Problem Solving: The Integration of Personality, Cognition, and Interest Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning

Richard L DeNovellis; DVM; Ph.D

Problem Solving: The Integration of Personality, Cognition, and Interest Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning

This book contains a comprehensive theory about subgroups of people and their problem-solving characteristics. The theory and data from 95 different studies by the author and others incorporate information about personality, interests and cognition integrated around various kinds of numerical, verbal, and spatial problems. Using a developmental perspective, the research illustrates how children, adolescents, adults and different subgroups of people apply knowledge to everyday problems and, at times, become stymied, slowed, or adept in the problem-solving process. Individual differences are characterized through a classification system of 36 problem-solving subgroups via machine learning-Naïve Bayes, support vector machine, and decision making trees.

Prepublication Copy Problem Solving: The Integration of Personality, Cognition, and Interest Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning Richard L. DeNovellis, DVM, Ph.D This book contains a comprehensive theory about subgroups of people and their problem-solving characteristics. The theory and data from 95 different studies by the author and others incorporate information about personality, interests and cognition integrated around various kinds of numerical, verbal, and spatial problems. Using a developmental perspective, the research illustrates how children, adolescents, adults, and different subgroups of people apply knowledge to everyday problems and, at times, become stymied, slowed, or adept in the problem-solving process. Individual differences are characterized through a classification system of 36 problem-solving subgroups via machine learningNaïve Bayes, support vector machine, and decision-making trees. Keywords: Individual Differences, Problem Solving, Neuroscience, Problem Solving (Education), Multidimensional Analysis, Nearest Neighbor, Support Vector, Subgroups, Classification b Prepublication Copy Electronic Book Publications First Copyright: Catalog of Copyright Entries. Third Series: A5112550: 1974: JanuaryJune Second Copyright: Catalog of Literary Works, TXu-2-061-201, July 2017 Richard L. DeNovellis, DVM; Ph.D RLDπ September 2019 b|Page i Prepublication Copy Problem Solving: The Integration of Personality, Cognition and Interests Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning Preface An Integrative Approach to Problem Solving (IPS) is not necessarily new, just a different perspective. People in education, business, psychology, and the sciences have spent many years studying the problem-solving processes of adults and children. Most of these studies have been useful, providing an extensive knowledge base. This book attempts to integrate both the author's studies and the studies of others to provide a cohesive, pragmatic, and useful theoretical foundation for studying the problem-solving process. The intent is to form a solid basis for the education of teachers, counselors, and others in the helping professions who are interested in the “how” and “why” of solving problems. A related purpose is to identify, classify, and describe different kinds of subgroups--how each differs in the solution of problems involving words, numbers, and spatial activities. Cognitive psychology, temperament, interests, physics, biology, and the concepts of information processing are the cornerstones of the IPS theory. The explosion of information in biology, especially brain research, may revolutionize the way that learning is conceived. Likewise, the new information from physics provides a foundation for the understanding of environmental /organismal interaction. Information processing, although relatively new, attempts to integrate the processes of thinking as descriptive and interactive. In the past, problem-solving has been conceived as more static, more as a concept related to ability and intelligence. This book characterizes the process of learning to solve problems as dynamic, changing, ongoing, and related to the process of aging and experience. Temperament, abilities, and interests have always been the foundations of career and vocational problem-solving. In the intelligence model, children and adults have more or less capability to solve problems. In this book, the emphasis is on continued experiences and ability which allow the practice of skills leading to the mastery of different kinds of problems. The present approach differs from past approaches in that ultimately, the problem-solving process is a product of motivation, personal orientation, and experience. IPS theory is based on an integrated and balance model that takes into account the experiential nature of problem-solving as developmental experiences i|Page ii Prepublication Copy contribute to the complex process of solving problems in schools, businesses, or chosen vocations. This book uses both empirical data and theory as a basis for its approach to problemsolving. The result is a three-tiered cognitive and affective model that posits how 36 “ideal” subgroups of people use individual differences to solve spatial, numerical, and verbal problems. The author (first educated as a teacher in the field of biological studies, later as a person interested in educational psychology as well as curriculum and instruction, and finally as a veterinarian) has never abandoned any of those historical roots. Forty years of data collection, which never produced anything not previously discovered, but provide an extensive database on children and adults from 3-78 years of age, has allowed the author the luxury of making extrapolations to the thinking and problem-solving process of children and adults. The first instruments developed by the author in 1975-1985 were integrated, using psychological style, embedded designs, interests, and cognitive tests as methods of categorization. The big four factors of the PTPI (an instrument developed in 1977) preceded the big five of Costa and McCrae by 10 years but the database was small (1600-2000 people), fragmented, and incomplete. During those early years, many master’s level students in my research and statistics, tests and measurement, and child development classes at California State Polytechnic University, Pomona, CA collected data from their classrooms as part of their graduate work. Other data came from university medical, dental, and veterinary students while I was teaching and working on my DVM at the College of Veterinary Medicine, Mississippi State University. Most data came from students working on their master’s degree theses, university grants, and the Psychological Research Institute for Business and Education in Claremont, CA (Associates for Human Perspective, Inc., 1984) during the early 80s and late 90s. The author is grateful to the Master level students (see Bibliography), students, staff, and friends of PRI (Linnea and Mark Brush, Simone Kim, and Ron). Each person contributed to some facets of what now is called the IPS model. However, the author takes responsibility for all assertions made throughout this book. Some of the 95 different studies (some published, many unpublished or written as research reports for aerospace and fortune five hundred companies in Southern California during the 80s and 90s) originally were designed to study other questions of interest or a particular population of people in their jobs. However, many people were assessed multiple times as the data were re-analyzed in light of the present model. The model for this book was developed ex post facto or "after the fact." The non-random database contains 5,500 people from which many individuals were randomly selected from all different ages and different kinds of work. In addition, in another database, 1500 managers from many Fortune Five Hundred companies were used as representatives of more expert real-life problem solvers. The author for 10 years had the privilege of ii | P a g e iii Prepublication Copy running a psychological and business research institute that generated considerable data from schools, colleges, and businesses. Groups of data, where possible, were randomly stratified based on age, gender, ethnicity, and socioeconomic characteristic. The data collection was not systematic and instead was based on “where” and “when” available. The data for four thousand people, which make up the normative database of the IPS model, was gathered during the late 70s as well as 80s, 90s, and early 2000s. These data were then re-analyzed in light of many of the facets of the IPS theory. Many items came from 7 different measuring instruments, including management tests, career tests, perceptual speed tests, ability tests, standardized academic tests, and learning style tests. Other kinds of data collection included observation or rating forms used by employees to rate others in their organization as well as personality inventories. Biographical data were collected from adults. All instruments were previously correlated with many different academic, and non-academic tests during the 40-year developmental period. The author’s interest in how problems are solved led to the collection of many types of problem-solving exercises. All this data provided a way in which to test many of the assumptions in this book. The collection of the data occurred mainly from 1976-2004; while the re-analysis of data and writing of the chapters occurred mainly from 2004 through 2017. The history of psychological testing which leads to the methodology of integrating these diverse areas is itself fragmented, diverse, and noncontiguous. Like all scientific endeavors, the result of integration is to provide illumination of an area defined often as the "black box"; the area of the brain. Our methodology is descriptive, and taxonomic and uses psychometric analysis. People who use psychometric techniques rely heavily on correlation and significance testing. The results of this research are descriptive as most samples are not random, but convenient. The author who personally oversaw the data collection is solely responsible for any errors, omissions, and theoretical interpretations. In my opinion, taxonomic classification can only be accomplished by algorithms that are constantly modified based on age, developmental level, educational background, the complexity of tasks involved as well as cultural heritage. Finally, the level of prediction based on items, subscales, and instruments has a tremendous error which was only decreased when extended scales and algorithms were developed for classification. The base scales which utilize basic psychometric principles are reliable and valid. The extended scales are composite scales that do well on test-retest over periods of months and years. Base scales tested for reliability and validity are useful in the identification, convergence, and explication of concepts. Extended scales do well in classification which requires a broad and inclusive measurement. Extended scales were derived from our “tried and true” psychometric instruments (items and subscales iii | P a g e iv Prepublication Copy tested for reliability and validity) and then combined across the domains of cognition, personality, and interests. Finally, one principle that pervades this work is summarized as: At this point in time, the current statistical method of analysis (multivariate, multidimensional, etc.) cannot accurately predict classifications of people, only theory and algorithms combined with statistical analysis based on feedback from real people in predetermined real situations can decrease error to acceptable levels). Enjoy! RLDπ/ March 2019 iv | P a g e v Prepublication Copy Table of Contents Contents Preface.................................................................................................................................................... i Table of Contents ....................................................................................................................................v CHAPTER 1 .................................................................................................................... 1 AN OVERVIEW OF THE INTEGRATIVE PROBLEM-SOLVING SYSTEM (IPS) ......................... 1 Introduction .............................................................................................................................................. 1 The thesis .................................................................................................................................................. 4 A concise summary of constructs ............................................................................................................. 5 Application of the 20 constructs to our problem-solving thesis............................................................... 6 Chapter summary .................................................................................................................................. 9 Chapter references ...............................................................................................................................10 CHAPTER 2 .................................................................................................................. 12 INTEGRATIVE PROBLEM-SOLVING THEORY................................................................... 12 Introduction ............................................................................................................................................ 12 Individual differences ............................................................................................................................. 13 Brain pathways ....................................................................................................................................... 14 Brain plasticity ........................................................................................................................................ 15 Conscious, unconscious, and subconscious pathways ........................................................................... 15 Environmental press ............................................................................................................................... 16 Modifications .......................................................................................................................................... 17 Filters ...................................................................................................................................................... 18 Layers ...................................................................................................................................................... 18 Surface characteristics ............................................................................................................................ 20 General and differential problem solvers ............................................................................................... 21 Concepts, and energy flow ..................................................................................................................... 22 SUBGROUPS AND SUBGROUP PATTERNS ..................................................................... 22 Chapter summary .................................................................................................................................24 Chapter references ...............................................................................................................................25 Further readings: ..................................................................................................................................25 v|Page vi Prepublication Copy CHAPTER 3 .................................................................................................................. 27 THE DEFINABLE CHARACTERISTICS OF THE IPS SYSTEM ................................................ 27 Introduction ............................................................................................................................................ 27 Defining environments ........................................................................................................................... 27 Defining speed of processing .................................................................................................................. 28 Defining other cognitive outcomes ........................................................................................................ 29 Defining preferences .............................................................................................................................. 30 Defining categories -problem-solving/personality ................................................................................. 31 Defining career and vocational preferences ........................................................................................... 32 The integrative model ...........................................................................................................................33 Elements of the IPS system ..................................................................................................................... 35 Defining style and mode ......................................................................................................................... 36 Defining the category framework ........................................................................................................... 37 The 36 subgroups descriptions ............................................................................................................... 39 The Mousetrap ....................................................................................................................................... 40 Chapter summary .................................................................................................................................41 Chapter references ...............................................................................................................................41 CHAPTER 4 .................................................................................................................. 43 PROBLEM SOLVING ...................................................................................................... 43 Introduction ............................................................................................................................................ 43 Historical view .................................................................................................................................... 43 Early examples of verbal, spatial, and numerical problems ...........................................44 Verbal Problem Solving...............................................................................................................50 Numerical Problem Solving .......................................................................................................52 Spatial Problem Solving ..............................................................................................................54 Factors influencing Problem Solving .....................................................................................55 Interaction of affective and cognitive states during problem-solving ..................................... 56 DIFFERENCES RELATED TO PROBLEM SOLVING ............................ 58 Age and neural development ........................................................................................................... 58 Gender differences in problem-solving .......................................................................................... 59 Expert (general) vs. beginning problem solvers (differential) ................................................ 60 Individual versus group problem solving ...................................................................................... 61 Chapter summary ..........................................................................................................................61 Chapter references: ......................................................................................................................62 vi | P a g e vii Prepublication Copy CHAPTER 5 .................................................................................................................. 71 ELEMENTS AND FOUNDATION OF SOLVING PROBLEMS ............................................... 71 Introduction ............................................................................................................................................ 71 IPS theory- energy production in problem-solving ................................................................................. 71 Origin of cell energy for language production ........................................................................................ 72 Competition in the brain......................................................................................................................... 73 Cognitive structure and cognitive processes in problem-solving ........................................................... 74 Levels of thinking .................................................................................................................................... 75 Cognitive ability ...................................................................................................................................... 75 Memory and fluid ability ........................................................................................................................ 76 A single thought ...................................................................................................................................... 77 Concept formation .................................................................................................................................. 77 Abstracting.............................................................................................................................................. 79 Speed of processing ................................................................................................................................ 79 Object processor vs conceptual (image) pattern processor ................................................................... 80 Chapter summary .................................................................................................................................81 Chapter references: ..............................................................................................................................81 Further reading .....................................................................................................................................84 CHAPTER 6 .................................................................................................................. 85 CODING, ENCODING, AND ENERGY IN PROBLEM SOLVING ........................................... 85 Introduction ............................................................................................................................................ 85 Encoding ...............................................................................................................................................85 Context ................................................................................................................................................... 86 Age differences in the encoding process ................................................................................................ 90 Symbolization ......................................................................................................................................... 91 Aural representations ............................................................................................................................. 92 Numeric and figural symbols .................................................................................................................. 93 Encoding with associations ..................................................................................................................... 93 Encoding with storage of emotions and feelings .................................................................................... 94 Memory ................................................................................................................................................94 Working memory .................................................................................................................................... 95 Features of working memory ................................................................................................................. 95 Central executive .................................................................................................................................... 96 The phonological loop ............................................................................................................................ 96 Visual-spatial sketch pad ........................................................................................................................ 96 Perceptual speed-speed of processing ................................................................................................... 97 Subgroup patterns ................................................................................................................................98 Chapter summary .................................................................................................................................98 Chapter references: ..............................................................................................................................98 vii | P a g e viii Prepublication Copy Further reading .....................................................................................................................................99 CHAPTER 7 ................................................................................................................ 100 PROBLEM SOLVING MODEL ....................................................................................... 100 Introduction ..........................................................................................................................................100 Problem-solving model .........................................................................................................................100 Process Terms in the Cognitive Model ................................................................................................101 Model characteristics ...........................................................................................................................102 Association ............................................................................................................................................102 Analysis and discrimination ..................................................................................................................103 Divergent thinking ................................................................................................................................105 Convergent thinking .............................................................................................................................107 Synthesis ...............................................................................................................................................107 Evaluation .............................................................................................................................................109 The logic system ...................................................................................................................................109 Conceptualization .................................................................................................................................111 Short-term or working memory............................................................................................................111 Working memory research ...................................................................................................................113 Bottom-up, and top-down processing ..................................................................................................114 Is the model useful?..............................................................................................................................115 Chapter summary ...............................................................................................................................116 Chapter references: ............................................................................................................................117 CHAPTER 8 ................................................................................................................ 119 PATHWAYS OF THE COGNITIVE MODEL ..................................................................... 119 Introduction ..........................................................................................................................................119 Time ......................................................................................................................................................119 A simple model pathway example ........................................................................................................121 Memory/limited memory pathway ......................................................................................................121 Associational pathways ........................................................................................................................123 Analytic pathways .................................................................................................................................124 Logical analytic or just analytical ..........................................................................................................125 Divergent pathways ..............................................................................................................................126 Convergent pathways ...........................................................................................................................128 Divergent/convergent logical pathway using comprehension .............................................................128 Complex and compound pathways involving comprehension .............................................................129 Interaction of social and different mental pathways ...........................................................................130 Chapter summary ...............................................................................................................................131 Chapter reference: ..............................................................................................................................132 Further reading ...................................................................................................................................132 CHAPTER 9 ................................................................................................................ 133 viii | P a g e ix Prepublication Copy KNOWN PATHWAY PROBLEMS .................................................................................. 133 Introduction ........................................................................................................................................133 Examples of mental slowing in everyday experience ..........................................................................133 Clinical neuroscience...........................................................................................................................134 Education ............................................................................................................................................135 Process theory/performance theory ....................................................................................................136 Test anxiety ...........................................................................................................................................137 LOST IN DIFFERENT NEURAL PATHWAYS .................................................................... 138 Perceptual/attention ............................................................................................................................138 Limited memories .................................................................................................................................139 Problems with associational pathways .................................................................................................140 Lost in pathways requiring logic ...........................................................................................................142 Lost in the complex pathways ..............................................................................................................144 Keys to pathway identification .............................................................................................................146 Chapter summary ...............................................................................................................................146 Chapter reference: ..............................................................................................................................147 Further reading ...................................................................................................................................147 CHAPTER 10............................................................................................................... 148 INTEGRATIVE PROBLEM SOLVING AND SUBGROUPS .................................................. 148 Introduction ..........................................................................................................................................148 Integrative problem solving ..................................................................................................................148 Pathways and our problem-solving subgroup ......................................................................................152 Control problem solvers .......................................................................................................................154 Flex problem solvers .............................................................................................................................155 Children’s Problem-Solving Subgroups................................................................................................155 General problem solvers.......................................................................................................................156 Differential problem solvers .................................................................................................................157 Descriptions ..........................................................................................................................................157 Chapter summary ...............................................................................................................................160 Chapter references .............................................................................................................................160 CHAPTER 11............................................................................................................... 161 THE NEONATE -BIRTH TO 24 MONTHS ....................................................................... 161 Introduction ..........................................................................................................................................161 Brain development ...............................................................................................................................161 Energy ...................................................................................................................................................162 ix | P a g e x Prepublication Copy Cognitive Model ..................................................................................................................................163 Diagram 2: The Cognitive Model (Neonate) .........................................................................................164 Perception ............................................................................................................................................164 Conception ............................................................................................................................................165 Motor ....................................................................................................................................................167 Analysis .................................................................................................................................................168 Social .....................................................................................................................................................168 Control (Structure) ................................................................................................................................169 Flex ........................................................................................................................................................170 Differences in Types of Problems Solved .............................................................................................171 Word problems solving .........................................................................................................................171 Numerical problem solving ...................................................................................................................172 Chapter summary ...............................................................................................................................173 Chapter references: ............................................................................................................................174 Further reading ...................................................................................................................................177 CHAPTER 12............................................................................................................... 178 INFANCY AND EARLY CHILDHOOD: 24 MONTHS TO 7.9 YEARS ................................... 178 Introduction ........................................................................................................................................178 Brain and energy .................................................................................................................................178 Energy as an activity level ...................................................................................................................179 Problem Solving Categories (Ages 24 months-7 years) ........................................................................180 Descriptive Problem-Solving Categories ..............................................................................................181 General problem solvers.......................................................................................................................181 Differential problem solvers .................................................................................................................182 Underachieving differential problem solvers .......................................................................................183 Perception (24-72 months) ...................................................................................................................185 Part-whole relationships.......................................................................................................................186 Perceptual speed ..................................................................................................................................186 Conception ............................................................................................................................................191 Motor ....................................................................................................................................................192 Analysis .................................................................................................................................................193 Social .....................................................................................................................................................194 Control and structure ...........................................................................................................................194 Flex ........................................................................................................................................................195 DIFFERENCES IN TYPES OF PROBLEMS SOLVED .......................................................... 197 Word problem solving ..........................................................................................................................197 Numerical problem solving ...................................................................................................................198 Spatial problem solving ........................................................................................................................199 Temperament .......................................................................................................................................200 x|Page xi Prepublication Copy Cognition and problem-solving development ......................................................................................201 Problem Solving Summary ....................................................................................................................202 Chapter summary ...............................................................................................................................204 Chapter references .............................................................................................................................204 Further reading ...................................................................................................................................205 CHAPTER 13............................................................................................................... 206 LATE CHILDHOOD: THE CHILD FROM 8 UNTIL 9 .......................................................... 206 Introduction ........................................................................................................................................206 Brain and energy ...................................................................................................................................207 Diagram 4: Cognitive model (Late Childhood) ......................................................................................207 Category System ...................................................................................................................................208 Demographic Factors ............................................................................................................................211 PROBLEM SOLVING CATEGORIES (AGES 8-9) .............................................................. 213 General academic problem solvers ......................................................................................................214 Differential problem solvers .................................................................................................................214 Perceptual problem solvers ..................................................................................................................216 Conceptual problem solvers .................................................................................................................218 Motor problem solvers .........................................................................................................................220 Analytic problem solvers ......................................................................................................................221 Social problem solvers ..........................................................................................................................223 Controlled problem solvers ..................................................................................................................224 Flex problem solvers .............................................................................................................................226 Role of interest on career paths and selection....................................................................................227 Differences in Types of Problems Solved .............................................................................................228 Word problems solving .........................................................................................................................228 Numerical problem solving ...................................................................................................................230 Spatial problem solving ........................................................................................................................231 Measurable differences?.....................................................................................................................232 Using the Problem-Solving Model .......................................................................................................233 Memory ................................................................................................................................................233 Comprehension ....................................................................................................................................234 Arrestment in problem-solving at 8-9. .................................................................................................234 Chapter summary ...............................................................................................................................236 Chapter references .............................................................................................................................237 Further reading ...................................................................................................................................237 CHAPTER 14............................................................................................................... 238 xi | P a g e xii Prepublication Copy EARLY ADOLESCENCE 10-13 YEARS OF AGE ................................................................ 238 Introduction ..........................................................................................................................................238 Biological and motor development ......................................................................................................239 Energy and physical development ........................................................................................................239 Energy and cognitive development ......................................................................................................241 The Measurement System for the Early Adolescent ............................................................................244 PROBLEMS SOLVING SCALES ...................................................................................... 253 General problem solving .......................................................................................................................253 Differential problem solver ...................................................................................................................257 Perceptual problem solver ...................................................................................................................258 Conceptual ............................................................................................................................................259 Motor problem solver...........................................................................................................................261 Analysis .................................................................................................................................................263 Logical analysis elements ......................................................................................................................264 Social .....................................................................................................................................................266 Control and structure ...........................................................................................................................268 Flex problem solver ..............................................................................................................................269 Extraversion/introversion .....................................................................................................................271 Differences in Types of Problems Solved .............................................................................................272 Word problem solving ..........................................................................................................................272 Numerical Problem Solving...................................................................................................................277 Spatial problem solving ........................................................................................................................281 Chapter summary ...............................................................................................................................284 Chapter references: ............................................................................................................................285 CHAPTER 15............................................................................................................... 287 LATE ADOLESCENCE (14-17)....................................................................................... 287 Problem Solving During High School Years ..........................................................................................287 Learning, problem-solving, and energy ................................................................................................287 Category Subscales .............................................................................................................................288 Gender differences ...............................................................................................................................290 A teaching example using the IPS Model ............................................................................................292 General problem solving .......................................................................................................................294 Differential PS .......................................................................................................................................295 Perceptual .............................................................................................................................................296 Conception ............................................................................................................................................297 Motor ....................................................................................................................................................299 Analytical ..............................................................................................................................................300 Social .....................................................................................................................................................301 Control/structure & flex .......................................................................................................................302 Flex ........................................................................................................................................................303 Flex and control interaction ..................................................................................................................303 Extraversion /introversion ....................................................................................................................305 xii | P a g e xiii Prepublication Copy Differences in Types of Problems Solved .............................................................................................306 Word problem solving ..........................................................................................................................306 Numerical problem solving ...................................................................................................................308 Spatial problem solving ........................................................................................................................310 Chapter summary ...............................................................................................................................312 Chapter reference ...............................................................................................................................313 CHAPTER 16............................................................................................................... 314 LATE ADOLESCENCE AND ADULTHOOD ...................................................................... 314 DATA FOR PROBLEM SOLVING IN OLDER AGE GROUPS .............................................. 314 Introduction ..........................................................................................................................................314 Gender differences ...............................................................................................................................315 Samples .................................................................................................................................................316 Problem Solving Categories ................................................................................................................318 General and differential problem solving .............................................................................................318 Perceptual .............................................................................................................................................320 Conception ............................................................................................................................................321 Motor ....................................................................................................................................................322 Analysis .................................................................................................................................................323 Social .....................................................................................................................................................325 Control and structure ...........................................................................................................................327 Flex ........................................................................................................................................................329 Flex and control patterns ......................................................................................................................330 Category and profile analysis ................................................................................................................331 Differences in Types of Problems Solved .............................................................................................332 Word problem solving ..........................................................................................................................332 Numerical and logical analytic ..............................................................................................................333 Spatial problem solving ........................................................................................................................334 Other important variables ..................................................................................................................336 Chapter summary ...............................................................................................................................336 Chapter references: ............................................................................................................................337 Further reading ...................................................................................................................................337 CHAPTER 17............................................................................................................... 338 THE CAREER SUBSCALES ............................................................................................ 338 Introduction ........................................................................................................................................338 Holland’s career patterns ....................................................................................................................339 xiii | P a g e xiv Prepublication Copy Picture 4 ................................................................................................................................................341 Analysis of gender and demographic response patterns .....................................................................343 Gender differences ...............................................................................................................................343 Table 76: Controlling Response Bias .....................................................................................................344 Table 77: Male Caucasian Responses ...................................................................................................345 Table 78: Female Caucasian Response Bias ..........................................................................................346 Summarizing Career Trends: ...............................................................................................................347 Education ..............................................................................................................................................347 Age ........................................................................................................................................................348 Culture ..................................................................................................................................................348 Chapter summary ...............................................................................................................................349 Chapter references: ............................................................................................................................349 Further reading ...................................................................................................................................350 CHAPTER 18............................................................................................................... 352 VOCATIONAL PROBLEM SOLVING .............................................................................. 352 Introduction ........................................................................................................................................352 IPS-interest theory ..............................................................................................................................352 Interest patterns ...................................................................................................................................353 Defining and Assessing Managers .......................................................................................................354 Assessing managers ..............................................................................................................................356 Measuring instruments .......................................................................................................................357 Cognitive and semi cognitive ................................................................................................................357 Primary goal ..........................................................................................................................................358 Validation ..............................................................................................................................................358 Results from basic scales .....................................................................................................................358 Results from ratings ..............................................................................................................................360 Anonymous ratings ...............................................................................................................................360 Results from extended scales ...............................................................................................................360 Management scores without ratings ....................................................................................................361 Management scores with ratings .........................................................................................................363 Chapter summary ...............................................................................................................................364 Chapter references: ............................................................................................................................364 CHAPTER 19:.............................................................................................................. 366 RESEARCH, CATEGORIZATION AND INTEGRATIVE MODELS ........................................ 366 xiv | P a g e xv Prepublication Copy Introduction ..........................................................................................................................................366 A cognitive model .................................................................................................................................366 A model of personality..........................................................................................................................369 A model for interests ............................................................................................................................369 Integrative models ................................................................................................................................370 Cattel’s 16 PF ........................................................................................................................................371 Our Research Integrated Model ..........................................................................................................371 Categorization model ...........................................................................................................................373 Chapter References:............................................................................................................................374 Further Reading ..................................................................................................................................375 CHAPTER 20............................................................................................................... 376 MEASURING THE PROBLEM-SOLVING CATEGORIES .................................................... 376 Introduction ..........................................................................................................................................376 Idiographic measurement.....................................................................................................................376 Base versus extended scales .................................................................................................................377 Item level scoring ..................................................................................................................................377 Scale level .............................................................................................................................................378 Profile selection. ...................................................................................................................................379 Subscales and selected examples of items ..........................................................................................381 General/differential problem solver .....................................................................................................381 Perceptual problem solvers ..................................................................................................................383 Conceptual problem solver ...................................................................................................................384 Motor problem solvers .........................................................................................................................386 Analytic problem solver ........................................................................................................................387 Social problem solver............................................................................................................................388 Control/structure ..................................................................................................................................389 Flex (cognitive flexibility) ......................................................................................................................390 Extraversion, ambivert, and introversion .............................................................................................391 Example: cognitive items: .....................................................................................................................393 Example: perceptual speed items ........................................................................................................394 Example: career and Interest Items ......................................................................................................396 Problem-solving categories defined by measurement .........................................................................397 Measurement issues using rank scoring ...............................................................................................399 Chapter references .............................................................................................................................400 CHAPTER 21............................................................................................................... 401 GENERAL MEASUREMENT CONCERNS ....................................................................... 401 INTRODUCTION ......................................................................................................... 401 Theory as known Information in class predictions ..............................................................................401 True and false positives ........................................................................................................................403 xv | P a g e xvi Prepublication Copy Factors of misclassification ...................................................................................................................403 Feature extraction ................................................................................................................................404 Feature extraction and dimension reduction .......................................................................................405 Representation in space .......................................................................................................................407 Correlated subgroups and distance profiles .........................................................................................408 Minimizing bias .....................................................................................................................................411 Our theory on how to find subgroups .................................................................................................412 Deconstructing and reconstructing our correlation matrix ..................................................................412 Writing the descriptions of subgroups: ................................................................................................416 Analysis of subgroups ...........................................................................................................................418 Rate of misclassification .......................................................................................................................420 Extended scales ....................................................................................................................................422 Measuring instruments (reliability and validity) .................................................................................423 Chapter references: ............................................................................................................................424 CHAPTER 22............................................................................................................... 426 PROBLEM SOLVING SUBGROUPS AND MACHINE LEARNING ....................................... 426 Introduction ........................................................................................................................................426 A brief history of machine learning ......................................................................................................426 Machine learning computer programs .................................................................................................428 Support vector machines (SVM) ...........................................................................................................429 Decision tree types ...............................................................................................................................431 The common methodology used in machine learning classification ....................................................432 Using a machine learning methodology ...............................................................................................433 Use machine learning to classify the subgroups...................................................................................434 Decision trees .......................................................................................................................................437 Chapter summary ...............................................................................................................................438 Chapter references .............................................................................................................................438 Further Reading: .................................................................................................................................440 CHAPTER 23............................................................................................................... 441 A DIFFERENT PERSPECTIVE ON PROBLEM SOLVING .................................................... 441 Introduction ........................................................................................................................................441 Higher dimensions ................................................................................................................................441 Law of parsimony..................................................................................................................................443 Energy ...................................................................................................................................................444 Different kinds of forces .......................................................................................................................445 Forces in higher dimensions .................................................................................................................445 Abstract, not spatial..............................................................................................................................447 Quantum theory ...................................................................................................................................447 xvi | P a g e xvii Prepublication Copy Quarks ...................................................................................................................................................449 Superstrings ..........................................................................................................................................450 Evolutionary remnants .........................................................................................................................451 Chapter reference: ..............................................................................................................................452 CHAPTER 24............................................................................................................... 453 REVIEW: BIOLOGICAL FOUNDATIONS......................................................................... 453 Introduction ..........................................................................................................................................453 Genetics ................................................................................................................................................453 Basic codes in genetics .........................................................................................................................454 Mitosis ..................................................................................................................................................455 Meiosis ..................................................................................................................................................455 The Cell .................................................................................................................................................456 Adenosine triphosphate .......................................................................................................................457 Enzymatic activity .................................................................................................................................458 Neurotransmitters ................................................................................................................................458 Picture: The “tree of life” ......................................................................................................................460 The brain ...............................................................................................................................................461 Brain regions .........................................................................................................................................461 Brain layers ...........................................................................................................................................463 Frontal lobes .........................................................................................................................................463 Brain pathways .....................................................................................................................................464 Sensory perceptions .............................................................................................................................465 Memory ................................................................................................................................................465 Embryological development .................................................................................................................466 Glia Cells ...............................................................................................................................................467 Neuronal degeneration ........................................................................................................................467 COGNITIVE THEORY ................................................................................................... 467 Early development of the brain ............................................................................................................467 Observing and executing ......................................................................................................................468 Learning ................................................................................................................................................469 Hierarchical organization ......................................................................................................................470 Brain processing....................................................................................................................................470 Origins of different types of problem-solving.......................................................................................471 Chapter References:............................................................................................................................471 CHAPTER 25............................................................................................................... 473 REVIEW: ENERGY AND COGNITION ............................................................................ 473 Introduction ........................................................................................................................................473 Historical view ......................................................................................................................................473 The energy at the origin of life .............................................................................................................475 COGNITION................................................................................................................ 477 xvii | P a g e xviii Prepublication Copy IPS theory-cognition ...........................................................................................................................477 Historical view ......................................................................................................................................477 Quantitative period ............................................................................................................................479 Intelligence as an ability .....................................................................................................................480 Speed of processing ............................................................................................................................481 The current research literature on the speed of processing ................................................................481 Historical view ......................................................................................................................................482 CATEGORIES OF PERCEPTION, CONCEPTION, AND ANALYSIS ...................................... 483 Introduction ........................................................................................................................................483 IPS theory- perception ........................................................................................................................484 Historical view ......................................................................................................................................484 ANALYSIS ................................................................................................................... 487 Analysis as logical thought ..................................................................................................................490 Historical view ......................................................................................................................................491 CONCEPTION ............................................................................................................. 492 IPS theory-conceptual .........................................................................................................................492 Historical view ......................................................................................................................................493 Animal research ....................................................................................................................................494 Evolutionary development ...................................................................................................................494 Philosophical period .............................................................................................................................495 Quantitative period ..............................................................................................................................496 Psychometric studies ............................................................................................................................496 Chapter summary ...............................................................................................................................497 Chapter references .............................................................................................................................497 Further Reading. .................................................................................................................................502 CHAPTER 26............................................................................................................... 504 REVIEW: PERSONALITY............................................................................................... 504 Introduction ........................................................................................................................................504 Historical view ......................................................................................................................................504 Personality Trait-Extraversion/Introversion ........................................................................................505 IPS theory-extraversion/introversion ..................................................................................................505 xviii | P a g e xix Prepublication Copy Historical view ......................................................................................................................................506 Allport ...................................................................................................................................................506 Early theorists .......................................................................................................................................507 McDougal and Kempf ...........................................................................................................................507 Other theorists......................................................................................................................................508 Personality Trait: Sensory Motor ........................................................................................................508 Historical view: .....................................................................................................................................510 Personality Trait: Social.......................................................................................................................511 Historical view ......................................................................................................................................512 Personality Trait: Control ....................................................................................................................514 IPS internal and external control ..........................................................................................................515 Personality Trait: Flex .........................................................................................................................519 Historical view ......................................................................................................................................520 Personality Trait: Achievement Motivation ........................................................................................521 Historical view ......................................................................................................................................521 Atkinson and McClelland ......................................................................................................................522 Interests..............................................................................................................................................522 Historical view ......................................................................................................................................522 Chapter Summary ...............................................................................................................................524 Chapter References:............................................................................................................................525 Further Reading ..................................................................................................................................532 CHAPTER 27............................................................................................................... 534 REVIEW: IDENTIFICATION OF SUBGROUPS ................................................................. 534 Introduction ........................................................................................................................................534 Overview of subgroup models ..............................................................................................................534 Unipolar or one-group model .............................................................................................................535 Bipolar or two-group models ..............................................................................................................536 MULTIPLE GROUP MODELS ........................................................................................ 536 Gregorc’s model ...................................................................................................................................536 Sternberg’s Model ................................................................................................................................538 Myers Briggs Type Indicator .................................................................................................................538 Sixteen Personality Factor Questionnaire (16 PF) ................................................................................539 Issues related to the measurement of subgroups ...............................................................................539 Our 36 subgroups................................................................................................................................540 xix | P a g e xx Prepublication Copy Picture 5: 36 Subgroups ........................................................................................................................541 Subgroups within subgroups ...............................................................................................................541 Picture 6: Analytic (A), Social (S), and Analytic Social (AS)....................................................................542 Picture 7: Motor (Mot); Conceptual (Con); and CM .............................................................................543 Picture 8: Centroid for Motor; Conceptual; CM ...................................................................................543 Chapter summary ...............................................................................................................................544 Chapter references: ............................................................................................................................544 Book references ..................................................................................................................................546 APPENDIX B ............................................................................................................... 582 General Problem Solver-1 .....................................................................................................................586 General Problem Solver-9 .....................................................................................................................605 General Problem Solver-19 ...................................................................................................................628 General Problem Solver-30 ...................................................................................................................653 Appendix C..........................................................................................................................................669 Analytic Items Version 2.0 Raw Score/Means, S.D. ..............................................................................669 Spatial items version 2.0: Age and Education .......................................................................................670 Cog flex .................................................................................................................................................673 Letter identification ..............................................................................................................................675 Embedded designs ................................................................................................................................677 Arithmetic Distraction ..........................................................................................................................678 Memory ................................................................................................................................................678 APPENDIX D ............................................................................................................... 679 Sample Sizes, Means, and Standard deviations from selected studies 1977 to 2002. .........................679 APPENDIX E ............................................................................................................... 691 Hierarchical Decision-Making Tree .......................................................................................................691 xx | P a g e 1 Prepublication Copy Chapter 1 An Overview of the Integrative Problem-Solving System (IPS) Introduction The dynamics of problem-solving begin at or before birth and continue until the last breath; therefore, the scope of this book covers all age groups from birth to senior citizens. Many of the problem-solving trends are easier to understand from a developmental perspective as the "The child is the 'father of the man” (Wordsworth, 1807) and of course, woman. What is meant by problem-solving? A problem is a question to be answered; problem-solving is a process by which the answer is derived. A problem can be viewed in many ways such as: • • • • A question---How can speed be defined in the universe? An obstacle or conflict--How can one travel from point “a” to point “b” without a source of locomotion? A goal---How can I achieve my career ambitions? An inner energizing force-My curiosity stimulates me to find the answer to a situation. Types of problems Duncker (1945), Newell and Simon (1972), and Maier (1931) use different terminology to describe a problem but the essence is the same. A problem has an initial state, a middle state, and an end state; each state must be defined and extrapolated to understand the dynamics of the problemsolving process. The solving of complex problems differs according to type, characteristics, situational circumstances, and the people who are solving them (Dostál, 2015). Problems can be simple, complex, abstract, compound, or part of the total problem-solving process. Simple problems that involve decision-making are the easiest to understand as most occur as part of everyday living. The problem is “what clothes do I wear in the morning or how do I go from the house to the car.” Compound problems are a little more complicated as they involve a series of many different kinds of simple problems. For example, assume you were asked to fix a broken handle on a toilet. The process could be involved, i.e., find the proper tools, remove the handle, find a proper handle, and use tools to replace the handle on the toilet. What often seems like a simple problem becomes compounded since each of the simple steps has 1|Page 2 Prepublication Copy another set of problems associated with it. Maybe a person could not find the right handle for the toilet, or one found the handle, but the connection was worn and the new one would not fit. The problem-solving process is the methodology for finding a solution to a problem or a series of problems. The methodology representing a series of steps or different courses of action (decisionmaking) is simple or complex, depending on the type of problem either tangible or intangible. The process of problem-solving involving tangible objects is more concrete and specific, while problem-solving involving intangible objects is generally more abstract. Try visualizing an abstract concept such as mass, perhaps the 'mass' of a rock. The process is difficult without a definition or an illustrative concept. Even if given a definition (i.e., mass is an integrated large body of matter without a defined shape), the concept of mass might be too abstract to interpret or visualize. Compare visualizing the ‘mass’ of rock to that of visualizing the rock itself. Which is easier? As another example, consider the problem-solving process of assembling a kite, i.e., using string to tie the wood frame and using paper to cover the frame. When assembling the kite, the problem solver must understand the purpose of the string, paper, and wood frame. Although the sequence might vary, a final solution in assembling the kite requires the paper to be attached to the wood frame. So, how does one assemble the kite? There are multiple ways to solve the problem, but the two main ones are to read the directions or to use trial and error. Reading the directions often leads to a simple logical solution that has been previously used by others. In contrast, the use of trial and error requires a different kind of thought process. Solving a problem by trial and error relies more upon experience and guesswork as well as divergent and/or convergent thinking. Regardless of which approach is used, an important point is that finding a solution via reading the direction is more efficient, feasible, and dependent upon others who have previously identified the steps in the process. Literature reviews of problem-solving often make distinctions between complex and simple problem-solving as well as problem-solving results studied in laboratory situations vs. those that are studied in situ. The reason for this distinction is easy to understand. Very defined simple tasks in the laboratory or regulated experimental situations requiring reasoning and inference are often correlated with intellectual ability. In contrast, complex problem-solving tasks, such as those found in ill-defined, real-life situations are more likely to be related to a host of factors such as previous experience, knowledge, expert performance, motivation, interest, and self-regulated disposition. In this book, the results from laboratory experiments as well as real-life problem solving are examined. Both are important. In the problem-solving process, both the characteristics and dynamics of the problem solver as well as the characteristics of the problem are important. The experiences of the person which contribute to understanding an abstract concept are as important as the problem itself. In the journey to understand the concept of problem-solving, characteristics of the problem and the 2|Page 3 Prepublication Copy problem solver are studied from many different perspectives, i.e., biological, environmental, social, and psychological. Limiting the problem-solving process The world of problem-solving is so extensive, so vast, that one could spend considerable time trying to understand it. Therefore, categories help to limit the process to the most common forms of problem-solving. The categories are numbers, words, spatial processing, and a mixture of all which is defined as performance. These categories are defined next. 1) Categories of numbers include problems using numeric calculations as in arithmetic (1 +1 =2). Examples are simple arithmetic tests (adding, subtracting, multiplying, dividing), standardized achievement tests, academic tests involving numerical operations, and numerical proficiency exams. 2) Word categories are defined as any problem which is comprised of letters (c, a, t). This includes word comprehension tests, reading tests, standardized tests in comprehension, reading, and literature as well as vocabulary proficiency tests. 3) Spatial processing involves any objects that require spatial manipulation, spatial visualization, and left or right brain spatial dis-embedding. Examples include spatial tests, object manipulation, perceptual speed processing, and activities that pose spatial problems. Often spatial relations and spatial visualization are inclusive of spatial processing. 4) Mixtures problems are obvious combinations of words, numbers, and spatial problems that result in an outcome or performance (expert performance in music, chess, subject matter domains), or other areas, i.e., repairing a car. By limiting the problem-solving process to these four categories, one can weave the study of individual differences around the complexities of personality, interests, and cognition. IPS is a descriptive system that allows us to separate people into subgroups and identify different types of problem solvers. Taxonomic classification is used to separate groups of people much as the biologist uses taxonomic classification to separate different species of trees. Although each category appears independent, as noted above, the continuum of abstractness to concrete 3|Page 4 Prepublication Copy contributes to interdependence. This property leads to the characterization of our theory of problem-solving as integrated. The thesis Before the thesis is explained, let’s acknowledge that any generalization has many qualifications. When making statements about human nature, think about how complicated and adaptive human beings are. For example, the human body has billions of cells that are constantly changing in various organs. Encoding of sensory information from the eyes, ears, nose, and touch occurs in millions of cells almost simultaneously. New cells in the brain and all organs of the body are developed every minute of every day. When stimuli from an outside source (threat, environmental change) occur, the mind and body are altered and change. What a person thinks now at this moment might be very different from the thoughts in a few moments, next week, next month, and next year. These continual adaptive changes allow individuals to constantly evolve and change throughout a lifetime and present many qualifications to any generalization or thesis. In a nutshell, our thesis posits that genetics, developmental experiences, and interactions of individual traits with the environment give rise to individual differences which can best be understood concerning subgroups of people who have similar demographics and problemsolving characteristics. Utilizing a 3-tier model of explanation, the patterns of problem-solving subgroups are captured by the interactions of personality, interests, and cognition with problems involving numbers, words, and spatial activities. By explaining the biological basis of our model in three tiers, either the efficiency in solving problems as well as the clinical symptoms of slowing and the effects of blockage in neurological pathways are better understood. Although the thesis is deceptively simple, the outcomes become quite complex as the basis of efficiency of problem-solving or slowing and blockage of neural pathways comes from both the environment and individual differences. Given the myriad of positive and negative experiences found in the environment and the tremendous differences among individuals, there are many possible outcomes. Think of how many different ways that experiences in the environment can shape the inherent approach and speed with which people solve problems. Also, consider how emotions of isolation, depression, and feelings of helplessness result in the slowing of decisions originating and involving neurological pathways! To understand the integrative process and IPS theory, Picture 1 shows a 2-dimensional nonmetric picture of how 20 variables representing the 4 groups of cognitions, speed of processing, personality, and interests are integrated. In Picture 1, notice how general cognition (small area of blue-C1-C2) and speed of processing (large area of blue S1-S4) is closer to the left of the plot while personality (P1-P8) and career dimensions (CR1-CR6) are around the perimeters of the picture. 4|Page 5 Prepublication Copy Using the non-metric distance measures, cognition and speed of processing variables seem to be embedded in and around measures of personality and interests. The non-metric picture shows how each of the elements is related to each other by a distance. Distance measurement assumes that those who are closer in distance have personality and cognitive attributes that are similar. The integrative nature of how these 4 groups influence the approach to solving problems of numbers, words, and spatial activities is explained in detail later in the book, but first, let’s try to represent how 20 different constructs appear. Picture 1: Non-metric Representation Personality (P1-P8), general cognition (C1-C2; small blue), career and interests (CR1-CR6) as well as Speed of Processing (S1-S4; large blue) A concise summary of constructs A concise summary of the constructs used in IPS theory suggests that during one’s lifetime some people excel at all types of problem-solving (generally integrated problem solvers) while many other people specialized in solving problems associated with their area of strengths and interests (Differential problem solver). Our experiences lead us to believe that some people excel at motor activities (coordination or manual dexterity) while others excel at perceptual (use of the eyes to see shapes and figures) or conceptual activities (use of memory, experience, and analytic thought to generate ideas). Some people are better at analysis (diagnostic ability); while others understand the dynamics of people and social systems (social). The capability to solve complex problems belies simple cognitive processing; the capability is based on the control and structuring of the mind and emotions so that one can focus and achieve success. However even control, by itself, is insufficient. Control, a method of structuring the environment, helps individuals to attend and plan, sharpen their minds, and focus on a goal, but 5|Page 6 Prepublication Copy another separate mechanism operates simultaneously. This other control mechanism which is very necessary for solving problems is denoted as “cognitive flexibility” or flex. Flex, at least academically, appears to be inversely related to structure and order at times. However, our studies have shown repeatedly that this varies considerably with individual differences. Flex or cognitive flexibility is the unconscious release mechanism needed to let the mind wander, to be creative enough to generate an alternative needed to solve a problem. Flex works in concert with ideation and conceptualization. Sometimes cognitive flexibility, when not controlled by analyzing events too much, represents both an impulse and an emotion. It seems that one neural network in the brain controls emotions so that one can focus while simultaneously a second neural network allows the mind to diverge, think of alternatives, or respond impulsively to external stimuli. At times both networks move together (coordination), and at times, each neural network acts separately (competition). Control is usually more conscious while flex operates at both conscious and subconscious levels. Continuing in our concise explanation of the 20 constructs of the IPS theory, we find that early in life, the genetic components of speed and inherited ability allow individuals to ferret out logical relationships and apply spatial thinking (fluid ability). These attributes are more likely to initially influence academic problem-solving of numbers, words, and spatial activities from birth to 16-17 years of age as the fluid ability declines with age (Bugga et al., 2006). Experience, familiarity with problems in an area, interest, and motivation, soon become the driving forces in problem-solving as the child matures into an adult and is exposed to the myriad of real-life problems found in a vocation. Application of the 20 constructs to our problem-solving thesis The ability to solve problems at a very young age is often the foundation for later career and vocational problem-solving. As children become adults, mastery and interest in different kinds of problems lead to and influence choices and opportunities which later result in different kinds of careers and vocations. Vocations and careers are the results of a myriad of things including happenstance, dedicated hard work, and interests—all necessary attributes to solve problems required by the job. Some careers require attributes of logical and spatial thinking and a realistic assessment of tasks found on the job. Other careers require mechanical, social understanding, and entrepreneurial instincts. Regardless of the attributes needed to accomplish the work, a primary need is the motivation and drive to finish tasks. Career pathways such as working in local food or department store are often opportunistic; while other career pathways, such as medicine or law are often dedicated. As children learn to solve and are exposed to different kinds of problems, their interests increase and become stronger. This occurs in many opportunistic ways, occasionally coming from parental guidance, experience gained during playtime as well as guided activities by social institutions such as schools, home, and church. Likewise, other individual interests strengthen by self-efficacy garnered through the 6|Page 7 Prepublication Copy mastery of numerical, verbal, or spatial kinds of problems that provide the basis for a career pathway. Children’s maturity, decision-making capability, and exposure lead to the solving of many kinds of problems. Cognition and decision-making capabilities increase as children grow older. In a career pathway, many current decisions are based on core values developed from the earliest moment of birth, while other decisions are based on immediate need and necessity. The experience of daily living makes it easy to identify the extremes, those who do not seem to solve problems easily or quickly and those who solve them very well; but the reality is that most people have dominant strengths, such as a faster-thinking process which increases their effectiveness in multiple problem-solving situations. This factor called the speed of processing becomes important in the solution of certain timed problems while in many untimed situations speed of processing has no effect. The complexity of the problem, as well as immediate exposure to the experiences involved in solving different kinds of problems, becomes paramount. Think about it! Young children who are taught how to pick pockets (a motor and perceptual skill) can exhibit a lot of expertise and dexterity. Adults whose strengths are dominant in the perceptual and motor areas may seem to do better at solving problems in the physical areas of engineering, construction, sports, truck driving, graphics, or repairs. Likewise, those who are conceptually dominant may do better in solving problems that require reading, extrapolation, and writing. Subgroups of people differ! General tenet and derivations of the thesis One purpose of this book is to explore and understand how people become dominant in their areas of problem-solving and how these strengths lead to different vocations, career patterns, and life choices. These dominant strengths are cataloged in the descriptions found in Appendix B. A second purpose is to increase problem-solving skills in areas of strength and areas of weakness. This can be accomplished by understanding the tenets of problem-solving. One major tenet of our thesis is: In early life, focused energy builds cognition. In later life, focused energy sustains cognition or problem-solving ability and affects the speed of processing and individual differences. Focused energy results in either adaptive or slowed problem-solving ability. Generally, focused energy is defined as the energy of the individual which is directed toward or used in the process of solving a problem. The concept of focused energy is not new; many theorists and theories have conceived of its effect. For example, Spearman (1927) proposed that the psychological meaning of the general factor of intelligence (g) was mental energy, concentration, or willpower. Rather than using focused energy, he referred to the physiological definition of energy as “neural energy.” 7|Page 8 Prepublication Copy In IPS theory, focused energy is emotional and cognitive energy (stored representation of episodic actions from interactions in the environment) which are structured (channeled) through the prefrontal cortex by repetitive experiences. Focused energy (cognition) is built and enhanced by personality, interests, and the speed of neural processing. At the cellular level, focused energy is the changing membrane voltage potential found within the neuron. Focused energy, at the cellular level, is constantly altered resulting in differences in neuronal conductivity. The differences in neuronal conductivity result in neural pathways which may increase or decrease response time to environmental stimuli. Differences in some instances are slowed or blocked thereby inhibiting problem-solving (Yizhar, O. et al. 2011). Now let’s be very exact about our thesis. Slowing or blocking the neurological pathway can simply be the result of many diverse things, including but not limited to perceptual differences. First, people‘s perceptions are both focused and diffuse. Becoming focused is a developmental attribute. Babies perceive things in gross, diffused ways while children and adults are more attuned to details. Development in the body and cells occurs from general to specific; from undifferentiated to differentiated. In general, people see many different things in the environment. As attention is focused, our sensory inputs are filtered. That is, information from multiple sources is either lost or becomes engaged as a subconscious or conscious action. Filtering is extremely important as the process allows small amounts of information to be processed instantly and simultaneously. As perception becomes focused, the details become clearer. Being able to focus on a particular attribute of a problem is necessary for the problem to be solved. The inability to focus is the result of many different biological, and psychological processes—emotions, hunger, anxiety, interest, etc. The lack of focus, goal conflicts, and degree of motivation increase response time in solving both everyday and specialized problems. Is there a neurological basis for differences in solving problems? Certainly, roadblocks or altered neural pathways occur frequently due to changes in the environment, individual differences, reproductive DNA, and even genes. Genes control early neuron development while daily experiences and interactions with objects of the environment control neuron-to-neuron conduction as well as pruning of neural circuitry. Differences in neuron conductivity occur frequently depending on developmental experiences, especially those experiences from birth to five years of age. Developmental experiences either strengthen or weaken neural circuitry based on repeated use or practice. A short explanation of our thesis is based on biomarkers and images as well as new medical research techniques. These theories suggest that neural pathways change constantly with neural conductivity. Neural conductivity is electron transfer along the axons and dendrites of the neuron. Images are the electrical patterns derived from Electroencephalography (EEG), magnetic resonance imagining (MRI), functional magnetic resonance imagining (fMRI), and positive emission tomography scans (PET). 8|Page 9 Prepublication Copy As an example, a biomarker can be an image, chemical, or substance that leads to a diagnosis of various physiological conditions. A well-known example of a chemical biomarker is cholesterol for heart disease, while a well-known image biomarker is a mammogram for breast cancer. Other types of biomarkers can be mapped with new medical techniques such as optogenetics (Zhang, F. et al., 2006; Deisseroth, K. et al., 2006). This procedure allows the mapping of circuitry in a neuron or group of neurons. In short, the technique uses light to control neurons that are genetically altered to show light-sensitive ion channels. Neural networks, using optogenetics, can be investigated via the introduction of proteins into the brains of mice for example. Since the proteins have been genetically modified, scientists can turn on and turn off functions and examine the results. This leads to the mapping of neural pathways for certain cognitive and affective responses. Techniques such as optogenetics allow scientists to manipulate circuits and understand explicit actions by changing the membrane voltage potential of excitable cells. Save the in-depth details of these complicated scientific explanations for a later discussion in the book but suffice it to say that, at this point, focused energy results in subgroup differences related to personality, interests, and cognition. These differences are manifest in the world of spatial, numerical, and verbal problem-solving. Our scientific theory is based on the foundations and pillars in many different areas of cognition, neuroscience, biology, and genetics as well as data collected on real people in real-life problems solving situations. Scientific information and data are the basis of an integrated problem-solving (IPS) theory. Why integrated? All of the achievement tests, and capability level data for children (birth to 17) are highly intercorrelated (usually above .75) suggesting a general integrative factor that can be deconstructed. IPS theory uses this, and other data explained in the next chapters to understand complex biological and psychological processes contributing to the integration of the problem-solving process. Chapter summary This is an introductory chapter that identifies, defines, and clarifies the concept of problems and the process of solving problems. The chapter also illustrates and defines the basic tenets, assumptions, and axioms underlying the theory of integrated problem-solving. A secondary purpose of our research is to classify subgroups of people and to show how taxonomic classification contributes to and influences the solving of problems. There are two classes of problem-solvers, general and differential. The scores on standardized outcome measures provide a basis for categorizing individuals by their scores on personality, cognition, and interests. One of the most important concepts in this chapter is that fluid ability (often called “gf” as explained in later chapters) declines as the maturity of the individual increases. Thus, problemsolving in the early years (birth to 16) gives rise to predictions based on various tests such as IQ. These predictions may have a basis in the early years for some individuals but as people mature 9|Page 10 Prepublication Copy the process of learning to solve problems becomes dynamic, changing, and ongoing, much more related to aging and experience. As an example, Tom Brady, the quarterback of the New England Patriots who has thrown 9600 passes may be better than a new quarterback who has never thrown a pass in the NFL. Ultimately, the problem-solving process, especially for many ill-defined and ubiquitous problems, is a product of motivation, maturity, familiarity with similar problems, personal orientation, and subgroup orientation. The author's background influences how this book is written. In medicine and veterinary medicine, there are the basic sciences that provide the etiology and mechanisms for diagnosis and clinical practice. Clinical science, the applied part of medicine, involves the diagnosis of disease. In the field of education, the same is true, psychology, and the social sciences are like the basic sciences. These foundational areas provide the basis for understanding the individual and solving problems. The first part of our journey called Tier One begins in Chapter 4. In Chapter 4, we review the literature about problem-solving, examine the processes involved, and pose a model to explain the process. In Chapter 7, Tier Two, the model representing basic physiological processes, begins. Tier Three, the chapters related to clinical practice or the daily life of solving problems at different ages, begins in Chapter 11. Chapter references Bugga, J.; Zook, N.A.; DeLosh, E.L.; Davalosa, D.B.; & Davis, H.P. (2006), Age differences in fluid intelligence: Contributions of general slowing and frontal decline. Brain and Cognition, 62, 9-16. Cattell, R. B., Cattell, A. K., & Cattell, H. E. P. (1993). 16PF Fifth Edition Questionnaire. Champaign, IL: IPAT (Institute for Personality and Ability Testing). Deisseroth, K. et al. (2006) Next-generation optical technologies for illuminating genetically targeted brain circuits. Journal of Neuroscience. 26(41), 10380-10386. Dostál, J. (2015). Theory of Problem Solving. Proceeding of Social and Behavioral Science. Published by Elsevier Ltd. An open access article under the CC BY-NC-ND license. Found online by Science Direct Duncker, K. (1945). On problem solving. Psychological Monographs, Number 58 (whole 270). Maier, N. R. F. (1931). Reasoning in humans: II. The solution of a problem and its appearance in consciousness. Journal of Comparative Psychology, 12, 181-194. Newell, A. & Simon, H. A. (1972). Human problem solving. Englewood Cliffs, NJ: PrenticeHall. Spearman, C. (1927), Abilities of man. New York: Macmillan 10 | P a g e 11 Prepublication Copy Wordsworth, W. (1807). “My Heart Leaps Up”; Poems, in Two Volumes, British Library, Public Domain. Zhang, F. et al. (2006). Channelrhodopsin-2 and optical control of excitable cells. Natural Methods, 3(10), 785-792. Yizhar, O. et al. (2011). Optogenetics in neural systems. Neuron, 71, 9–34 11 | P a g e 12 Prepublication Copy Chapter 2 Integrative Problem-Solving Theory Introduction IPS theory provides the foundations for understanding how environmental match or mismatch as well as learning modifications occur during the early years of development and contribute to solving problems academically and non-academically in everyday life. The problem-solving process begins at birth and continues through many different cognitive and affective phases of life. Consistency, adaptations, and change lead to many modifications of the conscious, subconscious, unconscious, and neural pathways. From the moment of birth, individuals filter information from the environment, determining whether the press from objects or people provides harmony or consternation. Layers, which are just neurological pathways that either facilitate or hinder information along nerve fibers, provide the basis for filtering in the conscious, subconscious, and conscious. A small number of layers contribute to more efficient problem solving while a large number of layers inhibits or delays problem-solving. Complex layers are formed when emotions and affective feelings are so constant as to inhibit or interfere with everyday problem-solving. Layers that are formed when there is a mismatch to the environment, either in terms of the child’s or adult’s intentions affect surface characteristics and one approach to solving problems. Complex layers result in neurons or brain networks holding memories with conflicting feelings, emotions, and information. Surface characteristics or how one appears to others are the direct result of the complexity of layers. When people approach everyday and academic problems, their methods, style, or habitual patterns are both conscious and subconscious. The conscious approach to solving problems results in adaptation and change to the existing problem. However, conscious patterns of approach are intertwined with autonomous actions learned from previous encounters. These habit patterns affect the surface characteristics of the individual and result in response patterns that form the basis of how subgroups of people solve problems. There are many ways to illustrate the IPS theory and its usefulness in solving problems. However, the process can be very complicated and technical; so, one simple method of conveying the essence of the theory is the following statement. How one acts, how one thinks, and the individual’s everyday interests influence how problems involving words, numbers, symbols, and combinations thereof are solved. The statement is quite straightforward; however, the application requires many limits and qualifications. 12 | P a g e 13 Prepublication Copy Data collected with multiple kinds of instruments and measurement constructs determine the boundaries of the IPS theory. One of our instruments measures interests while another measures the speed of processing and cognition in the brain. The instrument for measuring problemsolving uses 8 constructs denoted by the following subscales: Perceptual (Per-p1), Conceptual (Cn-p2), Motor (Mt-p3), Analytical (An-p4), Social (Soc-p5), Control/structure (Ct-p6), Flex (Fxp7), and Introversion/ extraversion (EI-p8). Cognition denoted by the terms Psa, Ps30, Pssp, and Pslap is measured by analogies, series, and spatial problems. Psa represents the total problemsolving score for the non-cognitive instrument while Ps30 is the total of analytic and spatial scores for the cognitive. Pslap is the summary score for analogies and sequence items while Pssp is a summary score for spatial items. Reviews of literature for all of these constructs are located in Chapters 23-27. Information gathered from these definitive problem-solving subscales along with data garnered from career and interests which, for this book, are conveniently named after Holland’s subscales (Realistic (CR1), Investigative (CR2), Artistic (CR3), Social (CR4), Enterprising (CR5), Conventional CR6) help in the prediction of subgroups problem-solving behavior. Although we developed completely different career items and subscales (see Chapter 19), six of the subscales, for research purposes in this book, use the same nomenclature as Holland’s RIASEC. Together, personality, cognition, speed of processing, and interests help to identify two different major groups of people—the general problem solver and the differential problem solver. The information from all of these combined instruments illustrates how subgroups have different propensities for solving academic, work, and practical problems in everyday life. The problem-solving process is contingent upon many unknown factors that exist as part of the person, the environment, and the interaction of both. IPS theory suggests that factors such as individual differences, environmental press, filters, and learning are at the heart of one’s propensity to solve a problem. Individual differences Individual differences start at the moment of conception. Prenatal ultrasound pinpoints gross biological developments in the early embryo and allows inspection of organ developments from an embryo the size of a pinhead. Technology provides ways to follow the effects of different genes on each part of the anatomy from the fingers to the brain stem. At the heart of this prenatal development is the differentiation and specialization of cells, particularly the neurons and cells in the brain. Our theory about individual differences begins with the energy passed to the embryo via the chromosomes of the mother and father. Energy, found in the mitochondria of the cytoplasm of the sperm and the egg, is the driving force and the impetus of all further interactions within the 13 | P a g e 14 Prepublication Copy embryo until the fetus is born. Energy in the form of sugars identified as adenosine triphosphate (ATP) and adenosine diphosphate (ADP) provides the fuel for the differentiation and specialization of cells. Energy forms the foundations of all individual differences resulting in cognition, emotional feelings, and interests. Individual differences from an evolutionary perspective begin with lifelong development. The long development history of homo sapiens provides a tremendous edge in the struggle for evolutionary survival. Most other species must instinctively find an immediate method of survival in a predatory environment while our species can develop under the care of many significant others (mothers, fathers, caregivers) for almost 18 years. This long developmental process gives each individual a way of finding the best path to longevity and successful problemsolving. At this point, the most important years in the development of individual differences and the solving of future problems extend from birth to approximately five years of age, the time before the entrance to formal schooling. This period of development is emphasized less by many parents as the neonate seems to be a morass of emotions, unintended consequences, and happenstance. Many parents underestimate the tremendous cognitive and emotional growth occurring during this time. The brain, during the first year of life, is similar to the proverbial sponge soaking up every possible source of environmental input. Constant neuronal additions of brain cells occur so rapidly as to defy imagination. The newborn is constantly learning new things. With each interaction comes memories, values, and cognitive experiences that form the basis of later problem-solving activities and individual differences. Constant interaction with people and things in the environment shapes the future. Brain pathways Brain pathway which results from constant environmental interactions established early in life contribute to measurable individual differences. Brain pathways consist of networks, fiber tracts, and neurons, places where memories and energy transformations are stored and processed. Some children and adults, due to individual differences in emotional and affective development, as well as experience, and maturity, become stymied, delayed, or have a deficit (lesions, trauma) in these pathways. These difficulties may impede the solution of everyday and academic problems. Whether it does or does not depends on a host of unknown factors that are experienced daily as neural plasticity (from the brain’s structure and function) adapts and changes. 14 | P a g e 15 Prepublication Copy Brain plasticity The brain consisting of fiber tracts builds numerous superhighways from birth. A superhighway is a neural pathway that connects networks of neurons for information transfer. The brain uses the same pathways over and over as long as the environment is consistent. Problems are solved via these pathways. However, if one superhighway becomes blocked, then a series of secondary roads are used. The brain’s changing neural pathways lead to the concept of neural plasticity which is the ability of the brain to rewire itself constantly. A more technical definition of plasticity asserts that neurons can change dendritic connections based on chemical gradients. Information coming in via the eyes, nose, and ears is constantly recorded over and over in many brain neurons and networks and contributes to brain plasticity. The brain’s ability to rewire, reroute, and use alternate pathways are methods of overcoming learning disabilities and delays which occur in problem-solving. Sometimes the brain can overcome immense difficulties by rerouting and rewiring as individuals with half of the brain have been successful in having a normal life. In other cases, the brain cannot adapt. Luria (1979) recounts the story of a patient wounded in the war with a piece of shrapnel lodged in the brain. The shrapnel was at the intersection of the occipital lobe (vision processing), temporal lobe (sound and language processing), and parietal lobe (sense processing). This man had difficulty telling time, reading, writing, and comprehending speech. In his case, the brain and its plasticity were unable to compensate for learning and neurological deficiencies. Brain plasticity is not the only method of overcoming delays and impediments to problemsolving. Individual differences give rise to other ways to compensate for and improve day-today functioning. Compensatory mechanisms occur daily in reactions to events in the conscious, unconscious, and subconscious minds. Conscious, unconscious, and subconscious pathways The conscious, unconscious, and subconscious pathways in the brain are active, constant participants in the solving of problems. Many of the mind’s problems are part of everyday living; while others are more abstract and academic. The conscious mind has neural pathways directly connected to the cerebral cortex and its auxiliary areas; while the subconscious mind is part of the autonomic nervous system. Both conscious and subconscious neural pathways differ from what is called the “unconscious.” The unconscious, as defined by psychologists, exists as thoughts that are not part of the conscious thinking process. These thoughts represent repressed ideas and feelings. The unconscious exists, in part, as representations from either short-term or long-term memory storage which have not been acted upon. 15 | P a g e 16 Prepublication Copy The subconscious mind exists in direct contrast to the conscious mind. The subconscious which is carrying out many mandatory functions keeps one alive and well. The subconscious mind is often called the “reptilian brain stem” because evolutionary heritage uses less energy, operates in the present, and controls many of the basic processes of daily functioning like breathing, heart rate, and movements. The subconscious mind accesses long-term memory to carry out many decisions related to events that occur repeatedly. The subconscious mind, using about 200,000 neurons, makes many decisions relative to what one eats, drinks, wears, and does at any moment of the day. The conscious mind works in concert with the subconscious mind to solve daily problems that occur repeatedly. Both are operating simultaneously but the conscious mind is active as brain pathways are constantly stimulated by environmental stimuli. The brain pathways for the conscious mind use about 15 billion neurons and fire with enough energy to power an athlete’s muscle. The conscious mind is extremely powerful, delays or expedites daily decisions, and controls voluntary muscle movement. Acting to overcome any existing threats, the conscious mind accesses memories of the past, makes decisions in the present, and plans for the future. The conscious mind feels the pressure and anxiety coming from the environment and reacts with other neural pathways to inform the amygdala (a place of feelings and emotions) to determine if there is a need to panic and then stores information in either short-term or long-term memory. Once the information is stored than the process begins all over again. The message becomes: “should I react to any new and existing pressures found in the environment?” Existing environmental pressures are defined in IPS theory as environmental press?” Environmental press The invisible pressures exerted from the environment are all-encompassing and are defined in IPS theory as ‘environmental press’; pressures that inhibit or facilitate problem-solving. Environment press is critical in problem-solving as it contributes to the molding and shaping of the child and adult in the same way that the energy of the universe shapes and molds the earth and its crust. Environmental press is the energy, pressure, and emotion exerted on the newborn and caregivers at any point in the developmental period from birth. Even from the beginning of life, the interactions of parent and child allow for the solution of daily problems based on immediate experience and abstract thought. Parents are often the mediators of experience as parents act to interpret, explain, and facilitate the daily interactions and events surrounding children in the first years of life. The amount and kind of interactions that children have with their parents are important in determining the child’s orientation toward solving problems. Each interaction cumulatively modifies existing behavior and the ability to adapt to new situations and solve new problems in life. 16 | P a g e 17 Prepublication Copy Environmental press which is facilitative in problem-solving leads to safety, awareness, and security. Security for the newborn child is based on consistencies, a response to the changing press of the environment. Consistency, especially in the early years, is the routine of everyday life, i.e., being the same so that expectations and trust for the caregivers are strongly developed. Consistencies which are the forerunner of control and structure in personality, are learned from everyday activities. However, consistencies should be balanced by adaptability, and the ability to learn quickly how to change and survive, not just by the child, but also by the caregiver. Consistencies at any age are based on many different things, but in particular, how thoughtfully parents adapt their parenting skills and approach to the changes that youngsters are going through and vice versa. Certainly, early training and interaction of both parents and children are important as the child undergoes modifications in behavior and thought. Modifications Modifications in behavior and approach are important in solving daily problems as some changes are adaptive or while many others are not. Modifications are changes in behavior, ideas, and thoughts that occur because of the environmental press. Modifications can be adaptive, harmless, or occasionally destructive. Changes in behavior and thought which are not adaptive result in resistance, obstructions, and sometimes negativity. Modifications take place as the parents or caregivers provide a ‘learning and living environment’; a place for the child to interact and change. Modifications occur when the environmental press is greater than the intentionality exhibited by the child. The child can intentionally react to the outer world. When the child exerts his or her ideas, thoughts, and energy on the problem-solving situation, the child exerts intentionality. Intentionality includes any form of emotion, cognitive thought, or interest. If intentionality is greater than the environmental press, the child has more control of the situation; while the converse is also true. Modifications necessitate internal and external control. Control of internal impulses is somewhat natural, but control is mostly from environmental sources (parents) in the early years of a child’s life. When a child is left to his or her own accord, internalization of values, attitudes, and beliefs occurs from the immediate environment. This includes values, attitudes, and ideas from the major caregiver(s) and non-caregiver(s) who spends more time with the child. Control or conscientiousness is an internal modification to external pressures from parents, significant others, church, and schools. Consistency in behavior comes from a match between the environmental press offered by parents and significant others and the internal modification made by the child. Modification is dependent upon the filters used by either or both the child and caregivers. 17 | P a g e 18 Prepublication Copy Filters Filters are the result of attention directed toward objects during the problem-solving process. At any given moment in life, sensory information from TV, radio, light, and people bombard the individual. The subconscious works overtime to filter all kinds of information, especially information temporarily stored before it is repressed or brought to conscious awareness. Blindsight is the term documented by Lawrence Keiskrantz, a British psychologist. His work reported how people can report details about events occurring around them, even events that are not part of conscious awareness. Studies such as this and others in neuroscience have noted how conscious awareness constitutes only a fraction of information being processed in the brain. During problem-solving situations, attention is directed toward the salient characteristics of the problem. Attention and filters can keep one on task or result in a diffuse focus. A diffuse focus that comes from holding multiple images, sounds, and feelings acting simultaneously usually confuses those who are very young. According to IPS theory, filters result in an energy transformation that skews or changes a neurological pathway. A filter, a precursor to a neurological layer, begins to form if the behaviors, attitudes, and internal representations of the child are inconsistent with the desires, wishes, and actions of the caregivers or others. Filters funnel subconscious and unconscious impulses, thoughts, and feelings while the brain is on automatic pilot. Filters also give rise to inconsistent behaviors such as feelings, impulses, and thoughts which may be contrary to actions in the environment. Inconsistency from parents and others in the environment often leads to confusion and difficulty in problem-solving on the part of the child. Inconsistency from parents results from a parenting system that is different each time that a parent offers rewards and punishments to the child. Parents often punish children for actions which at the child’s intellectual stage of development, are not comprehensible. (Most very young children do not understand “why” they are being punished; only that they can “feel” the punishment). Short-term memory traces and layers are formed in the early stages of birth. Layers In IPS theory, layers result in a slowing of decision-making and are detrimental to the problemsolving process. Layers in the child occur when the inclinations of the child are contrary or opposite to the inclinations, control requirements, and values of the adult or the family in which one lives. Layers (as a result of modification or changes) are part of growing neurological shells in either the parent or the child. Layers, physiologically, are just neurological fibers, networks, and tracts that have emotions of pain, suffering, and abuse stored in long-term memory. 18 | P a g e 19 Prepublication Copy A simple layer can result from the emotional memories and affect associated with loud noises exhibited simultaneously with screaming words such as No! No! No! Autobiographical memory becomes replete with painful memories that are networked via groups of neurons in various brain regions. Although at the time of this writing, science suggests that long-term memories do not exist in children less than two, our contention is that painful episodes that occur in the neonate (12-24 months) are stored and may resurface in later years. This contention is similar to many early theorists such as Carl Jung (1916/1920) and Sigmund Freud (1905/1961). The greater the number of networks and neural regions involved, the greater the number of layers that must be traversed via problem-solving interactions. A large number of layers leads to slowness in problem-solving as the child or adult must resolve internal emotions before cognitively processing external stimuli. Neurological layers result from conflicting sets of long-term memories that come from inconsistent actions and behaviors occurring in the environment. Thus, cognitive information pulled from one set of memories can be in direct contrast with cognitive information and emotional feelings existing in another set of memories. An unstable environment where conflicting messages relative to stimulation and affection form a neurological layer which increases the disparity of internal actions and thinking between significant others and the child. A very young child (0-2) can store memories but cannot control emotional reactions. (The assumption is that the child wants to receive love and affection and avoid harsh punishment. Between the ages of 0-2, the child does not think ahead as he or she has just reached a stage of internal representation and responds mostly to external pressures which are a part of the environment). A harsh parental control system, an unstimulating environment, and abusive conditions do not produce the foundations for problem-solving behaviors since the child becomes reluctant to interact with the things in the environment. Interactions from the environmental press can be too strong and negative and inhibit a child's movement and exploration of the current environment. This causes the child to act more on internal representations and move away from the reality of events in the environment. An environmental press that is too stressful, not stimulating, and occurring over a long period leads to greater passivity and conformity or reliance on internal representations as a source of stimulation. Too much reliance on internal representations at an early age leads to withdrawal and a lack of understanding of how to deal with everyday problems in the real world. This can be observed in slowed responses (confusion, hesitation, bewilderment) as young children solve very simple problems such as trying to put a round block in a square hole. This confusion directly relates to the amount and kind of internal layers formed. Layers continue to develop if the child does not have some success in solving simple problems in daily life. Success in various kinds of motor actions is necessary from birth to two years. Simple problems, as stated earlier, occur in daily life and are associated with survival such as eating, drinking, and breathing. Almost all early kinds of success in the first 12 months of life are motor in origin. However, behind every motor action is a smile and a thinking process that forms the 19 | P a g e 20 Prepublication Copy foundations for social and abstract thinking. The brunt of the IPS theory is left for later chapters (9-16) which explore the developmental years and problem-solving from neonates to senior citizens. For now, let us now examine the concept of surface characteristics which provide the window to personality and cognition. Surface characteristics When solving simple and complex problems, each person brings to the problem-solving process their thoughts, values, ideas, personality, and interests. Together, all of these characteristics represent the persona and are expressed as surface characteristics (Gittenger, 1992). Surface characteristics are important when teams or groups solve problems. Surface characteristics are the cues that bring bristles to the back of the neck or feelings of warmth and satisfaction to the heart during the problem-solving process. Surface characteristics are directly affected by the size of the developed layers. Layers continue to form as conflicting information about joy, sadness, and pain are stored in memories in different places in the brain. Cognitive dissonance comes via the conflict in information about the pain or its stored affective emotional feelings. Shells or layers influence the ability or inability to solve problems. An association from an episode of pain causes emotional reactions that can completely interfere with cognition thereby stirring some rational and other times irrational actions. What one sees is not what one necessarily gets! Surface characteristics are especially important when trying to classify individuals or their behaviors. Surface characteristics are likely to represent true feelings, behaviors, and thoughts when layers are thin and pliable. As the depth of the layer increases, surface characteristics are false representations of thoughts and ideas which cause misclassification, and misrepresentation of the individual. That is, thick layers or complex and multiple neurological pathways filtered through different parts of the brain may produce responses that are not representative of the individual’s true feelings, ideas, or thoughts. A young man or woman who is continually fighting internal emotions may not have the energy to deal with problems in the outer world. This is often exhibited in children who are withdrawn, not interactive, sullen, or difficult in general to reach. It is almost impossible to teach children how to solve problems in their daily life if they are mentally and emotionally unavailable. Feelings, emotions, interests, and cognitive processing interfere with or facilitate problem-solving and lead to identifiable differences in types of problem solvers who are classified in our system as general and differential problem solvers. 20 | P a g e 21 Prepublication Copy General and differential problem solvers In IPS theory there are two general classes of problem solvers. One is designated as a general problem solver and the other as a differential problem solver. The general problem solver has some different experiences in school, life, and career patterns than a differential problem solver; however, many experiences may overlap. Both general and differential problem solvers have success in life with similar and different kinds of problems. The definitions, which differentiate the general and differential problem solvers, are based on both cognitive and non-cognitive interests and personality characteristics. Since a lot of our data was collected on students in grades 2 through 12, a general problem solver was defined and operationalized as a child scoring higher on problems related to words, numbers, and spatial objects as well as scoring higher scores in areas related to self-concept, learning self-concept and speed in the solving of complex problems. In contrast, differential problem solvers scored well in some of the same areas but not all of them. Utilizing normal curve results in a rather small number of general problem solvers (about 14 percent) and a large number of differential problem solvers (about 86 percent). Both groups contribute substantially to society. When academic schooling is over, education begins. It is the education of individuals in the world of experience that assists in clarifying the characteristics of the differential problem solver who begins to “shine” in many different real-world careers. Differential problem solvers are often the pillars of many communities, providing service and assistance in solving many daily problems. Differential problem solvers often excel in specialized areas of math, science, and history after choosing or being selected for a work environment. In some cases, the general and differential problem solver ends up in the same kind of career. A differential problem solver may solve some career problems better than a general problem solver. There are no limitations on hard work, industriousness, and experience as this book illustrates how problem-solving is the product of exposure, interest, self-efficacy, identity, and practice. Extreme individual differences show vast differences in problem-solving ability. Different kinds of problems found in everyday life have different levels of task simplicity and complexity. This suggests that people who can solve very abstract academic verbal, numerical, and spatial problems are going to have different experiences and different kinds of daily interactions than those people who solve very real and practical problems in the world of everyday life. However, the spectrum of the numerical, word, and spatial problems which exist between the extremes of task complexity leaves plenty of opportunity for success in solving problems for all types and kinds of individuals and their subgroups. 21 | P a g e 22 Prepublication Copy Concepts, and energy flow Many experiences in life are the result of the application and solution of problems encountered either as part of the work experience or in daily living. Our thesis and theory are applied in reallife situations by information from the multiple concepts which clarify the problem-solving process through quantification and classification based on our measuring instruments. Each of these constructs is integrated around cognitive, personality, and interest patterns which help clarify the complexity of problem-solving. The key to solving problems is that learning and adaptive changes occur constantly over a lifetime. Each person’s individual experiences hone skills in solving both general and specialized problems and lead to many individual career paths. The brain has many different kinds of networks that function simultaneously in different regions. In later chapters, there are explanations of how parts of the brain work in competition with each other. This unique ability of homo sapiens give rise to competition from flex and control, from thinking and feeling, and from the sensory-motor to conceptual processing. These checks and balances provide a realistic explanation of how differences occur in energy flow throughout the body. Energy flow is the process by which internal thoughts move from the brain to the outside environment or continue to be processed repeatedly in the brain. Energy flow gives rise to personality characteristics such as introversion and extraversion. Subgroups and subgroup patterns Whenever possible the characteristics of the dominant individual differences are examined through a taxonomy that places individuals with similar characteristics together in a subgroup. Our premise is that similarities in approach to solving problems bring about habitual patterns that help define definitive subgroups. It is almost impossible to categorize any single individual as individuals change and adapt so rapidly. However, by grouping individuals into a subgroup, one can better understand the single case, the person. This occurs by comparing and contrasting how the person differs from his or her idealized subgroup. Let’s repeat that axiom since it is so important. Accurate predictions of individuals cannot be made, especially where actions, thoughts, ideas, and values of a person change quickly in daily activities. However, one can define a prior meaning of the person’s subgroups and then compare how each person differs from the “ideal” cognitive, personality, and interest pattern exemplified by the subgroup. In Appendix B, 36 ideal subgroups have different cognitive, personality, interests, and cognitive patterns. Each subgroup has been carefully constructed over 40 years from the 20 variables which define the measuring instruments and the correlations which interpret the direction of 22 | P a g e 23 Prepublication Copy interactions. The process of classification occurs through machine learning programs defined and elucidated in Chapter 22. How does one define and build a descriptive subgroup? First, determine a person’s score on cognitive and non-cognitive assessments. Different kinds of items, preferences, and academic tests are used to assess verbal, numerical, and spatial cognitive as well as non-cognitive skills. The combination of scores from personality, interests, and cognitive items helps categorized children and adults into major groups and then subgroups. Those individuals who score higher in all areas (personality, interests, cognition) are categorized as general problem solvers while those who score higher in just some of the areas are classified as differential problem solvers. Then, using various subscales, we identify a subgroup pattern. The subgroup pattern comes from the deconstruction of the intercorrelations of the 20 variables identified by the different measuring instruments and the individual’s responses to those instruments. The process of grouping individuals who are more alike as a method of understanding individual differences is certainly not new or different. The history of psychological assessment is rife with groups and subgroups of people. Many researchers use profiles; however, the number of subgroups is usually very small. One exception is Raymond Cattell’s 16 Personality Factors (Cattell et al., 1993) which attempts to capture the complexity of human nature with multiple subscales and categories. Anytime, profile patterning is used, the number of possible groups can be astronomical depending on how the groups are exhibited by the standard unit scores. Picture 2 below shows how the 36 different subgroups (labeled 1 through 36) are distributed by distance measures based on their standard scores. The objective is to get as much separation as possible between all different subgroups while having those subgroups which are more similar being closer together. 23 | P a g e 24 Prepublication Copy Picture 2: Subgroups 2-Dimensional Picture of the Distribution of Subgroups by Non-Metric Distance As an example, subgroups 1 and 4 are very close; the profile scores differ in only a few areas. However, subgroups 1 and 4 differ considerably from subgroup 30 and subgroup 28. Subgroup patterns are based on standard scores of personality, cognition, and interests. The standard or raw scores of any new person can be compared to the subgroup pattern with the assumption of likeness in groups. However, as expected, it is very difficult to classify subgroups or individuals when surface characteristics are not congruent with true underlying feelings, thoughts, and ideas. Or when an individual purposely falsifies a response. In such cases, usually, the individual vigorously objects stating that the descriptive subgroup has no relation to his or her person. True enough!! Chapter summary IPS theory drives the 3-tier model built for understanding the differences in the solving of everyday problems using numbers, words, and spatial activities. IPS theory is based on scientific assumptions from many areas, including but not limited to psychology, physics, education, information processing, and biology. Individual differences highlight a basic style and solution to problems; however, the brain pathways, brain plasticity, and conscious, as well as unconscious 24 | P a g e 25 Prepublication Copy elements drive many automated functions of everyday life. Every approach to a problem whether simple, complex, or compound is filtered by previous experience in solving similar problems. IPS theory encompasses both individual and the environment as both are important in solving any problems. Environmental press leads to modifications in behavior and thinking patterns. Layers are built through emotional trauma and pain from the earliest moments of life. Each person displays the surface characteristics of his or her persona. When there are few layers and few modifications, surface characteristics mirror underlying values. In such cases, the categorization of individuals is possible. However, when surface characteristics resulting from modifications and filters of the environmental press are too great, the categorization of problemsolving characteristics of the individual is usually in error. IPS theory is based on the notion that the present stage of research has established at least 5 foundational areas based on the work of Costa and McCrae (1995) as well as others. Integrating cognition and career with personality to obtain more precise measurements of subgroups in the world of problem-solving can provide a fresh look and a different perspective on existing areas of research. Chapter references Freud, S. (1905). Jokes and Their Relation to the Unconscious: Translation, Penguin Modern Classics Paperback: International Edition. Freud, S. (1964) The Psychopathology of Everyday Life. Strachey, James (Ed), Oxford, England: Macmillan. The standard edition of the complete psychological works of Sigmund Freud. Gittinger, John, (1992) PAS Atlas, MARS Assessment Technology Inc, Sterling Virginia, Edwin W. Gunberg editor. Jung, C. G. (1916). Collected Papers on Analytical Psychology (tr. by C. Long). London: Jung, C. G. (1925). Problems of Personality. Studies in Honor of Morton Prince. New York: Harcourt, Brace. Luria, A. R. (1971). A man with a shattered world: The history of a brain wound., Harvard University Press, Cambridge, Mass. Translation by Lynn Soltaroff. Republished 1987. Further readings: Blech, C. & J. Funke (2010). You cannot have your cake and eat it, too: How induced goal conflicts affect complex problem solving, Open Psychology Journal, 3, 4 25 | P a g e 26 Prepublication Copy Funke, J. & P. A. Frensch (2007). Complex problem solving: The European perspective – 10 years after, in D. H. Jonassen (ed.), Learning to Solve Complex Scientific Problems, Lawrence Erlbaum, New York, 25-47. Funke, J. (2010). Complex problem solving: A case for complex cognition? Cognitive Processing, Vol. 11, 133-142. Klieme, E. (2004). Assessment of cross-curricular problem-solving competencies, in J. H. Moskowitz, M. Stephens (eds.), Comparing Learning Outcomes. International Assessment and Education Policy, Routledge Falmer, London, 81-107. Maier, N. R. F. (1931). Reasoning in humans: II. The solution of a problem and its appearance in consciousness. Journal of Comparative Psychology, 12, 181-194. Mayer, R. E. & M. C. Wittrock (1996). Problem Solving Transfer, in R. Calfee, R. Berliner (eds.), Handbook of Educational Psychology, Macmillan, New York, 47-62. Mayer, R. E. (1990). Problem solving, in W. M. Eysenck (ed.), The Blackwell Dictionary of Cognitive Psychology, Basil Blackwell, Oxford, 284-288. Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving, Instructional Science, Vol. 26, 49-63. Scott, B. K. (2015). What's the correct spelling: ExtrAversion or ExtrOversion? Online Retrieved on 10/1/2016 from http://blogs.scientificamerican.com Winne, J. F., and Gittinger, J. W, (1973a) An introduction to the Personality Assessment System, Journal of Clinical Psychology, Monograph Supplement, 38, 1-68 Winne, John F.; Gittinger, John W. (April 1, 1973b). "An introduction to the personality assessment system". Journal of Community Psychology. 1 (2): 99–163. doi:10.1002/1520-6629(197304)1:2<99: AID-JCOP2290010202>3.0.CO;2-U . 26 | P a g e 27 Prepublication Copy Chapter 3 The Definable Characteristics of the IPS System Introduction Our quest for understanding is inherent in the Integrative Problem-Solving System (IPS). The working model has different components similar to a model train which has an engine with different kinds of railroad cars. Each component has a different name and contributes to the total understanding of the IPS system. The foundation of the problem-solving process is based on categories. Categories signify the broad thinking constructs which integrate the overall manner in which people approach problems. Categories are interwoven with smaller building blocks called elements. Elements are interests, thinking mechanisms, and emotions designated by labels from instruments such as career and interest, personal style, speed of processing, and cognition. Elements are generated from the daily experiences of people from childhood to adulthood. Each daily experience influences a person's perceptual process; that is, how each sees the world around him or herself. Ultimately, the cumulative effect of these daily experiences is the ability to solve problems which leads to a strong career and vocational path. Defining environments There are two environments emphasized throughout this book: traditional and non-traditional. A traditional environment encompasses the events associated with school and classroom-based learning while a non-traditional environment encompasses learning which takes place outside of schools and classrooms. Traditional environments, as currently taught in American schools, have learning outcomes or skills which are unipolar-right and wrong. Learning in traditional environments is measured by achievement and power tests in school-based situations. School-based learning occurring in a traditional environment is often domain-specific as the problems and knowledge are organized structurally and sometimes hierarchically in books. For example, the knowledge of mathematics is organized by books found in courses in general mathematics, algebra, trigonometry, and calculus, while the knowledge of history is found in books entitled “American history”, “World History, European History, etc.” School-based learning is often domain-specific and hierarchical in the sense that knowledge found in one course is the foundation for knowledge in another course. Likewise, traditional classroom environments emphasize verbal, numerical, and spatial problems and solutions. 27 | P a g e 28 Prepublication Copy A non-traditional learning environment is an experience that is outside the formality of traditional school-based learning. This includes problems found in the shop and homemaking classrooms, as well as non-classroom settings such as jobs, companies, church, home, and daily living. This book is based on the assumption that developmental learning and experiences take place “inside” and “outside” the classroom. Ultimately, we measure the validity of IPS based on solving problems in real-world environments. Our choice was the decision-making capabilities of managers who had to solve everyday problems in companies. The three-tiered model used to explain problem-solving is all-encompassing as it gives credence to learning and problem-solving in traditional and non-traditional environments. Non-traditional learning environments have a powerful effect on the individual and subgroup. Non-traditional environments provide the skills of problem-solving for both the general and differential problem solver. Learning at home before entering the classroom for the first time has the greatest effect as it sets the foundation for lifetime learning. Classroom learning also has a powerful influence as it provides the basis for organized knowledge and further education. Defining speed of processing Speed of processing is a psychological construct that has been studied for over a hundred years. In physiology, the speed of processing is a form of electrochemical activity, which flows along neural pathways and becomes the basis of mental speed. In a narrow and reductionist context, That processing is heralded as a major contributor to individual differences. The dictum, whether true or not, is that intelligent people process information faster and solve problems quicker and more efficiently. The reason for these statements is based on many reviews of research literature (See Chapters 25 & 26 for a review). In IPS theory, brain processing speed, either fast or slow, contributes but is not essential to the solution of problems. Our construct of the general problem solver is based on those who process well-defined numerical, verbal, and spatial problems faster and more efficiently; while our construct of differential problem solving is based on those who spend long hours on problems of interest or problems of necessity, either in academia or not. In this book, the speed of processing (S1-S4) is defined by four different kinds of data assessments: Perceptual Flexibility (S1-PF); Scanning a field of curved and straight lines from an exemplar. Letter identification (S2- Letid); Picking out a specific letter such as an ‘x’ or ‘e’ from a crowded field of many lines of random letters (measures the discrimination of letters). Embedded Designs (S3- Emb) Having the individual circle an embedded figure in a group of embedded designs (measures dis-embedding of the part from the whole). 28 | P a g e 29 Prepublication Copy Arithmetic distraction tests (S4-Arith). Performing a simple arithmetic operation such as adding (1 + 5 -2) in a distracted field. Data has also been collected using a 2-minute memory test (M1-M2) to assess the ability of young children to hold letters and symbols in short-term memory. Defining other cognitive outcomes In our model, the outcome of solving problems is skill-based where a skill may be either unitary or part of a set of skills. The skill might be a special talent or a special ability but, in most cases, the skill comes from repeated skill building, exposure, and practice developed over time from birth. Skills result in mastery which increases self-efficacy and self-confidence. Skills can be academic, motor, physical, or combinations thereof. An example of an academic skill is solving a mathematical equation, writing a paper, or developing a project. A motor skill might be throwing a football, performing a floor gymnastic exercise, or painting a picture. Emotional and cognitive energy is transformed into focused energy as the person is rewarded or not rewarded for a particular skill set. The most prolific theorists in the areas of cognition are Carroll (1993), Horn (1965), Vernon (1950), and Cattell. (1971/1987). From a measurement standpoint, when modeling intelligence, most cognitive theorists have the general ability (“g”) as a major factor followed by broad groups of second and third levels. Carroll’s explanatory model has wide acceptance. Carroll’s intelligence model incorporates two concepts originally coined by Raymond Cattell called fluid intelligence and crystalline intelligence. Fluid intelligence is composed of sequential reasoning and inductive reasoning while crystalline intelligence includes verbal and reading comprehension. Another factor of Carroll’s is knowledge and achievement which incorporates general school achievement as well as verbal information and knowledge. Perceptual speed memory and mental reasoning are also separate factors. Finally, there are two closely related vectors named visual perception and closure. If “g” is a part of problem-solving, then data collected over many different age groups should suggest the “how” and “why. “In IPS theory, two different kinds of assessments, logical analysis, and spatial reasoning are used with achievement tests and teacher observations to assess skill development. Logical analysis (C1-Pslap): A series of 6 analogies and 6 sequence problems that are untimed. Measures logical thinking (Examples in Chapter 20) Spatial analysis (C2-Pssp): A series of 5 pictures of blocks arranged in various spatial configurations and 3 drawings that require perceptual and spatial reasoning. (Examples in Chapter 20) 29 | P a g e 30 Prepublication Copy Ps30: A composite measure of logical and spatial analysis Psa: A composite measure of problem-solving derived from non-cognitive variables which correlate with teacher observations, and achievement test data When teacher observations are combined with cognitive assessment and achievement tests, the results help define the limits of early problem-solving skills (ages 7-11). As noted, throughout this book, early problem-solving skills are the foundation of later problem-solving skills and in some instances, define the major differences between older general and differential problem solvers in the solution of verbal, spatial, and number problems. In the early developmental periods of life, skills are developed in the home, church, or areas of exposure such as pre-school. Later, schools use standardized tests that represent one measurement of skill development in academic subjects such as English, math, and science. Many other types of artistic and manual skills are developed in music, art, and vocational classes or outof-school experience. To define categories for taxonomic purposes, all types of problem-solving outcomes must be used and related to the elements (personality, interests, and cognitive processes). IPS theory suggests ways that elements become variables that define skill-based outcomes. Later in the book (Chapters 13-16), many different types of problem-solving outcomes related to the speed of processing and standardized testing are examined. Defining preferences So, what are preferences? Preferences are conceived as how individual emotional and cognitive differences (hence energy) are accentuated in the environment. Preferences come from individual choice and experience in the selection of activities in the environment. For example, a child who prefers to spend most of his or her time outside running, jumping, and engaging in play activities has different preferences than a child who prefers to spend most of his or her time inside reading books. Likewise, a parent who prefers not to have their children outside in uncontrolled situations presents a different environmental press, and therefore a different modification of their children's behavioral patterns than a parent who prefers to let their children play in uncontrolled situations. Each different parenting activity contributes to and interacts with a child’s preference pattern. Preferences incorporate both interests and values and are reflections of personality and cognition. Often time what the child or adult prefers to do (their interests) also determines or reflects what each person values. If one spends a lot of time playing chess, then presumably one is interested in the cognitive activity and enjoyment of various strategies, and competition. Likewise, if one spends a lot of time in church-related activities, this reflects values related to religion and social 30 | P a g e 31 Prepublication Copy aspects of living. Thus, preferences help to define the temporary or core level of interest or values that a person holds. However, as is expected, core levels of interests and values are very difficult to uncover. The use of items on objective tests as well as personality and interest questionnaires is one method of defining preferences. Item preferences by the individual are unidirectional and unipolar for cognitive power tests while non-cognitive items reflect bipolar scales and sometimes multidirectional orientations. Inherent in the choice of items is the assumption that if a person selects one preference over another then this represents a reflection of their values, ideas, personality, or modes of thinking. Defining categories -problem-solving/personality In the IPS model of identifying different categories of problem-solving behaviors, there are 10 personality and cognitive scales of measurement known as the perceptual, conceptual, analytic, social, motor, control, flex, extraversion /introversion, general and differential. Simple definitions for each of the scales are presented here; while other chapters explain the constructs in detail. Perceptual(P1-Per): use of the perceptual senses (eyes, nose, hearing, smell, touch) to perceive changes in shapes, figures, objects, and people; Conceptual(P2-Cn): use of memory and cognition to associate and generate concepts; Motor (P3-Mt): reliance on physical and motor coordination and manual dexterity to solve problems; Analysis (P4-An): diagnostic and analytic orientation used to understand and dissect problems; Social (P5-Soc): understanding of the problems inherent in the dynamics of people and social systems; Control/Structure (P6-Ct): a method of planning and structuring the environment to affect a problem solution, an individual attribute used to attend, to sharpen their mind and focus on a goal related to solving problems; Flex(P7-Fx): unconscious release mechanism; sensitive to impulse and idea generation Extraversion (P8-EI): the flow of mental and emotional energy from the individual to people and objects; General problem solver (G): people who solve number, word, and spatial problems quickly and easily; 31 | P a g e 32 Prepublication Copy Differential problem solver (D): people who specialized in solving practical and ill-defined problems associated with their area of strengths and interests. These scales, which are augmented by cognitive and non-cognitive assessments, illuminate developmental differences which are evident at an early age and have implications for solving problems. Some scales are extended; others are simple, primary subscales. In our theory, a measurement scale represents a category related to the problem-solving process. For example, the measurement scale called general problem solver represents a group of people who are better at solving different kinds of general problems while the measurement scale of differential problem solver represents a group of people who solve very specific kinds of problems better. The measurement subscale of introversion and extraversion are simply personality elements that push energy flow either inward or outward. When energy (internal thoughts, emotional energy) moves inward, introversion results. When energy (internal thoughts emotional energy) moves outward, extraversion results. When energy moves sometimes inward, and sometimes outward, this results in ambiversion. During the problem-solving process, energy flow is dependent upon many practical factors such as the differences in situations, kinds of problems, and the influence of the environmental press. Defining career and vocational preferences In 1986, two separate career instruments (Career and Interest Inventory, Vocational Inventory) were developed by us using Holland’s RIASEC categories. Each instrument was validated by comparing the subscales against samples of items from COPS (Knapp et al.,1974) Strong (Strong,1994), and Holland’s (Holland,1965). These instruments were tested with the Career Center at Cal Poly, Pomona from 1986-1992. The career instruments had 9 subscales of which 6 were similar to Holland’s. For convenience and ease of understanding in reading this book, the subscales are labeled with a well-known RIASEC acronym. This is to provide a comparative basis for those who do research. The career and interest instruments have 232 preference statements about problemsolving in different vocational activities. The definition of these scales is similar to Holland’s classification but has different items than Holland’s instruments. (See examples in Chapter 20). Realistic (R-CR1): Prefers applying knowledge and emotional interactions to objects in the environment. Objects can be machinery, pots & pans, kitchen utensils, toys, trees, tools, or anything living or non-living Investigative (I-CR2): Prefers to find out how things work and what they are made of. Likes to trace lines of thought, patterns of objects, and basic assumptions of what makes an object work. Artistic (A-CR3): Prefers creative, divergent thinker, enjoys using the mind and hands in crafts, or the Arts. 32 | P a g e 33 Prepublication Copy Social (S-CR4): Prefers to engage objects and work which has social value; helps another or has altruistic aims. Enterprising(E-CR5): Likes things that involve business, trade, or influencing others in business transactions Conventional (C-CR6): Prefers jobs or vocations which are characterized by internal structure and order. Work such as accounting or clerical. Other subscales (CR7-CR11): An additional 5 career problem-solving subscales which are referenced in this book were also developed. They are important for classifying others and are integrated with the six subscales referenced here (again: different items, different subscales than those of Holland but similar in emphasis). The integrative model Our integrative model for problem-solving suggests that components of “g” are intertwined with emotions, memory, and constant environmental actions in an interactive process. This produces a cognitive and affective model that is fluid and changing as people solve different kinds of word, number, and spatial problems and interact with the environment. These active elements can be modeled in many different ways. Using Carroll’s (1993) seven categories described in Chapter 19, an integrated model might be displayed as follows: 33 | P a g e 34 Prepublication Copy Figure 1 (Derived from Carrol, 1993): Math Reasoning Arithmetic Fluid Intelligence (Gf) Logical Analysis Visual Perception Closure Spatial Embedded Designs Perceptual Speed Speed of Processing/Letter Identification/Cogflex Problem Solving Learning Memory Knowledge and Achievement Problem solutions, Achievement Motivation, Knowledge Behavioral Control (Control/Analysis/Social etc.) Knowledge of Interests Ideational Fluency Divergent thinking/Conceptual Flex Crystallized intelligence (Gc) Reading Comprehension Communication/Listening Notice that knowledge of Behavioral Control is categorized under Knowledge of Achievement. In our theory, this is also where the constructs related to interests are located. 34 | P a g e 35 Prepublication Copy Elements of the IPS system Earlier in Chapter One, Picture 1 showed the broad-brush strokes of how cognition (C)and speed of processing (S) were integrated into and around personality (P) and interests (Cr). Picture 2 indicated the subgroups. In this chapter, Picture 3 provides a label for each of the 20 constructs and how each is related to the other by distance measures. In the picture below, a metric system was added using a principal component analysis in 2 dimensions (PC1 x PC2). Again, to avoid confusion with so many letters. P stands for Personality; S for the speed of processing, C for Cognition or thinking, and CR for Career and Interests. If you enjoy reading the history of these 20 Constructs, after finishing this chapter, read the literature reviews found in Chapters 24 & 25. Picture 3: Elements Spatial Representation of 20 Elements in the IPS theory The upper right quadrant displays: Extraversion (P8-Ex), Conventional (CR6-CN), Social (P5Soc), and Flex (P7-Fx). The upper left shows, Conceptual (P2-Con), Artistic (CR2-A), Social (CR4-S); Cognitive Flexibility Speed (S1-CF) and Embedded Designs (S3-EB), and Letter 35 | P a g e 36 Prepublication Copy Identification (S2-LD) The left lower quadrant displays: Logical analysis (C1-Pslap) Spatial Analysis (C2-Pssp), Control (P6-CT); Analysis (P5-An)). and Arithmetic Distraction (S4-AD). The lower right quadrant is Enterprising (CR5), Realistic (CR1), Motor (P3) Perceptual (P1-P), and Enterprising-(Cr6-E); Picture 3 shows how cognition (C1 and C2) and speed of processing (S1-S4) are related by distance to each other. The same is true for personality (P1-P8) and interests (C1-C2). Of importance is that there are more personality variables in the upper right quadrant, more speed of processing in the upper left, more cognitive processing in the lower left, and more career variables in the lower right quadrant. Some individual interest and personality variables are more related to cognitive processing while others are related to each other. For example, i.e. control and structure (Con) in the same quadrant as the speed of processing (LD; Emb; etc.) and preference for analytic thought (An) is in the same quadrant as logical and spatial processing (C1-C2). Defining style and mode Style is another term used throughout this book and has a distinct definition that influences our developmental model. Style refers specifically to groups of categories (Conceptual, Perceptual, etc.) that consistently act in concert to influence a person’s approach to the problem. A style is a habitual way of approaching various kinds of tasks in the world (Messick, 1976). Consistency in style suggests repeated use of the same methods, strategies, and ideas in approaching a task. When a style becomes ingrained in early developmental stages and used through most of life, it is conceived of as habitual or trait-like. In this context, a problem-solving style becomes habitual when a person uses the same personal characteristics, and interest patterns to engage in the systematic use of behaviors each time a problem is encountered. Experience helps build a preferred way of doing things. When daily experiences, education, and training influence problem-solving behavior in such a manner that one utilizes the same mental and behavioral pathways over and over, then an identifiable subgroup develops. Everyone uses multiple styles in solving problems, especially over a lifetime. There is a greater tendency to use trial and error as an approach in the very early stages of life (0-5). As the number of learned abstract concepts increases, a child uses more implicit memory and cognition to discriminate between alternatives and choices. The fewer alternatives or abstractions available to synthesize information from long-term memory, the more likely a problem-solving style relies heavily on immediate experience leading to a trial and error approach. A trial and error approach can be impulsive--try this, try that, see if it works. Or an approach may be reflective, that is, using long-term memory, reading, and analysis to approximate a solution, even if the alternatives are limited. When reading and investigation are combined either with a trial and error approach, 36 | P a g e 37 Prepublication Copy either impulsive or reflective, the number of abstractions increase and the style becomes more reflective, analytical, and less impulsive. Style is different from problem-solving modes. A mode is a combination of categories that act in concert to solve a problem but are not adopted over long periods. Modes are temporary. Modes refer to states or transitions over short periods, i.e., a child tries out a mode (use of different problem-solving strengths) temporarily trying to develop a consistent style. For many children, a mode does not become dominant until late adolescence. Defining the category framework The Category Framework (See Appendix B for a description of the 36 different subgroups) is a way of organizing many different problem-solving characteristics into subgroups. It is also a way of noting the interrelationships of all the categories in problem-solving The Category Framework denotes ideal subgroups of people, not single individuals. Experience and dominant skills developed over a lifetime lead to some very interesting differences in each subgroup. A group of artists who use a pencil to sketch a cartoon is going to be different from a group of engineers who use the same pencil for writing formulas or reports. A group of differential problem solvers with dominant scores on perceptual and motor are going to be different from a group of general problem solvers with dominant scores on analysis. In short, there is a need to define a subgroup according to very specific demographic and cognitive criteria and then compare the scores of individuals to these criteria. In practice, the general subgroup is identified by the first three letters of the problem-solving categories. Each letter indicates a dominant characteristic. Therefore, a general problem solver (G) who had one high score in Perception is designated as simply GP. A differential problem solver who had high scores in generating ideas (Conceptual), analysis (Analysis), and social interaction (Social) is denoted as a DCAS problem-solving style. Most of the time, individuals have none, one, or two high scores that define their group. In practice, these dominant subscale scores can be interests, personality, cognition, or a combination thereof. This is very important in classification as an interest category may be more dominant than a personality or cognitive category, especially in differential problem solvers. Introversion, ambiversion, and extraversion are the result of how neural energy flows through pathways and provides one of the criteria for dividing subgroup. Not all subgroups are useful or have equal importance. Empirically, people’s responses show different frequency patterns. That is, people choose different items with different frequencies based on social acceptance and true representation of their belief system. Therefore, the frequency of one minor subgroup may appear 1 percent of the time while another 4 percent of the time. Having 10 different categories of problem solvers categorized by only certain combinations of introversion, extraversion, and ambiversion leads to many different groups. Many categories overlap, especially during early 37 | P a g e 38 Prepublication Copy ages and stages of development. Thus, the category of GA may be difficult to mathematically separate from GC in a 7 or 8-year-old child. When this occurs, the result is a classification of a single general category noted as G or general problem solver. That is, in our process of classifying individuals, rather than using a more definitive category with more letters, a single letter is more appropriate. When an adult has many years of experience, the categories are more mathematically distinct and allow more definitive labels: As an example, to illustrate the process, group labels in the category framework might be first divided by introversion or extraversion and then subdivided by General (G) or Differential (D). Or then again, the process could be reversed. First by G or D than by introversion. The other categories change according to dominance in score patterns. Conceptual (C): Motor (M): Social (S): Analytic(A): Perceptual (P): C MC SCA APM PAS CPM M SA AMS PMA CSP MSA SLM ACS PM The letters at first may not seem very important. They are important to the classification algorithm since each letter denotes a special distinction in the group of problem solvers. In the first column, three groups of conceptual problem solvers are noted--C, CPM, and CSP. In the second column, three groups of motor problem solvers are MC, M, and MSA. An unstructured motor problem solver (M) is denoted as M-u. Mathematically, there are distinctions between some of the groups of problem solvers which have important for us. Thus, the group noted by CAS, or conceptual, analytic, and social may be more mathematically independent and distinct from the group denoted as CPM or Conceptual, Perceptual Motor, depending on other factors such as age, gender, or ethnicity. Controlled versus flex tendencies can be found in many different problem-solving modes. Their impact is extremely important as structuring leads to a definitive kind of thinking, easily identified as part of the problem-solving orientation. Flex operates on both conscious and subconscious levels. Later in Chapter 3, two specific types of structuring (internal control versus external control) are introduced. Each directly affects the problem-solving process. In the past, one of the major problems of people who were using the subgroups or profiles was the difficulty in understanding that each profile, subgroup, or pattern was an “ideal or composite” which was to be used as a level of comparison. People tend to use the profiles as “stereotypes etched in stone” rather than as a fluid composite for comparison. Individual people differ from each subgroup in major ways based on individual scores. A difference in scores is 38 | P a g e 39 Prepublication Copy paramount as each discrepancy represents “an individual difference.” Likewise, people change subgroups as they age. A person may reflect certain problem-solving characteristics at a young age and other characteristics at an older age. The 36 subgroups descriptions The descriptions found in the Framework describe the similarities or differences in approach to solving problems. These same descriptions give rise to 36 subgroups found in Appendix B. Their hierarchical relationship of the 36 subgroups for both the Differential Problem Solver and General Problem Solver is found in a separate pdf entitled DeNovellis’ 36 Problem-Solving Subgroups. Descriptions allow for a better understanding of the people and processes involved. Descriptions are also based on composite profiles and represent “average or ideal representations.” and not any particular person. The descriptions are like a taxonomic classification in biology. Biologists describe a human system (integumentary, alimentary, and nervous) that provides a generalization for others to follow and expand. Order and sequence for the broad inclusive categories of personality, cognition, and interests are also important. For example, for one group solving problems, the use of cognition in problemsolving can be dominant, thereby stimulating and driving personality and interests. In contrast, in very young developmental age groups and situations, cognition may be secondary to personality and interests. When emotional energy is unbridled, unchecked, and not focused (fear, anxiety), feelings take the driver's seat and cognition becomes a sweet second. Depending on the situation, type, and complexity of the problem, the framework allows for a simple taxonomic classification which aids in understanding the contributions of the problem solver in the problemsolving situations. In Appendix B, each of the subgroups is labeled from one to thirty-six. Each is preceded by measurement categories from different measuring instruments such as Cattell’s 16PF (Cattell et al., 1970); Jackson’s Personality Form (Jackson, D.,1967); Holland’s Interest Categories (Holland, J. L., 1965); Problem Solving Categories (DeNovellis, 1984); Perceptual Speed Tests (DeNovellis and Dehler, 2002) as well as categories for verbal, spatial, and numerical strengths. This latter group of scores corresponds to instruments like Wechsler’s Adult Intelligence Test (Wechsler, D., 1939) or Wechsler’s test for children. The use of scores for these instruments is meant solely as guides. For people who interpret patterns, the scores represent ways of conceptualizing what the ideal composite profile description represents. Each cognitive, interest, and personality tests define a level or strata. Consider a stratum to be similar to a geological stratum in the crust of the earth. Each geological stratum gives clues to the previous history of the earth and its formation. These levels or strata are used by the computers to identify the subgroups patterns from 1 to 36. 39 | P a g e 40 Prepublication Copy Many of the measuring instruments have as many as 7 different levels labeled from A through G. Each level has either a plus, minus, N or A. The plus indicates above average; the minus is below average while N or A stands for average. The stars listed on the levels indicate a level used to identify the subgroup description which identifies each pattern from 1 to 36. The computer program does all of the work in selecting the correct category for each respondent and distinguishing how each person differs from the subgroup. In essence, each individual set of scores is compared to one of the patterns from subgroups 1-36. Patterns 1-18 are extroverts while patterns 19-36 are introverts. Patterns differ first by general vs. differential problem solver and then by dominant characteristics of the other 8 problem-solving concepts. Once the pattern is selected than comparisons are made via demographic characteristics and the profile is interpreted. Each respondent is compared not to an overall group norm for each instrument but subgroup norms for a particular group. Each subgroup norm can be further analyzed if the information is available. The information provided in this book represents two groups of problem solvers, general and differential. Data for these groups were gathered at many different ages. The classification of a subgroup followed a very specific pattern. In terms of correctly classifying a problem solver, the first step is important; i.e. one must accurately determine the age and general category of problem solvers: general vs. differential. The next step is to add the dominant characteristics from the other areas such as perception, personality, and interests. During the long developmental history of the IPS theory, one thing became patently clear, when defining a subgroup, the ultimate goal is differentiation by age, gender, ethnicity, socioeconomic status, as well as problems solving characteristics. The Mousetrap Recently I listened to a discussion on the radio about a person who was building a mousetrap. His mouse trap was built out of wood--having a lever and a spring on the top. The mousetrap was useful as it worked to catch mice. In the discussion, many different kinds of mousetraps were discussed. Some mouse traps had special springs; others used metal. Even though each mousetrap was composed of different parts, the outcome was catching a mouse in the trap. The lever was tripped on the mouse trap; all parts of the mousetrap worked in concert. By analogy, even though all the elements of the IPS model are separate and defined, each works in concert while solving a problem. Thus, the problem-solving process can be considered as either holistic based on the outcome or atomistic, based on how the parts work in concert. Certainly, if every part is operating at maximum capacity, then the overall holistic outcome is maximum. However, one or more parts of the brain or system may not be optimal, thus interferences from different neural pathways affect the outcome of the whole. 40 | P a g e 41 Prepublication Copy That is what is emphasized in the IPS model, even though all the parts (preferences, categories, style) are interrelated, the outcome is solving a problem. However, anyone who has taught individual learners knows that all the parts do not function as a whole in both children and adults. Some children have strengths in reading but not in computation, others are impaired physically (visual, hearing, walking, moving) while others are born with genetic predispositions (autism, color blindness). Some children are better with their hands, while others are better with their minds. Some children do well in playing musical instruments while others do well in sports. Different modes and different styles contribute to solving a problem, depending on the task characteristics and environment of the problem. In other words, how problems are solved differs by age and developmental level. Are there other factors that are important in solving problems? Yes, to name a few, the list includes previous experience, the capacity of working and long-term memory, domain-specific knowledge, processing speed, level of expertise, type, and complexity of the problem. Chapter summary Chapter Three provides an introduction to the basic elements, principles, and tenets of the Integrated Problem Solving (IPS) theory and further clarifies the use of the Category System. Each of the individual components is specifically defined and operationalized so there is less discrepancy in interpretation. The Category system is integral to the IPS system and is used to determine the mathematical separation of different subgroups. Of particular importance is Picture 3 which defines the metric relationships of all four groups of elements (speed of processing, interests, cognition, and personality). By themselves, relationships are mostly expected. Later, we will show a picture of how the 36 subgroups are integrated into and around these same 20 constructs. This becomes significant only when one understands each of the 36 subgroups and their relationship to solving problems. Previously, Chapter Two provided the theory of IPS while Chapter 3 provides definitions and explanations of the characteristics of the IPS. Next, in Chapter 4, we begin a historical overview of problem-solving. Chapter references Carroll, J.B. (1993). Human cognitive abilities: A survey of factor-analytical studies. Cambridge, United Kingdom: Cambridge University Press. Cattell, R. B., Eber, H. W., & Tatsuoka, M. M. (1970). Handbook for the Sixteen Personality Factor Questionnaire (16PF). Champaign, IL: IPAT. DeNovellis, R. L. & Dehler, C. (2002). Speed, Ability, Achievement, and Student Growth Scores. Paper (Division C). American Educational Research Association, New Orleans, Louisiana. 41 | P a g e 42 Prepublication Copy DeNovellis, R. L. (1984). Personality Type Preference Indicator. Journal of Psychological Type, 7, 6,14-28 Holland, J. L. (1965). Holland Vocational Preference Inventory: Manual. Palo Alto, CA: Consulting Psychologists Press. Jackson. D. N. (1967). Personality Research Form. Goshen, N.Y.: Research Psychologist Press. Wechsler, D. (1939). Messick, S. (1976). Individuality in learning. San Francisco: Jossey-Bass Publishers. Wechsler, D. (1939). Wechsler-Bellevue intelligence scale. New York: The Psychological Corporation. 42 | P a g e 43 Prepublication Copy Chapter 4 Problem Solving Introduction Our journey in Tier One begins! The study of problem-solving has a long and varied history. At the heart of the journey is the quest for survival. This chapter provides a sociological, psychological, and historical review of the myriad obstacles to understanding the research associated with the problem-solving process. To the best of our present knowledge, the generic problem-solving process extends back to the beginning of civilizations. In contrast, the domain-specific reviews of problem-solving are identified under the separate nomenclature related to each category of problems; i.e., verbal, spatial, and numerical. Domain-specific refers to a particular area of expertise; i.e. knowledge about the brain or subject matter (math, chemistry, etc.); while generic refers to general knowledge such as knowledge about history, literature, or the world. Furthermore, information about verbal, numerical, and spatial problems is found under diverse topics such as text comprehension, spatial visualization, mathematical understanding, and ability. Has the bridge between knowledge of the brain and the solving of verbal, numerical, and spatial problems narrowed the gap so issues related to solving different kinds of problems are more easily understood? The following review provides some insight. Historical view Problem-solving has been a part of our history as long as people faced everyday dilemmas related to living and survival. According to geological evidence, fossils, and other artifacts, early Homo neanderthalensis and Homo sapiens faced extinction many times. Neanderthals (Homo neanderthalensis) lived 100,000-200,000 years ago. This seems like a long time ago until one contrasts that date with the “day of the dinosaurs” who lived 65 to 100 million years in the past. Today, modern people differ in DNA in only 1 to 4 percent of segments from the DNA found in Neanderthals (Prüfer et al., 2014). Uncontrollable weather, harsh living conditions, and disease influenced many historic problematic situations. The average lifetime of the Neanderthals was about 30 years. Survival was based on adaptation and finding solutions to the problems of everyday living, i.e., gathering food, finding shelter, and avoiding danger. 43 | P a g e 44 Prepublication Copy The early cave dwellers of 40,000 years ago, and social workers today find commonality in solutions to well-defined and ill-defined problems (Brabeck, et al., 1990). Well-defined problems such as getting dressed in the morning have a boundary--a way of determining if the goal is met. Ill-defined problems, such as those involving changes in the weather, have either no boundaries or boundaries which are constantly changing. Adaptive methods for solving ill-defined and well-defined problems are necessary for survival. Evidence from fossils and geology suggests that in recent years from 6000 to 3000 BCE, many aborigines were present in all parts of the world. Early migration of species related to homo sapiens occurred between seventy to one hundred sixty thousand years in the past. These migratory groups traveled on land from Asian, African, and European continents to North and South Americas as well as islands of the Pacific Ocean and Australia. Each early group carried solutions to problems related to their culture and everyday life in the form of tradition, customs, and oral stories. Early examples of verbal, spatial, and numerical problems Each migratory group developed its system of solving spatial, numerical, and verbal problems in everyday life. Three thousand years ago, in the Egyptian tomb, written history in the form of hieroglyphics (spatial problems) was recorded on the walls of caves. Other recordings were found on papyrus, and clay tablets. Counting and measurement in these early times were necessary for daily life. Numerical formulas, such as areas (length times width) of land were calculated for paying taxes on the quantities of food raised. Drawings and symbols provided substantive examples of practical solutions concerning building, construction, and daily life. Symbolic problems and solutions embodied in the mathematical and astronomical writing of the Egyptians were also found in other historical relics and documents such as the Rhind papyrus (Gillings, R. 1972). Early history provides a plethora of other examples of verbal, numerical, and spatial problems denoting scientific and pseudo-scientific solutions to practical problems during its millennia. Examples of academic problem solving come from the fifth and fourth centuries (BCE) in the Greco-Roman period. The mathematics of the Greeks, geometry, and arithmetic (number problems) were applied to scientific formulations such as astronomy, optics, and harmonics. Aristotle, in Posterior Analytics, discussed issues that reflected the contemporary mathematics practiced in Plato’s Academy. Symbolic abstractions in technical work showed the use of letters to identify pictorial representations of buildings and construction (Heath, 1949 & Allen, 1969). Of course, many literary (verbal) forms of problems were commonplace in earlier times, as seen in established forms of writings and symbolic activities in various 44 | P a g e 45 Prepublication Copy languages. Examples included literary symbols found on the walls of caves. Egyptian treaties were written on literary papyrus, and early forms of Chinese writing, middle to late Shang dynasty, were etched on turtle shells and animal bones. In Medieval times, especially from the 10th to 12th centuries, Christian writers as well as those representing Jewish and Arabic traditions composed all forms of dialogues representing solutions to existing daily problems (Maxfield, 2008). Problem-solving in the late 1800s In the tradition of domain-specific knowledge, the work of Benjamin Rush during the early 1800s provided historical evidence of psychological issues related to the mind in solving everyday problems. In 1812, Rush’s textbook on Medical Inquiries and Observations on Diseases of the Mind suggested that many problems in the mind were due to a lack of circulation of blood to the brain or sensory overload. In the late 1800s, the Behaviorist, or empiricist, as some called them, wanted to avoid the mind/body black box phenomena. Issues were not grouped by problems to be solved but by schools of thought, i.e., Behaviorism, Gestalt, and Psychodynamic. Groups of scientists studied reflexes, the physiology of neural circuits, and various forms of conditioned behavior. Their focus was on the behavioral aspects of observed phenomena. The work of Thorndike (1911) typified the early thinking of the Behaviorist who relied on a stimulus-response (S-R) model. In the problem-solving model, the “problem” is the stimulus and the response is the goal. The S-R model suggests for every stimulus there exists a response that may or may not be reinforced. According to Thorndike’s law of effect, if the response is satisfying, the response is reproduced or replicated in a similar situation and is likely to occur again. Later, Thorndike’s law was used by B.F. Skinner in his development of operant conditioning, “a learning process by which the effect, or consequence, of a response, influences the future rate of production of that response (Grey, 2008)” Other Behaviorists, such as Clark Hull and Pavlov, adopted principles from Skinner’s work. While Thorndike (1921) was pursuing the experimental and empirical aspects of psychology, the psychologists at Würzburg such as Oswald Külpe, Karl Bühler, and Otto Selz focused on defining problems by analysis of the whole form or “gestalt.” Earlier in 1893, Von Ehrenfels introduced the concept that the conscious state of the mind could not be decomposed. The mind was too powerful and the task of psychology was to describe cognition rather than explain the physiological aspects of human informational processing. Mental laws and perceptions determined how objects were perceived. The Gestalt psychologist influenced many researchers, especially those who studied insight problems. The most common insight problems according to Dow and Mayer (2004) are verbal, mathematical, and spatial. 45 | P a g e 46 Prepublication Copy Problem-solving in the middle 1900s Problem-solving is highly dependent upon experience, knowledge, and memory. In 1932, Frederick C. Bartlett published his first book called Remembering: A Study in Experimental and Social Psychology. In 1958, he published a second book called: Thinking: An Experimental and Social Study. According to Henry Roediger, Bartlett’s work was the forerunner of many ideas in cognitive psychology which came to the forefront in the early 1960s and 1970s (Wheeler and Roediger, 1992). Most of the current psychology textbooks cite three important problem-solving exercises which initially contributed to the literature on problem-solving during the 1900s. These three exercises were: Maier’s (1931) pendulum problem, Duncker’s (1945) tumor radiation problem, and Newell and Simon’s Tower of Hanoi. These different problems solving exercises have a wealth of literature contributing to analogical transfer in problem-solving and are still used today by researchers in the field (Simon, 1975). In 1945, Duncker, a pioneer in the study of problems, describe problem-solving as a goal that does not yet have a solution. Most of Duncker’s observations came from the laboratory where he found results from practical and mathematical problems. In his experimentations, he had his students “think aloud” as a method of reaching their goals. This process, in his words, was different than introspecting as the student could not divorce him or herself from the problem at hand. “Thinking aloud” allowed the student to reach the restructuring necessary for a solution to the problem. In the 1960s, Herbert Simon and his two colleagues, Shaw and Newell studied the solving of complex problems. Complex problems were different from insight problems in that there was not a crucial element leading to the solution. Simon (1971) was interested in the process, that is, the cognitive strategies, mental operations, and how problems were solved. Since the computer was used to simulate human problemsolving, the protocols involved the concept of searching problem space. This led to algorithms that could be programmed to solve these well-defined human problems (Simon, 1961; Newell et al., 1960). In 1972, Newell and Simon proposed a comprehensive theory of problem-solving that still contributes to problem-solving models today. These researchers used the complex problem known as the Tower of Hanoi, a well-defined problem with a solution or endpoint. The problem was to move disks located on three pegs to a known configuration. The solution involved 27 steps. Three of the theoretical components were described as an initial state (all the disks on peg 1), a goal state (how the disks should look for the final solution), and operators used to move from one state to 46 | P a g e 47 Prepublication Copy another (mental representations by the participant to figure out the solution). The problem space encompassed the total process; that is, the beginning, the end, and all the operations which occur in between. Theories of problem-solving Recently, many authors and researchers have written profusely on thinking, problem-solving, and cognition (Mayer, 1983, Sternberg, 1994, Davidson, J. E. & Sternberg, R. (2003) ). Theories Abound! A textbook could be written on each facet. Each theory of problem-solving may have components, meta-components, or even supra structures that define the problem-solving process. The supra structures are planning, monitoring, and evaluation of the problem solution and are components of metacognition. Metacognition occurs when the individual becomes conscious of the problem-solving process and thinks about ways to strategize and monitor one’s behavior. For example, Nietfeld and Bosma (2003) found that explaining how the problem was solved (not just the solution to the problem) improved task performance as individuals could monitor their performance. Of particular importance was one theory of the mind which utilized the idea of association and came from the early philosophy of Aristotle. This theory denoted as associationism suggested that thinking could be explained in terms of ideas (elements) and associations (links). Cognitive thought was the result of habits families developed by trial and error over time. A stimulus (S) gives rise to various responses (R1, R2, R3, R4); the links or associations are in the problem solver’s head. For any given problem-solving situation, there is a family of responses, one that is either strengthen or weakened. The differences in the strength of response lead to a hierarchy. This hierarchy of responses becomes habits that are conditioned by reward and therefore are likely to occur with a greater frequency of response. In the language of the IPS, a habit is a response that occurs over defined neural pathways. (Mayer, 1983).) The practical application of the theory was found in studies of anagrams, analogies, puzzle boxes, measurement of the electrical activity of muscles, and studies of braindamaged patients (Mayzner & Tresselt, 1958; Devnich, 1937 Gick & Holyoak, 1983). The essence of those studies was data on the median solution times in seconds. Therefore, the researchers noted how many seconds were required to transform an anagram from “beahc” to beach. Likewise, the probability of letter transitions, the number of moves, and the order of transition from one form of anagram to another were calculated. This research provided benchmark data for those interested in the speed of processing. 47 | P a g e 48 Prepublication Copy Later, theorists concentrated on the components of problem-solving. Components of problem-solving include problem definition, problem representation, and all the intermediate steps needed to arrive at solutions. Knowing which components are involved in the problem-solving process helps define the pathways that are involved. Meta-components include workable mental strategies (stratagems) to arrive at a solution. The choice of cognitive processes depends upon which theory has immediate practical value. Problem definition Researchers agree that problem definition, problem finding, and problem formulation are difficult and dependent upon many theoretical and practical factors, particularly whether the problem was ill-defined or well-defined. Newell and Simon (1972) used a clearly defined problem (Tower of Hanoi) that had a beginning and an end with an area that could be searched (problem space). Well-defined problems can be solved more easily via computer programming. Ill-defined problems involving differences in time, space, and environmental constraints are more difficult for problem definitions, problem finding, and problem formulation. Getzel (1982) gave three examples of ill-defined problems. The first was: problems discovered. Did the problem already exist in the environment or was it discovered during a problem search? Second, was the problem created as a result of other known problems? A scientist is especially good at discovering new problems in a field as well as solving those which already exist. For example, artists spend considerable time finding and creating problems. Both of these classes of problems are different from Getzel’s third class—the problem presented. How is the problem presented to the subject? Problem definition, in all classes of problems, is based on a concise definition that illustrates all conditions necessary for a solution. For the problem to be accurately defined, it must be recognized and described with a knowledge of all constraining factors. Problem representation When a problem is found, formulated, and defined, it can be represented mentally in some form. Representation is constrained by the cues in the environment that present the problem. In general, the representation is either verbal, numerical, visual-spatial, or any combination thereof. An example is indicated by early studies which asked people to illustrate how the following phrase was encoded in their minds. “plus, over a star.” Think about how you would encode the phrase. The most common 48 | P a g e 49 Prepublication Copy responses were either verbal or visual. The people who responded visually saw a picture with a plus sign over the star. The people who responded that they verbally encoded the sentence saw words. That is, they responded that the representation was a verbal sentence indicating a plus over a star. The sentence did not lend itself to a numerical representation; however, the phrase {what is the sum of a ‘plus over a star’ added to a ‘plus over a star’} could be represented numerically. Problems given by researchers to subjects are usually represented in four different forms-verbal, spatial, mathematical, or a mixture of each. The mixture can be represented as a complex measure such as an outcome or performance (playing a musical piece, repairing a car, etc.). Examples of each of the different forms are listed below: A simple mathematical problem (usually presented in a distracted field with all kinds of squiggles and marks). (1+ 5-6+2=?) A verbal problem is represented in the following form: Misha and Marjorie were born on the same day of the same month of the same year. Their other sister was born on a different day in the same month of the same year: How is this possible? A spatial (visual-spatial) problem: Place a line through all 9 dots without lifting your pencil once you have selected a beginning point. A mixture requiring both verbal and mathematical representation: 49 | P a g e 50 Prepublication Copy There are 10 bags, each containing 10 gold coins, all of which look identical. In 9 of the bags, each coin weighs 16 ounces, but in one of the bags, the coins weigh 17 ounces each. How is it possible, in a single weighing, on an accurate weighing scale, to determine which bag contains the 17-ounce coins? The second type of mixture problem might read as follows: A mechanic reads the computer codes for a problem with a Ferrari engine. Consulting his manual, he finds a process flowchart illustrating 20 possible problems for the single code that was selected. Eliminating the first two possible problems, what is the minimum number of codes that are left to check? Since our thesis revolves around neural pathways and the solving of verbal, spatial, and numerical problem solving, the next three sections provide an up-to-date review of these 3 areas. Current studies do not refute prior research but add to the growing body of important ideas on the state of the art. Verbal Problem Solving Words, text, or any similar structure of letters that convey meaning can be defined as verbal. Comprehension is defined as understanding the meaning of words, letters, and anything literary in form. Lucangeli, Tressoldi, and Cendron (1998) demonstrated in a research study that text comprehension is a necessary component of problem-solving. Generally, the accepted notion is that text comprehension preceded the components of problem representation, problem solution, and tentative problem solutions as well as the meta-components of problem evaluation. In other words, one must understand the meaning inherent in the words before the rest of the problem can be solved. Many studies have documented that a broad knowledge base influences text comprehension (Cote, Goldman & Saul, 1998; Kintsch, 1998, Voss, J. F. & Silfies, 1996). Differences are based on the type of problem (domain-specific vs. generic) and type of knowledge base (domain-specific vs. generic). In other words, there is a difference in understanding words in a specific subject matter area versus words in a general sense. Researchers (Kintsch, 1998; Graesser, Millis, & Zwann, 1997) have developed many different classifications of words and their organization in written form. Each category has specific implications for comprehending the meaning assumed by the text in question. According to Brooks & Warren (1972), different kinds of texts such as scientific articles, comic books, novels, and science fiction can be interpreted differently. For example, in the category known as discourse genre, students report 50 | P a g e 51 Prepublication Copy a difference in long-term memory representations depending on whether they thought they were reading literature or a scientific article. This particular kind of filtering (differences in memory representations) gives rise to our assumption that filters are the precursors to layers as layers are developed when specific instances of mental pain are filtered and remain in long-term memory. According to Brooks and Warren, each different classification of text is affected by the manner of the structural representation of letters. If there is insufficient information due to missing letters, improper syntax, or poorly written text, then the processes in the brain responsible for activating the memory storage necessary for matching the level of representation are lost and the meaning is not conveyed. In other words, one’s brain can understand this “all c_ts purr when content” but not this “all __s bite when angry. The assumption, of course, is that the reader possesses the necessary skills and relevant previous knowledge. When words or text in problem-solving are categorized as textbase (Perfetti and Britt, 1995), then the form is known as propositional. Propositional suggests that the manner and form of the written text provide information about the meaning. For example, a verb provides knowledge of a goal, action, or state while a noun provides information about objects of action. Likewise, the place of the verb or noun in the sentence provides clues to the meaning of the word. These 4 different theoretical considerations highlight how words, texts, or the structural denotation of letters increases the difficulty of understanding how problems are solved. Research on verbal problem solving The process of reading a sentence, story, or book highlights the issues involved in text comprehension for younger children. Neurobiological evidence on reading suggests that MRI activation for normal readers occurs in the inferior frontal gyrus during word analysis while occipital/temporal lobes are activated during skilled, fluent (automatic) reading. These results come from neuroimaging studies that compared dyslexic and normal children. The dyslexic readers did not show activity in the left hemisphere posterior brain system (McCrory et al., 2005; Paulesu et al., 2001; B. A. Shaywitz et al., 2002; S. E. Shaywitz, et al., 1995. ; Simos et al.,2000; Temple et al., 2000). The anterior lateral occipital-temporal system has been called the visual word-form area (Cohen et al., 2000; Dehaene, Cohen, Sigman, & Vinckier, 2005; McCandliss, Cohen, & Dehaene, 2003). Gray and Thompson (2004) assume that verbal tests of any complexity involve contributions from both hemispheres. However, in general, the function of the left hemisphere is verbal and logical while the right hemisphere 51 | P a g e 52 Prepublication Copy is more non-verbal, and spatial (Gray, 1999; Hugdahl, 2000; Toga, & Thompson, 2003). However, these results are often disputed by many neuroscientists who do not classify functions by hemispheres. Instead, functions are classified by structure (anatomy) and knowledge of where they occur. The psychometric viewpoint provides different evidence than neuroscience. Psychometrics often use descriptive data for understanding the influence of verbal text and measurement techniques of data to objectify findings. For example, factor analysis is used as a methodology to understand differences related to verbal comprehension, spatial abilities, and the general education of individuals. What is left over after factoring out the correlations of residuals related to g, leaves two groups? One is designated as (verbal: education) and the other is (practical: mechanical). Verbal and educational ability is based on learned content while practical and mechanical abilities are based on spatial, practical, and mechanical abilities. One interpretation of these results suggests that a kind of fluid ability (“gf”) has less influence in older adults. Why? As people are exposed to the world of reallife problems in different career fields than education (non-traditional environment), reading, learning as well as practical and mechanical knowledge become more important (Vernon, 1950). The acceptance of either a neurobiological or psychometric model depends on one’s goal (Garlick, 2002). A model of individual differences (measurement within the individual) varies from a psychometric model (measurement across people). An individual difference model designed to explain the structures of the brain suggests knowledge and skills are built through specific neuronal connections in association with trait-relevant environmental stimuli. Individual variation in mental ability tasks is due partly to genetics and environmental experiences develop through the task being measured (Bouchard, Lykken, Tellegen, & McGue, 1996). The psychometric model attempts to explain how groups of people differ on these same tasks. Numerical Problem Solving Simple numeric skills in calculating ordinary arithmetic are necessary for vocational, and everyday problem-solving. The ability to add, subtract, multiply and divide is required in managing money, using a calculator, or measuring things. The use of arithmetic in selecting economical items at the grocery store or in calculating interest on the loan is a prime example. The inability to perform simple arithmetic calculations is evident in preschool and school-age children. It occurs also in patients with cerebral lesions. 52 | P a g e 53 Prepublication Copy Henchen (1919) performed one of the first systematic studies of impairments in calculations. By investigating patient records, patients, and brain lesions in over 300 cases, Henschen noticed a co-relationship between reading and language disorders. He argued that difficulty in numbers could be identified and named the condition acalculia. Berger (1926) extended the idea that a specific disorder in calculations could occur. In his small study of 18 patients, he identified 3 patients in which there was an impairment in the ability to carry out simple calculations. He termed the disorder anarithmetria. In the literature, today, there are many examples of children who do well in reading and verbal studies but have impairment in mathematical calculations and vice versa. Converging evidence demonstrates that children’s mathematical performance is supported by cognitive abilities such as working memory, executive functions, semantic long-term memory, and processing speed (e.g., Andersson, 2007; Berg, 2008; Bull et al., 2008; Geary, 2004; Passolunghi, Mammarella, & Altoè, 2008; Passolunghi & Pazzaglia, 2004; Swanson, 1994). The role of short-term memory, however, is still in dispute. Some authors argue that short-term memory is more important as an indicator of fluid intelligence. Others define short-term memory as dormant or “the subconscious” acting within a theoretical framework of support and not actively involved in the manipulation of any representation. Often the question is whether verbal and numerical propensities are separate skills functioning in brain pathways. Many studies have shown that mathematical skill is supported by general cognitive abilities when researchers use standardized tests to measure mathematical performance. A few studies have used relatively speciﬁc measures of arithmetical calculation and problem-solving (e.g., Andersson, 2008; Maybery & Do, 2003; McLean & Hitch, 1999; Swanson & Beebe-Frankenberger, 2004; Wilson & Swanson, 2001). When using specific arithmetical calculations (Swanson & Beebe-Frankenberger, 2004; Wilson & Swanson, 2001) found that tasks requiring verbal working memory could predict skills in calculation---reading and fluid IQ were held constant. However, these results differ from other researchers (Durand, Hulme, Larkin, and Snowling, 2005) and Swanson (2004) who did not find any relationship between the calculation skills of children and verbal memory. Conclusion: the jury is still out. 53 | P a g e 54 Prepublication Copy Spatial Problem Solving Spatial cognition is the cognitive interpretation of spatial information in the environment by distance, direction, and typology. Spatial cognition begins at birth. The use of spatial cognition in the solving of simple and complex problems is defined as spatial problem-solving. As a simple example, an infant in a crib attempts to find an object such as a finger. The problem is solved when the finger is located and grasped. Almost all actions from birth involve sensory information as the first step in spatial problem-solving. The eyes, ears, and hands are often used to perform tasks in space. The application of spatial problem-solving in simple everyday life is common and becomes more complex as the use of abstractions increases. Spatial representations involve the use of long-term memory to store information about objects in the environment. At birth and during early infancy, representations about the environment are continuously stored, rewritten, and utilized. In our theory, any interruption or delay in a processing system leads to an interruption in problem-solving. In the case of spatial problem solving, there is a long list of interruptions or impairments that can be defined. This includes difficulty in shape or object discrimination, impairment of hue or colors, as well as deficits in the associative meaning of objects. Individual variation in spatial problem solving occurs based on memory, representation, the speed of processing, and pathways utilized for encoding information. Many researchers find significant differences related to these three areas of problem-solving. Does individual variation extend from spatial problem-solving to an analysis of spatial perception? Spatial perception is perceiving the relationship between objects in the environment while solving spatial problems. Impairments in spatial perception include both simple relationships (single points) and complex relationships (spatial analysis). An impairment related to a single point has been described by Holmes (1918/1919). He cited an example related to a patient who could not move from one area of the room to another without bumping into furniture. The patient could not judge the distance and depth of perception between himself and the objects. Paterson & Zangwill (1944) cited examples of patients who made errors in simple spatial tasks such as copying objects. They also could not count blocks in a 3x3x3 cube. Noteworthy is that some children in the age group of 3-5 exhibit similar problems in copying, counting, and analyzing spatial patterns. Are these impairments only found in a single individual? Or are there differences in subgroups of children and adults who display similar characteristics when given spatial problems? The answer to the latter question is a resounding, “yes.”; subgroups of people have been defined by results from spatial problems. Some differences extend 54 | P a g e 55 Prepublication Copy from early childhood. Others are found in adults who suffer impairments in neural functioning due to trauma. Some of these differences are perceptual while others are conceptual and sensory-motor. Conceptual and sensory-motor abnormalities become more evident as the complexity of the problems increases. The concepts of field independence and field dependence which were introduced in the review of the literature in Chapter 24 are just one example. In simple problems with little complexity, differences in either perceptual, conceptual, or sensory-motor are not as evident. However, when there is an increase in problem complexity and the addition of a time limit, the speed of processing becomes an important variable that separates groups of individuals. Many different types of tests have been developed to measure spatial processing. Poppelreuter (1923) developed a “search” test designed to locate a single target among a background of distractors. The main objective was to quantify the amount of spatial bias. Others (Albert, 1973; & De Renzi, 1983) have similar objectives. That is, using different kinds of search tasks, they were able to differentiate patients who searched one-half of a target rather than both sides. This led to considerable differences in time differentials related to spatial bias. In cognitive neuroscience, reference frames are used to distinguish different parts of space in constructing spatial configurations. Different spatial frames constitute different spatial representations. One current theory from animal studies suggests there is not a single Cartesian coordinate system in the brain. Instead, multiple areas of the brain appear able to process visual data. Each of the individual areas seems to have its maps and methods of orienting the stimulus based on the source. Other groups of cells, in another cortical area, make a wide receptive field that locates features within an object. In other words, specialization occurs with groups of brain cells and regions of the brain. This contributes to a spatial representation. How do affective and cognitive factors interact during the process of solving problems? Is motivation just as important as cognition? Factors influencing Problem Solving The energy of the individual is the impetus for moving toward problem resolution. Many characterize this energy as motivation. The easiest method of studying motivation in problem-solving is in the formal context of laboratory problems or a defined research paradigm. The formal context can be controlled and defined by boundaries. Can the results from these types of studies be generalized to the broader types of open-ended problems which require information seeking, competence in problem 55 | P a g e 56 Prepublication Copy solutions as well as intense recurrent motivation to find a problem solution? This kind of question is asked often as many people want to understand the context of problem-solving in everyday life. What happens, for example, if a person falls and breaks a leg and is the only wage earner in the family? Think about how you would respond to this type of problem. Is it a complex problem? Motivation to succeed comes in multiple attempts over a sustained period. Zimmerman & Paulson, (1995) suggests that this motivation can be summarized as a form of self-regulation. Self-regulation is a process of harnessing one feelings, thoughts, and actions to obtain personal goals. Self-regulation is a cyclical process that relies on prior performance, goal orientation, and affective feelings such as satisfaction and anxiety. Self-regulation is an adjustment made to maximize effort as a problem-solving skill. Any effort to solve problems is worthless if the motivation is missing. Bandura (1997) suggests that the motivation for solving a problem or reaching a goal is related to the person’s belief about themselves and their ability to solve the problem. In essence, this self-efficacy is central to the problem-solving process. Belief in self helps to accomplish the task and solve the problem at hand. Support for the concept that self-regulation is related to problem-solving tasks comes from three studies (Zimmerman and Ringle, 1981; Bandura, 1997; and Zimmerman & Paulson, 1995). Schunk (1983abc) and Schunk, Hansen, and Cox (1981) gave support to the notion of self-efficacy as a motivating force in the solution of a problem. Interaction of affective and cognitive states during problem-solving So far, the discussion has concentrated on the cognitive aspects of solving problems as the literature is mainly concentrated on cognition and problem-solving. One important assumption relative to this IPS theory is that cognition is modified substantially when interaction with the affective system occurs (Schwartz and Clore, 1996). If one could isolate just the cognitive components of thinking, then one scientific description would result. However, there is another entirely different outcome when cognition interacts with the affective system. Affect includes social concern for others, emotions, moods, and feelings. What happens when affect is combined with cognition during problem-solving? To answer that question requires some insight from a recent study by a group of neuroscientists. Kosslyn et al. (2009) have identified two general levels of brain functioning called top-down and bottom-up processing. Kosslyn’s group based their 56 | P a g e 57 Prepublication Copy assumptions on Miskin and Ungerliger’s 1982 study with Rhesus monkeys. This study surgically removed parts of the brains of the monkeys who were taught two different kinds of tasks. One task required learning shapes while the other required learning location (spatial). When the bottom part of the brain of a monkey was removed, the animal lost the ability to identify shapes (objects) but still could perform tasks or relearn the tasks which required knowledge of location (spatial). Likewise, the removal of the top part of the monkey’s brain resulted in the inability to relearn tasks requiring knowledge of location but the monkeys could do tasks requiring knowledge of shape (objects). In another experiment, the researchers were able to monitor individual neurons. Neurons in the top part of the brain were activated in decisions about the location (spatial), and neurons in the bottom part of the brain were activated in decisions about shape (objects). Spatial vision is part of the top-down system while object memory is part of the bottom-up system. Information from many later research studies (Wilson et al., 1993) now has documented, in general, how the two systems, top-down and bottom-up, coordinate and work together. The top brain is dorsal from the temporal and occipital pathways while the bottom brain is ventral via lower temporal and occipital pathways. Information flows from the bottom to the top and vice versa. For example, information coming via motor and sensory is organized, compared to the object in short-term or long-term memory, and then classified and interpreted. Information coming via the temporal and occipital pathways may go to the frontal lobe. With this new information, many studies suggest that the top brain and bottom brain provide feedback loops from the environment about the correctness of a problem solution. New information constantly shapes and modifies current thoughts and ideas. Top-down processing, when juxtaposed and interacting with the affective system, results in global cognitive processing, such as metacognition, component selfregulation, and active meta-components. Meta-components are supra structure, such as planning, and forethought. Top-down processing, when combined with environment feedback systems, affects one’s feelings (affective system). Thus, the two systems (top-down and affective) acting simultaneously result in global processing which is more ideational, and intuitive. When emotions or feelings are blocked, or held at a repressed level, then cognitive systems may rely more on logical thought. Repressed feelings may lead to cold hard logic or then again repressed feelings may lead to a complete lack of logical thought. Being in a happier mood may make a person less attuned to negative threats in the environment. Therefore, in less stressful problem situations, individuals usually rely on subconscious automated response mechanisms to obtain their goals. The top-down system can bypass the data-driven detailed-oriented bottom-down system and use a 57 | P a g e 58 Prepublication Copy simple heuristic (rule of thumb) to meet current goals. This happens frequently to the introverted individual who is an image or pattern processor as is described in a later section and our 36 subgroups. Being positive, and less attuned to the problems of the outer world, the pattern processor skips over details of their immediate environment as is evident in their global speech and writing. This pattern is particularly evident in aging senior citizens whose speech and processing become more nondescript. “Get that thing over there for me, will you?” Anxiety, an affective response, can keep the data-driven bottom-up system from finding an inferential principle to help in any given situation. Even though the two systems work in a coordinated manner, the top-down system can dominate or interfere with a bottom-up system under certain situations (euphoria, distress, anxiety-driven, morose, sadness (Schwartz, 2002). Of course, the reciprocal is true. Differences related to Problem Solving Age and neural development Age and neural development are extremely important factors in problem-solving, especially if the theories of Piaget are followed. In Piaget’s theory, children develop general and specific cognitive processes and abilities in different stages (differentiation). The differentiation hypothesis suggests that people acquire specialized abilities with age, experience, and neural development. It was Cyril Burt, 1919 who proposed the idea that differentiation occurs with increasing age (Anatasia, 1970). Early studies supported the idea (Bayley, 1955; Burt, 1954; Garrett, 1946), but later studies found contradictory evidence. Perhaps differentiation occurs in different stages, or then again, maybe differentiation is so individually based as to obscure the stage. Many researchers suggested there were issues related to methodology and choice of measuring instruments (Bickley, Keith, and Wolfe, 1995). Current neuropsychological studies suggest that abilities become more specialized and increase in complexity over time (Kolb & Fantie, 1997; Kolb & Whishaw, 1996). Therefore, age is important as a form of maturation when considering early childhood. Epstein (1979) is one of the main supporters of the notion that Piaget’s stages of cognitive development coincide with stages of brain maturation. The work of Thatcher (1991, 1997), as well as Hudspeth & Pribram (1990), provide some supporting evidence. Does the aging of the brain occur in phases? Current theories suggest that phaselike development in different cerebral systems occurs in response to environmental 58 | P a g e 59 Prepublication Copy influence. At some developmental stages, which are labeled critical or sensitive periods by Anderson et al. (2001), the organism is more vulnerable to environmental inﬂuences. Most critical periods are paralleled by rapid neurological development in myelination and synaptogenesis and thus visual-spatial and verbal systems develop through the interplay of functional systems that mature depending on these underlying processes. Piaget suggests that sensory-motor is the first stage of cognitive development and occurs from birth to around two-three years of age. In this stage, most children’s visual activities are dependent upon reflexes, neural feedback, and movement, especially in the lower body regions. Memory, processing speed, and visual-spatial functionality are just beginning to develop. (Anderson, Northam, Hendy, & Wrennall, 2001). The brain functions found in the right and left hemispheres overlap. Most of the processing occurs as reflexes, and lower-level sensory-motor. Piaget’s second stage (pre-operational from 3 to 7) is regarded as an especially important phase of brain development, during which neurons and synapses necessary for the rest of one’s lifetime are selected and organized (Sanes & Jessel, 2000). The basic assumption is that changes in psychological test performance are a reﬂection of brain maturation and experience. Most studies indicate that by age 5, each hemisphere is more differentiated and higher-order cognitive processes are less likely to overlap. This is supported by correlational data between cognitive processes of verbal items and arithmetic processing and/or verbal items with test performance, especially tests involving the Wechsler (Kolb & Whishaw, 1996). Also, as the child ages, processing speed and executive functions are more multidimensional. (Bjorklund, 1989; Kail, 1986). Human beings have longer development periods, a process that separates us from many other species. Gender differences in problem-solving Gender differences are often found on many standardized test instruments, especially at an early age. The literature reviews are certainly controversial with some favoring females on certain kinds of numerical and spatial tests; while other reviews favor males on the same standardized instruments. What we do know is that tests score, specifically verbal, numerical, and spatial, can be combined across measures. According to Deary et al., (2007) as well as Strand et al. (2006), gender differences are quite small when scores are aggregated. Recent results suggest that males exhibit a slight advantage on measures of ﬁgural reasoning like the Raven test (Irwing & Lynn, 2005) and quantitative reasoning (e.g., Hulick, 1998), whereas females often achieve better results in verbal reasoning tests (e.g., Strand, Deary, & Smith, 2006). 59 | P a g e 60 Prepublication Copy In early research reviews, girls do not score as high on spatial problems in mathematics as boys (Linn & Peterson, 1985; Waber (1977); Voyer, Voyer, & Bryden 1995). According to Casey (2009), support by mothers during their early formative years is more important than early exposure to spatial problem-solving. Other researchers (Levine, Ratliff, Huttenlocher, & Cannon, 2012) who examined early home environments found that parental support and parents’ spatial language at ages 2-3 were predictors of later spatial performance at 4.5 years of age. Reviews and results change when real-life situations are used for analysis. Complex problem-solving tasks, such as those found in real-life situations, are more likely to be related to a host of factors such as previous experience, knowledge, expert performance, motivation, interest, and self-regulated disposition. In this book, the results from laboratory experiments as well as real-life problem solving are examined and used. Both are important. Expert (general) vs. beginning problem solvers (differential) The research literature on problem-solving attempts to address problems solving capabilities by contrasting expert performance with beginners or novices. This characterization does not fit our definition of a differential problem solver as the differential problem solver with interest and experience can sometimes solve complex problems better than the expert, especially in non-traditional environments. In such cases, the differential problem solver is the expert. However, the literature does help explicate differences for those who solve problems better than others. In summary expert performance (specialization) in solving problems is obtained over an extended period and is gained through the mastery of complex and difficult challenges, usually within domain-specific areas or traditional environments. In many cases, expert performance (specialization) encompasses multiple skill acquisitions as well as complex learning. The cognitive processes which underlie expert performance encompass an extensive structured knowledge base and semantic memory which are applied to problems through reason, creative thinking, text, numerical and spatial comprehension, as well as decision making. Expert performance changes with the type of tasks and subtasks involved in the domain of expertise. Experts and beginners do not approach problems in the same manner. A mental set and previous experience with similar problems influence the outcome of an individual problem-solving situation. 60 | P a g e 61 Prepublication Copy Individual versus group problem solving A group of people solves a problem differently than a single individual. Groups of people are more likely to engage in divergent thinking and generate a plethora of alternatives compared to a single individual. In a group of people, each representation of the problem is different and the group is likely to converge to a single solution, depending on the constituency of the group. The group often performs better than any single individual since the thinking processes involving causal reasoning, logical alternatives, inductions, and evaluations are distributed more amongst members of the group with each member contributing based on strengths rather than weaknesses. (Dama & Dunbar, 1996) Are groups more successful? That depends upon the composition of the group as groups that are from the same background tend to represent the problems similarly and arrive at the same outcome. Groups composed of members from different backgrounds tend to generate many different kinds of problem representations (D). Chapter summary Our theory suggests that groups of people show differences in the solving of problems depending on whether the problem is verbal, numerical, or spatial. Based on this basic review, what does your intuition about the literature suggest? Problem-solving is an adaptive behavior necessary for survival and longevity. It is a process that has been with us since the beginning of our species. Studies in the past have tried to unlock the mystery and have succeeded in dividing the process into many subcomponents, including a beginning, middle, and end. A problem can be defined, presented, formulated, and reformulated in many different ways. 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Sex differences in mental abilities, hemispheric lateralization, and rate of physical growth at adolescence. Developmental Psychology, 13, 29-38. 70 | P a g e 71 Prepublication Copy Chapter 5 Elements and Foundation of Solving Problems Introduction Any discussion of problem-solving should incorporate the biological and psychological foundations of how people think and how the brain functions during the problem-solving process. This chapter provides basic information about cognitive structures, functions, and abilities as viewed through the lens of IPS theory. IPS theory- energy production in problem-solving Before birth, the embryo develops into a fetus that can hear, and see. Studies have suggested that physiological changes such as the rate of the heartbeat react to sounds in the fluid environment of the womb. For example, one study measured the heart rate when the fetus was exposed to music. The heart rate fell when the same music was played repeatedly, suggesting acclimation to the sound and a calming effect (Aniruddh, D., & Patel, E. M., 2011). In contrast, other studies suggested that worry and stress from the mother resulted in a decrease in important chemical constituents such as folic acid and vitamin B12. These chemicals ultimately affect life after birth, including the ability to solve life and academic problems. Vitamin B12 and folic acid act as supplements that help in methylation, a process needed to sustain brain cell networks (Scholl and Johnson, 2000). The capacity to solve problems shortly after birth relies on proprioceptive memory found in muscles and the brain (Gundersen, K., 2016; Egner, I. M., 2013; Sharples, A., 2015.). The very first actions of the neonate are related to motor functions such as moving the arms, grasping the fingers, and walking. Short-term memory drives motor functions until about 17-28 months when long-term memory begins to develop. In the developmental process of children, the structures of the frontal lobes only become mature during the fourth and fifth years of life (Sapir and Nitzbury, 1973). In other words, the structural basis for solving complex kinds of problems is not available until many children are starting preschool. Development is speeded by oxygen, glucose, and other elements in the brain. Development is increased by motor or physical activities occurring at an early age, usually before four years of age. 71 | P a g e 72 Prepublication Copy Even though the capacity for solving more abstract complex problems is not available early, the foundations are established at or before birth. Problem-solving is based on experience, exposure, and practice which leads to language development such as the first words of” mother” and “father”. According to IPS theory, how does this occur? Origin of cell energy for language production Biological evolution occurs over billions of years with energy transformations occurring as slowly as the half-life found in strong nuclear forces. Although biological energy is different from the physical energy of light, the concepts of energy transfer share similar characteristics. At the heart of both energies, reactions are quarks, quantum theory, and electromagnetic forces. The world of the particle/strings is not very predictable but the characteristics of self-consistency, resonance vibrations, higher dimensions, tunneling, and mathematical equilibriums in electron movements could provide the neurochemical basis of memory traces and electron movement. Electrons exist on all atoms, moving in orbits around the nucleus filled with protons and neutrons. The electron is held in orbit by energy. As electrons shift from orbit to orbit, energy is lost or gained as electrons bump into each other, repel each other, and exchange packets of energy. Electrons are part of the neural network in the body. The movement of electrons through a conductor such as copper wire is called electricity. The electron movements through a conductor such as a nerve cell or its myelin sheaths create electrical transmissions. Guess what, every cell in the human body has an electrical field created by potassium, calcium, and sodium ions (Fish and Geddes, 2007). These electrical fields are often stimulated by changes in ion concentration causing action potentials, and electrochemical changes. Energy is created in almost all forms of life by the same process of chemical gradients. According to the recent article published in the Journal of Molecular Evolution, by Barry et. al. (2014), an acid/alkaline pump similar to those found in hydrothermal vents was a parallel precursor to energy production in early evolutionary history. The universal process of chemical osmotic coupling occurs through an electrochemical proton gradient used to drive Adenosine Triphosphate Phosphate (ATP) synthesis. Again, in the theory of the IPS model, at the subatomic level, energy forces are created from the exchange of discrete electrical packets (Read the reference Chapters 23 - 25 if you want to know how!). As the frontal lobes develop, the energy forces (let us for lack of a better name call these discrete electrical packets "neuphons") in the cellular neurons are rapidly transferred to all different areas of the neural network. The neuphons can be stored (short-term, long-term, or episodic memory) or transferred to different parts of the brain's lobes. The storage components can be in parts (individual neurons) or wholes (networks of linked neurons). With this information, it is easy to postulate that language development occurs over a period of time, usually through exposure and experience. Neural networks do not contain whole language 72 | P a g e 73 Prepublication Copy components such as the word "mother" but instead have neurons with representations of the smallest phonetic unit capable of providing the whole word. For example, the word "mother" is assembled individually based on the sensory transmissions converted from the experiences that the child undergoes. To assemble the word "mother" from individual neuronal cells or parts of a network requires electrical packets to move from place to place transferring energy and effort. Knowledge of language becomes an individual reconstruction of experiences as is evident from the many dialects and languages found in different regions of the world. The reassembling of the experience in the form of knowledge and language is not the same for everyone but has a common core based on shared experiences as each person solves daily problems. Competition in the brain Problem-solving involves choice and decision makings. How and where does this occur? Electroencephalography (EEG), magnetic resonance imaging (MRI), functional magnetic resonance imaging (fMRI), and positive emission tomography scans (PET) are ways of visualizing the flow of energy (electrons) in the brain. Many of these electronic methods use flashing imagery to show pathways and neuronal activity. Neural networks, coordinating different structures and functions, are everywhere in the body. The speed of electrons parses many networks activating emotions, non-emotions, functions, hormones, as well as physiologic and skeletal components. Given the nature of any situation, the flow of energy is either outward toward the environment or inward as part of the brain functions (introversion vs. extraversion). This results in different areas of brain competition such as sensory-motor activation versus conceptual activation; control of focused thinking vs. adaptable flexible thinking; or even a rational response versus an emotional response. All functions can be in either opposition or synchronization. This occurs through the involuntary autonomic nervous system along with the voluntary central nervous system which controls many simultaneous actions in the conscious and subconscious. One of the fascinating findings from EEGs and other similar methods is that during many daily activities of the person, multiple areas of the brain are involved. A fact more fascinating is that some of these areas or neural networks are engaged in cooperation and competing functions simultaneously. That is, one area of the brain may reflect choices based on the memory of core values (democracy, home, family) while another area may reflect choices based on peripheral values (how much things cost). Information is stored in different areas of the brain and reassembled. If the information comes from networks that are competing, cognitive dissonance occurs. When multiple areas of the brain are activated, the voluntary CNS system must make a decision which ultimately results in a choice or a selection. As an example, assume one is in the supermarket. A choice must be made between two different brands of ketchup. One is a wellknown brand and costs more and the other bottle is a lesser known brand and costs less. The well73 | P a g e 74 Prepublication Copy known brand has a better taste; while the lesser brand does not. What is the basis of one’s choice? That is the question but unfortunately, the answer is not the same for everyone. For one person, maybe taste from a well-known brand is more important than cost. For another, the lesser cost outweighs any increase in value related to taste. Based on current knowledge, the choice depends upon so many different factors; there is never a single correct answer. For some people, in certain situations, a choice might reflect lifetime core values. For others, one person’s lifetime values may be tremendously outweighed by another person’s lifetime values. For the rest of the people, the choice might not hold any value as “time” may be more important and thus, the selection is based on necessity. How quickly can one obtain a bottle of ketchup and return home and watch the Dodgers play on TV! Competing networks lead to discriminating differences and discriminating differences in choice lead to individual differences in problem-solving. Individual differences are found between people with similar values, similar ideas, and similar personality characteristics. Similar groups of people can make different decisions based on different choices from similar neural pathways. In psychological terms, decisions based on neural pathways require different levels of experience and choices to solve similar and different kinds of problems. Cognitive structure and cognitive processes in problem-solving Confusion often results as many authors use cognitive structure and processes and cognitive ability interchangeably. How each of these concepts is modeled is based on theory. That is, theory represents how functions related to the structure of the brain occur. A structure can be the neural networks carrying electrical charges operating in an area such as the temporal lobe. Theory suggests that the transformation of the information coming from the senses can be represented as hierarchical or recurrent, i.e.; being sequential with known steps occurring at a point in the network or moving in multiple networks in many different directions simultaneously. As such, converging evidence suggests that the capability to solve problems is related to both cognitive structure and function. What exactly is meant by that statement and how does the structure and function of the brain directly influence the solving of problems? Cognitive structure is often used to identify a part of the brain. In problem-solving, cognitive structures are numerous (frontal lobe, etc.), depending on which cognitive processes (analogy, verbal semantic interpretations) is identified. Scientists and psychologists have many names for very similar processes. Even then, there is not a one-to-one relationship between cognitive structure and cognitive processes. In the previous chapter, two levels of processing (top down and bottom up) were identified by Miskin and Urlinger in 1982. Motor and sensory information were classified and interpreted via 74 | P a g e 75 Prepublication Copy comparison to object memory at the same time as information went to the frontal lobe. Both systems simultaneously provided feedback during problem-solving situations. Problem solution comes in response to feedback in degrees, depending on the amount, type, and stage. Information is available in each feedback loop. The amount of information can be very small (not enough), very large (information overload), or somewhere in between. The type of information represented by the environment can be classified into three categoriesverbal, numerical, or spatial. The stage of the problem solution can be the initial, middle, or end. In the initial stages of solving problems, perception and attention are extremely important while the intermediate stages include the cognitive processes of analysis, and synthesis, as well as the interactions with long-term memory and short-term memory. The ending stages require evaluation and reflection. The difficulty in understanding cognitive structure and function in the problem-solving process comes from the many feedback loops which shape and modify each process at each of the 3 stages. Even a short, simple, perceptual task such as discriminating between two letters may require many millions of neurons interacting in competing networks via the process of feedback. Many of the above authors cite the frontal lobes as one of the major structural and functional areas related to problems solving. Regardless of how cognitive processes are measured, either separately or individually, they contribute to the concept known as levels of thinking. Levels of thinking Levels of thinking that are represented as hierarchical are more easily interpreted. For example, in Bloom’s taxonomy (1956), the lowest levels of thinking (Knowledge) include facts (very defined) and connections such as associations. The levels above Knowledge are usually characterized as critical thinking processes (Comprehension, Application, Analysis, and Synthesis). The top level includes the metacognitive component called Evaluation. While Bloom’s taxonomy is excellent and useful for conceptualizing cognitive processes, most scientific studies suggest that there is not a bottom or top. Instead, there are many pathways through the brain with different levels of experience and interaction which contribute to levels in processing information (thinking). Cognitive ability Earlier, it was noted that many authors when describing the solving of problems use cognitive ability in place of cognitive structure. So, what is cognitive ability? Cognitive ability is related more to functions than to structure. Today, many authors (Andersson, 2007; Berg, 2008; Bull et al., 2008; Geary, 2004; Passolunghi, Mammarella, & Altoè, 2008; Passolunghi & Pazzaglia, 2004; 75 | P a g e 76 Prepublication Copy Swanson, 1994) suggest that cognitive ability is a combination of multiple processes such as working memory, verbal (semantic) long-term memory, processing speed, and actions of the executive functions found in the frontal lobe. These summary statements are probably a good assessment of cognitive ability as cognitive ability, at least initially before complex life experiences, appears to be more generic. Many authors suggest that cognitive ability subsumes a concept called fluid ability or “gf”; i.e. spatial and analogical reasoning, as well as analogical transfer. According to Cattell’s investment hypothesis (1987), fluid ability (Gf); a genetic component, is used to solve verbal, numerical, and spatial tasks. Over time, children through practice and experience learn perceptual, discriminatory, and executive skills that are integrated into their particular repertoire of ability. Because of the uniformity of the curriculum, crystallized knowledge (nongenetic) such as reading writing, and arithmetic is learned during the school years. What is known at the present is that the influence of fluid ability differs by age, experience, and sometimes gender. The analogical transfer seems to be more common as a person goes through the developmental stages of infancy, adolescence, and adulthood. According to most studies, general cognitive ability is established before learning domainspecific knowledge. That is, children inherit some general cognitive ability and later, through study and exposure to feedback from parents and caregivers, establish the foundation for general knowledge in the early years of life (birth-4 years). From preschool to grade 4, some children, especially by asking questions or receiving corrective feedback, amass a large amount of general knowledge in math, literature, and English (domain-specific knowledge) and use both cognitive ability and knowledge to solve new problems. McArdle et al. (2001) addressed the relations between memory (short term), verbal (vocabulary tests), and non-verbal indicators (spatial block design) tests for age groups 16-68. All subtests were significantly related. His results suggested that processing speed, short-term memory, and fluid ability signified changes in time intervals for older groups. In the early age groups, the ability to understand spatial relationships inversely predicted word and vocabulary comprehension. In his words, non-verbal indicators were negative leading indicators for vocabulary in the 6-11 age groups. Memory and fluid ability Is there a relationship between memory storage for words and fluid ability? Again, the results vary. In some studies, verbal working memory appears to be dependent on skills in reading and fluid intelligence (Swanson & Beebe-Frankenberger, 2004; Wilson & Swanson, 2001); while in others, there is no relationship (Andersson, 2008; Fuchs et al., 2006; Swanson, 2006). 76 | P a g e 77 Prepublication Copy The influence of fluid reasoning (Gf) is very identifiable from 2-10 years of age. Assuming that fluid ability plays some part in academic learning, the influence is greater upon mental manipulations and quantitative learning and stronger during the age period of 5-16 when standardized test taking is apparent. There is a decline in the influence of fluid ability from ages 16 to 31 and even weaker relationships in the age group 32 to 60 (Ferrer & McArdle, 2004). The decline in the influence of fluid ability is directly related to the individual’s ability to solve more complex problems using the experience gained from everyday work or living activities. A single thought To produce a single thought, such as lifting the arm, the brain works in a coordinated fashion. That is, the flow of energy through the neuron pathways occurs at a very fast rate. Give yourself a command to lift your arm or think of a fighter who must interpret the actions of his or her opponent. A poor fighter who does not interpret the action of his or her opponent is in real trouble. One neuroscientist suggests that the neuro-circuitry in the brain should be conceived similarly to an ice cube being moved along a flat surface. When water is frozen (an energy transformation) in the form of an ice cube, thousands of molecules change form. This energy transformation from liquid to solid allows the new form (ice cube) to act differently than the old form (water). When the ice cube is pushed, all the molecules in the ice cube move simultaneously. An energy transformation in the electrochemical pathways allows the neurons to act as networks. Networks, like the atoms in the ice cube, act in concert and all move simultaneously. In IPS theory, energy transformations give rise to memories, analytic thought, divergent thinking, and convergent thinking almost simultaneously. Energy transformations are the basis of what is often called “conceptualization or thinking.’ Concept formation The classical view of concept formation suggests a pathway approach. In other words, neuronto-neuron or network-to-network processing can only occur simultaneously in different areas of the brain (as seen in magnetic resonance imaging) if multiple connections exist. The multiple connections of neurons or networks are designated as neural pathways which are modeled as cognitive and personality pathways. Concept formation concerns how the brain represents conceptual knowledge or objects or events and actions seen in the environment. In the classical view, there is an input, processing, and output. If someone wanted to open the door, the visual image is processed through the visual system and the output would be the “action” of opening the door. The brain represents the process as seen with the visual system (forming a mental image); relays the information through the prefrontal cortex, and finally, the motor neurons implement a command to open the door. 77 | P a g e 78 Prepublication Copy Opening the door is not a high-level cognitive abstraction but instead represents a combination of low-level sensory and motor actions under the control of the subconscious system. Remember in Chapter One, that the decisions made by ANS and the reptilian brain are automated. Experience or activities associated with real objects in our environment provide the basis of everyday low-level conceptualization (reflex actions) about events associated with survival, and reproduction while the depth of processing is associated with higher levels of concepts such as time spent reading, writing, and manipulating abstract symbols. The prefrontal cortex is involved in planning and manipulating areas if repetitive actions occur through symbolization. Depth of processing assumes repetitive actions are associated with practice, rehearsal, and repetition. Depth of processing is extremely important as the “thinking through” of complex problems requires it. Depth of processing requires a greater expenditure of energy and focus as there is a greater amount of time spent individually thinking about multiple actions or objects in the environment. The depth of processing is associated with the individual processing of manipulating real concrete objects and abstract symbolization in the environment. For example, what happens if I throw this ball and it hits the window? The window breaks. How do you know this? Have you seen what happens when a ball strikes a window? Was it in real life or did you watch the scene in cartoons as a child? Have you internalized the sound, the mess created? Can you picture what happens? Again, stored memories from your experience recreate the answers to all of these questions. Memories come from all parts of the brain. Sensory neurons hold information about sound, vision, and smell. The neurons in the occipital lobe provide information about visual memories, while the neurons in the limbic system provide memories about an emotional response. Sound and vision memories are processed simultaneously in the parietal and occipital lobes. In total, the memories, the processing of visual information, and abstractions constitute the depth of processing. Depth of processing ultimately requires analysis in the prefrontal lobes which manipulates the concrete objects and symbols through energy transformations. The number of abstract symbolizations and concept formations developed during a single thought process about concrete objects is based on how people in the environment (i.e.; father, mother, caregiver, and schooling) provide early enrichment opportunities. The number of abstract symbolizations could be in the millions if the environment provides numerous opportunities for practice and interaction during enrichment. PS: Let your children ask questions as they encounter new situations. Either give them a complete answer or find the answer with them on the internet! Enriched environments are those which provide more opportunities for manipulating concrete objects. Enriched print and object environments give children an understanding associated with abstract symbolization. 78 | P a g e 79 Prepublication Copy Abstracting Long hours of conceptualization lead to abstracting. Abstracting is a cognitive process that cuts across the details in the environment via the sensory-motor systems (see, heard, touched, and noted). People, when conversing, often use the lowest level of detail and abstraction as a method of description. For example, one might ask another “Where did you get that coat?” Because the words are non-specific and general, the lowest level of physical detail which might be accurate is obtained from the label on the coat. That is, a person might respond “I got the coat from Bushranger.” On the other hand, a simple answer could be “from the closet or the store.” All responses are accurate when the question contained non-specific information. Children who grow up in environments where non-specific language is used often retort with non-specific language. Mother says to the child “Go get that.” The child thinks, “What is that?” Mother points out “that.” Child retorts, “get that yourself.” Children mimic adults, especially in verbal and grammatical language. Children, who grow up in environments where very specific language (nouns, verbs) are used, tend to abstract based on the object of the noun. For example, the following example is a sentence with a specific language. Question: “From which store did you buy the coat that you are wearing?” Response: “I bought the coat from Bushranger.” Abstract logical thinking is processed in the prefrontal cortex. The work of Piaget (1954) suggested that children first use abstract logical phrases around 11 or 12 years of age. Although studies in literature now contradict that age range, children develop different levels of abstract thought at different ages. Very few children can logically use abstractions as young as 5 or 6 years of age. The literature reviews of individual differences suggest “less of stage approach” and more of an “it depends on the experiences” when denoting the age range of developmental behaviors. In essence, categorization, inferences, abstractions, logical thinking, and almost all other highlevel processes are a function of time and development. Think of the varied experiences that occur between the ages of birth and five. Children exposed to an enriched environment with lots of reading are more likely to develop the ability to conceptualize on abstract levels earlier in life. Speed of processing There is another kind of neuronal processing called the speed of processing. The speed of neuron processing probably has its origin in evolutionary genetics. One is born with a natural speed based on neuronal interconnections; however, that speed can be increased through practice. In the infant, developmental speed is associated with moving of the arms, grasping, eye movement, and other motor functions exhibited at birth and beyond. Speed of processing in its simplest form is manifested as a reflex; while in the more complex form speed of processing represents memorystores accessed via proprioceptive and sensory functioning. Neuronal motor speed in networks 79 | P a g e 80 Prepublication Copy travels along the ventral pathways while the depth of processing interacts with networks in dorsal pathways. Have you ever played the game of trying to catch a piece of paper as it is dropped between two fingers? Are some people better at catching the paper than others? What if there were 100 people (3 different time trials) trying to catch the paper as it is dropped? Could this exercise separate people into groups by time? Probably! Speed in processing is real; differences are measured daily in athletes and other individuals whose lives depend on motor agility (military, firefighters, etc.). Think about the reactions of a goalie in hockey who must react to a puck traveling over 100 miles an hour. Speed of processing, in many instances, is a function of reflexes, proprioceptive actions, and low-level conceptual processing found in sensory and motor neurons. Depth of processing and abstracting is a function of memory, image formation, and executive forebrain activities. Object processor vs conceptual (image) pattern processor Are there people who process information differently than others? All people use multiple neuronal processes simultaneously; however, the time spent processing the information as required by tasks and work situations establishes neural patterns and habits. These neural patterns are dependent upon short-term and long-term memory patterns. When people share common memory patterns because of schooling, culture, and recent training, automated habitual mental and motor actions are similar. The habitual effects of these patterns are then explicated when individuals are asked to solve a particular kind of number, word, or spatial problem. In essence, the speed of processing and emotional affect interacts using different brain pathways as people perceive objects and images related to the problem. In IPS theory, this results in patterns of people who are designated as object processors or image pattern processors. These patterns are woven into the descriptions of the 36 problem-solving subgroups found in the appendix and the separate documents “DeNovellis’ Description of the 36 Problem-Solving Subgroups”. How does this occur? Each person uses both the top-down and bottom-up processing systems simultaneously. Over time and based on individual propensities, cognitive processing changes. That is, some people become more attuned to objects, shapes, and things in the environment; while others are more likely to abstract patterns in their environment. Differences are based on experience, memory, affective feeling, and propensities for abstracting objects and or processes. Object processors become more concerned with the characteristic of objects, things, shapes, and details about those objects while pattern processors are globally processing the patterns, commonalities, and abstract relationships associated with related objects. These differences can be easily seen in the style of writing and pattern of speech used by various people. Some people respond to test questions with short, curtailed logical phrases; while others 80 | P a g e 81 Prepublication Copy use image-laden responses. Some people write a full paragraph explaining an answer while others write a single sentence. When listening to patterns of speech, some people use very globally, non-descriptive language, while others use detailed descriptive responses. In IPS theory, in non-threat environments, object processors are more likely to be motor oriented while pattern processors are generally conceptually oriented. However, changing the environment from nonthreat to threatening and both object processors and image processes become more realistic, practical, and detail-oriented. The need to survive becomes paramount and both groups move from more global to more focused. Chapter summary Cognitive processes and structures influence the levels of thought which in turn define different subgroups of people who solve problems differently. The are many terms (concept formation, levels of thought, depth of processing) that describe the processing of information transfer during the solving of a problem. Problem-solving is dependent upon memory, abstracting, cognitive structures, ability, and changes or modifications which take place in a nanosecond or longer depending upon the complexity of the problem. Long-term modification can only occur with repeated instances of practice. Chapter references: Andersson, U. (2007). The contribution of working memory to children’s mathematical word problem solving. Applied Cognitive Psychology, 21, 1201–1216. Andersson, U. (2008). Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions. British Journal of Educational Psychology, 78, 181– 203. Aniruddh, D., & Patel, E. M. (2011). The Power of Music: Pioneering Discoveries in the New Science of Song. Bloomsbury Publishing. United Kingdom. 9780802719966, 263pps. Barry H., A. Whicher, A., Camprubi, E. Watson, C., Dartnell, L., Ward, J., Evans, J. R. G. & Lane, N. (2014). An Origin-of-Life Reactor to Simulate Alkaline Hydrothermal Vents. Journal of Molecular Evolution, 78(5-6), 213-227. Published online 2014 Nov 27. doi: 10.1007/s00239-0149658-4 PMCID: PMC4247476 Bartlett, F. C. (1932). Remembering: A Study in Experimental and Social Psychology. Cambridge: Cambridge University Press. 81 | P a g e 82 Prepublication Copy Berg, D. H. (2008). Working memory and arithmetic calculation in children: The contributory roles of processing speed, short- term memory, and reading. Journal of Experimental Child Psychology, 99, 288–308. Bloom, B. S.; Engelhart, M. D.; Furst, E. J.; Hill, W. H.; Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: David McKay Company. Budni, J.1., Zomkowski, A.D., Engel, D., Santos, D. B., dos Santos, A. A., Moretti, M., Valvassori, S.S., Ornell, F., Quevedo, J., Farina, M., Rodrigues, A. L. (2013). Folic acid prevents depressive-like behavior and hippocampal antioxidant imbalance induced by restraint stress in mice. Journal of Experimental Neurology, 10, 240,112-121. Bull, R., Espy, K. A., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33, 205–228. Cattell, R. B. (1987). Intelligence: Its structure, growth, and action. Amsterdam: North-Holland. Dow, G. T. & Mayer Egner, I. M., Bruusgaard, J.C., Eftestøl, E., & Gundersen, K. (2013). A cellular memory mechanism aids overload hypertrophy in muscle long after an episodic exposure to anabolic steroids. Journal of Physiology 591(24):6221-30. doi: 10.1113/jphysiol.2013.264457. Epub 2013 Oct 28 Ferrer, E., & McArdle, J. J. (2004). An experimental analysis of dynamic hypotheses about cognitive abilities and achievement from childhood to early adulthood. Developmental Psychology, 40, 935–952. Fish, R. M. & Geddes, L.A. Conduction of Electrical Current to and Through the Human Body: A Review. Eplasty. 2009; 9: e44. Published online 2009 Oct 12. PMCID: PMC2763825. Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., et al (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98,29–43. Geary, D. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15. Gundersen, K. (2016) Muscle memory and a new cellular model for muscle atrophy and hypertrophy. Journal of Experimental Biology. 235-42. doi: 10.1242/jeb.124495 Kosslyn, S. M., et al. (2009) Two forms of spatial imagery: Neuroimaging evidence. Psychological Science, 20, 1245-1253. McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural analysis. In R. Cudeck, S. du Toit, & D. Sorbom (Eds.), Structural equation modeling: Present and 82 | P a g e 83 Prepublication Copy future. A Festschrift in honor of Karl Joreskog (pp. 341–380). Lincolnwood, IL: Scientific Software International. Miskin, M. and Ungerliger, L. G. (1982). Two Cortical Visual Systems. In D. J. Ingle, Melvyn A. Goodale, and Richard J. W. Mansfield (Eds.) (1945) 1959 Productive Thinking. Enl. ed., edited by Michael Wertheimer. New York: Harper. → Published posthumously. Contains a bibliography of Wertheimer’s publications. Reprinted in 1961 by Tavistock. Cambridge, MA: MIT Press: 546-86. Mumford, M. D., Reiter-Palmon, R., & Redmond, M. R. (1994), Problem construction and cognition: Applying problem representations in ill-defined domains. In M. A. Runco (Ed.), Problem finding, problem solving, and creativity (pp. 1-39). Norwood, NJ: Ablex. Passolunghi, M. C., & Pazzaglia, F. (2004). Individual differences in memory updating in relation to arithmetic problem solving. Learning and Individual Differences, 14, 219–230. Passolunghi, M. C., Mammarella, I. C., & Altoè, G. (2008). Cognitive abilities as precursors of the early acquisition of mathematical skills during ﬁrst through second grades. Developmental Neuropsychology, 33, 229–250. Piaget, J. (1954). The construction of reality in the child. New York: Ballantine. Sapir, Selma G, & Ann C. Nitzburg. (1973). Children with Learning Problems: Readings in a Developmental-Interaction Approach. New York: Brunner/Mazel. Scholl, T. O. & Johnson, W. G. (2000). Folic acid: influence on the outcome of pregnancy1,2,3,4. American Journal of Clinical Nutrition.71,5 ,1295s-1303s. Sharples, A. P., Polydorou I., Hughes, D.C. Owens D. J., Hughes, T. M., Stewart, C. E. (2015). Skeletal muscle cells possess a 'memory' of acute early life TNF-α exposure: role of epigenetic adaptation. Biogerontology. 2016 Jun;17(3):603-17. doi: 10.1007/s10522-015-9604-x. Epub 2015 Sep 8. Sternberg, R. J. (1985). Beyond IQ: A triarchic view of human intelligence. Cambridge, England: Cambridge University Press. Swanson, H. L. (1994). Short-term memory and working memory: Do both contribute to our understanding of academic achievement in children and adults with learning disabilities? Journal of Learning Disabilities, 27, 34–50. Swanson, H. L. (2006). Cross-sectional and incremental changes in working memory and mathematical problem solving. Journal of Educational Psychology, 98, 265–281. Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difﬁculties. Journal of Educational Psychology, 96, 471–491. Wertheimer, M. (1945). Productive Thinking. New York: Harper. Reprinted 1961 (Tavistock). 83 | P a g e 84 Prepublication Copy Wilson, K. M., & Swanson, H. L. (2001). Are mathematics disabilities due to a domain-general or a domain-speciﬁc working memory deﬁcit? Journal of Learning Disabilities, 34, 237–248. Further reading Bourzac, K. (2007) Lightning Bolts within Cells. Biomedicine, Retrieved on December 10, 2007, https://www.technologyreview.com/s/409171/lightning-bolts-within-cells/ 84 | P a g e 85 Prepublication Copy Chapter 6 Coding, Encoding, and Energy in Problem Solving Introduction One reason for using cognitive processes and information processing as a foundation for the Integrative Problem-Solving Model is the fluidity and potential elicited by the cognitive approach. Most people, especially in business and education, are interested in remediation and modification as a method to improve performance. Understanding the encoding processes helps in diagnosis as well as developing constructive remediation in the solving of common problems. So, what exactly is meant by the encoding process? Encoding Encoding information from the environment is central to the Integrative Problem-Solving Model. In our theory, encoding leads to differences in subgroups, and the model pathways used. Common environmental stimuli are encoded by sensory neurons over pathways that are heavily traveled and not blocked by emotions and/or feelings. Encoding is primary since encoding is the foundation of memory retrieval and the basis of context comprehension. Encoding occurs as a result of the filtering of information which can be related to habitual actions, especially in restricted environments where there are limited interactions. Encoding is based on the transfer of energy from either outside or inside sources to a form that the neurons can utilize. In theory, encoding stops once an energy stimulus originating from the environment or the brain is processed either in a single neuron or a group of neurons representing a network. However, the process is ongoing as energy stimuli are never-ending. Encoding at the level of neurons and neural networks is measured by non-linear spikes representing electrical impulses. The output of neuron firings consists of a lot of noise (error) depending upon where the neurons are located and what type of task is involved. Extrapolation of information about environmental occurrences comes from different patterns and firing of the neurons (Butts et al., 2007). Whatever the form (text, aural, numeric, image, or smell), the encoding process is short and difficult to isolate. Therefore, from a practical point of view, the process of encoding is usually extended from symbolization and mental representation to a form of output (behavior, image, or product). Symbolization precedes mental representation as symbols in the various forms (text, numbers, signs, etc.) must be stored or processed before any of them can be represented. 85 | P a g e 86 Prepublication Copy Most of the information about encoding is inferred from observed actions and responses of an individual during controlled situations using fMRI (functional magnetic resonance imaging) or positron emission tomography (PET). Both are used to map areas of the brain. Specific areas of the brain responded to specific tasks. According to studies in fMRI, encoding takes place in the neurons of the brain in different places. The places depend upon the kind (text, aural, numeric, image, and smell) and the action required by the task (Petersson, et al., 2000). Encoding or coding is an energy transmission related to the five senses: hearing, sight, touch, smell, or kinesthetic. Encoding via the senses is crucial. A person, for example, has about 5 million smell receptors while a Bloodhound has 220 million. Guess whether a Bloodhound or a person does a better job of encoding smell! For a person to encode (hear) a sound stimulus, it must originate from someone or something (person, radio, TV, etc.). The process is straightforward. Let’s suggest that another person vocalizes the word "mother.” The impetus for the saying “mother” comes from that person’s brain to the voice box (membrane stretch over the epiglottis which vibrates when words are formed). The vibration of the membrane is based on the total coordination of the muscles, nerves, and vocal structures. The sound is carried as sound waves (energy transformation) through the medium of air and received by the tympanic membrane in the eardrum of the receiver. The vibrating tympanic membrane stimulates nerve activity in the ear (small bones-stapes, incus, and malleus) which allows for the transmission to the brain. In our theory, the energy packets (neuphons) like those associated with quantum theory are responsible for energy transmission at the subatomic level. The brain's neural pathways become the processing system where storage, encoding, and processing occurs, an action necessary to understand how the context of the situation is important for the basic understanding of the problem-solving process. Context First, incoming verbal and aural stimuli, ignited and controlled by arousal and attention, must be organized based on contextual circumstances. This is called situational comprehension (Beck et al, 1997). Context is necessary for meaning. The context suggests that existing simultaneous conditions that influence outcome help define meaning. For example, if I say: “Bring me a plate.” What is your first thought? How did you encode the information---a dinner plate? Consider the word "plate" used in many different fields or circumstances (context) with a variety of definitions and meanings, eleven of which follow: Metallurgy. A thin piece of metal used for armor. b. Armor made of such pieces. Printing. a. A sheet of metal, plastic, rubber, paperboard, or other material prepared for use as a printing surface, such as an Electrotype or a stereotype. b. A print of a woodcut, lithograph, or other engraved 86 | P a g e 87 Prepublication Copy material, especially when reproduced in a book. c. A full-page book illustration, often in color and printed on paper different from that used on the text pages. Photography. A light-sensitive sheet of glass or metal on which a photographic image can be recorded. Dentistry. A thin metallic or plastic support is fitted to the gums to anchor artificial teeth. Architecture. In wood-frame construction, a horizontal member caps the exterior wall studs, upon which the roof rafters rest. Hotel Management. A shallow dish in which food is served or from which it is eaten. b. The contents of such a dish. c. A whole course served on such a dish. Service and food for one person at a meal Religion. A dish is passed among the members of a group or congregation for the collection of offerings. Sports. a. A dish, cup, or another article of silver or gold is offered as a prize. b. A contest, especially a horse race, offering such a prize Anatomy & Zoology. a. A thin, flat layer or scale, like that of a fish. b. A plate-like part, organ, or structure, such as that covering some reptiles. Electricity. a. An electrode, as in a storage battery or capacitor. b. The anode in an electron tube Geology. In the theory of plate tectonics, one of the sections into which the earth's crust is divided is in constant motion relative to other plates, which are also in motion. Which meaning of “plate” is important during encoding? How many did you know? In most cases, an individual encodes the meaning of a word such as plate in one of two ways: 1) encoding from episodic memory, i.e. a meaning important for the individual, or 2) semantic--a meaning which is shared by many others (dictionary definition). Neurologically, both methods involve the transfer of energy in a group of neurons somewhere in the brain. The encoding mechanism is based on how the individual most generally codes. Yes, individuals have a favorite method of encoding. President Regan preferred information presented to him in the form of visuals such as movies, diagrams, and overheads. He did not prefer to read long documents. Thus, in our model, encoding for him is more sensory involving both eyes and ears rather than just eyes for reading. Repetition and experience provide the opportunity for encoding. This suggests individual differences in the manner of encoding. What is your favorite method of encoding? Are you more likely to listen to what other people say or are you more likely to go and find a source to read? Would you rather have an Audio-Visual presentation or just an oral presentation? Children, such as those that were measured in detention centers, grew up organizing information mainly based on what is seen and heard. Individuals encoded information in a predominant aural and visual form simultaneously—image processing. They are extremely sensitive to any change in nonverbal expressions which may pose threats. Of course, many young children use some 87 | P a g e 88 Prepublication Copy combination of visual and aural forms; however, sensory input in juvenile delinquents seems to be amplified. A child, who has been exposed to reading from age three and reads continually for pleasure, encodes information primarily in the text (written form--plate), secondarily in image forms (visual image of a plate), or lastly in numerical! Repeat, if one continually uses neural pathways related to a particular action such as reading, that influences the form in which information is stored or encoded. Those who continually work with numbers or symbols which require rules and syntax, encode information in that form first, and later into other forms. Encoding can shift from one form to another—from symbolic to verbal and back again. Consider the person who is always diagramming, or writing images and symbols of what is read to conceptualize or further extrapolate ideas. Once the symbols make sense, the same person may write the ideas in verbal form. Coding in different neurons has a plethora of associations which, when recalled, allow an individual to retrieve the code from any of the forms just mentioned-text, numeric, aural, or image. At present, science has not determined whether or how verbal, aural, or image forms exist. Studies involving literate and ill-literate subjects have clarified that encoding in the human brain changes as a result of acquiring orthographic language skills. In particular, the process of becoming literate, i.e., reading and writing, influences the architecture of the adult brain ((Petersson, et al., 2000). According to many studies (Petersson, K, Reis A, & Ingvar M.,2001; Castro-Caldas A. L. et al., 1998; Dehaene S.L. et al., 2010), the brain is rewired during the process of achieving literacy. When applying previously learned information over and over, the practice effect strengthens the neuronal activity involved. This results in automation, a response that requires less energy. Yes, less energy. That is, the action is easier to accomplish without the focused energy of attention and perception. As an example, simple motor activity such as swinging a bat and hitting a ball is easier to accomplish with practice. By practicing an activity over and over, the neurons act differently, i.e., changing shape, firing in a new way, or coordinating with other neurons. One neuron may send a message to the forebrain about the speed of the ball coming toward you while another may send a message about moving your muscles to hit the ball. The same is true for more complicated actions such as studying for a test, learning to play a new musical piece, or writing a story. Practice (repetition) does have a cumulative effect. Practice makes the brain becomes rewired and can change the encoding process, i.e., the brain forms a new connection to other neurons, when repetition occurs. Neurons become more efficient, and faster with practice. When new information is encoded, learned, then practiced, and relearned, the neurons may use a new route. (Since neurons form a new connection in learning, the route of transmission also changes as memory is rewritten). This process occurs throughout our lives but is particularly important in the ages of birth to five. New cells are formed; old ones die; new connections are made; new routes are developed. In this book, the assumption is that children who encode a lot of aural information and little written information differ from those who encode aural and verbal written information equally. Why? Many of the delinquents that were measured by our group have little or no capacity to read, yet they can solve problems based on aural and perceptual encoding. Their problem-solving capability is dependent upon 88 | P a g e 89 Prepublication Copy perceptual encounters (especially under threat conditions), past experience, as well as the aural transfer of information. For delinquents, events and actions from past experiences seem to be encoded more holistically much like the visual information which they see in the environment. By holistically, one infers that a child or adult reacts to past information in a form that evokes mental images similar to those seen in the environment. For example, when a child is given a picture of an animal--a bear-- if their previous visual experience includes an association with a sight/sound picture of a bear, they verbalize the word “bear.” If asked to describe a bear without the picture, children tend to evoke a mental image and globally describe components of the mental image. The description does not have all the details of a real bear as it is processed from a mental image. This is the inference given by “holistic.” Holistic encoding lacks details! When an approach to problem-solving is related to information stored in the brain and retrieve from the mental image and its parts, for most people it is “holistic.” Guess what! Subgroups (i.e. artists for instance) differ in this characteristic method of encoding, especially people who have a dominant perceptual mode that retains detail through practice. This is seen in various problem-solving subscales in later chapters. In summary, encoding is affected by previous cumulative experience and knowledge. Coding or encoding does not occur in a vacuum but is strengthened by a repeated number of instances, especially when related to other events, occurrences, and instances in a network. If a child sees a plate on his or her table every night, he or she is more likely to recall associations with the word 'plate' related to food or the process of eating. Likewise, the next associations are based on the most recent experiences, i.e., for instance, if the child plays baseball--home plate is a likely association or if one watches an earthquake on TV then the “a shifting plate of the earth” might be a possibility. Encoding and storage of more recent information are likely to overshadow retrieval of past stored information. Memory evolves and is very subject to influences and errors! If a person has limited previous experience, encoding, interpretation, and organization of events may be difficult. For example, soccer is just beginning to become popular in the US; however, the parents of many children do not understand all the facets of the game. By not being aware of the rules including the number of players, scoring opportunities, and other similar aspects of the game, misinterpretation and slow encoding of different visual information associated with soccer plays is likely to occur. What is the most important part of encoding? Remember our general thesis is one associated with energy and impediments to processes. Energy is necessary for the entire encoding process. A lack of energy contributes to a lack of attention, lack of concentration, or perhaps in some cases, sheer exhaustion. In contrast, a greater amount of energy could lead to hyperactivity where attention is problematic since it cannot be controlled. Likewise, at the cellular level, an increase in energy could cause an improper balance of intracellular activities, decreasing the electrical impulse or ionic activity needed for encoding. Encoding at the micro level of cells requires energy transformation, processing of energy changing to a form that cells can use. This results in the formation of chemical bonds and electrochemical gradients in the neuron. For 89 | P a g e 90 Prepublication Copy example, let us assume that ribonucleic acid (RNA) is primary in memory transfer. If RNA is prominent in memory transfer, then the enzymatic activity necessary for energy transformation to form the electrochemical charges necessary for images to be stored in their proper location in long or short-term memory is of paramount importance. In the next sections of this chapter, some of the pertinent aspects of encoding in the Theory of Integrative Problem Solving are examined thoroughly. Some of these terms are new, thus an expository approach is used. Let's start with an oversimplified scenario for four different age groups—a child at 3 months, a child at five, a person at twenty-two, and perhaps fifty-five. Each person is given a set of things (rattle, keys, etc.) by a fifty-year-old man. The encoding process is vastly different for each of the five as encoding varies with differences in development---monthly and yearly. The following scenarios are fairly superficial but demonstrate the point. Age differences in the encoding process A 3-month-old baby is given a rattle for the first time. When the attention of the baby is diverted, the rattle is hidden from sight (behind a pillow for one minute). What happens? When first given the rattle, the infant has very few memory stores and an immature nervous system. The baby shakes the rattle, stimulated by sound and touch. The stimulation is exhilarating to the auditory nerves while the touch is processed by the sensory nerves of the hands as the baby shakes the rattle vigorously. The optic nerves focus on the movement while the hand moves rapidly back and forth. The experience is encoded as emotionally pleasurable and the baby starts to cry when the rattle disappears (removal of an emotionally pleasurable object). Since the object is out of sight, the baby quickly stops crying when a new object--a light--is introduced. The working memory was short. Few previous associations were available. When the rattle is visually introduced in the corner of the bed two days later, the baby does not even recognize, grasp or pay attention to the object. A five-year-old is given a set of keys that are jingled in front of him or her for a few minutes. The keys are then given to the child. The child, saying nothing, but having previous experience with the keys, jingles them once or twice, looks around the room, grabs a single key, and tries unsuccessfully to fit the key into a keyhole of the door (imitation using a previous store memory). During the next few minutes, various keys are tried on the door, attention wanes, the keys are dropped on the floor and the child engages in new behaviors. Physiologically short-term memory exists. An attempt to fit the key into the keyhole is a problem-solving attempt but is based on associational thinking (imitation). A short attention span, a very short working memory, and associational thinking, all are common in five-year-old children. The twenty-two-year-old, when the keys are first sighted in the hands of his girlfriend, ignores them and continues talking. Then, after being handed the keys by his girlfriend, he asks what they are for; acknowledges their purpose; puts them in his pocket, and continues talking. Physiologically, working 90 | P a g e 91 Prepublication Copy memory exists and the process has been encoded. There must be a reason (logical analytic thought) for being given the keys. Spontaneous problem solving (trying the keys in different keyholes based on associational thinking) is less likely at twenty years old under these circumstances. A twenty-two-year-old can solve problems logically, although one might not use that ability. Therefore, less trial and error are tried, and more automation exists. The fifty-five-year-old, when the keys are first sighted, asks what they are for, attempts to fathom the reason or purpose for giving him the keys, then either acquiesces to your wishes or finally gives the keys back and says--"do it yourself." The encoding process and the working memory are different for each of the individuals in each scenario which is why there are different chapters for different age groups. At different ages, people are at different stages of cognitive maturity and development. Cognitive, interest, and personality theory address these differences. To fully understand why, let’s explain some of the following concepts used in the encoding process. This includes symbolization, aural representations, emotions, and the kinds of information encoded. Symbolization Symbolization is the property of the human brain which distinguishes us from many other species. Homo sapiens have evolved based on two important processes-language and symbolization. Symbolization is an encoding process that occurs early in life where a form of the object from the environment is encoded in an iconic form. Consider a child at an early age who first encodes a physical object such as a tree that is either seen or touched. Does this encoding process differ from the first encoding of a non-tangible object such as the concept of "beautiful?" Yes, but this is explained later when discussing concepts. In the vocabulary of the IPS system, symbolization means that the visual or aural form of the object has been encoded (transformed into an iconic form) from any of the five senses to the memory. Symbolization is the translation from the environment through the senses to either processing or temporary storage in the memory. Mental representation is different from symbolization. Mental representation is a further step where linkage takes place. The iconic form is linked by association. This association takes place between information from either a) more than one form of the senses or b) different kinds of information already stored in the brain via the senses. Linkage of the symbol with the phonological action can be simultaneous with storage or processing in short-term memory. The association links the stored form and any objects from the senses: two objects of touch (touch a hot object, touch a cold object), two aural forms (hear the word ‘mother’, hear the word 91 | P a g e 92 Prepublication Copy ‘father’), two visual forms (see mother, see father), or an aural (hear the word father) and visual (see father), a form from touch, visual, and aural. In any of the examples, the symbol of the tree can become a memory trace (iconic engram stored in memory). The association is the linking process to a stored component of the word through a sensory component (sound, smell, touch, etc.). Thus, the tree is the icon linked to another visually stored component, i.e., a picture, a signed image of a deaf person, or something in a book). An association is strengthened by the child saying the word from memory (using his or her energy) in a constructivist manner, as a way of linking the aural form with a stored memory trace (icon), i.e., a language utterance (tree) to visual storage, such as a tree. At present, research does not distinguish adequately whether there are separate forms of memory storage for the different types of visual representations (image processing and lexicon). Research suggests only that the forms are stored. When an association has been formed, one can recreate the actions in the environment through a mental process, a mental voice--a voice inside of the mind. This mental voice is often called thinking, a cognitive thought process. The following are examples of iconic visual symbols which might be encoded in memory but have no representations by themselves in the first years of life: g e j p * ( ! @ → To better understand, look at the first symbol at the left of the group, the letter "g." When you encode the letter "g", a mental voice inside your brain seems to verbalize the sound associated with the sight of the symbol "g." Try to look at the next letter, without hearing the mental verbalization of the letter "e." It is almost impossible to do. The association from repeated instances (stored in many different neurons or a whole network sometimes) or use is so strong that the mental voice is extremely difficult to eliminate. Look at the last symbol, did you hear "arrow" from your mental voice or nothing? For objects that you have learned, when the stored verbal symbol is united with stored aural sound, mental representation is present. The representation is the association of the previously heard aural sound with previously stored visual form. Different mental representations form the basis of each person’s thought processes. Aural representations Language is the second major process of evolution and is keyed by energy stores. Yes, the process of using language is an energy process; just ask any teacher who has talked all day. A person says a word such as "ho.” What do you hear? Has the sound or visual image been previously stored? When? How? If you heard your mental voice, then you know that it was previously stored. What about the word "uxg?” Uxg is a nonsense symbol. By itself, it is a visual symbol. Did you hear the nonsense sound 92 | P a g e 93 Prepublication Copy “uxxxg” from your mental voice as you tried to determine its meaning? When seen as a visual, but not combined with aural storage forms, the memory trace is weak. Uxg means nothing to you. There is not a strong representation, other than the letters. What about the word "xenophobia?" Have you ever seen, smelled, heard, or touched xenophobia? If you have previously been introduced to the word "xenophobia", a mental voice would have sounded out the word Xeno (zee no) and the word phobia (fo be a). Words that do not have visual representations are generally considered to be abstract. Abstractions require more rehearsal and time for encoding. Numeric and figural symbols Numbers and figural symbols (5, 6, 7, or /\, +, -) are encoded in the same manner as the iconic visual symbols (→) above. There is a little difference; the distinction between numbers (5, 6, 7) and sign elements (^, +, -) is explained later. Encoding with associations Associations related to encoding occur via integration. The brain contains many complex paths such as the arcuate fasciculus pathway and the association pathways. The bundles of nerves connect various regions of the brain so that information flow can occur at multiple places which is why oxygen consumption and blood flow in those areas are identified by fMRI. While an individual is working on a problem related to one idea, the association in episodic memory produces images or patterns which have been previously bound up by the hippocampus. Since there are two different parts of the hippocampus, a right and a left, each part seems to work independently with functions occurring differently for men and women. Recent research suggests that the right hippocampus is associated with the memory of spatial visuals and locations while the left is associated with words, episodic memory, and autobiographical memory. Remember the hippocampus is part of the old cortex and in animals and other species works to bind memories that are related to survival. The old or paleocortex stores memories related to emotions and visual representations felt in the episode, especially in situations involving fear. Decisions about what to do are taking place in the frontal lobes (rostral prefrontal lobes) at the same time the hippocampus is binding the memories together. The binding process occurs over a period of time, maybe even while we are sleeping. If the emotions associated with the episodic memory are strong enough then the binding continues for a long period of time. By theory, one presumes that working memory is located somewhere close to the dorsal lateral prefrontal cortex. If the information from optogenetics is accurate then the neurons which are closer in juxtaposition become active and link with other neurons to form associations where the binding process occurs 93 | P a g e 94 Prepublication Copy in the hippocampus. Repeated encoding processes that stimulate representations (visual icons transferred into various chemical substances via protein transcriptions and enzyme interactions) are then stored. Encoding with storage of emotions and feelings Encoding does not occur in a vacuum. Encoding occurs simultaneously with all the feelings, emotions, and environmental stimuli, especially when a recording of the event occurs in episodic memory. Thus, storage in memory contains not only the encoded image, action, and perception but also the feeling attached when the event occurs. (Remember, the storage is not just one neuron, but a group of neurons or perhaps a whole network). When the event stored is not immediately (short-term memory-15 to 30 secs)) at a level of perception and attention, then the event moves to the subconscious level until recalled with a similar stimulus, i.e. original carrying of the stimulus is an electrochemical event occurring at synapses or junction boxes. When recalled or moved from temporary storage, the emotions and feelings come to a conscious level with an event stored either in the hippocampus memory or the area associated with the specific sensory cortex (cognitive processing of echoic, visual, touch, etc.). This is, one of the reasons, “why” the IPS theory specifies both cognitive and affective neural pathways in response to environmental stimuli. Where and how are memories stored? Memory is stored as part of neuronal activity in multiple places in the brain. There is a memory for the smell in the olfactory neurons, a memory of physical activity in motor neurons, a memory for sensory neurons in the visual cortex, a memory for emotions in the limbic system, and an autonoetic self-awareness in the uncinate fasciculus. When stimulation of single network neurons occurs in experimental conditions, the growth of neuronal axons and dendrites occurs as messenger RNA moves from the nucleus to build proteins and extend neural networks. Memory For research purposes, memory is often divided into three subunits-short-term memories, working memory, and long-term memory. In IPS theory, the most important is long-term memory as it supports both short-term and working memory. Long-term memory results from the cognitive processes of encoding and the permanent storage of information. Long-term memory is the result of encoding processes that are repetitive and take place over a long developmental period. In IPS theory, short-term and beginning long-term memory is an extremely rapid neuron and network process which occur with extremely rapid feedback loops that constantly modify sensory information in nanoseconds. Thus, both short-term and working memory are not independent processes but are affected and supported by feedback from storage in long-term memory. This feedback process occurs before language development but is more obvious after language development occurs. Why? The answer is found in Chapter Seven which examines how language is stored in neurons and networks in different areas of the neocortex. For 94 | P a g e 95 Prepublication Copy now, let us define encoding as the process which facilitates the storage of symbols either verbal or nonverbal associated areas. Any information in a sensory form that is attended by any individual must be represented in some form (iconic, image, verbal). Repetitions from the environment facilitate the encoding and storage process. Working and short-term memory are hypothetical constructs utilized in research to determine the duration and limits of memory retention. The cumulative effect of time (decay as well as retention) is important in assessing individual differences. Working memory in almost all research studies is different from short-term memory. The cumulative effects of feedback loops from long-term memory result in distinctive differences that give rise to assessments of working and short-term memory. Short-term memory is a subconscious or conscious process that brings sensory information to attention in 15 to 30 secs, resulting in a decision to retain or not retain the information for more than a fleeting second or nanosecond. A short memory is a useful memory that allows one to attend to the car behind you and in your blind spot so you do not turn the car into that lane but is lost quickly as other actions and cars are on the road. Working memory is often measured by asking a person to remember numbers, letters, words, or objects in particular sequences and then to cognitively manipulate the information. For example, present a person with a series of 7 numbers, and have them repeat the numbers in regular or reverse order. Or: 8 objects are flashed on a screen for 20 seconds; a person gives the name of each object in the original or specific order Working memory Working memory requires cognitive processing of both incoming stimuli as well as stored information so that other motor and cognitive actions may take place. Research on working memory has been reviewed by Baddeley (1999). Baddeley’s model is represented by tier two. That is, his model is a pictorial representation of how the brain functions. Actual brain functions can be mapped by tier two models, however, error results. In Baddeley’s model, new information is cognitively processed as soon as it is received. The meaning is determined prior to the transfer to more permanent long-term memory. A practical feature of working memory is its limited capacity and the vulnerability to loss of information when displaced by further incoming information. Features of working memory The working memory system comprises three components: the central executive, and two slave systems - the phonological loop and the visual-spatial sketch pad (Baddeley,1986; Baddeley & Hitch, 1974). Information is processed by either the phonological loop or the visual-spatial sketch pad, or by both. The 95 | P a g e 96 Prepublication Copy central executive is responsible for the control and integration of information from the phonological loop and visual-spatial sketch pad. In Baddeley's theory, the three components-central executives, phonological and visual-spatial sketch pad are a model like those found in our tier two. Models are a method of conceptualizing the functions of the brain. Any model of actual events has lots of error and the error increases as the model form move to tier three Central executive According to Baddeley, the central executive functions as a control system. It is a limited capacity attention system, responsible for coordinating the input and output of information to and from the subsidiary slave systems, and for selecting and operating control processes and strategies. The central executive is assisted by the operation of the two slave systems, the phonological loop and the visualspatial sketch pad. The phonological loop The aniculatory or phonological loop is a system specialized for the storage of verbal information over short periods. According to Baddeley (1986) and Gathercole and Baddeley (1993), the phonological loop has a limited capacity and is assumed to comprise two components: (a) a temporary store that holds information in phonological form and an articulator control process, which serves to maintain decaying representations in the phonological store. It has been argued that the simple model of the phonological loop can account for a range of factors that affect memory span in terms of phonological similarity, word length, articulatory suppression, and irrelevant speech (e.g., Baddeley, 1986, Baddeley, Gathercole, & Papagno, 1998; and Gathercole & Baddeley, 1993). Visual-spatial sketch pad The third component of the working memory system is the visual-spatial sketch pad. It is a slave system specialized for the processing and storage of visual and spatial information, and verbal material that is subsequently encoded in the form of images (Gathercole & Baddeley, 1993, p- 17). However, the visualspatial sketch pad is in some respects similar to the phonological loop, because it can handle more than one stimulus at a time and can rehearse information. Using the model of the visual-spatial sketchpad and the phonological loop, two assumptions are possible. The first concerns the phonological loop which is the loop of echoic memory moving between Broca’s area and Wernicke’s areas. Remember, from the review of the literature, Broca discovered an area of the brain which was non-functional in patients who could understand 96 | P a g e 97 Prepublication Copy speech but could not speak while Wernicke found an area that was the basis of understanding speech. fMRI shows oxygen consumption in these areas. Since the visual-spatial sketch pad is related to icon memory, when a person is trying to recall words, the areas associated with visual (i.e. optic nerve conduction through lateral geniculate to the occipital lobe) processing via oxygen consumption is active. This suggests that the “image processor” is using the memory associated with words. Perceptual speed-speed of processing The mystery of problem-solving and encoding relies heavily on the structure and function of the biological systems of the body. The structural components of the brain are designated by areas such as lobes (parietal, occipital) as well as individual parts (neuron cells, white, matter, myelin sheaths, etc.). White matter is a composite of a large number of myelin sheaths bundled together in gables. Why is all this important? Because the structures and functions of the brain are used in the process of solving different kinds of verbal, numerical, and spatial problems. This led to measurable individual differences. The gables or bundles of myelin sheaths contribute to differences in speed and efficiency of processing and are referred to as “speed of processing or perceptual speed.” Remember our thesis is that differences in speed of processing influence problem-solving in timed situations. Under timed situations, the speed of processing allows multiple attempts of finding a correct answer but does not influence the “correctness” of the response. If that is true, one of the issues is the sources of speed and how it influences problem-solving. Therefore, the next important question is: “Where does the myelin sheath come from?” One kind of non-neuronal cell in the brain is called an oligodendrocyte. This type of cell (Schwann) extends thin processes of their cell membranes to form the myelin sheaths that wrap around neuronal axons. The myelin from oligodendrocytes forms a coat called a sheath around the axon which is the extension of the nerve cell. The myelin sheath has gaps and acts as insulation and increases the speed of electron transmission along the nerve fiber. Myelin, composed of lipids, proteins, and water, keeps the action potential and the ions that jump the gaps firmly encased in the axon. Recent research suggests that there is a vast difference in the speed of electron and ion transmission between myelinated and non-myelinated fibers and between different animals whose myelinated sheaths have varying degrees of widths. Learning which is at the heart of problem-solving does not depend upon the myelinated sheaths but the speed of learning information is influenced by the amount of myelin. Therefore, the reality is that the brain is composed of thousands of large myelin sheaths that influence the speed of neurotransmission of electrons and ions and the learning of new things (neural pathways). Differences in speed of processing are a function, in part, of the differences found in the myelin sheath. 97 | P a g e 98 Prepublication Copy Subgroup patterns Remember in Chapters 4 and 5, the study of Kosslyn’s group which identified two basic kinds of processing (top down and bottom up) based on Miskin and Ungerliger’s 1982 study was introduced. The results from that study suggested separate brain pathways were used for spatial location and object pathways when parts of the brain were removed from monkeys. In this Chapter, elements (speed of processing, text comprehension, symbolization, sensory information related to emotions and feeling as well as the memory of numeric and figural symbols) are related to the processing of encoding. Encoding is primary for both spatial and object pathways. Individual differences are the result of all different kinds of encoding interactions between people who use focused energy to process the perceptual properties of objects and shapes and people who use focused energy to process abstractions related to the objects. If one combines these inclinations with the individual differences of control, structure, and flex as well as external environmental stimuli of threat and security, then different pathways are going to be used over and over. Likewise, add the tendencies toward logical thinking and spatial analysis, and these differences result in habitual subgroup patterns. Chapter summary In this chapter, the emphasis is on the various biological functions necessary for the process of encoding, as encoding is paramount to solving problems. Humans have evolved through the use of language. Language is the written or oral form of either symbol or concrete referents in the environment. The concrete referent of the chair is expressed in symbolic form (icon), written form (chair), or oral form (chair). The linkage of any of the forms is mental representations. Since people encode images, text, and aural forms in different manners and at different speeds, this contributes to individual differences in problem-solving and is the basis of our assumption that groups of people are going to manifest measurable differences. Common to all forms of mental representations for the individual is a context that provides meaning for communication. In later chapters, statements that subgroups of people (remember the category system –CMS) solve verbal problems differently than another group of people (MSP) are made. The basis of such statements is individual differences in biological functioning due to encoding, language, symbolizations, energy, mental representations, and neural pathways. Chapter references: Baddeley, A. D., & Hitch, G.I. (1974). Working memory. In G. 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Brain, 121, P (6),1053-63. Conway, M. A. (2001). Sensory-perceptual episodic memory and its context: Autobiographical memory Philosophical Translations of the Royal Society of. London, B356,1375-1384. Dehaene S. L., Pegado, F, Braga, L. W., Ventura, P., Nunes, F. G., Jobert, A, Dehaene-Lambertz, G, Kolinsky R, Morais, J., Cohen L. (2010). How learning to read changes the cortical networks for vision and language. Science. 330(6009):1359-64. doi: 10.1126/science.1194140. Epub 2010 Nov 11. Gathercole. S. E., & Baddeley, A. D. (1993). Working memory and language. Hove: Lawrence Erlbaum Associates. Miskin, M. and Ungerliger, L. G. (1982). Two Cortical Visual Systems. In D. J. Ingle, Melvyn A. Goodale, and Richard J. W. Mansfield (Eds.) Analysis of Visual Behavior. Cambridge, MA: MIT Press: 546-86. Petersson KM1, Reis A, Askelöf S., Castro-Caldas, A., Ingvar, M. (2000). Language processing modulated by literacy: a network analysis of verbal repetition in literate and illiterate subjects. Journal of Cognitive Neuroscience, 3, 364-82. Petersson KM1, Reis A, & Ingvar M. (2001). Cognitive processing in literate and illiterate subjects: a review of some recent behavioral and functional neuroimaging data. Scandinavian Journal of Psychology, 3, 251-67. Further reading 99 | P a g e 100 Prepublication Copy Chapter 7 Problem Solving Model Introduction Finally, Tier Two of IPS theory presents a model that is easier to understand as it explains the complex thinking process in everyday language. The first series of chapters (1-6) and the four reference chapters (22-26) explained the biological functions of the brain and problem-solving. We could have developed the cognitive and affective model without a link to biological functioning, but the model would not have any continuity. That is, statements made in Tier Two and Tier Three of the IPS theory would appear to lack any factual basis. This chapter describes a model of the cognitive processes which mirror biological functions. The chapter illustrates the thought process involved in problem-solving and explains each of the different terms of our cognitive model. Remember Tier Two is representative of biological functioning in Tier One. Likewise, Tier Three is representative of the biological functions of Tier One and cognitive and affective processes in Tier Two. Why? Why spend a whole chapter explaining the terms associated with the problem-solving model? Simply, the processes that occur in the brain are complicated and an ongoing mystery. The so-called ‘black box’ contains many different functions which are based on the biological structure and neural functioning. As noted in the last chapter, simultaneous cognitive processing combined with emotional reactions contributes to individual differences. Individual differences in problem-solving rely heavily on the uniqueness of the individual developed over a vast period, a uniqueness that comes from experience, practice, the firing of neurons in the brain as well as the brain’s structure and function. In this chapter, the explanations move up a symbolic level from just biological functioning to functional processing to make the process easily comprehensible for those who have less background in biology and science. Problem-solving model Elements of the cognitive and affective processes have been written about for many years. In a simple model, there are three steps--input, process, and output. Input represents incoming sensory information relative to the problem encountered, the process represents different pathways through the brain, and output represents the behavioral responses, images, or products of thought. The input and output are rather easy to follow. How information is processed provides the greatest mystery. The elements used in our problem-solving model follow Bloom (1956) & Guilford (1967) in part as well as Gardener (1993). 100 | P a g e 101 Prepublication Copy The cognitive model is diagrammed below. In the diagram, there are different elements of input, process, and output. Each is explained in the chapter. The one aspect which is not present in the model is the affective component of emotions. In reality, the affective components are just as important as the cognitive parts of the model but are so much more difficult to model as the control of emotions differs greatly from person to person. Also, the cognitive problem-solving model does not contain categories relative to the 36 subgroups. These super-ordinate constructs, explained in later chapters, are found in Tier Three in later chapters. Diagram 1 Process Terms in the Cognitive Model 101 | P a g e 102 Prepublication Copy Model characteristics Our cognitive model can be hierarchical, linear, or recursive. Various strategies used by people, such as trial and error, make it that way. Oftentimes, the strategies used by individuals complicate the process of understanding the model. Notice that any stimulus can be internal (stored memory) or external related to the environment. Information can go directly from memory (emotions, feelings) to muscles or motor actions thereby bypassing analysis, comprehension, and other forms of mental activity (a person experiences a feeling of anger and swings his arm). Or the form of the image encountered in the environment (perceptual) can stimulate an idea (memory to conceptual) which results in the person drawing a picture. Likewise, an unknown “sound” in the environment can cause a person to start analyzing different contingencies (bypass long-term memory as no representations of the sound are available). Just how these processes occur is based on the model terms defined and explained next. Association Find the term “association” in the middle of the cognitive model above. Analyze where the term ‘association’ in the model is placed (input, process, or out)? Try to figure out why it is placed as ’process’ as opposed to input or output. Now define the term of association in your own language. Great. Now compare your definition to our explanation. The term “association” in our model of thinking and problem solving has many verbal, spatial, and numerical nuances. Let’s start with the word “Drunk” and do a word association. Notice the two words below. Drunk vomit Did those two words conjure up vivid memories or associations? Did you ever have an experience with a person who was drunk and vomited? Which concrete object do you most associate with the written letter “a?” Is it an “apple?” Consider which word you associate with the word “'mother.” Was the response 'father?' Or did the word evoke something entirely different such as an image (picture stimulus) of a 'mother with a child?’ The problem, of course, is that any association is difficult to categorize as it comes from memory. The only way to fully understand an association is to question people about its meaning. Are there associations that do not involve simple memory? In our view, it is less likely. A response to an outside stimulus must originate from someplace so the assumption is either long or shortterm memory. In IPS theory, associations are a process that links a group of symbols or ideas together in a related but not necessarily meaningful manner. 102 | P a g e 103 Prepublication Copy In one of the oldest and most influential theories of learning (Thorndike, 1911), the principle of association, suggests that when 2 or more events repeatedly occur together and are reinforced or rewarded, a bond occurs. Although Thorndike’s definition of associations is widely accepted, we add additional criteria. That is, to establish a baseline measurement, one must judge the semantics of the association. Therefore, any association given by a person is evaluated as 1) common 2) unique 3) logical 4) illogical 5) reality-based, or 6) non-reality based. Common/unique: A response or singular thought given in an association test may be very unique, unusual, or common. For example, one person may associate “love” with "mother" which is assessed as common. Another person may associate love with "towels or thunderstorms.” This association is unique. Any association is considered common if other people respond with words that have a common relationship. Using another example: what if the association for the word "love" was "thunderstorm." That particular kind of association requires the observer to ask a question to determine the associative meaning. In most cases, that particular association is individual, unique, less specific, and therefore less common. Logical/less logical: What determines if an association is logical or less logical? Good question! One person may judge the association of love and “mother" to be logical; then again, maybe the same person would suggest that the association of love with "ice cream" is also logical. Our criteria are simple. If other people can verify that the response is normative and follows normative logical rules, then it is assessed as logical. Logical responses often involve symbols that follow logical outcomes (1+1+1 is equal to 3) or involve expressions that others can judge. Such expressions are happy is to ‘sad’ as hot is to ‘cold’? Based on our data, 97.8% of the people make the correct logical association when either word is left out of the parenthesis (hot is similar to cold as happy is similar to ____. If one cannot answer this logical relationship, then a red flag is raised about the data. Reality-based/non-reality based: Association may either be 1) reality-based or 2) non-reality based (fantasy). Reality-based suggests that the associations have a common reference or a physical basis. For example, ask a child, “What is a tree?” A response that a tree has branches, leaves, and roots is considered reality-based while a response such as “a home for ants” may be considered non-reality based. These 6 different examples are a way of explaining that the term “association” in our cognitive model may have many different meanings both for the individual and for a group of people and therefore multiple criteria are used to judge the associative meaning. Analysis and discrimination In the two references (Chapters 23 and 24), the mechanisms, basic processes, and theory of analysis are described in detail. In this chapter, the emphasis is on the components pertinent to our cognitive model. 103 | P a g e 104 Prepublication Copy In the IPS theory, the concept of analysis is primary and relates to thinking. When making a simple analysis, the use of a neuro pathway results in discrimination, the distinction between objects. Discriminations may or may not be related to reasoning or logical thought. Individuals discriminate between objects, ideas, and thoughts daily but the discrimination may not be logical at all (verified by others). Analysis occurs as a separate cognitive process, as explained in the reference chapters, but is simultaneously related to other ongoing personality traits such as introversion and extraversion, motor or conceptual, control and flex. In IPS theory, two qualities related to the strengths and frequency of functions such as analysis and social concern occur in neural pathways. The qualities are described as dominance and auxiliary. These two qualities are based on habitual use. Both qualities may begin as either unconscious or subconscious and provoke actions that vie for entrance into the conscious mind. Pathways that are primary and enter into the conscious more often are dominant. Pathways that are less prominent in the conscious and therefore surface less often are auxiliary. Analysis can be dominant and conscious when the neural pathways are not slowed or blocked by simultaneous actions related to social concerns, emotions, and feelings. When neural pathways are slowed thereby causing new and secondary pathways to be used, then analytic thought is regulated by the direction of energy flow either to the environment or internally to other thoughts and ideas. Extraversion suggests that the person is wearing one’s feelings on one’s sleeves while introversion hides the feelings and ideas behind a non-discerning face. Control and flex are two related personality traits influencing the outcomes related to analytic thought. Control and structure are imposed when analytic thought in the conscious mind is directed toward an object. Control and structure result in focus and attention. When control and structure are mediated simultaneously by impulses (flex), analytic thought is redirected from an idea or object to the impulse (the mind wanders as physiological processes increase). When analytic thoughts or actions related to the analysis of ongoing perceptual and environmental stimuli are slowed by emotions and feelings, then feelings become dominant and analytic thought is auxiliary. Although many definitions exist, depending on the field of study, analysis, in general, is the process of breaking a whole unit into parts. Biologically, analysis is probably a mechanic-biochemical process whose exact mechanism is not known but can be hypothesized. In our theory, analysis is an energy action. Stored ideas, concepts, and images are retrieved from memory where each unit can be rotated, divided, subdivided, or transformed into another form Are there analytic processes in the solving of problems? Anytime one accesses memory, energy is required. This energy is used in the process of discrimination, decision-making, and making choices. Analysis is the energy process breaking down any complex unit into the sum of its parts and at times, the energy unit is used for decision making and discrimination. When energy is redirected to feelings and emotions, the process bypasses analytic and logical analytic thought. Many children and adults have been tested over the years. In some cases, our perceptual, spatial, and analogies tests have exercises that required finding targets that must be rotated and matched. 104 | P a g e 105 Prepublication Copy Finding rotated targets requires associations and analysis. When associations found on the perceptual test are rotated or turned, then some action must take place from the moment of perception to the moment of finding and circling the same object on a written page. This mental manipulation requires holding the figure in short-term memory and then rotating the first perceived figure to mentally match the second perceived figure in a different location. This output action requires an energy transformation or analysis, a chemical energy process that occurs in neurons stored in the brain. In our cognitive model, notice how numerical, spatial, and verbal representations occur prior to analysis. This suggests that the representation in the memory precedes analysis. Also, notice how the use of logic occurs as a process separate from the analysis. Associations can be at the same level as analysis in the process model. Analysis, Associations, and Divergent and Convergent thinking can result in only partial comprehension of the situation, context, or semantic meaning. Incubation or the serial process of asking questions, receiving information, and asking further questions are necessary for the complete process of problem-solving Divergent thinking The psychologist J.P. Guilford (1967) used the term divergent and convergent thinking in his book The Nature of Human Intelligence. Guilford gave his subjects a pen with the instruction “generate as many associations about the pen as possible.” Each person listed multiple thoughts and perspectives which were perceived to require divergent thinking. Then each response was evaluated for its relationship to the object. Our notion of divergent thinking is similar in many respects. Divergent thinking involves an energy process much the same way that energy was used in defining the term “analysis.” Divergent thinking is not just an association but also discrimination (analytic action) between multiple objects of the association. For example, look at an object on television. In a flash of a second, subconscious thought eliminates some associations before reaching conscious thought. Likewise, simultaneous discriminations (analytic actions made by the subconscious) eliminate other alternatives. Divergent thinking with comprehension involves multiple associations from memory with associative and analytical thinking involved. Divergent thinking, like analysis, requires a series of energy actions, not a singular energy reaction. In our subgroups, some people are conceptual or image pattern processors. These people used concepts to skip over ideas and make associations quickly. For the pattern processor, divergent thinking is the result of abstracting common attributes over multiple objects in the environment. Pattern processors are often not attentive to the details of objects; instead, the pattern processor processes common attributes through analytic and divergent actions. The pattern processor differs from the object processor. For the object processor, divergent thinking is processing the perceptual characteristics of the object (shape, size, distance, a process that results in applied creativity. 105 | P a g e 106 Prepublication Copy Remember that applied creativity is processing perceptual objects in a manner that extends, modifies, or redefines existing characteristics in a manner that creates a new perception of the object. Divergent thinking is a response to mental representation and occurs after the comparison to the memory component. Divergent as well as convergent thinking are rapid response mechanisms occurring many times in the space of microseconds, especially if a complex problem is posed. If the problem is not complex but rather simple or mundane, the response pattern can be very slow deliberate, and more infrequent or it can be very quick. For example, suppose someone asks you to give 5 words associations with “mother.” What happens? First, there is a comparison to memory representation which evokes several different images, emotions, or feelings simultaneously. Each of these representations, either written or verbal, is slow and deliberate or is elicited at the speed of the individual. Each association with the mother can be evaluated similarly to Guilford’s exercise. i.e., each group of representations, whether verbal or written becomes an example of divergent thinking. Studies have suggested that divergent thinkers score higher on reading ability and word fluency (Clark et al., 1965). The reliability of the concept of divergent thinking which is broad as opposed to narrow was established early by the studies of Guilford (1967) as well as Wallach and Kogan (1965). Certainly, in the early days of measurement, there were differences in the tests used to measure the construct. Today’s theorist who currently defines divergent thinking (Runco et al., 1987; Silvia et al. 2008) suggest that divergent thinking has more to do with originality than creativity. Other authors (Sawyer, 2006; Weisberg, 2006) argue that divergent thinking is related to creativity. Runco (2008) argues that divergent thinking is not related to creativity. His argument is based on discriminant validity between the two concepts. Data from EEG patterns (Razoumnikova, 2000) suggest that better performers on divergent thinking tests have more connections between central parietal areas of both hemispheres. Likewise, the cortex of the right hemisphere has more ipsilateral connections. When a person has more connections, IPS theory suggests more concepts are held in memory. Recently I told a 68-year-old person who I met while playing handball that he looked older and wiser. He responded with: “I wonder if a person can look younger and wiser.” His thinking diverges into a host of different associations. He then responded: “Wise people do not look older or wiser, nor younger and wiser.” He diverges with his first response and then converged and evaluated with his second response. One of our guides in Berlin was challenged with a question about the ways that now-a-day Germans have changed their ways to adapt to the monetary policies of the European Union. He rapidly named 12 different ways in less than 2 minutes. He responded with ideas from a preconceived knowledge base with differences due to finance, societal norms, and historical facts. His response suggested that the question was posed also in earlier sessions by other travelers and that he had plenty of opportunities to formulate an answer. 106 | P a g e 107 Prepublication Copy Convergent thinking Convergent thinking is just the opposite of divergent thinking but the two processes are connected. Often in the game of brainstorming, people come with a laundry list of things from which to choose. The list is generated quickly (divergent thinking). However, each of the alternatives is not as useful so a decision is made about which alternative is better. This process illustrates convergent thinking-narrowing down a list of alternatives to a single answer which may or may not be the best or the correct answer. Convergent thinking is the selection of an alternative (from multiple associations) to determine a single choice. Convergent thinking involves an energy transformation as the choice between multiple associations also involves multiple discrimination. Many object processors converge quickly to an answer based on discriminant characteristics of the object choices while pattern processors are converging based on abstractions seen in the objects What is the opposite of cold? A single response occurs after considering the meaning of cold and its attributes. Regardless of how one argues the semantics of the question, most children over five years of age, as well as adults, answer with the single convergent response of “hot.” What about a single convergent response to the question, "When is a door, not a door?" Response: "When it is ajar (i.e. a ‘jar’). This response requires many feedback loops of divergent and convergent thinking. Why? A person must generate the alternative and give a selected response or simply give an answer stored in memory. For instance, the first non-verbal thought might be “How can a door not be a door?” “Must be a play on words or something similar?” “OK, a trick question based on sound.” “Oh, I got it--a glass jar is not a door. Etc.” If there is a single choice, that choice may be reworked, redone, or elaborated. If there are multiple choices, then one of the many can be selected. Clark et al. (1965) studied convergent and divergent thinkers. After analyzing biographical material, Clark concluded that convergent thinkers had higher grades. Synthesis A simple statement: if analysis breaks things down into components, then synthesis puts them together as a whole. Although the statement might be an oversimplification, its application is not. In our complicated world, information is available from a lot of different sources. Some people suggest that there are not any new ideas; only ideas that are generated from other sources. Others suggest that new ideas are just the reformulation of older ideas. Regardless, the integration of ideas into a form different from the source is defined as a synthesis. Sometimes the synthesis is a picture or song; other times it is a paper or written work. The form can anything—a model, a diagram, or even a group of squiggles if the whole is the sum of the parts. 107 | P a g e 108 Prepublication Copy In the world of theory, the Analysis by Synthesis Theory for a speech by Stevens and Halle (1967) has quite a following. The theory suggests that the incoming auditory signal is encoded, represented, and analyzed. Then analysis follows a series of generative rules which activate a motor pattern. The motor command produces a hypothetical auditory pattern that is matched to the original signal. A mismatch (lack of understanding) continues until a match is made. This iterative procedure (feedback loops) occurs continuously. Thus, both auditory analysis and motor activation are necessary for speech development. For those who follow evolutionary theory closely, the auditory bones of the middle ear which are used for auditory reception were developed over millions of years in vertebrates. Thus, speech development is a relatively new process in mammalian species. There is support for this theory in both infants and adults when considering data and experimentation from magnetoencephalography (MEG). A recent study (Kuhl et al., 2014) examined auditory and motor brain activation during the discrimination of native and non-native syllables in infants. Their results suggested differences in infants' processing at 7 and 11/12 months. The almost 8-month infant group activates both auditory and motor areas for native and non-native sounds. For the group of 11–12 months old infants, there was greater activation in auditory brain areas for native sounds. In contrast, at the same age, for nonnative sounds, there was greater activation in motor brain areas, the same pattern that exists in adults. Based on their experimentation, they concluded that their results suggested both areas are important in the development of speech and that (paraphrased) auditory analysis of speech, when coupled with synthesis from motor areas, is necessary to produce the speech signal. Notice in our cognitive model that a representation can bypass synthesis and directly output to products. This process occurs via brain pathways and is the same process that representations use when bypassing the logic system. Inferences that bypass the logic and synthesis components are intuitive. Intuitions are feeling about things that may not appear to have a factual basis. Many people rely primarily on their intuitions (feelings about things) as well as their values when making a decision. In IPS theory, divergent thinking, analysis, and synthesis involve multidimensional processing. Multidimensional processing has a mathematical basis and provides a world for complex systems and network theory (Bose, 2013). The energy process of analysis and synthesis is far too complex to delve into at this point. Just suffice to say that advances in n-D; n>3 polynomial matrix theory and matrix fraction description have led to a greater understanding of dimensionality. System theory for many years before 1985 was based on 2-dimensional deterministic systems while today’s multi-dimensional modeling spans both deterministic and stochastic processes. This increases our understanding of spatial-temporal modeling and allows us to understand how energy works in the brain to break things up and put them back together. Our statements about n-dimensional space and rotation of electrons have only a partial mathematical base of reasoning and are intuitive but 108 | P a g e 109 Prepublication Copy new mathematical theories and applications are expanding rapidly. Back to the world of facts, assumptions, logic, and evaluation. Evaluation Evaluation is an important factor in the problem-solving process. Evaluation is a process that determines how well the selection of choices meets the outcome or goal of problem-solving. The process of evaluation occurs often and requires the simultaneous use of all the processes— association, analysis, logic, etc. A lot of researchers conceptualize evaluation as one of the components of meta-cognition, occurring at the superordinate level of processing. In IPS theory, evaluation occurs simultaneously with the desire to improve, correct, or modify a convergent response. This action can occur at any time during the process of solving a problem, although, for most authors, the action occurs at the end of the following series -representation, analysis, and product in some form which is evaluated. The more steps involved in the thinking process, the more likely several alternatives (divergent thinking) are generated as possible solutions. Discriminating among alternatives is a choice that can require evaluation as long as a product or outcome is generated. Convergent thinking, which occurs as a result of discrimination, can also require evaluation to determine if the alternative generated is the best choice. Is the choice or solution an endpoint or a temporary intermediate point? Even an intermediate tangible product such as a drawing, or representation (idea) should be evaluated to determine the degree of correctness for the problem posed. Evaluation, at any point in the process, can result in a single solution being overturned as less appropriate. Progress toward a complex or compound problem-solving solution requires constant evaluation. The logic system The logic system in the brain is not a place or anatomical structure. The logic system is an energy representation acted upon by the very nature of people being able to store and retrieve symbols, numbers, and letters. Logic is applying an energy action in the brain according to a pre-existing verbal, numeric, or symbolic rule. Rules are applied only after comparison with temporary or longterm memory storage. Comparisons are based on either text comprehension or symbolic extractions. “Do not put your hand in the fire as the fire is “hot” is a verbal rule that can govern behavior. The rule is stored in memory either through repetition or experience. The development of a logical rule occurs over time by practice, an iterative process that occurs when given many examples. Rules are developed inductively and deductively. A single rule might 109 | P a g e 110 Prepublication Copy involve the operation of numbers such as (5+5). The numeric example of (5 +5)/2 can be a two-rule operation. Within any individual, the logic or rule-based system is built and developed depending on interest, reward, exposure, experience, and circumstance. The time frame might be a second, a minute, a day or a span of years as logic can be passed from generation to generation by symbolsverbal, or written means. Conceptual logic, in IPS theory, is defined as a particular kind of reasoning or thinking. Logic is represented by syntax, semantics, and proof theory. The syntax is based on grammatical expressions or symbols used to model the thought processes. Semantic refers to meaning while theory is a verified system of proof that others may follow. When a symbol (figural, or numerical) is transformed (turned, divided, or rotated) in a direction other than its original form or position and that form can be recognized by others, then the process, in our theory, is a logical conceptualization. The symbol is garnered by syntax (a person writes the symbol and its accompanying forms on paper). The rotation is semantic (a person identifies, according to our thinking, how the symbol was turned or twisted, and its meaning is captured by comparison to memory). The identification of the rotation is by proof theory (others can verify that the symbol was turned in the direction specified). As an example, in many of our cognitive tests, a person is required either: 1) to develop a symbolization of a figural stimulus, search a target field in which the figure is duplicated exactly, or 2) to find a figure which is turned or reversed, then circle it. The former process (1) is deemed a representation through an associational process when an exact copy of the stimulus is located and circled in the stimulus field while the latter (2) is considered logical when a matching rotated figure is found. In other words, conceptual logic involves acting mentally (energy action) on the stimulus figure by rotating or turning it. This turning of the stimulus figure to a position other than what it was originally encoded requires more energy. The representation of the stimulus is first developed through focus or attention and then carried out until encoding occurs. Finally, this becomes an action or product when the stimulus is correctly circled by the respondent. Verbal logic involves words associated with a pattern according to rules within a word system. For example, word analogies such as: ‘stamp is like an envelope as butter are similar to bread’ involves rules such as "is similar to" which suggests a logical analogous relationship exists between pairs of words. In the example, the assumption is that the terminology of a ‘stamp placed (spread) on an envelope has a word relationship between elements similar to ‘butter is spread on bread.’ The analogy is not exact but some of the same procedural elements exist in both. Luria's (1959) explanation of the brain has two types of information processing--serration and simultaneous. Some people consider ‘analogies’ to be a kind of processing known as simultaneous. Serial processing is when information is processed in a series or sequence. Information from reading a book or sentence is sequential, left to right. Verbal logic, which is serial, requires that information be interpreted in a manner where the end activities such as reading a single paragraph are dependent upon the words at the beginning and how they are interpreted. 110 | P a g e 111 Prepublication Copy Conceptualization Conceptualization suggests that others can interpret the significance of associative linking, i.e., there is a common frame of reference (not necessarily logical or verified as logical by others) held by other people through the experience. One can interpret or comprehend symbolization and its properties through his or her own experiences. When the discernment of properties common to a class of stimuli is made, then additional rules relating to those properties can be elaborated. For example, if an individual describes their concept of the California flag--the following might be acceptable--a piece of cloth with various kinds of symbols-a bear, multiple stripes, or multiple stars. It is easier to judge the correctness of a concrete descriptive conceptualization (describing the concept of the flag) but more difficult to assess the correctness of an abstract descriptive conceptualization such as "democracy." In your own words, define the concept of democracy, then have someone assess it! Short-term or working memory Deep in the brain, the hippocampus helps to store memories. Of course, the hippocampus is not the only place as described earlier, memory is stored in many different places simultaneously. So, how important is memory in problem-solving? Extremely!! Try solving problems without memory. Many people do not have good short or long-term memories. Such people are limited by the amount of information they have at the moment to solve problems. Limited problem solvers (àla some senior citizens and young children) may have abbreviated long or short-term memories and therefore process everything from the bottom up in a new way each time the objects are encountered. Therefore, objects which are part of the everyday experience such as keys, eyeglasses, pens, and pencils are lost from working memory and reprocessed each time that attention is focused— “What did I do with my eyeglasses?” Short-term memory is different from working memory. Short-term memory is denoted as the storage of temporary memories which acts like a compact disc that can be written over and over but not necessarily retained. Encoding takes place in short memory as every representation which is generated from temporary storage has a match as long as a previous encounter with the object has been stored. Scientists describe working memory as a place where problem situations are generated. As noted in the next chapter, each encounter in the environment generates thousands of feedback loops of sensory information replacing short-term memory with new information; however, the moment that a problem (goal, question, obstacle posed, etc.) is generated then shortterm memory becomes working memory as an action is required. If the problem is simple, only an association is required but as the problem increases in complexity, then analysis, convergence, 111 | P a g e 112 Prepublication Copy divergence, synthesis, and evaluation are activated. Working memory requires actions while shortterm memory does not. Complex problem solving requires a strategy, a plan as well as storage in short and long-term memory. That is, the more complex the problem, the greater the necessity for writing down intermediary steps and/ or practicing or inferring the intermediary steps and how each relates to the problem. For simple problem solving, short-term memory such as remembering a seven-digit number, suffices. For complex problem solving, rehearsal or chunking, i.e., repeating the information, over and over to remember it (practice), is necessary. Without this process of breaking information into small chunks to facilitate understanding and retrieval, the average person has difficulty remembering or even working with large amounts of information (cognitive overload). Information remains in short-term memory from fleeting nanoseconds to minutes, a period in which the information may be processed, changed, or forgotten. If it is processed, the information proceeds along the neurons to the brain where electrochemical energy performs the transformation. Most of our perceptual speed tests utilized working memory and short-term memory, not long, term memory. Working and short-term memory are important since that is where most sensory transactions first occur. Does short-term memory account for different learning capacities? There is no doubt that some differences in individual learners in the school situation can be accounted for by problems in short and long-term memory, depending on the type of problems and which timed testing situation is involved. If information cannot be retained, found, or retrieved for at least a minute, can a quick solution occur? The differences in the capacity to remember are illustrated by our myriad of short-term memory tests. The nervous system is not fully developed around 12 years of age as the brain reaches developmental maturity at roughly 22 years of age. Should one expect young children to solve complex problems? The answer is certainly not. The work of Case (1985), Roth (1991), and Seigler, (1978) suggest that until adolescence, children can only execute strategies that require three steps. About the age of 12 and 13 or the maturational age of Piaget's formal operations, the child can execute more than 3. Should one only propose short 3 steps problems for younger children? Giving problems to children who are age appropriate is important. Young children can practice the processes of problem-solving--generating hypotheses that need to be tested. Age-appropriate problems are necessary to stimulate the process of thinking; therefore, it is good practice to ask young children (ages 5-11) problems where they must guess or hypothesize about the answer. Ask them for their “theory” about events. 112 | P a g e 113 Prepublication Copy Working memory research Working memory is a construct used for research that is embedded within a theoretical framework. For most authors, working memory requires the active manipulation of a representation found in short-term memory (15-30 seconds) which is supported by long-term memory. Since working memory has a limited capacity and is crucial in information processing, individual differences in memory capacity are likely to be reflected in performance. Daneman and Carpenter (1980) & Daneman and Tardif (1987) argue for the importance of individual differences in working memory efficiency during reading comprehension. They suggest that when information is processed, the two product components---processing and storage--- compete for the limited capacity available in working memory. They hypothesized that a part of working memory implements the strategies and skills used in a complex mental task such as reading, while the remaining capacity stores resulting information related to reading comprehension. They conclude that individual differences in reading comprehension are due to the variability between readers in the “efficiency” of their processing and storing capacities. There is evidence that effective working memory capacity differs among individuals. This difference affects a wide range of cognitive tasks such as problem-solving, reasoning, acquiring new vocabulary words, and reading comprehension (e.g. Cantor& Engle, 1993; Conway & Engle, 1994; Daneman & Carpenter, 1980, 1983; Engle, Cantor, & Carullo, 1992). Daneman and Tardif (1987) suggest that working memory differences reflect the efficiency of processing strategies or skills rather than differences in working memory capacity. In practice, it appears likely that there are differences both in capacity and skill efficiency, although this is an ongoing issue (see Baddeley, 2000, pp. 86-87). Earlier in the chapter on the biological development of the brain, memory was depicted as a set of neurons that are linked serially and associatively in the brain. Thus, structurally, long-term and working memory are found in a network of neurons. Biochemically, memory is a functional store associated with messenger ribonucleic acid (mRNA) building proteins in the cytoplasm of the cell. Functionally, memory is based on how information is stored using electrochemical gradients. Although a lot of controversies exist as to the exact nature of storing information in the brain, current theories suggest the form of storage is either episodic, autobiographical, or semantic with some overlap. Episodic refers to the storing of information about events. Events can be part of one’s personal life. Autobiographical refers to the storage of information about our personal lives and experiences. A simple example relates to a song or music that one may have heard recently. Did the song stimulate memories based on where you were the last time that you heard it? Were there a series of events or episodes that were elicited? Did you think about the person that you were with or the events of the day that transpired? In episodic memory, the meaning is retrieved in the brain in the form of small episodes or associated events. When these personal events become a part of long-term memory, they are defined as autobiographical. (Conway, 2001). 113 | P a g e 114 Prepublication Copy In contrast to the research above, the second theory of memory suggests that the method of encoding is semantic or based on a network of meaning. Both theories, in our view, have some validity. The network of neurons in the brain indicates where the activity is occurring by imaging techniques. Semantic activity such as differentiating between different words occurs in the different areas of the brain from simple memory retrieval. Information stored in the brain to solve problems is generally stored as semantic knowledge. Repetition and practice add internal organization to memory! The internal organization of memory has levels and layers. How the memory is organized, i.e., procedural, declarative, semantic, or episodic--is based on how the individuals learn to process information. A person can process information incorporating many forms -recitation, easy retrieval, and rehearsal. Procedural memory suggests the organizational structure is sequential, with information in a linear sequence. Declarative is memory structure in almost word-for-word form so that information can be retrieved in a form for recitation. As noted earlier, long-term memory, especially that which is related to declarative memory, is a process that is consolidated during sleep. The constant polarization and depolarization of neurons occur in waves that originate in prefrontal areas and are spread across the neocortex. This synchronizing process which is seen as a slow oscillation on EEG creates spindles in the thalamus. The work of Mednick et al. (2013) suggests these spindles are related to efficient storage of memories and therefore learning. In our model, all the predominant forms, episodic, semantic, declarative, procedural, and social are used and distinguished by examining their relationship to problem-solving by the individual or based on the subgroup in which he or she is involved. Bottom-up, and top-down processing Without beating the concept to death, top-down processing is the ability to encode perceptual images from the environment in a manner that enhances object recognition. For example, see the rock, touch the rock, smell the rock, and then store the memory of the rock in memory. Once the concept of rock, an average of all kinds of rocks seen in the environment, is stored then the concepts of rock are processed bottom up. When another rock is seen or touched, the memory stored from bottom-up processing is combined with the abstracted elements (about rocks) processed from topdown processing via the prefrontal cortex. However, when one is operating internally, inside the head, with little focus on external events (writing, imagining), then top-down processing becomes global processing, a process of abstracting with images transferred to the writing process or the memory without the necessity of bottom-up processing. Some people, either by choice or by the nature of work, spend a lot of time inside their head processing information via top-down 114 | P a g e 115 Prepublication Copy processing; other people spend equal time processing both ways, while the task characteristics of some types of everyday work (building a house) require more object processing. Is the model useful? It depends! The cognitive and affective model depicts several different processes. The model is useful if the terms can explain diverse kinds of real-world actions involved in the solution of complex and simple problems. The first comment often received is “Where is the pattern in the model? Arrows seem to go in all different directions.” Sorry, that is the reality of how the brain processes information in all different directions, especially since the most often used strategy is trial and error. Useful patterns come from the individual’s subsequent and frequent use of neural pathways to solve a problem, based on learning and training. Useful patterns come as one gets older, works, and solves the same kinds of problems over and over. The familiar terms called “topdown” and “bottom-up” processing provide some semblance of a useful pattern. Notice that the cognitive model relies heavily on memory. As noted earlier, memory can be procedural, factual, episodic, or semantic. For example, answering the question “What is the capital of California?” is easy. The response is factual--Sacramento. But memory is more than recitation as is evident in this saga. When an object of value such as eyeglasses are misplaced, a person starts to recall the last place the object was used. “I remember taking off my glasses in the doctor’s office.” Subconsciously a value is placed on the object lost as well as the conditions under which the object was lost. All that information is stored in conscious and subconscious memory with the object “glasses.” The gist of the saga is that recalling information changes its priority level and hence its value as processing occurs. A high-priority item (value placed by the individual) is remembered more often than a low-priority item. Why? It is stored repeatedly through rehearsal and associations in short-term memory for entry into long-term memory. Thinking is a process. If one looks in the brain to find the memory of where the glasses were last used; one finds neurons, fibers, tracts, and a host of other things. So, there is not a single place or thing called memory (although the hippocampus is mentioned more often). The model gives credence to the many layers in our brain which are part of neuron processing. So, again, is the model useful? If the model clarifies the complicated process of solving daily and complex problems, then it becomes useful. It is quite easy to use the simple model (input/process/ output) without terms like association, divergent thinking, etc. However, problem-solving becomes more difficult and complex when there is an increase in the number of steps to solve the original problem. Problems become compounded as extensions of the original problem. The vast majority of people use trial and error as a method of finding a solution to compound problems. How would you approach the following problem? 115 | P a g e 116 Prepublication Copy Suppose you want to build a go-cart that can travel at 15 miles per hour and holds two riders. Have you ever built a go-cart? Think about the complexity of the problem. The results or the product depends on which neural pathway is used at each step of an exceedingly long problem-solving process. The first step in the process might be an extraordinarily complex problem, deciding on the shape of the go-cart? However, deciding on the shape may suggest many other compound problems. Is shape related to the speed of the go-cart? How does one maximize the shape of a go-cart to obtain a speed of 15 miles per hour and hold 2 riders? What material is best to maximize speed? How many wheels should the go-cart have? How do you handle the disappointment if you fail and have to begin again? The questions are boundless! Before building the go-cart, an understanding of all the factors related to the goal is necessary. Partial and complete comprehension could involve any one of many different processes listed in the cognitive model— “analysis”, “logical approximation” and/or simple “association, etc.” Interruptions, inhibitions, and stoppage can occur at so many breakpoints. Would you use a strategy of trial and error, intuition, analysis, or logic? Note, that according to our cognitive model, verbal, numerical processing, and spatial pathways do not necessarily involve logic! Likewise, analytical, emotional, and associational pathways can be separate and simultaneous. How many intuitive notions might you express in the problem-solving process? During this complex process, neural pathways are accessed and processed many times per sec, analogous to a computer processing numerical calculation at a rate of millions of times per sec. Of course, the brain is not as fast as a computer, but the focusing, converging and coordinated interactions contribute to different outcomes. Mental representations generated during the process of constructing the go-cart vary depending on the process used, the amount of processing done, and the level of processing necessary to achieve a successful goal. Faulty memory, inaccurate logical analysis, inaccurate analysis, or a lack of proper simple associations can result in partial comprehension or lack of understanding. The problem is not solved; the go-cart does not work. The thought process is complicated by differences in age, and distinct levels of maturity. Is the problem about go-karts approached differently by 12-year-olds versus 30-year-olds? In the next chapters, some of these questions are answered by focusing on known problems that interfere with the process. These answers are not simple since they are confounded by all kinds of individual differences-maturity, ages, and stages of development. Chapter summary In this chapter, the first tier of biological processing is organized into a simplified model of cognitive processing. It is much easier to understand the complicated process of solving problems if they are organized around input, processing, and output. Again, our assumption is that there is some method to the madness of various kinds of simultaneous biological functioning. The method, 116 | P a g e 117 Prepublication Copy or perhaps the madness, is the similarity and differences by which groups of people process the forms of information (verbal, numeric, and spatial). In the next two chapters, by observation and previous research, the places in the cognitive model where people get “hung up” or blocked are explained. This provides information on individual and group differences and is the basis of our category system (CAS-u) which follows in subsequent chapters. Chapter references: Bose, N. K. (2013). Multidimensional systems theory and applications. New York: SpringerVerlag Bloom, B. S.; Engelhart, M. D.; Furst, E. J.; Hill, W. H.; Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: David McKay Company. Cantor J, Engle R. W. (1993). Working-memory capacity as long-term memory activation: An individual-differences approach. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19, 1101–1114. Case, R. (1985). Intellectual development: Birth to adulthood. Orlando, FL: Academic Press. Clark, C. M., Vedman, D. J., & Thorpe, J. S. (1965). Convergent and divergent thinking abilities of talented adolescents. Journal of Educational Psychology, 56, 157-163. Conway ARA, & Engle R. W. (1994). Working memory and retrieval: A resource-dependent inhibition model. Journal of Experimental Psychology, 123,354–373. Conway ARA, & Engle R. W. (1996). Individual differences in working memory capacity: More evidence for a general capacity theory. Journal of Experimental Psychology, 4, 577–590. Daneman, M., & Carpenter, P. A. (1983). Individual differences in integrating information between and within sentences. Journal of Experimental Psychology, 3, 561-584. Daneman, M., &Tardif, T. (1987). Working memory and reading skill re-examined. In M. Coltheart (Ed.), Attention and performance XII (pp. 491–508). London: Erlbaum. Daneman. M., & Carpenter. P. A. (1980). Individual differences in working memory and reading. Engle, R. W. Cantor, J., & Carullo, J. J. (1992). Individual differences in working memory and comprehension: A test of four hypotheses. Journal of Experimental Psychology: Learning. Memory. and Cognition, 18. 976-992. Gardner, H. (1993). Multiple intelligences: The theory in practice. New York: Basic Books. Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw Hill. Journal of Verbal Learning and Verbal Behavior, 19, 450-466. 117 | P a g e 118 Prepublication Copy Kuhl1, P. K., Ramírez, R. R., Bosseler, A., Lotus Lin, J. & Imada, T. (2014). Infants’ brain responses to speech suggest Analysis by Synthesis. Inaugural Articles by members of the National Academy of Sciences elected in 2010. Cross Mark. Luria, A. R. (1959). The directive function of speech in development and dissolution. Word,341– 452. Mednick, S.C.*,1,2,3, McDevitt, E. A. 1 Walsh, J. K. 4,5, Wamsley, E., Paulus, M.2,3, Kanady, J.C. 7, & Drummond, S.P.A.2, (2013). The critical role of sleep spindles in hippocampal-dependent memory: A pharmacology study. Journal of Neuroscience, 33(10), 4494–4504. Razoumnikova, M. O. (2000). Functional organization of different brain areas during convergent and divergent thinking: an EEG investigation. Cognitive Brain Research, 10(1–2),11–18 Roth, W.-M. (1991). The development of reasoning on the balance beam. Journal of Research in Science Teaching, 28, 631-645. Runco, M. A., Okuda, S. M., & Thurston, B. J. (1987). The psychometric properties of four systems for scoring divergent thinking tests. Journal of Psychoeducational Assessment, 5, 149 –156. Runco, M.A. (2008). Commentary: Divergent Thinking Is Not Synonymous with Creativity. Psychology of Aesthetics, Creativity, and the Arts Copyright, 2(2),93–96 Sawyer, R. K. (2006). Explaining creativity: The science of human innovation. New York: Oxford University Press. Siegler, R. S. (1978). The origins of scientific reasoning. In R. S. Siegler (Ed.), Children's thinking, what develops? (pp. 109-149). Hillsdale, NJ: Lawrence Erlbaum Associates. Silvia, P. J., Winterstein, B. P., Willse, J. T., Barona, C. M., Cram, J. T., Hess, K. I., et al. (2008). Assessing creativity with divergent thinking tasks: Exploring the reliability and validity of new subjective scoring methods. Psychology of Aesthetics, Creativity, and the Arts, 2, 68 – 85. Stevens, K. N.& Halle, M. (1967) in Models for the Perception of Speech and Visual Form: Proceedings of a Symposium (Ed.) Waltham-Dunn, MIT Press, Cambridge, MA, 88–102. Thorndike, E. L. (1911). Animal intelligence: Experimental studies. New York: Macmillan. Wallach, M. A., & Kogan, N. (1965). Modes of thinking in young children. New York: Holt, Rinehart & Winston. Weisberg, R. W. (2006). Creativity: Understanding innovation in problem solving, science, invention, and the arts. Hoboken, NJ: Wiley. 118 | P a g e 119 Prepublication Copy Chapter 8 Pathways of the Cognitive Model Introduction In a review of the cognitive model in Chapter 7, a simple pathway is input-process-output. As an example, perception can be 'input', memory encoding can be 'process', and verbalization can be 'output'. Few people argue over the simple pathway but as the complexity of the problem increases so do the arguments, but again, that is the purpose of theory. Since our cognitive model is recursive, any number of the brain or neural pathways, as well as elements, can be involved. We use the term “Tier Two” to explain the meaning and importance of neural and brain pathways and possible interruptions to the problem-solving process. Our thesis is that particular pathways are used more than others, and some pathways are more habitual and efficient than others. The use of pathways is important and helps defined groups of problem solvers. Problem-solving can be slowed for any number of reasons: cognitive dissonance, aging, the complexity of the problem, interferences from environmental stimuli, learning difficulties, and neurological deficits. Identifying pathways, using measurements of time and function, can facilitate understanding of how problem solutions are efficient and habitual as well as interfered with, arrested, or slowed. Time Is time an important variable in traditional and non-traditional problem-solving? Of course, it depends!! Time is not a factor in many cases related to school, work, or home where constraints are not imposed by other people, events, or situations. However, when a constraint, limit, or pressure is imposed by significant others or environmental situations; time becomes an issue. Time measurements are based on the difference between when a process starts and ends. Thus, in most of our examples below, the simple pathway (see-encode-represent) can be measured. Children push a computer button to start a clock indicating that they have perceived an object and then push a computer button indicating that they have encoded or represented the object of the perceptual situation by name, i.e., dog, cat, or mass. Sometimes this occurs in milliseconds. In situations where a start and a finish cannot be precisely timed, the time measurement is implied. For example, an event becomes timed when a teacher imposes a time limit on an activity by stating that a classroom test must 119 | P a g e 120 Prepublication Copy be finished by the end of a school period which is 45 minutes long or a standardized test must be finished at an identified time Many unstructured events in life involve time management. Usually, during work, a person does not have a stopwatch or there is not a person keeping time; however, companies and people have deadlines that must be met. Events associated with work or employment have implied time constraints. People are given directives to accomplish a task and the manager must assess whether the task was accomplished efficiently. In some cases, a person is given a task and must work overtime as not enough time exists during the work day to solve the problem. Examples in everyday situations are numerous. Have you ever delivered your car to a shop and the car was not fixed within a reasonable time limit? Recent studies about experts and others in different skill areas suggest that individuals, categorized by different levels of cognitive skills, achieve problem-solving solutions based on time differentials. Many outcomes based on time are logarithmic (experts vs. novice) rather than linear. Many assessments are group-based (sanitation workers, plumbers, electricians, accountants, etc.), suggesting that certain occupational groups solve problems in their profession faster than other occupational groups. A person who spends more time thinking about problems in one’s area of expertise is more likely to reach a better problem resolution quicker than a person with less experience. However, efficiency does not necessarily imply quality! Many quick solutions may be inferior to solutions taking more time. A fact! Individuals differ in the speed with which they conduct various cognitive activities. A slow time for completion of a task could simply represent more time spent processing various logical alternatives or time off-task, i.e., daydreaming. In our experience, the time required to converge to a single best response for a divergent thinker can be relatively long compared to a person who spends less time examining alternatives converging to a single response. However, the time spent to achieve problem resolution may not necessarily be directly associated with output. Think about a student who has not studied the classroom assignments and spends a lot of time trying to answer questions on a test. Since information-related concepts are not in memory, time spends processing the test questions may not be related to responses given on the test. Because of the great variation in time differentials situations, many studies suggest that either time is not variable in problem-solving or that faster times are equated with better problem solvers. Of course, this is very controversial as explained in many sections of this book. In the next section, many examples illustrate how many different kinds of situations and approaches to problems cause time differentials in individual responses. This time differential can be associated with arrestment or slowing in the problem-solving process!! 120 | P a g e 121 Prepublication Copy Time measurement along with deep levels of processing help to differentiate the problemsolving process. By examining the following model pathways, the amount of time required to solve complex problems becomes apparent. A simple model pathway example In the process model of Chapter 7, the simple terms of input and output are used. Many important cognitive and affective processes occur in milliseconds or maybe nanoseconds. If the amount of time in either perceiving or hearing is increased, then processing time can increase substantially until either confusion subsists or comprehension takes place. The outcome depends on the task complexity as well as the number and kind of neural pathways that are used. To understand how a child may exhibit different degrees of efficiency in response to a problem-solving situation, consider the number of different kinds of mental model pathways that a child may use in the following scenario. A child sees the cover of a book with a picture of Mary walking ahead of her little lambs. Each of the little lambs is covered by a large heavy cloth and has its tongues hanging out, depicting exhaustion and thirst. The book cover reads, "Mary had a Little Lamb." The following possible response patterns are based on the cognitive diagram in Chapter 7 and indicate where in the model various individual thought processes could be arrested so that a problem resolution can or cannot be efficiently reached. These response patterns occur with many recursive iterations between neural pathways so a linear sequence is illustrative but difficult to quantify. Memory/limited memory pathway Perception- attention--memory at a subconscious level. The simplest problem-solving pathway involves perception, encoding, and then output, either from a memory source or by passing a memory source. The typical scenario is--see an object, encode the object, name the object and/or continue perceiving other objects. The child sees a book, and consciously encodes 'book' in the brain, but looks at other objects without focusing or directing attention specifically toward the book. Perception-memory or memory first then perception. An extremely important point is that in all pathways, the stimulus can be initiated either internally or externally. This can occur in any order. For example, a conversation stimulates a memory, which is initiated internally, followed by perception. Or vice versa, memory follows perception which is 121 | P a g e 122 Prepublication Copy initiated externally. Remember our cognitive model is recursive with many feedback loops. As an example, think of a situation where an idea “pops” into your mind but has nothing to do with what is happening around you. Perhaps you are sitting on the couch watching television and from your subconscious comes a new thought associated with your job. That is “memory first” and then perception. If the thought is keyed by what you are watching on television, then it is ‘perception first’ than a memory. The internal stimulus for action is usually an emotion and a memory stored in traces while an external stimulus for action is sensory (hearing, feeling, touching, and seeing). An external stimulus is first temporarily stored in memory where it may or may not be represented (working memory vs. long-term memory). For example--a child sees a book cover and stores the picture of the book cover in memory but does not recall the memory trace except when memory is desired because a question is asked or a problem is posed. This memory-perception pathway is important as complex problems are not usually solved by a simple memory pathway. Identification of memory impairment is also important as memory precedes the outcome of most problem-solving activities. In a second example, the student sees the book, consciously encodes the picture on the book cover, and says "book" when asked for a response of what he or she sees (output). Little comprehension may exist at this level. The book represents a memory stimulus. A problem is not generated until the student is asked: “what do you see.” Little or no time is needed for solving this simple problem which is based on a memory or perceptual response and the problem-solving process is unlikely to be arrested. However, as seen in later examples, the more complicated the problem, the more likely a process may be arrested, delayed, or terminated or that a person adapts to the complexity and the person becomes more adept and efficient in solving the problem. In your experience as a youngster, was there a child or friend whom others might have characterized as “slow?” Can you remember his or her name? Were other children aware of this “slowness?” What about senior citizens? Many times, arrestment (stoppage for a short period while struggling to recall) occurs as people age. For some senior citizens, memory recall is affected. In the course of a conversation, it is not unusual for an arrest to occur. If a place, name of a store, event, or location cannot be recalled, then the pause (arrestment) is obvious. Sentences, word fillers, and sounds require time for a person to remember. “Oh, what is that person’s name?? Do you know? Ah, ah, ah, or silence.” Take a minute, ask anyone a question, and watch for arrestment (pauses for a short period before a response) to occur. Listen carefully for differences in the kind of questions that are posed. Try it and note simple differences between members of your family or friends. 122 | P a g e 123 Prepublication Copy Associational pathways A second pathway involves a mode of limited comprehension called associations. Earlier a mode was described as a temporary process. The child perceives a book, encodes the stimulus, then gives a verbal response associated with the stimulus. For example, the child sees a book, encodes the picture of Mary and the little lambs on the front cover, and gives a response-- a nursery rhyme such as "Ba Black Sheep- have you any wool?" related to the title or picture. In other words, the response was associational. Some time was needed to generate a response, but only slightly more than the previous example. The difference in the amount of time needed to generate the response helps define the pathway. For example, the difference in a pathway from memory to association can be defined in nanoseconds and the difference is real and sometimes measurable, depending on the amount of slowing or searching for the association. In many people, the amount of separation time (ask the question- receive a response) is very close, almost identical. Everything depends on age, experience, the complexity of the question, and language familiarity. One can measure the time of the pathway but not its route through the brain, unless, of course, one is using fMRI. The exact pathway itself cannot be determined as it may be sequential, recursive, or non-sequential. However, in our model, the pathway is associated with the kind (type) of response received---for example, analytic vs. association vs. memory. Repeat: The pathway is associated with a categorization of the output (analytic response, divergent thinking, singular convergent response, emotional feeling response, etc.). A singular pathway could also be designated as Perception-memory-association with another stored memory: An individual sees an object, stores it in memory, and associates it with an existing stored memory to form a representation but does not comprehend the meaning of the situation. Example: - an 18-month-old child sees a box, moves to the box, and lifts the lid to see what is inside. Comprehension may or may not occur, depending on whether an association is present. Note: The child must have some association with an object (box) to lift the lid. He or she would not know how to lift the lid to look inside without some association. This process is elementary and is the first stage of problemsolving. Animals use this pathway as a form of imitation or general association; In psychology, the pattern is usually designated as S-R or stimulus-response pathway with different forms of conditioning based on rewards and goal objectives, i.e., a Pavlovian response such as parrots responding with speech to a command, a dog getting a paper, etc. Assume there are a series of numbers such as 5, 10, 15, 20, and 25. An 8-year-old child perceives the 5 number symbols (previously stored) and makes an association that 5 123 | P a g e 124 Prepublication Copy separate numbers exist but does not see a simple pattern or relationship which exists (seriation-increases by 5 between each number). There is only partial comprehension if the child recognizes that the numbers vary from 5 to 25 by association only. If there was complete comprehension, the child would see the existing pattern of 5 separating each number using the process of analysis (an adult assumption, I admit). The pathway is denoted as associational with partial comprehension, rather than analytical with complete comprehension if seriation is not recognized. Or as another example, the child does not see his or her mother, thinks of or says "where is a mother?" In other words, the child associates the mother with a representation in memory and makes a query. One assumes an association as sensory input was such that the mother was not present. My daughter's friend (10 years old), who was staying the night, went into a dark bathroom besides me to wash her hands. After washing her hands, she exclaimed! "Who turned out the light?? The light was never on. She had used the light from the room next to her to see how to wash her hands. She only realized that the light was not on as she was about to leave the room and reached for the light switch (memory association). Recently my 9-year-old son heard a Dodger baseball radio announcer indicate that all the outfielders were "straight away." He heard the information, checked his memory store, and did not understand the idiom "straight away." He was perplexed; with partial comprehension. Many examples of idioms in language exemplify an associational pathway. Associational pathways in many instances do not encompass understanding or comprehension. Again, two of my older friends from the Philippines did not laugh at one of my jokes since it involved the phrase “wondering about a person stealing a hubcap”, a phrase which did not match their experience (many vehicles did not have hubcaps in their younger years). A lack of common associations results in a lack of communication, and oftentimes, comprehension. Analytic pathways In this pathway, the child perceives the book cover, encodes the stimulus, and gives a verbal response to the following question “What is happening?” Instead of giving an associational response when seeing the book cover, the child says, "Mary is being followed by the lambs who seemed to be hot." Wow! This response required an interpretation of the events on the cover based on the lambs having their tongues hanging out. Since the event was interpreted, there was some comprehension (text comprehension) which led to the analysis (which seemed to be hot). An analytic response requires about the same amount of time as an associational response. Therefore, the content of the response has 124 | P a g e 125 Prepublication Copy to be interpreted. In this example, the first part of the response is descriptive, while the second part (seemed to be hot) is an inference (analysis required) based on the observation. Remember that in our cognitive model in Chapter 7, discrimination (simple analysis) is a process whereby a child discerns the differences between objects. The process of deciphering the differences by relating them to other associations is a more complex analysis than simple discrimination. When analysis involves comparison and contrast, it is more complex. To make comparisons requires the person to use words (simile) such as "fire is like melting iron as both tend to destroy the surface with which each comes in contact." Or “the point of a needle hurts like the tip of a knife blade." Or “this rock has more color and striations than that rock. Analysis can be simple discrimination, or an inference, a statement indicating the decomposition of complex thought into simpler components. The pathways of perception-memory analysis can be illustrated with different kinds of examples but are easier to understand by using words. Words have many meanings and although a person may understand your reasoning, they may not agree with it. In the previous example related above, attempts by the child to fathom the meaning of 'straight away' by attempting to give meaning to the words constitutes a form of analysis. The problem was not solved since the meanings were obtuse, and not part of his vocabulary. Logical analytic or just analytical Many examples below illustrate the difference between similar kinds of thinking; i.e., analytic and logical analytic. Analytic: If the response is purely associational and an interpretation or inference is made, then the classification of the response is analytical. There is a difference between analytic and logical analytics. Analytic pathways are used often by children from ages 5 to 11 or by adults (ages 11-90); however, these same pathways do not always involve logical analytic thought. Simple discriminations, as well as the dissecting of an argument, are valid analytical responses that may or may not be logical. An analytic response to the lamb story above might be: “It feels like the lambs want to go home.” Is that response an inference or an intuitive notion? Lots of people analyze situations and their analysis contains little logic, yet their solution or conclusion is correct. Maybe the lamb wants to go home but the outcome was determined by a feeling. Can one find a solution to a problem through intuitive thinking based on many observations of a pattern of events? 125 | P a g e 126 Prepublication Copy Logical analytic: Our definition of logical analytical involves examples using analogies and seriation. For example, determine the relationship (similarity) between this set of words—the dog is similar to the house and the elephant is similar to a circus. How would judge the following response by a child to this analogy 1) dog is to house as the elephant is to ________? The response by an 8-year-old: a dog plays in the house and the elephant plays at the circus. Likewise, what about this response: A dog lives in the doghouse while the elephant lives in his house at the circus. If the response requires the respondent to give a relationship and it has a common reference that can be verified by others, then we classify the response as logical and analytical. What about the example above: "Mary is being followed by the lambs who seemed to be hot?” The first part of the response was descriptive, while the second part (which seemed to be hot) is an inference (analysis required) based on the observation that the tongues were hanging out-- common reference verified by others but is it logical analytic or just analytic? Divergent pathways Problem-solving situations in high school often exist as part of a narrow context, within a confined subject matter area, discipline, or set of circumstances. For instance, a problem given in an English class might require the student to write a literary character portrayal. An activity such as writing uses many divergent pathways. Think about your favorite TV character (Sherlock Holmes, for example). How would you write a characterization? First recall the character’s multiple activities, expressions, and ways of behaving. Now transfer these images, icons, or mental representations into written words on a piece of paper, a very divergent and convergent activity. Often in the later years of one’s life, a person, after seeing many problems in their area of specialty, moves into management. Having many different and varied experiences provides the new manager with many alternative solutions when a problem arises. Divergent thinking in this sense allows the mind to think of more than a single alternative. In earlier chapters, the process was described as making decisions between competing pathways that provided different mental representations. In the university system, I have met many students who were extremely perplexed because they did not score well on an exam. They had studied long and diligently. Many of these students when questioned orally could give analytic explanations about the material. However, these same students could not interpret what was required by a written question on the exams. That is, their thought pattern was: What is being asked by this question? If the teacher would verbally clarify, explain, or narrow down the options, 126 | P a g e 127 Prepublication Copy then the question could be answered correctly by the student. In other words, the teacher acted as the intermediary in converging the vast number of divergent possibilities Likewise, many students were unable to choose a correct answer between alternatives on a multiple-choice exam, especially if the alternatives were written in a similar style and manner with words changed for logical inference. Their divergent thinking and method of networking information contributed to their confusion on tests. In many instances, they failed to converge quickly. When they analyzed each alternative on the multiple-choice test, the number of associations they created as possible answers was so great that they were overwhelmed. Their thought process was: “Well, it could be this or then again maybe this.” “Well if this is true, the answer might be?” The answer required on the multiplechoice test was logical, convergent, and time-dependent. Of course, my colleagues would suggest that they did not study long enough to comprehend the complexity of the question. Our system of education places emphasis on problem-solving but usually in specific settings and within defined parameters of subject matter such as math, science, English, reading, social studies, or social relations. Often, this emphasis requires convergent analysis and memory, not divergent thinking. Perception (Ideation)-memory-divergent –association) In this next pathway, the child perceives the book, encodes the stimulus, diverges to ideational content in the brain, and then converges to a single response. This is a recursive response where converging to a single response requires time to go back and forth between many different divergent thoughts. This cognitive process is time-consuming, especially if the student can generate many different divergent thoughts which may pose plausible solutions to the stimulus situation. Some of the most recursive, divergent thinkers that we have measured have jobs in advertising and writing. They develop and write jingles, and scenarios for radio, television, and newspapers. As an example of this pathway, an older child may pose his or her problem based on seeing the picture of Mary and the little lambs on the cover, "I wonder if the author of the story Mary had a Little Lamb was a man or a woman?" or "Was Mary a real person and where did she live?" Or "Was wool a necessary commodity at the time in which the poem was written?" These responses are rather sophisticated for a child but they illustrate the point. The more creative or divergent the student, the more likely the response is unique. 127 | P a g e 128 Prepublication Copy Sometimes my colleagues when hearing such divergent responses characterize the same person as “spacey.” Remember, that children (and adults) spend a lot of time daydreaming, reading books, or just thinking about things that may seem ridiculous to others. Their fantasy-land thoughts may or may not have real components that aid in the solution of a problem. The more divergent the thinking process of the individual, the greater the number of alternative responses that are generated, and the more time required to think about which alternative is useful in the solution of a problem. Convergent pathways Perception-memory, analytic, convergent. An individual sees a math problem on a sheet of paper, stores that perception in memory, thinks about which the single best response is, and answers. Example: The child sees a math problem, remembers the previous day’s lesson, decides which answer is best, and gives the single right answer. A teacher writes on the board, "How many 5's are contained in 25? The child thinks: What does she mean? Multiplication, division, addition, subtraction? This question requires a divergent response to answer unless one assumes that only an operation, such as division exists and responds with an answer of five to that operation. People make assumptions (i.e. convergent answers based on division by 5). However, a divergent thinker might think of multiple operations before answering: multiplication (5x5); subtraction (25-5-5-55-5); addition (5+5+5+5+5); or division (25/5) before deciding on the single convergent response of 5. A teacher writes on the board, "How many 5's are contained in 25? Use division for your answer?" The child remembers the form of the problem presented in the previous day’s lesson and applies the same method of dividing 5 into 25 and converges to the single right answer of 5. What would be the response to the question: “How many times is 5 contained in 25? Use addition to answer this question Notice that the constraints (use division, use addition) limits the divergence and allows for quick convergence. Were these logical responses posed by IPS theory? Divergent/convergent logical pathway using comprehension The perception-memory-logical analysis is also a type of analysis that is considered by many to be a premium pathway of thinking since the elements of logical analysis can be verified by others as a correct response. The key is ‘verified by others.’ This pathway is not often 128 | P a g e 129 Prepublication Copy used until the developmental age stage of 10 or 11 or cognitive developmental stages between 13 and 22. A child is given a math problem, stores or draws from memory, and then analyzes what is needed to solve the problem. The child sees a problem in the following form. "How many fours are found in the following problem (24 + 12)." The child remembers a sequence of addition from memory but must analyze and comprehend the meaning of the word problem- how many fours? One answer might be (6 + 3) or another is 9. The answer can be verified by others since there are mathematical rules used to solve the problem. As noted earlier, our model allows for partial and complete comprehension. Comprehension suggests that the meaning of words is either individualistic or common. When people diverge with multiple associations, comprehension is individualistic until another person interprets the meaning. How many times during your lifetime has a member of a family said something to you and you had to ask several questions to understand what the family member is saying? There was partial comprehension until the statement was clarified and finally there was comprehension. Perception-memory-(association-divergent)-analysis-divergent/convergent) A person sees something, stores it in memory, thinks of different ideas which are related, imagines some possibilities, and thinks about which one is best. Example: (Obviously, this is a complicated example for an older child). The child encounters a math problem with the instructions: Using any set of numbers and arithmetic operations, generate a problem with a numerical solution of 4. The child stores or draws from memory (addition, subtraction multiplication, divisions?), finds an association with different memory ideas (6-2=4, 4 x 1=4, 16/4 = 4), generates different ideas (6+2-4=4, 12x4/9=4), examines different ideas and finally chooses one. The student must comprehend the operations to use them properly and all of the outcomes are verifiable according to mathematical rules. Complex and compound pathways involving comprehension People contribute substantially to society by solving immensely complex problems that are not constrained by time. Often these same people use their time at home or away from school or work to solve complex or compound problems. Some of the previous problems in this section are classified as complex and compound. Remember that any problem requiring multiple mental operations is complex, while a compound problem requires a series of steps involving divergent, convergent thinking, and an evaluation of the results. Does evaluation imply the answer makes sense in the context of the question posed? Compound problems are often found in fortune five hundred companies where 129 | P a g e 130 Prepublication Copy expansion and maintenance issues require solutions to problems that have many steps. In Chapter 17, managers in organizations are representative of complex and compound problem solvers. As many senior managers are aware, complex problems in business are usually solved by teams of people. For younger problem solvers, complex problemsolving pathways are often part of math and science or project-oriented curriculums. Perception-memory association. Linkage, analysis, complex association (understanding) divergent -convergent -evaluation- Recursion. An individual sees an object, stores the object in memory, thinks about the characteristics (with or without analysis) and links thoughts with other characteristics that are stored in memory. Example: The child is given a math problem, remembers the previous lesson, relates to other images stored in memory, and links up many different parts from the lesson read the previous day. Then the child analyzes the best response and then diverges to several different possible solutions by trial and error. Finally, after many recursive iterations, he or she converges to a single solution and evaluates the response--starting the process over. The process is often called simultaneous thinking. Perception-memory-(association-divergent)-analysis-convergent-evaluation. A person notes something, stores that image in memory, and thinks of different ideas that are related. He or she imagines other possibilities, decides which is best, writes the response down, and evaluates its appropriateness. He or she starts over, thinks of another particular response, tries to decide which is the best alternative, and finally makes a decision. Wow! Does this happen? Ask any student who had tried to solve a complex, math-related word problem or any history student who had tried to put everyday observed situations into a historical context! If the problem is very complex, there are many situations where a problem-solving individual becomes arrested in a stage or pathway related to a problem. The more complex the problem, the more likely that some form of arrest may occur in the process. In fact, in some cases, a solution cannot be synthesized, even if one is given all the elements and unlimited time. The solution to a problem might be a paper, an equation, a new project, a work of art, or fixing a car. Interaction of social and different mental pathways Association-affective: Any of the pathways may be affected by emotions, threats, or external factors such as hunger, fatigue, or environmental interference. Almost everyone is aware of how an emotionally laden response skews or biases the meaning of the verbal content 130 | P a g e 131 Prepublication Copy offered with the information. All kinds of emotional responses can occur based on how the following words are uttered— “get out of here.” A blocking or suppressing of the emotional content or affect is just as diagnostic as the actual emotional content itself. It is possible to suppress affect and feelings when dealing with problems. The suppressing of feelings is more likely as egocentricity increases. That is, the more egocentric the person, the less likely that a pathway includes an initial emotional response. The reason: egocentric individuals tend to interpret almost all responses in terms of their perspective; how it affects them. One cannot discuss all the relationships of social and mental pathways but some are more important than others. Suffice at the present that perception memory-affective-association-analytic is important when the ‘social context’ of a problem needs to be understood. Association-biological factors: Hunger and fatigue are obvious biological factors that slow the problem-solving process. Children are especially vulnerable to feelings of fatigue and hunger. Children who cannot pay attention because they are sleeping in class are not good at solving problems. Have you ever stayed too long in the sauna? The blood flows to the extremities and when getting out, one feels faint and the sensory-motor system fails. There is great difficulty in doing much of anything, much less solving any type of problem. How about when a child is scared, try asking them to solve a simple problem. Most of the time, one gets a blank stare, garble response, confusion, or panic. The more egocentric a person is the more likely they have difficulty dealing with social cues. Egocentricity can occur as a result of many things including being in an education setting for long periods, especially for those graduate students in disciplines that require a structured knowledge base. Developing a structured knowledge base requires that the individual spend many hours reading, thinking, and organizing. Spending hours away from social interaction with other people (social isolation) can lead a person to more focus on self-needs, self-gratification, and social awkwardness. Chapter summary In this chapter, using the terms in the cognitive model, many different scenarios and examples illustrate how pathways affect the problem-solving process. Some of the examples are very simple while others are quite extended. The purpose of these examples was to illustrate, using model pathways, how normal individuals solve a problem with differences in time delays. At any stage in the process, a person can use a different strategy or pathway and become slowed or arrested as a partial solution is obtained. This is very true when affective pathways coincide with cognitive pathways. The second purpose of the chapter was to illustrate the complexity of thought processes that occur in 131 | P a g e 132 Prepublication Copy nanoseconds. By illustrating how thoughts move quickly from different kinds of thinking, it is easier to understand how interruptions and terminations can occur. If our thesis is correct, the next two chapters should illustrate known pathways problems that have been researched over time. If a group of individuals has similar methods of approaching problems and over time tend to develop a style or consistent way of handling problems, then they constitute a subgroup. Subgroups of people using their dominant mode (skill sets, integrative thinking processes) often approach problems similarly but end up with different solutions. Chapter reference: Kosslyn, S. M., et al. (2009) Two forms of spatial imagery: Neuroimaging evidence. Psychological Science, 20, 1245-1253. Further reading Mednick, S.C.*,1,2,3, McDevitt, E. A. 1 Walsh, J. K. 4,5, Wamsley, E., Paulus, M.2,3, Kanady, J.C. 7, & Drummond, S.P.A.2, (2013). The critical role of sleep spindles in hippocampal-dependent memory: A pharmacology study. Journal of Neuroscience, 33(10), 4494–4504. Conway, M. A. (2001). Sensory-perceptual episodic memory and its context: Autobiographical memory. Philosophical Translations of the Royal Society. London, B356,1375-1384. 132 | P a g e 133 Prepublication Copy Chapter 9 Known Pathway Problems Introduction The medical model is clinical. In a real-life setting, a doctor uses observation and clinical assessment to provide diagnosis and treatment. Clinical assessment must be continuous, building a realistic case for diagnosis from the three tiers of anatomy, physiology, and presenting symptoms. Similar to the medical model, the IPS model is also three-tiered. The IPS model uses anatomy, physiology, and presenting symptoms to elicit the processes of problemsolving. The lack of efficiency or effectiveness by various student and adult problem solvers relates to the specific use of pathways in the brain. The pathways may be habitual or not. In Chapter 8, the cognitive pathways used in various kinds of problem-solving were illustrated. In this chapter, we examine some of the most obvious problems that occur in daily life as well as problems found in the field of education, and medicine. Examples of mental slowing in everyday experience Goal conflicts are very common. Several choices may have equal appeal. Given a choice, especially one which involves children, family, or life, one has difficulty finding a problem solution because of the importance of the decision and its outcomes. These types of problems often result in extended time to solve the problem as the outcome has monumental significance. Slowness in processing is often seen in children and sometimes in adults when confronted with a simple problem that is new or different from previous experience. People, especially as they age, are usually slow to process new information and even slower to act upon it. When confronted with a situation that is new or different from previous experience, the solution for many people is to ask someone else, do nothing, or wait for help. Many other examples of time differentials are a part of everyday experience. For instance, a person who thinks of many alternatives to a problem (divergent thinker) is differentiated by time from their counterpart, the quick convergent thinker. The divergent thinker wants more information for alternate solutions or to generate more alternatives; while other people have converged on a solution long ago. Many quick 133 | P a g e 134 Prepublication Copy convergent thinkers get upset with divergent thinkers or think of them as “indecisive or slow.” Slowness in the solving of problems can come from personality tendencies such as showing cognitive rigidity or being to rule-based behavior. From the moment of birth, self-regulation, based derived on parental rules, is encoded in the brain. A child learns to follow the rules and to be self-regulated. Rules, over time, become encoded in neurons based on the action potentials and experience. Rules are sometimes based on simple associations-fire: hot: burn-don’t touch and later on analysis. For instance, one sees a burner on the stove. If the fire is turned on and one touches a hot surface, it burns. Once an experience is encoded then other experiences can change the rule but change requires multiple neurons to be encoded and processed. This involves time, as the changing of a rule in a simple problem situation requires further encoding and processing. The process of self-regulation requires following the rules. Following the rules ad nauseum invites rigidity, less cognitive flexibility, and slowness in the solving of everyday problems. Well-known problems which are the result of obstructions, slowing, and lesions in neural pathways are reported often in the field of clinical neuroscience. Clinical neuroscience Let’s start with the most obvious cases of cognitive delay, i.e., accidents. In brain trauma resulting from the brain moving forward and backward during car accidents, delays in cognitive functions are common. Delays are the result of either brain or vascular injury. When one car rear-ends another car and causes neck and brain injury, the brain and neck joints move forward or backward for several millimeters. Injury to the blood vessels causes ischemia or reduced blood flow which results in microinfarctions. Reduced blow flow causes a problem with cellular metabolism and neurons do not carry brain signals as easily. A loss of brain neurons, fibers, and tracts retards signals from auditory, visual, or cognitive areas. Obvious clinical signs are slurring of words, inability to speak, lack of motor coordination, and inaccurate word associations. Pet scans and fMRIs indicate areas of malfunctions and delays. From clinical neuroscience, there are other known problems in neuropathways that apply to the IPS theory. The first is Apperceptive Agnosia or the impairment of seeing objects. Milner (1958) noted that lesions in the right hemisphere, specifically the temporal lobes, caused difficulty in matching overlapping figures. The inability to make visual shape discriminations (Wesikrantz, 1980) is associated with bilateral posterior cerebral lesions. Disorders related to the meaning of objects are known as Associative Agnosia (Lissauer, 1988). This was studied post-mortem but confirmed by other single cases (Ferro & Santos, 134 | P a g e 135 Prepublication Copy 1984). There are many studies on impairments in visual perceptual abilities (Taylor & Warrington, 1971). Many other documented studies in clinical neuroscience suggest impairments in neural pathways lead to processing difficulties and slowness of response. Impairments are defined as anything which causes a delay, or malfunction of normal problem-solving. Impairment occurs as a result of interferences with neuron transmissions, lesions, deficits, emotions, and incorrect use of cognitive patterns due to emotions and feelings. Impairments in seeing objects clearly, difficulty in matching overlapping figures, as well as disorders related to the meaning of objects have been found in many single cases by clinicians and researchers. The IPS theory extends the single case evidence to the idea that different groups of people, who are not impaired with cerebral lesions have delays in the processing of information. In IPS theory, rather than being abnormal, these delays are related to the process of growth and differentiation as well as the repeated use of sometimes incorrect pathways to solve problems. What are other causes of impairment? Alzheimer’s, anxiety, aging, head trauma, strokes, developmental delays, emotionality, impulsiveness, and impatience are just a few of the well-known causes which can result in cognitive interferences. Alzheimer’s disease through the spread of amyloids in the brain impairs the functioning of the hippocampus in the limbic system causing problems in learning and memory and the recognition of novelty and spatial relationships. Aging is a common cause as many senior citizens can attest. Likewise, many examples of emotionality interfering can be seen on the nightly news. Road rage, fights, and police shootings are common examples. Education In education, developmental differences accentuate individual differences in the solving of school-related problems, particularly those measured by verbal, numerical, and spatial tests through standardized testing. Developmental differences may result in lifelong vocational differences that affect career pathways. Developmental delays in neuro pathways may contribute to difficulties in problemsolving and affect general life functions. Because of neurodevelopmental problems that are caused by differential functioning, children may develop identifiable characteristics. Autism is one example of a neurodevelopmental delay that can cause social ineptness, difficulty in processing environmental stimuli, and a host of related symptoms. Less serious problems are also evident as a result of other problems in neuro pathways. Children who have simple cognitive and affective processing difficulties may have 135 | P a g e 136 Prepublication Copy problems in processing language, speech, words, numbers, and images. These simple cognitive and affective delays lead to identifiable differences in standardized testing which are manifested early in age development. The field of education is full of children who are developmentally delayed in one form or another. The most obvious example is children classified as special education and resource-dependent (RSP). The least obvious examples are illustrated in the following story. Recently I talked with a third-grade teacher who taught advanced students in a higher average income area. I questioned him about the student’s capability of solving math problems in the third-grade curriculum. He stated that 14 of the 26 students were fine but 12 were behind. Twelve advanced students behind, I gasped! When I asked him the reason, he stated that, in his opinion, they were developmentally delayed! Think about an 8-year-old student in an advanced class being developmentally delayed in math. To me, this statement was the equivalent of stating that neurological cognitive interference, deficits, inhibition, and developmental cognitive growth patterns contributed to neural pathways that were less efficient in problem-solving in comparison to other children of the same age, mental maturity, and experience. One does not think of children who score in the 90th percentile and above on most standardized tests as being developmentally delayed. Most often, the standard of ‘developmentally delayed’ is applied to those who score in the lowest 30th percentile of standardized tests. Can the “case” be made that there are just different normal degrees of developmental delays in children that contribute to differences in problem-solving? Process theory/performance theory Two of the dominant theories in the literature address both the processes and outcomes of problem-solving. The Attentional Control Theory (Eysenck, Derakshan, Santos, & Calvo, 2007), was developed from the earlier Processing Efficiency Theory (Eysenck & Calvo, 1992). Both theories were developed based on empirical data. Processing Efficiency Theory explains how well the resources (encoding, memory, neural tracts) are used to effectively process information while Attentional Control Theory is a performance theory that relates to the quality of the outcome of a problem-solving situation. Research on these two theories is usually laboratory-based. High anxiety and low anxiety subjects are given performance tasks under threat and non-threat conditions. In general, time-related processing shows high anxious subjects are usually slower in processing information, especially under threat conditions. High anxious subjects are more likely to process task-irrelevant information during an exercise. This is a simple example of 136 | P a g e 137 Prepublication Copy cognitive interference. Time to reach a problem solution is increased by emotional interference which results in a time differential. Test anxiety Test anxiety, a known impairment in neuropathways, is an emotional condition that often results in a lower grade on tests. High levels of anxiety occur simultaneously with or before a cognitive problem-solving operation thereby impeding or interfering with cognition. Anxiety is emotional electrical energy that cascades through the brain, internal organs, and integumentary system. The source of anxiety depends upon whether it is a state or trait. State anxiety is a temporary condition that increases motivation and often prevents failure in goal attainment. That is, “I better study tonight to keep from failing the test tomorrow.” Trait anxiety is less situational, more enduring, and occurs with greater frequency in the everyday behavior of an individual. Trait anxiety comes from reoccurring situations which increase stress, expectations, pressure, and the need to succeed. Trait anxiety becomes destructive when emotional electrical energy impedes cognition and prevents problem-solving. State anxiety and trait anxiety are interactive as perceived threat conditions increase. Emotional energy, filtered through memories representing stored images in episodic behavior, removes or alters the condition of threat or stress. How does cognitive interference occur? Both the Process Effectiveness Theory and the Attentional Control Theory assume that there is a fundamental distinction between “performance effectiveness” (quality of performance) and “processing efficiency” (the relationship between performance effectiveness and use of processing resources), and that anxiety impairs “processing efficiency” more than “performance effectiveness.” According to theory, the constant thoughts resulting from anxiety are off-task (irrelevant) during a problem-solving situation thereby shifting attention from the task at hand. This self-preoccupation is a strong and impulsive force. When taking a test, if one is constantly worried about the baby at home, this worry shifts attention from the ongoing task or questions posed on the test. This can result in a lower test grade. This single case of evidence is extended to the concept that different subgroups of people are not impaired but show delays or increases in the processing of information. Four examples are often given. First, the nature of the problem causes delays or increases in processing time, thereby causing individuals to shift to other mental resources such as focusing on existing social processes rather than the problem being presented. That is, when emotional content is provided with the problem, the affective nature (threat, hostility, or anger) impedes the cognitive processes causing people to focus on social outcomes rather than cognitive problem outcomes. The second alternative suggests that when so many cognitive resources are available and a problem is presented, favorite 137 | P a g e 138 Prepublication Copy pathways (habits) are used by different people. That is, the divergent thinker, focusing on other alternatives related to the problem, fails to respond with an immediate solution as their favorite pathway “thinking of multiple alternatives” is used. The third and most often cited example is that changes occurring in the environment (from verbal, and nonverbal situations) affect processing time. One of the most often cited examples is environmental conditions in the classroom that affect and interfere with individuals who are taking a test—lights, noise, other students talking or shifting their bodies, etc. Fourth, delays are related to the process of growth (not having reached a neurological endpoint). This is often cited as a “readiness” factor. Rather than being abnormal, biological delays are normal occurrences but are often overlooked especially by parents. Ultimately, delays or increases in neural pathways and processing lead to compensations, habits, or repeated use of neural pathways that provide information about characteristics of personality, interest, and cognitive subgroups of people! In the IPS model, Tier One and Tier Two are just as important as Tier Three. That is, understanding the theoretical foundations of neural functioning is important in understanding how cognitive interference, growth differentials, deficits, and pathway inhibition influence the solving of problems. In the research literature, one of the oftenstated axioms is that once a neurological pathway is used or developed, then it is easier to reuse. The difficult process is developing the energy, resources, and time to cut a new neural pathway! Learn something new! After a pathway is developed, the repeated practice increased memory usage, and structured recall from an ordered knowledge base to increase efficiency and performance quality. What happens when a person is stymied or lost in a pathway, either by cerebral lesions, brain trauma, aging, or just normal interference from one’s own emotions? The answer to that question requires a textbook on clinical cognitive neuropsychology so we focus on how children or adults become lost in different neural pathways. Lost in different neural pathways Perceptual/attention In the early stages of adolescence and late childhood, many students get lost in certain neural pathways while attempting to solve typical school problems. The results are much more devastating as the teachers are more discipline or subject matter-oriented, i.e., teaching history, teaching math, etc. The pathway in which adolescent children are lost, impeded, or blocked is generally perceptual/attentional or memory (see Attentional Control Theory above) 138 | P a g e 139 Prepublication Copy Perceptual/attentional problems are those associated with not being able to attend to the information being presented. When information is presented, the ultimate requirement is the ability to focus on what is being said or seen. When the “mind wanders” or attention is focused away from the source, either internal or external, interference occurs. The brain is not going to register the information in a form that can be retrieved or recalled. Especially in elementary school a lot of information is “presented” either by worksheets, books, the teacher, movies, computers, slides, dance, orally, or otherwise. When perceptual/attentional problems occur with too much frequency, then a slowing or arrestment is possible. Limited memories As one would expect, students with limited memories, students slow at processing memory, or those less willing to practice memorization for tests, are bound to have difficulty in achievement-related situations. Each of these students represents a different group. 5 or 6 percent of the students who previously have not been motivated to study at school are less likely to start at this point. This group of students has problems often described as attention deficit, hyperactivity, low motivation, or truancy. Even if these students are good at analysis, their faulty short-term memory or concomitant emotional problems keep them from getting average or better scores on an examination. Many teachers want to keep these children in school but find it difficult since each child requires an immense amount of personal attention since the areas of distress are often emotional not cognitive. Limited memory, which is really poor or conceptually dearth long-term memory, may also show limited short-term memory capacity. Usually, students with limited memories learn orally from other students or the teacher right before the examination. Many teachers, especially in the lower grades, review the subject matter as a “show and tell” prior to giving a test and those with limited memories do best with the review. Slow processors with limited memories generally have special classes or resources teachers to help them. Children who just do not care, have something else on their minds, or won't memorize are designated as having motivational problems. When children devote some effort and time to work on the memory requirements, often they get a passing grade. Even if their grades or answers on quizzes are not of exceptional quality, teachers find a way to accommodate them. Teachers want students to exert effort and motivation. An increase in short-term memory activation which results in a better score than in the previous testing situations is indicative of effort. Effort is generally rewarded by teachers. 139 | P a g e 140 Prepublication Copy Remember that getting things into memory occurs by activation of any of the senses, active interaction with objects in the environment, creating abstract scenarios, or just plain rehearsal. General life activities (getting dressed, eating breakfast, etc.) become part of the experience by repetition day after day. Experience with motor activity and interaction (hands-on) learning is the easiest method for most children as it matches the learning which occurs in daily life. Since there are many ways to get things into memory rather than just rote memorization, some teachers use homework, practice sheets, videos, movies, and other multimedia formats. All of these are useful formats if the learner spends time processing the information; however, as one expects, those who have attention or motivational problems are less likely to focus on homework or practice sheets. Other formats including computers, videos, slides, and movies are useful since animation and sound become associated with the concept being presented. Active learning comes from children's interactions, working on practice sheets, doing homework, or having a discussion in the classroom. Children with good memories learn the subject matter, or the procedure for solving problems just by listening, discussing, or reading. They integrate verbal discourse in the classroom with previously learned concepts or homework previously read. Homework for them is a reinforcement of something already known and learned earlier in class. Children with average memories require more interaction-listening, discussion, or reading. Homework supplements their classroom activities and embeds the new information into neural traces. Children with poor memories feel overwhelmed, learning only some of the material because of their cognitive overload associated with new neural pathways that have not been previously stimulated. Children with poor memories require many interactive repetitions so that information "sticks with them." Due to a lack of focus, interest, or attention, their time on task is often not long enough. For us, these students are “lost in the memory or perceptual pathways.” Problems with associational pathways Are there other ways to get lost in the neural pathway? Certainly. All of us are familiar with students who spend time learning classroom material but still do not test well. Why? In some cases, their method of association is unique rather than common. That is, many students, in our opinion, store information in a manner that does not analytically allow fast retrieval of facts. These students are called image or pattern processors as they store written material as patterns or sometimes pictures rather than facts. Their cognitive patterns are comparable to a concept linkage board with arrows between words or concepts going in all different ways. These students can learn facts through repetition and 140 | P a g e 141 Prepublication Copy rehearsal; however, they do not prefer to store facts. They spend time and prefer to learn the “big idea.” The “big idea” is linked associations, which when one questions them orally, allows them to skip quickly over many important concepts. Wow! Great. They understand the lesson well. However, they did not memorize details or supporting facts and receive lower grades. Some students like to memorize facts since they have great memories. Sometimes the problem is that they try to answer all test questions with facts, i.e., by association and memory. In essence, in earlier grades, these students relied heavily on recognition memory associated with a stimulus or prompt and were rewarded. They were rewarded with high grades by questions requiring a factual response. However, these students do not make good grades when the test questions required an analytic response rather than a memorized response. In essence, they are lost in associational pathways! Why do students try to memorize facts? Many tests administered in the elementary grades use matching questions, fill-in-the-blank, or true-false. Although these same questions can be written to require inference, and complex thought, most of the time, in lower grades, the questions are written for memory association or recognition. Match the stem with alternatives to the right 1. _____ First President of US a) Jefferson 2. _____ Signed Declaration of Independence b) Washington Or Fill in the Blanks 1. The first president of the US was __________. Or True False 1. T or F The first president of the US was George Washington. Prior to 11 or 12 years of age, many questions can be answered by association and memory, since association and memory are the predominant modes of testing in elementary school. In late adolescence (13-17), the academic stakes have changed but many children still rely on association and memory. That is, when a person reads or hears information in a text form, the ideas are remembered in an associational form (first president--George Washington). Associational thinking and memory are often the basis 141 | P a g e 142 Prepublication Copy of inference, but many classes require the use of other parts of the brain. For example, algebra, trigonometry, and physical science usually seem foreign to many students. They have less exposure and experience with new and difficult science and math concepts. Often, students must first learn new vocabulary, think through what the application of the new vocabulary means, and then apply these concepts to abstract problems. Impedance is the pathway that comes from using an associational and memory method of recall while studying and then not being able to apply the information in a problemsolving situation since they did not get beyond memorizing the information. “Time on task” is a necessary prerequisite since there is one method of learning new more complex material—spend time studying. However, for some students, spending time is a ‘waste of time’ not because of ability, but because they lack the reading skills, background, and motivation necessary to learn the concepts. As problem complexity increases, the more likely these students to falter. The lack of everyday experience with concrete objects poses a gigantic obstacle to many students since their primary method of learning is concrete to abstract. In fact, as a generalization, about 70 percent of the children learn from concrete to abstract while the other 30 percent can learn abstract concepts without hands-on experience. Concrete learning is learning through examples--touching, feeling, and observing. Concrete learning includes visual presentations such as films, computer programs, and slideshows. The problem that many students have is basic reading skills. The students lack some concrete referents (bottom-up processing). They cannot make a connection or association between the concrete world to the abstract world without support from other sources (i.e., the teacher, movies, slide shows, and hands-on experience). These students are lost in the pathway of associations. Lost in pathways requiring logic How can a person become lost in a neural pathway which requires logic? In a sentence or two, some people cannot fathom the underlying logic required to solve the problem as the algorithm and rules are too complex. When the underlying logical rules are too complex, an intermediary such as a teacher or support system (books, audio-visual materials) is needed. Becoming lost means that the intermediary did not provide an adequate explanation of the logic; the instructor did not show adequate examples, or the student did not spend the time to ferret out the logic. This next section explains how one can get “lost.” Most high school-based subjects in grades 9-12 have an inherent structure that is organized by assumptions, concepts, relationships, sequence, and logic. A typical example involves chemistry where the primary assumption might be that "the smallest unit of matter could be a meson." Formerly the assumption might have been that the 142 | P a g e 143 Prepublication Copy smallest unit of matter is the atom. Knowledge is based on assumptions. The assumptions are that atoms compose molecules, molecules compose compounds, and the compounds comprise larger units of matter such as rubber. Students studying complex subjects such as algebra or chemistry typically do not encounter practical, hands-on experience in these areas prior to entering a high school course. Instead, they study and learn the basic relationships of the discipline through written materials, teachers, or intermediaries (except when laboratory experience is available). They usually draw, explain, or reconstruct material from a book after an instructional period. The book is the base of knowledge and requires reading. Further understanding of the subject matter discipline is dependent upon more courses and other books (for example, an introduction to chemistry, organic chemistry, inorganic chemistry, biochemistry, etc.). Mastery of the academic discipline becomes dependent upon the mastery of a number of courses in that discipline. Since the basis of any subject matter discipline is knowledge, assumptions, concepts, relationships, sequence, and logic, most students learn complex vocabulary and attempt to understand the interrelationships of those concepts to solve problems. Most of the vocabulary and interrelationships require organization, structure, and logic created in the mind of the student based on the logic created by the writer or intermediary. The problem is that knowledge created in the student’s mind might be very different than the knowledge created in the mind of the teacher or the book of study. Problems, illustrative of discipline and created in a textbook, as well as examples and explanations given by the teacher, are the method of synchronizing the student’s mind with the textbook and teacher. This synchronization can only take place with time, study, experience, and practice. If synchronization does not take place, the student learns unique and individual relationships and scores low on examinations. There is no way to verify the logic created in the student’s mind except through the book and the teacher. A lot of chemistry, physics, and other science subjects have a mathematical base as well as a conceptual knowledge base. Students who do not understand how to read the textbooks well, or solve the problem independently often rely on the instructor as the person who simplifies information. In these instances, the teacher becomes more important. The intermediary is the person who clarifies what is important, uses examples of logic to teach simple concepts, and provides the key to solving more complex problems. For most students who are not independent learners, the teacher must assist in knowledge clarification. If not, the student becomes lost and exhibits only partial knowledge. Students who have difficulty in subject matter disciplines often have problems either with the logic of the mathematical problems or the logic inherent in relating complex concepts together based on the assumptions in the text. For example, a simple formula in chemistry is: 143 | P a g e 144 Prepublication Copy H20 + CAS04= CA(0H)2 + H2S04 This simple equation is based on assumptions about the valence of atoms in the compounds. The equation indicates how atoms with different valences are combined under specific catalytic conditions. The transformation of symbols can be memorized. But eventually, a teacher gives similar examples that test the student's understanding of the use or meaning of the equation. If students do not spend enough time and practice working with similar equations, then they are unable to apply or perform logical operations. They have only partial comprehension which interferes with the performance of logical operations. These students are impeded or lost in the logical pathway. Often, being lost in the pathway is the result of spending less time understanding the logical rules and operations in solving the problem or not being shown how to perform the operations. Lost in the complex pathways In adolescence, the fifth pathway, complex problem solving, requires a complicated response that involves many steps of analysis, synthesis, and evaluation. A problem is usually posed prior to the stimulus which was encoded and analyzed. An appropriate strategy or series of higher-order steps must be used to arrive at a solution. Each step may require divergence, convergence, synthesis, and evaluation. As an example, solve the following mathematical problem for a solution involving x: 3= (6x+6+8-15). The complexity of the problem increases as the difficulty level to obtain a solution increases. Earlier, house building was used as an example of “compound problem-solving” as it involves many steps. In schools, the analogy encompasses a science, literature, or history project or its equivalent. Think about the following scenario. Before the student can perceive a solution, a problem must be posed. What if the teacher posed the following question to her students? Using the picture on the cover of this book that I am holding, what kinds of ‘social and economic conditions might have been prevalent at the time the author wrote the poem called "Mary had a Little Lamb.” This type of ridiculous contextual problem posed by the teacher requires considerably more time for the individual to give a response. Individual differences do play a part. Does the student have enough prerequisite information? If a student has the prerequisite contextual information, can he or she process it efficiently? Was there partial or total comprehension of the question? Some adolescents might not answer because they are slow to process information. Such as, ”what does the teacher mean by the words ‘social and economic conditions?’ In this 144 | P a g e 145 Prepublication Copy case, the individual's general speed of processing is slowed. Slowness is related to cutting new neural pathways as the meaning of the words (social and economic) may be new and difficult to comprehend. For a student, each new concept must find an association, meaning, and relationship either logical or not. This process takes time. Some students fail to answer since their time of divergence to reach realistic or unrealistic alternatives is too great. That is, think of all the ways that social conditions can be interpreted. Simply put, some students cannot reach an efficient solution as fast as other students. These students are slow in response to divergence (trying to understand the meaning of the words ‘social and economic conditions). Or then again, many students diverge and converge well but have difficulty at the evaluation stage. What is meant by the following statement? A person can diverge well, and converge sometimes but fail at the stage of evaluation? That is, the response to the problem may be simplistic, erroneous, or inadequate when evaluated by another person. As a person converges to a solution, the standard of evaluation might be very high or very low. If one’s internal standards are very high, each time that the student converges on a solution, their high achievement standards might prevent them or others from accepting the convergent solution. Rewrite! Redo! In many instances, this same person, due to a lack of time, accepts an inferior solution. Recently my daughter was writing a graduate paper for a course she was taking. She has very high standards. Having read and thought a lot about the concepts in her paper, she was nearing the deadline for submission. Did she submit her paper? Yes. Did it meet her standards? I don’t think so but I did not ask. I just listen to her response about having to submit the paper because of the deadline. Later, I surmised that the paper did not meet her expectations and standards. She had spent a long time evaluating all the alternatives. Without the deadline, she could have spent another year contemplating the issues in the paper, just like her father. Another illustration of being lost in a complex neural pathway comes from the reading of textual or contextual material. Often words stimulate multiple ideas in the mind of the person. The ideas which are stimulated are only tangentially related to the problem. As the person examines each of the different ideas that were generated, time marches on! A person might converge to a wrong solution or converge too slowly or sometimes never converge at all. This method of processing information is extremely inefficient and/or time-consuming. Models help in the identification of pathways when problem-solving of children and adults become arrested (slowed in terms of time measurement) or accelerated in a particular stage based on experience with different kinds of problems. An important 145 | P a g e 146 Prepublication Copy point in this chapter is that slowing occurs in a manner of nanoseconds, especially when complex and compound problems are solved. The following examples are illustrative but not exhaustive. Keys to pathway identification For us, the quick speed of processing tests, as well as simple analogies, memory distraction, sequence problems, writing and drawing assessment as well as spatial analysis, are useful in identifying problems in pathways. Children who received special help from a resource teacher or those classified by special education usually have difficulty (low scores based on time differentials) on all kinds of assessments when developmental age is taken into account. Children (based on age) who have lower grade point averages but score average or well on the speed of processing, as well as the other tests, are usually differential problem solvers. Children who have higher grade point averages and score higher on all speed, spatial, and logic problems are usually general academic problem solvers. A problem in any single area (memory, logic, speed) may not be indicated as a pathway problem and should be assessed over time. We use our problem-solving instruments to identify the subgroup to which children belong and then assess the speed of processing, arithmetic processing, and logic to understand the keys to solving problems for their subgroup. Chapter summary Known neuropathway problems are very evident in daily life, clinical neuroscience, and education. Often doctors in neurology utilize paper and pencil tests of diagrams and puzzles to identify problems on a case-by-case basis. In education, known pathway problems occur in children, especially those diagnosed by an educational psychologist. The field of special education has many examples. Many cases of children who are not referred to educational psychologists are only globally identified by teachers and educators. Often teachers determine the reasons that children cannot solve a problem by questions or observation. In work, college, and graduate schools, the inability to solve problems is not as obvious. The problems can be memory, test anxiety, inappropriate selection of strategies for achieving an outcome, time management, lack of study, clinical signs and lesions, or unknown reasons. Regardless, most pathway problems can be identified with appropriate diagnosis and training. During the elementary years when problems were simple, many children bypassed the analytic stage in their reasoning of problems and relied heavily on memory and were rewarded for it. Since the teacher was interested either in memory responses or 146 | P a g e 147 Prepublication Copy developing a foundational stage for problem-solving, children learned that memory was one key to academic success. In late middle school and high school, children who rely a lot on memory to solve problems meet with only average success which is why a lot of students drop out of school. In subjects requiring complex thought and solutions, text material cannot be memorized but must be understood to reach tangible results. In other words, the answers to a complex problem cannot be memorized. Chapter reference: Eysenck, M. W. & Calvo, M. G. (1992). Anxiety and performance: The processing efficiency theory. Cognition and Emotion, 6(6),409-434. doi: 10.1080/02699939208409696 Eysenck M. W1, Derakshan N, Santos R, & Calvo, M. G. (2007). Anxiety and cognitive performance: attentional control theory. Emotion,7(2),336-53. Ferro, J. M. & Santos, M. E (1984). Associative visual agnosia: A case study. Cortex, 20, 121–134. Lissauer, H. (1890). Ein Fall von Seelenblindheit nebst einem Beitrag zur Theorie derselben Archiv fur Psychiatrie, 21, 222-270. [edited and reprinted in translation by Jackson, M. (1988). Lissauer on agnosia. Cognitive Neuropsychology, 5, 155-168. Milner, B. (1958) Psychological deficits produced by temporal-lobe excision. Research Publications-Associations for Research in Nervous and Mental Disease, 36, 244-247. Taylor, A.M. & Warrington, E. K. (1971). Visual agnosia: A single case report. Cortex, 7 152-161. Wesikrantz, L. (1980). Varieties of residual experience. Quarterly Journal of Experimental Psychology, 32, 365-386 Further reading 147 | P a g e 148 Prepublication Copy Chapter 10 Integrative Problem Solving and Subgroups Introduction Finally, Tier Three! For nine chapters, the foundational knowledge necessary for understanding the complex web of personality, interests, and cognitive constructs and their relationship to solving everyday numerical, spatial, and verbal has been developed and expanded. These constructs and others are pertinent to understanding the slowing or arrestment of children and adults as they solve problems. In this chapter, the tenets of integrative problem solving, pathways, and categorical subgroups are explained in more detail. Integrative problem solving Integrative Problem Solving is at the macro level and transcends many biological systems in the individual. Personal characteristics, interest patterns, and cognitive/affective processes of thinking have been studied for many years as isolated elements. Studies found in books, research articles, and literature provide many conceptual ways of viewing problem-solving. At the macro level of integration for the individual, the problem-solving process, utilizing all biological systems, interacts and functions holistically. As noted, many times earlier, encoding, representation, and neural feedback provide thousands of neural firings simultaneously in nanoseconds causing cognitive processes to appear integrated. When integration occurs, individual differences are amplified. When a problem is being solved, especially under a threat or anxiety-created situation, the interaction between all biological systems as well as the environmental task makes it almost impossible to separate or isolate individual elements, except when previous processes unique to the individual’s problem-solving process have been identified. In an integrative model, many questions about the speed and duration of solving problems are relevant as decisions are made quickly. For example, assume one is flying a Boeing 777 and two out of three engines are on fire or failing. Is it possible to isolate the problem-solving characteristics of a pilot in the cockpit of a plane carrying 200 passengers in such a situation? How do decisions regarding speed, duration, and maneuverability of the airplane change for the pilot who is under threat? What happens as new information becomes available? Under such conditions, the slowness or quickness of a decision is 148 | P a g e 149 Prepublication Copy related to the complexity and nature of the problem, the experience of the individual, and the nature of the environmental consequences. What is presently known is that for almost any individual, the integrative factor makes it almost impossible to divide the whole into the sum of its parts in such dire circumstances. Sometimes the only visible factor of what happens is the outcome—the plane crashes or not. However, the influence of the individual’s background (training, motivation, prerequisite knowledge, natural ability, comprehension of the problem, amount of time practicing similar examples, and cognitive factors) is paramount in defining and contributing to a problem-solving outcome. Example: To make the argument more explicit, let us use an example from math. Math is the easiest to track and understand as the outcome is more likely to follow logical rules. Consider these directions found on a recent achievement test--"factor this algebraic expression into 2 different components: (x2-y2). The answer is (x + y) times (x-y) where the middle term disappears or is canceled. For a child to answer the question, the child’s background and personal characteristics, as well as the question given on the achievement tests, should be considered. First, based on personal characteristics, children differ in their motivation to solve such a problem. If one does not like math, then solving quadratic equations is not fun. Second, the children who desire or have the motivation to solve the problem may not have the foundation of quadratic equations (prerequisite knowledge) necessary to determine a solution. Third, if the knowledge (skill or information base) was not present, then a natural ability to detect or recognize patterns could be involved. In such a case, the person might give the correct answer but not know how it was obtained. And finally, there are children who through teaching and study have prerequisite information. They practice the skill; give the correct answer but do not have any understanding of its use. They perform (that is, recall with automatization of the skill) but do not understand how the material is applied. When is the last time that you used a quadratic equation? The skill is automatized by practice from familiarity with similar problems found in math books. In essence, as shown in the next paragraphs, many invisible integrated factors contribute to the correct solution to any problem. Axiom At any given moment when an individual is solving a problem, the interdependence of emotional, physical, and biological systems in the normal individual is considered, for all practical purposes, single, interdependent, and integrative. Remember the mousetrap in Chapter 2. In other words, all the individual systems function as a whole at higher levels of thought—ala “energy.” combined with emotions. This axiom holds “true” except when 149 | P a g e 150 Prepublication Copy any of the biological systems are malfunctioning due to a lack of attention, normal attrition, or energy deprivation. Or then again, perhaps the exception is an environmental cause (rain, sleet, snow, earthquake) or when other people intercede causing interference with problem-solving activity. Consider as a concrete example: when I am sitting in my easy chair writing this book, I am not worried about or cognizant of actions occurring at a micro atomic level in any of the objects in my immediate environment. Quantum physics and the influence of energy and light in my environment concern me only to the degree that they impact my writing on my computer. However, if my wife should throw a pillow at my head, I am going to quit writing and duck. As another case in point, if I do not eat for several hours and I become hungry and tired, the loss of energy from one of my biological systems becomes important to the degree that there is interference in the writing of the book. I cannot write since I am hungry. I have to go to eat. The interface between biological functions and cognitive functions is so great that should a malfunction occurs in one area; there is a direct influence in another. A pain in my stomach when I have the flu keeps me from doing my best work. So why all the fuss? This information seems like common sense. The emphasis here is on solving problems. In our research, the integrative nature of biological systems functioning holistically can be better understood by using a variety of measurement subscales that address problem-solving activity in a complex and multifaceted way. Knowing both the problem solver and the problem-solving activity as well as the environmental circumstances helps to understand the complexity of the problem-solving process and the subgroup to which each person belongs. The characteristics of different biological systems and the physical environments can be better understood by understanding the interactions which occur; however, problems are particular to the individual or groups of individuals. When one goes to the doctor for a problem, the fact that smoking leads to a greater probability of cancer influences the doctor in his physical exam if the patient is a smoker. However, the influence of smoking on any patient is unique to their particular immune systems and to the group of people who smoke! Cancer can be but is not necessarily an outcome. The same is true for solving problems. Some people are better problem solvers than others since they have an experiential history of solving similar kinds of problems (Captain Chelsey Sullenberger landed an Airbus A320 with failing engines on the Hudson River in 2009. Another pilot may have crashed.). This leads to a second axiom regarding the integrative nature of solving problems. Integrative systems have multiple functioning dependent and independent units which act in concert but simultaneously function antagonistically to the whole. A cell might function independently and dependently on the organ in which it is contained; a hormone 150 | P a g e 151 Prepublication Copy may increase or decrease the function of the whole. Thus, the brain contains physiological and structural systems that are competitive and antagonistic but function holistically as an integrative unit. No doubt, the experiential history of children and adolescents relates to the development of the biological and neurological systems. For the child, any teacher of any sport or subject recognizes that "readiness" or the time when children are ready to learn or engage in certain motor or mental activities is important. In teaching youngsters, there is a readiness stage for solving different kinds of problems which involve verbal, numerical, and spatial problems. The readiness stage is different for different people or groups of people. Example: I tried to help my older daughter learn simple mental arithmetic operations, i.e., the multiplication tables (6x9=?). We spent hours going over examples while we drove to many different places. The number of mistakes that she made was great. I was astounded that she could not do simple multiplication mentally (times table) at the chronological age of 10. Emotionally, she took everything in stride. Developmentally because her neurological systems had not reached a maturational stage of readiness, this contributed to her not being able to remember the ”times tables” and calculate mental arithmetic. So, don’t worry. At age 17, she was taking advanced courses in mathematics, and having little trouble with any kind of mental arithmetic. The biological systems are unique. Her problem was that she was arrested or slowed in a developmental pathway (readiness!) related to memory and analysis. The problem was primarily related to slowness in neurological development and experience. In the common vernacular, developmentally she had not reached a biological readiness stage. Teachers see this problem all the time but have a difficult time explaining the phenomena to a parent or an administrator. The proper neurological pathways had not been developed through experience, practice, or use. She was not yet ready to make mental transformations. Remember that mental transformations (rotating objects mentally performing operations, writing sentences) such as multiplying mentally are developed from birth through exposure, practice, and experience. Readiness assumes that mental operations increase with biological development and that age-wise cognitive acumen varies with previous experience, exposure, and mental development. This may seem difficult to accept, especially for test developers who develop tests by age groups that schools use to pigeonhole children. Both schools and test developers should consider writing academic tests for developmental groups, rather than by age or grade level, especially if an achievement test is used as a basis for assigning students to educational activities. The interaction of energy reactions in motor and neural pathways, as the result of practice and exposure, helps to develop readiness characteristics. 151 | P a g e 152 Prepublication Copy For the adult, complex and compound problem solving is the result of years of experience and tenacity in solving particular kinds of problems. Very few people can ascertain the number of hours and the work ethic needed to solve unique problems. Many of the complex problems of society have been solved by people who have dedicated their lives to solving problems related to their interests or work. So, what are other background factors, besides readiness and individual motivation, that can help in determining outcomes for problem-solving? Our thesis is that identifying subgroups of people who may similarly solve problems, then this process can increase our knowledge of the problem-solving process and the people that solve them. In this next section, many different kinds of subgroups of children and their problem-solving capabilities are identified via patterns related to the measurement subscales. Pathways and our problem-solving subgroup The integrative nature of problem-solving allows the identification of subgroups of people as groups of people tends to solve problems similarly. Differences begin in childhood and become more evident in adulthood. We explore the beginning of individual differences in childhood, but first, a little background is necessary. In Chapter 3, the category system was used to identify and explain the actions of a subgroup. The subgroups are an ideal composite pattern. Subgroups represent a category just like fruits represent a category. The concept of fruit allows one to better understand the elements (apples, pears, and oranges) which comprise the category. Our subgroups have characteristics in common, particularly ways of identifying problem solvers as general and differential. The sources for the adult profiles which are extensions of the children subgroups are found in Appendix B. Some of the original data for these descriptions were gathered using observational instruments in middle school classrooms in 1974 (Lawrence & DeNovellis, 1974). From that study, the author developed other instruments to measure high school, veterinary, medical, and dental students while teaching at the College of Veterinary Medicine at Mississippi State University (Toal et al., 1985; DeNovellis, 1976, 1974). The classrooms of schools provided us with an insight into the problem-solving capabilities of children and young adults. In most cases, children in a class generated profiles based on many subscales. The descriptions below were written from the scores on these subscales. The category framework assumes that one is classified into one of two groups based on performance, interests, and personality derived from school-related problems. In any one classroom, some children are designated as general problem solvers and others as differential problems. 152 | P a g e 153 Prepublication Copy Some people inquire, why divide the children into subgroups-they are all capable of solving problems? True, however, the expectations of academic achievement and practical solutions to problems change over time as children mature into adults. Sometimes these expectations of success occur with an associated set of difficulties (fear of failure, need for achievement, competitiveness, and egocentrism) which are different for the two groups. Our goal is to show how the strengths of the differential and general problem solvers contribute to the solutions of traditional, non-traditional, and ill-defined problems. Both groups, because of their creativity, analytic ability, motor skills, and the vast number of jobs, tasks, and opportunities available, are going to solve different and similar kinds of problems. We have seen the products and outcomes of problem solutions in many different classrooms, organizations, and work environments. There are not any limitations on problems that can be solved by either group. Why? Because problems solving outcomes are not dependent solely upon ability but occur by practice, exposure, and experience which results from the integration of personality, interests, cognition, and semi-cognitive characteristics. In Chapter 1, the different categories of problem solvers were defined by the 8 supraordinate measurement subscales: Conceptual, Analytic, Social, Motor, Perceptual, Control, Flex Introversion/ Extraversion (P1-P8) which integrated interests (Car1-Car6), and cognition (C1-C2; S1-S4) into 2 different groups called Differential and General Problem Solving. Each of the different subscales measured the results of individuals using similar and multiple neural pathways. The category framework described different groups of problem solvers with labels such as DC (Differential, Conceptual) which displayed the largest preference scores of the individual in the order of dominant to less dominant. We use these pattern descriptions to understand the characteristics of the problem solvers as they are engaged in solving numerical, verbal, and spatial problems. One pattern does not fit all! These general pattern descriptions, follow, apply to very young children and the patterns change with age, maturity, and situations. These small snippets are for the reader to get a notion of individual differences and are, of course, gigantic generalizations! As with adult profiles, these are idealized personifications and subgroups, not intended to describe any individual. What is important is how individuals differ from the subgroup. The profiles for any age group differ according to age, pattern, gender, ethnicity, and task orientation. Changes due to development necessitate different pattern descriptions for different groups and ages! Children can move from one subgroup to another subgroup as each matures. Likewise, the patterns must be associated with learning numerical, spatial, and verbal problems. We make these pattern distinctions as neonates, toddlers, adolescents, and adults are examined in later chapters. Measurement subscales identify problem solvers. With young children, each preference as described by a subscale can be depicted on a continuum. Multiple preferences described by two or more subscales can be depicted in many different ways but are 153 | P a g e 154 Prepublication Copy written as interactive. It does not matter whether a child scores low, medium, or high on any subscale; the descriptive results capture the rank order of results. Later in the book, we show how differences are narrowed from general descriptions to more precise descriptions by incorporating more detailed attributes of age, education, socioeconomic status, ethnicity, and cultural group. That is, based on the kind of subscale (personality, cognitive, and interests) as well as normative demographic factors such as age groups, gender, socio-economic differences, ethnicity, logical and spatial analogies, and speed of perception, it is possible to make more definitive statements about problem solvers. There are numerous permutations and combinations of types of problems solving styles but based on real data collected over the forty years, the most common patterns occur in about 36 different adult profiles (See Appendix B) with dominant interest patterns and problemsolving styles. Before we discuss the category of subgroups, let us re-emphasize how the children’s subgroups differ from adolescents and adults. The subgroups of children greater than 11 years of age are based on integrative scales of interest, personality, and cognition while below 11 years of age, the measurement subscales are based on non-cognitive subscales. In other words, performance for younger children is based on how children select preference items, not on actual performance scores (logical and spatial analysis). The younger children’s subgroups below are represented by high scores on learning selfconcept and other non-cognitive scales. For our work in classification at this age, interests, and cognition are excluded since the scales are less reliable, less stable, and less useful for age groups 11 and under. Observations by teachers in the classroom are combined with children's personality scores for validity. Only high scores (one standard deviation above the mean) are used in the classification. The goal of our work is to understand how the “child is a father (or mother) of the man.” The saga continues. Control problem solvers Adding an ‘s’ to a particular problem-solving category reflects a high score on control and structure. Control, as well as flex, are more likely to be mechanisms moderating cognitive and affective processes. By adding a letter after each group of problem-solving styles, the tendency to structure (s) and control the outcome is evident in a particular style. That structure is often found in the planning orientation of the person. When energy is channeled into visible products such as a work of art, the problem-solving process is focused. The more a person thinks and plans, the more control is likely. However, that control is balanced with the tendency to give up a preconceived plan so that inflexibility will not result. Because thinking is a conscious process, control and flexibility are related but not necessarily opposites. Control and flexibility are inversely related when the 154 | P a g e 155 Prepublication Copy interaction in problem-solving situations is more at the conscious level and less at the unconscious level. A group and a person can show both structure and flex as each is a competing function. Flex problem solvers By adding an (u) after a particular style, we are noting that a person often thinks 1) in an unrestrained manner (uncontrolled emotional response) 2) in a spontaneous manner to solve the problem at hand or 3) with multiple possible divergent thoughts simultaneously. The degree, either unrestrained or with multiple divergent thoughts, is based on the degree of control or energy focus and the consciousness of the thinking process involved. The greater the control exhibited by the individual, the more likely the divergent thoughts are channeled to the problem situation. On the other hand, the less control, the more likely the flex behavior is unrestrained by the problem situations. Some people may solve problems better by being spontaneous and less encumbered by pre-planning strategies. On the other hand, such spontaneity could be disastrous as others may not be able to judge the efficacy of strategies and therefore not take the possible alternatives seriously. Children’s Problem-Solving Subgroups In Chapters 13-18, a tremendous amount of numbers and data are presented for different age groups to establish the validity of the descriptive categories. Whenever, there is an interpretation of numbers, a difference of opinion often results. There is sufficient repetition in the explanation of concepts to form your interpretation of these subgroups. If, in your opinion, the descriptions need expansion or change; then suggest improvements or write your own. Chapters 13-18 indicate that one’s descriptions of problem-solving behaviors and processes should change with different age groups 8-9; 10-11; 12-13; 14-17; 18-22; 23-32; 33-52. 155 | P a g e 156 Prepublication Copy General problem solvers As noted earlier, the criteria for selecting young general problem solvers on the PS instrument were based on non-cognitive (higher scores on the perception of learning ability, self-concept, and achievement motivation). These subscales were generally significantly related to higher achievement in grades 2-5 using standardized tests, teacher observations, and preschool learning experiences. The dominant subgroups are listed below GS: This is the dominant group in younger children. Socialization has been well developed during the early years before entering school. The subgroup is more extroverted generally with a greater emphasis on being structured and organized. Memory is well developed and exposure to different experiences and different kinds of objects is greater. In this group, motor pathways (perceptual memory-motor-social) are developed first and social skills are next. Analytic pathways are emphasized less than social pathways as the child prefers more motor and social interactive skills. This group of generalized problem solvers is quite facile at learning new things. These children often excel in academic work in response to social expectations. For this subgroup, a lot of individual differences depend on the energy flow, that is, the tendency toward introversion or extraversion. GCS-u: (perception-memory-association-conceptual) This group of children uses divergent pathways more often. The use of divergent pathways results from reacting to impulses and the preference for diversity. Their motivation to succeed is usually social, not wanting to disappoint parental expectations. GCA problem solvers read well since their conceptual orientation is stimulated by verbal and written ideas (ideation and conceptual use of words). Children in this subgroup are better verbal learners since the internal structure is greater (long-term memory helps to develop complex schema over time). They enjoy ideas, different and novel experiences, and people since their unstructured internal environment thrives from rich external experiences. Analytic tendencies are often hidden under a social veneer. Likewise, they are more likely to be image processors, focusing on the big idea, not facts. They are less likely to argue semantics or nuances in the interpretation of single convergent responses. GMA: This group of motor-oriented individuals utilizes motor pathways to increase comprehension- (perception-memory, social, association, motor, conceptual) about objects in the environment. They prefer to solve problems with objects found in their environments. They are more likely to rely heavily on bottom-up processing which is confirmed through top-down processing. Motor Problem Solvers have many important skills, utilizing either their social, perceptual, or analytic pathways to help them accomplish their daily tasks. Motor pathways are enhanced by experience. These 156 | P a g e 157 Prepublication Copy children score well on the academic test as they are often conscientious and apply their skills to school-related projects. GAM-s: Dominant characteristics of this analytic group include the ability to extract common principles from experiences that occur in the environment. Some use logic early; others use approximate logic, and others analyze but do not use logic. Analysis is the ability to inductively or deductively derive a generalization. A generalization is defined by Webster as a general statement, law, principle, or proposition. General analytic problem solvers with structure and social skills are involved in many different kinds of activities as they arrive at principles or generalizations. A few excel at logical approximation and logical thought. Their analytic tendencies are applied to all sorts of problems both academic and non-academic. Children in this group also have very good memories of what is seen and heard in the environment. Athletics, manual use of the hands, and crafts are activities where this group of problem solvers is more likely to find vocational opportunities. Differential problem solvers This set of descriptions is based on 8-11-year-old children. The samples had a greater number of Caucasians and Hispanics with a much smaller number of Asians and African Americans. There were slightly more boys than girls. The D suggests that this group solve academic problems (verbal, spatial, or number) differentially. Some do well with numbers, for example, others do not. The P denotes a high score on perception. The “u” denotes a high score on cognitive flexibility but not a very high score on control of impulses. Even though this perceptual subscale is higher, probably just as important is the fact that according to individual preference, other subscales are not high. Children at a young age do not always answer questions well due to a lack of understanding, social maturity, and motivation to respond. So, we confirm each child’s individual preferences with the observation made by teachers. Descriptions DS: This is the largest subgroup of children whose age is less than 11. These social problem solvers (perception-memory-social-motor) are great at solving social-related tasks and rely on basic motor skills, whenever possible. They enjoy talking, socializing, and being with others. The solution to a problem is usually by talking about it and discussing it with others. By preference, they depend heavily on the association, discrimination, and analysis. Social interaction is extremely important to these children. They learn best in a supportive environment. Their reliance on perceptual phenomena 157 | P a g e 158 Prepublication Copy keeps them oriented toward the outer environment thus they utilize their skills to help others accomplish tasks. They do well in activities that they enjoy and relate to. They enjoy and do well in their area of choice. In many cases, their preferred method of learning is “show or tell me how” and I can do it. DM: These differential problem solvers have a major preference for the use of motor skills. Children in this group are average, above average, or below average in problem-solving. This group often excels in athletics, dance, gymnastics, and other motor areas but may block occasionally analytic conceptualization when experience and practice are not available. Kinesthetic and motor skills are dominant in life. Without exposure to academic problems that use rules as the basis for decision making, their affective systems dominate causing interference or occasional blockage in everyday problem-solving. DA-s: This group of children has analytic skills that may or may not translate into extended conceptual reading skills. They use their power of analysis to achieve immediate goal-oriented satisfaction. When personality attributes are combined with structure-these problem solvers use convergent analytic pathways more often (perceptualmemory-association-analysis-motor output). Occasionally, control and structure facilitate the learning of concepts that provide the basis for logical approximation and occasionally logical analysis. Their strength in problem-solving is based on discrimination or logical approximation in areas where they have an interest. In introverted children, highly developed control systems and an analytic approach help them develop a vast internal cognitive structure. They are often rewarded in schools for their analytic ability and less for use of social problem-solving. DP-u: Children in this subgroup use perceptual skills in very task-specific kinds of problems. Flex or impulse utilization is higher suggesting less ability to control emotions and feelings. A lack of exposure or constant use of specific neural pathway problems (perceptual-memory-association--motor) could limit their skill sets. Often social skills are less developed usually because of less impulse control. In the early stages of life, this group could require long-term developmental help. These children are less structured in their approach to problems. Many children with special needs and emotional problems often select a preference for perceptual scales but have average or below scores on other subscales. Sometimes short-term memory problems are responsible for a lack of comprehension. DC-u: Children in this group use the following neural pathway (perceptual-memoryassociational-conceptual with output). Their problem-solving ability may be in the average range however, on occasion, they may have difficulty converging to a single right answer. Consider the child who is great with ideas, and likes to create things, but may not have a good long-term memory. Their motor skills are average or less since they spend more time on conceptually related projects such as reading and art. They are great 158 | P a g e 159 Prepublication Copy at simple discrimination between objects in the environment as well as the capability to see objects for different uses. A person in this subgroup can make a Halloween costume out of different size boxes with artwork painted on the side. A game can be constructed out of odds and ends found in the garage. Fine motor skills with the hands increase their ability to construct different kinds of things. DMA: For this group of problem solvers (perception, memory, association, analytic) there is increased perceptual awareness combined with analytic pathways, Motor skills increase their motor skills awareness. Think of a good team player on a boy’s football team or a girls’ basketball team. Major skills are developed over a period of time. Analytic skills are used to obtain personal goals, especially in motor-related competitions. DM-u: (Differential-Motor and higher flex) problem solvers use- associational combined with emotional pathways more than others. These students might be designated as special students with special talents. Most of their energy is focused on motor activities with less impulse control. Occasionally, children may have less motivational, and physical energy, a factor that affects their developmental history and contributes to less structure and organization (internal or external). With normal developmental history, these children can achieve with less effort in perceptual-motor tasks. The special talents come from artistic instincts in both fine motor and gross motor activities. As noted earlier, their problem-solving experience may be very task specific and if accompanied by memory impairment results in less analytic experiences, or uneven development. DM-s: This group of problem solvers can be observed during playground interactions, school breaks, and athletic competitions. Compare classroom interactions with motor performance in a variety of activities. As expected, as a group, they are quite competitive, finding ways to be first in line or to be the best at games, sports, or whatever their interest is at the moment. Gender differences are apparent in their approach to everyday tasks. For those who are less competitive, motor and physical actions seem to be more important. DS-u Social conceptual problem solvers who have higher flex scores (perceptualmemory-social-association) focus a lot of energy on social experiences. Their orientation can be more ideational with less focus and structure. Sometimes, they utilize perceptual pathways more and motor skills less. 159 | P a g e 160 Prepublication Copy Chapter summary The first part of the chapter summarizes the basic tenets of an integrative system. Integrative systems are difficult to break apart when functioning at an optimal level. This is very true of the system which involves human decision-making. This leads to the primary axiom. When a problem is being solved, especially under a threat or anxiety-created situation, the interaction between all biological systems as well as the environmental task makes it almost impossible to separate or isolate individual elements, except when previous processes unique to the individual’s problem-solving process have been identified. This last part of the chapter delineates how groups of children's problem solvers differ in the dominance of preferences preference patterns and therefore, based on IPS theory, uses different pathways to solve problems. Dominance is indicated by the first letter of the category system. Therefore, a person with a category system of G has a dominant preference and/or cognitive score on general problem-solving. A category system of PM has a dominant preference score on Perceptual and Motor scores. We have emphasized the use of problem-solving categories as general constructs to help conceptualize the problems of a different group of people that we have encountered trying to solve simple and complex problems. The theory might seem abstract, complicated, and perhaps obtuse. However, think about the complexity of the subject matter (people solving problems). The measurement system and data explained in the next chapters (13-17) give credence to the theory. For continuity, we start with the child at birth and move through different stages of development to adulthood. Chapter references DeNovellis, R. (1975). Characteristics of students identified as inaccurate perceivers. Retrieved from http://uf.catalog.fcla.edu/ University of Florida: Gainesville, FL. Collection UFRDS; univ_florida_smathers; Americana. DeNovellis, R. L. (1976). Catalog of Copyright Entries. Third Series: A5112550: 1974: January-June: Index: https://books.google.com/books. Lawrence, G. & DeNovellis, R. (1974). Personality Variables and the Middle School Teaching Learning Process. Paper presented at the Annual Meeting of the American Educational Research Association (Chicago, Illinois). Toal, R. L. Losonsky, J. M. Coulter, D. & DeNovellis, R. (1985). Influence of cardiac cycle on the Radiographic appearance of the feline heart. Onlinelibrary.wiley.com/doi/10.1111/j.1740-8261. 1985.tb01118.x/abstract 160 | P a g e 161 Prepublication Copy Chapter 11 The Neonate -birth to 24 months Introduction Our measurements of young children begin at age 5, not the neonate, but for the sake of continuity, the tenets of the IPS system are followed from birth. Are there research studies that give credence to the speed of processing, problem-solving, and neuronal pathways of the brain found in the neonate from birth to two years of age and as late as five or seven years of age? Conjectures are based on the best available evidence as one moves from the abstract theory to concrete examples to show how the integrated superordinate constructs of personality, interests, and cognition as well as the 2 groups of problem solvers are a part of the daily life of the neonate. Energy, brain development, and the cognitive model suggest how each process influences the process of solving problems even at the beginning of life. Based on IPS, these early years represent the primitive stage of development. Compensation and modifications occur in all facets of the neonate. Filters set the foundation for differences in approach to everyday interactions and problems. Focused energy comes to fruition through constant practice and interaction. In the living organism, all systems interact but the focal point is the brain. Brain development Chapter 23 examines the general growth pattern of the central nervous system (CNS) during embryological development. The developmental pattern suggests that nerve cells that control the head, arms, and upper trunk movement mature faster than those of the lower body. Overall movement occurs in a cephlo (associated with the head) caudal (associated with the body) manner. Within the brain, the development of the cortical areas occurs in many different directions but generally follows cephalo-caudal patterns. Particularly interesting is the process of lateralization. Lateralization is the specialization of the areas of the cerebral cortex. The findings of Fox and Davidson (1986) on the right and left-brain EEG activity suggest that verbal or linguistic ability is present in the left 161 | P a g e 162 Prepublication Copy hemisphere while spatial, and certain emotions are present in the right; some researchers dispute this observation. There are important critical periods in CNS development, especially in the third trimester of pregnancy. Each cell's development is dependent upon energy, either electrical, enzymatic, or weak forces. Glia cells, which are increasing at a fast pace, have axons and dendrites continuing their growth while other neurological structures are in various stages of development. The cells of the fetus increase at a rate of 250 thousand a minute (Dekaban, & Sadowsky, 1978). The mother's psychological well-being drastically influences her progress in development. For example, at the University of Washington, researchers found that a mother who prolongs depression can significantly reduce the cellular activity in parts of the infant's brain. Conditioning takes place before birth! After birth, stimulation, a form of environmental energy, is still critical for growth in cortical structures. With stimulation, the neurons blossom in the brain like a flower responding to water and the sun’s rays. By birth, the neonate has an entire cadre of brain cells, shaped by more than 50,000 cells from the human genome. The greatest postnatal spurts of brain growth occur from birth to 2 years. In the early years, an infant generates up to 15,000 connections to each neuron. As those neurons enlarge, the dendrites and axons have 1,000 billion interconnections. From about 2 months of age, the areas associated with myelination continue to develop; this process continues well into adulthood. Notice that external sources of stimulation are via the senses (eyes, ears, smell, etc.). Each one of the senses is, in fact, an energy reaction from the outside which is transferred via the nervous system to the inside. One of the most overlooked forms of stimulation is touch. Massaging newborn babies increases cortical stimulation. Massage or touch decreases the stress hormone and increases the sense of well-being. The infant is programmed for a healthy beginning (Hold, 1996). Energy Certain principles related to the energy growth of the ovum are evident in molecular biology and embryology. From the moment of conception and cellular division, gradients are important. Gradients are a series of progressively increasing or decreasing differences in the growth rate, metabolism, or physiological activity of a cell. The progressive differences are due to energy differentials inherent in certain chemical combinations (proteins, RNA). When certain proteins (messenger RNA) in the cell begin their replication phase, the chemical gradient and the amount of chemical concentration 162 | P a g e 163 Prepublication Copy determine the direction of development (anterior, posterior). Each energy combination contributes to the overall development of the embryo. Energy reactions are synonymous with internal stimulation (Nüsslein-Volhard, C., 1996). Our model posits the need for stimulation and affection as basic ingredients for the growth of the neonate’s problem-solving. A deprived environment with little social contact and sensory stimulation results in cognitive and emotional delays (Johnson, 2000; Ames, 1997). The importance of stimulation during the time in which the neonate is developing has been shown in many different studies involving sensory deprivation (Collard, 1971). This is true, especially for the development of the cortex. Critical periods of stimulation must occur if the visual cortex is to develop and function adequately. Many widely- heralded studies have examined humans reared in isolation or with sensory deprivation (Dennis & Najarian, 1957). The lack of mental and emotional development in children without stimulation is obvious; some children never attained normal development after being exposed to a negative and stressful environment. Any infant, who is raised in an atmosphere of fear and neglect, experiences a rise in bio-chemicals associated with stress. Stress produces an overdose of corticosteroids from the adrenal glands. Corticosteroids decrease the leukocytes or white blood cells. This overdose of bio-chemicals damages the brain circuitry of young children. Affection, in our terminology, assumes that the neonate is being touched, coddled, and stimulated. Connections with the outside world are crucial while the neonate goes through the basic stages of survival (eating, drinking, and breathing). The term "failure to thrive" is given to infants who show retardation in growth or mental development when no obvious nutritional or organic disease is noted as the cause. Passivity and apathy are hallmarks of behavior. The child exhibits little smiling or vocalization and does not react to the cuddliness or being picked up. Such children often die, showing signs of weight loss, and emaciation (Galler, Ramsey, & Spolamono, 1985). Cognitive Model The cognitive model of the neonate has many missing labels and functions compared to the adult model. Logical rules, advanced analytic thought, evaluation, and synthesis, all processes designed for higher-order thinking, are missing. Are the frontal lobes intact and functioning? Even though the child probably enters the world with some minute representations and short-term memory, the long-term process of cognition is just beginning. The senses are intact with perception, hearing, touch, kinesthetic, and smell providing sensory information. Language processing occurs anywhere from 8 months to 16 months depending on the child. Mental representation and imitations (long-term 163 | P a g e 164 Prepublication Copy memory) appear also from 21 to 28 months depending on the exposure and experience (Liston and Kagan, 2002). Spatial processing is evident in the first 3 months after birth. Discrimination, a simple form of analytic thought, is present, but the exact age has not been determined. Notice that divergent and convergent thinking are both evident as studies suggest occurrence during the first few months. Spatial, numeric, and verbal representations are present at different times depending upon stimulation and exposure. A lack of stimulation, exposure, and experience results in the uneven development of problem-solving capabilities. Diagram 2: The Cognitive Model (Neonate) Cognitive Model: Neonate (Birth to Age 2) Perception Perception is the active process of interpreting and organizing incoming stimuli or sensations. The newborn is actively engaged in gathering information about light, sound, aroma, taste, and touch. Attention is estimated by the amount of time processing all these stimuli as indicated by behavioral scanning. 164 | P a g e 165 Prepublication Copy Neonates do not have good vision when they are born. Faces are fuzzy shapes. Vision increases with time and the resulting attention and perception help define the image, identity, and self-knowledge during the first years of life (Gibson, 1969, 1995; Lewis, 1994: Neisser, 2003; Rochat, 1995; Rochat & Morgan, 1995a; Schmuckler, 1995, Vander Meer & Van der Weel, 1995). The simple act of a newborn varies from grasping a finger to sucking on everything. A newborn turns his head to look for a nipple, touches his or her body, and moves the arms and legs. Neonates gain knowledge of their bodies. Each baby tries to coordinate hand/mouth movements and spends time visually observing the environment. Neonates use perceptual information to adapt their posture (e.g., Bertenthal & Bai, 1989; Butterworth et al., 1982; Lee & Aronson, 1974) and to avoid reactions to objects in the environment (Ball & Tronick, 1971; Nañez, 1987; Yonas, Pettersen, & Lockman, 1979). As time goes on, vision and perception are intimately tied to sensory-motor input and influence all actions of the growing child. In a study by Lewis and Brooks-Gunn (1979), 3-month-old children showed individual differences in visual attention and recognition memory. The same children who were rapidly habituated at 3 months also had high scores on the Bayley Scales of Infant Development. The flexibility associated with shifting one’s attention is evident toward the second month of life, but that flexibility increases and decreases over time. Conception Each association that a child makes from birth can result in some form of conceptualization. Most researchers prefer pre-concept learning for the time before long-term memory formation. Comprehension is related to concept development although it is not the same. Comprehension for most researchers is based on memory, encoding, associations, and concept development. Concept development is the ability to group and sort by features, properties, or common themes. Concept development occurs early; perhaps 21 to 28 months as studies have shown this is the time that long-term memory also develops (Liston & Kagan, 2002). Concepts increase the speed of processing. Taxonomies allow for understanding and comparison with known objects and ideas. Studies have noted the neonate’s resourcefulness in classifying and categorizing things that have perceptual similarities. As noted earlier, perception precedes concept development. At this point, given what is known, almost all internal motor-related concepts originate initially from "bottom-up processing." Concept formation probably occurs simultaneously for all practical purposes with bottom-up and top-down processing. Bottom-up processing, as cited in Chapter 6, occurs in the ventral pathways of the brain and is sensory-motor. Bottom-up processing with encoding and memory storage allows categorization, a process evident by 17 months as the child sorts and categorizes similarly 165 | P a g e 166 Prepublication Copy shaped blocks. Children begin to fill in the gaps developed from bottom-up processing by storing long-term memory information. The child encodes information from the environment via sensory-motor innervation and combines that information with memory as he or she reacts to sensory-motor encoding. Remember there are different kinds of memory, even memory specifically designed for the proprioceptive muscles. That is, the arms and legs in the child’s body remember what sequences occurred in muscle movement. The parent or caregiver provides the sensory environment as the neonate lacks mobility. That is, an outside source of stimulation provides all forms of sensory input. Sensory information is processed with environmental labels if the parent talks or converses in normal language with the child. Before the child talks, she or he makes associations with sounds, faces, smiles, touches, and feelings. Problem-solving by the child can occur as early as three months as the child lays in the rocker, basket, or crib. The earliest forms of problem-solving occur as the child looks for familiar objects in the environment. A simple object, such as the toy ring partially grasped by small fingers waving in the air, is moved from hand to mouth or shifted from one hand to another. If the same favorite toy ring is shown to the child at a later time, their fingers reach out to grasp the object to move it to their mouth or other hands again. Sensory information changes with physical development as the child interacts with objects in the environment by crawling and finally by walking. Walking occurs from nine to twelve months. Each stage of physical development contributes to conceptual development as more and more sensory information is available. The changes are so great from birth to 18 months; it is difficult to account for all of them. In the latter stages of development, perhaps 8 to 16 months, the results of cognition manifest themselves in various forms of imitation, play, and imagination. Imitation such as pretending to shave or verbalizing like daddy or mommy is important. Imitation is performance via a pathway of perception, and memory. It becomes a symbolic, and abstract representation of the person, being imitated, who is not present or shaving. In the IPS theory, the forms of play, the type of imagination exhibited, and the degree of imitation are excellent forerunners of problem-solving behaviors. Only when the child exhibits some form of intentionality (internally or externally) does problem-solving truly occur. Intentionality is exhibited by the child doing something which represents an internal action or displaying active behavior, even if the behavior is a by-product of some other action. For example, suppose a 10-month-old child wants to get a toy doll out of a box that is constructed with removable plastic sides. The child picks up the box and dumps the toy doll out, then attempts to take the box apart. In our view, problem-solving has occurred as the child has a goal (problem) to get to the toy doll. The solutiondumping the toy doll out of the box -- involves a series of steps to achieve the goal. There 166 | P a g e 167 Prepublication Copy is “intentionality” on the part of the child. The intent of the child is based on the actions to retrieve the object. From a cognitive standpoint, in this previous example, the child does not think in the traditional method outlined but instead uses a) memory or perception to find the toy, b) trial and error to turn the container upside down, and c) interest in continuing to take the sides of the box apart. Intentionality is exhibited because the child is actively doing something to or with the box. A form of comprehension exists at 10 months since some form of discrimination was involved in getting to the box to turn it upside down. However, one could not ask the child to explain or articulate any information about the objects involved--box, or doll. The child could not, for example, conjure up a picture of the doll that he or she did not see. Only later does the child develop this capability. What if the child thinks of a plan but has no immediate product? My 10-year son is always lying in bed thinking of new designs for spaceship motors. He seldom develops or makes anything other than the design on the computer at a later date. For him, problems solving has occurred when the design on the computer was produced. Intentionality resulted in an observable outcome. An excellent method of a child's representation is drawings. Ask an 18-month-old child to draw a dog. Trying to interpret the mass of scrawls is an artful adventure. The child, who at 24 months, can verbalize the representations, of dog, cat, mother, etc. has developed many memory stores and concepts. Motor Sensory-motor actions and physical development are rapidly changing during the period of birth to 18 months. Neonates move from limited body actions and self-exploration to movements associated with crawling, walking, and running. Early movements are restrictive, such as raising the forearms while being on the tummy. Each child in a crib can hold his head up at 6 months. The neonate moves from the actions of rolling over to standing alone and finally cruising. At about 18 months, some children can push and pull cars or hold objects while walking. Other children can assist with dressing and undressing, hold a crayon and scribble, and walk downstairs if holding someone’s hand. All these events are motor events that directly influence self-confidence and selfmotivation. Motor actions in the environment directly affect cognition. The encoding process of the newborn gradually develops from birth and changes daily as new information becomes available. Often the only way for a newborn to verify the information is via sensory input (seeing, touching, hearing, feeling). Motor actions increase the tendency to use sensory input as the best method of verification. This later leads to children being quite practical 167 | P a g e 168 Prepublication Copy and concrete about objects which exist as reality or exist only in fantasy. Children who continue to focus, sharpen, accentuate, and improve motor functions and their associated conceptual referents develop a preference for motor-oriented and concrete activities. This preference is the basis of our classification of a child being in the Motor subgroup (DM or GM). In the next chapters, the common assertion is that motor-driven children are more practical, hands-on, and reality-oriented. This sensory-motor experience develops from birth as children have a long developmental history of dealing directly with objects in the environment. What is seen, touched, and felt contributes directly to the knowledge base of motor children. The motor-driven child has strengths in object processing and proprioceptive memory. Analysis For the neonate, simple discrimination and association are at the heart of the thinking process. Analysis constitutes the first step in decision-making. The neonate is born into a world of sounds, sights, and touch, all of which require simple discrimination. After one month, there is recognition of sounds and voices. The neonate recognizes and responds to his or her name by the fifth month. At six months, objects are being studied and at 7 months there is evidence of anticipation of feeding or events which have been established by routine. The hallmark of new events is finding hidden objects at 10 months. Of course, all of these descriptions are arbitrary and vary with the individual child. At what age does problem-solving begin? For us, the child’s action at three months is a sign of problem-solving based on intentionality. The intent to grasp a favorite toy and shift it to another hand suggests a goal has been reached. Studies show that a child can recognize the simple differences in categories of food items, furniture, and stuffed animals by 12 months of age (Younger, 1985) while at 18 months, the child can sort objects in different groups. This suggests that some form of simple and perhaps compound analysis can occur by one and a half years of age. Social The social behaviors of the child have received the most attention from the scientific community. One is less likely to see a child smile during the first month. Around 2 or 3 months of age, smiles increase and continue throughout the first year (Robert, 1989). In the first months, physical manifestations are everywhere, cognition is less evident. Crying, anger, and frustrations are easy to identify. According to some researchers, anger 168 | P a g e 169 Prepublication Copy follows a U-shaped curve with a decrease in anger in the second through the sixth month and an increase in anger when a child cannot grasp what is wanted. Many studies show that newborns are more responsive to their mothers than strangers. Evidence of maternal touch is negatively associated with indicators of distress (Stevenson, Thompson, & Sonuga-Barke, 1996). Shyness, which is based on observed behaviors, is only evident in some children. When seen, the observed behavior is assessed by speed (slowness-caution), especially when a child is approaching situations that are novel or uncertain. The behavioral repertoire of the neonate includes a host of social behaviors such as making eye contact, laughing when tickled, and showing affection by looking, smiling, and kicking. In the second six months, there is a definite fear response with strangers and an awareness of social approval. Anger is expressed more dramatically while acts of pride in personal accomplishments are evident by 18 months. Stubbornness increases from 12 months to 24 months. The inability to share is different based on familiarity with social situations. Children around 12 months of age seem to enjoy the opportunity to interact with other children who are their age. Control (Structure) Control and structure are related to co-regulation, especially in the neonate. Co-regulation is a process of helping children internalize rules, regulations, and social behaviors (Maccoby, 1984). For the neonate, co-regulation involves a parent or caregiver and occurs early--- usually at the beginning of the physical movement (Kopp,1987). When children endanger themselves or engage in the behaviors of hitting, throwing, or kicking caregivers, the behavior is restricted. Parents or caregivers espouse many “no-s” or “don’ts.” The internalization of verbal rules begins to take place. The neonate’s normal behavior is impulsive and inquisitive. Control is the structuring of events and actions by parents or the structuring required for goal attainment in the neonate. In many cases, the neonate does not understand the reason for the control and structuring from the outside. The association of names, labels, and actions does not lead to comprehension in the first 18 months. The development of language begins with the process of self-regulation and self-initiation, but its completion is many months away. Two kinds of control: one kind of control is from the parents or caregiver and the other is from the child seeking a solution to a goal (hungry-get food). External structuring (and in some cases the lack of structuring) is instituted from the outside in the form of routine or habits. Control from the inside is the series of steps necessary to maintain basic survival (eat, drink, and be merry). When the basic survival needs are fulfilled, control from the 169 | P a g e 170 Prepublication Copy inside is still based on goal attainment, fulfilling the need for mental and physical stimulation. Think about the routine. Routine is doing things the same way at the same time, establishing a form of control. Routine forms patterns and expectations that events are going to occur in the same manner. Routine has advantages as it is a method or way of handling common problems Routine requires less energy of thought as automization occurs. The routine involves fewer errors and faster task completion. Parents, teachers, and caregivers are masters of establishing behavioral routines. Behavioral routines influence mental behaviors as they also establish mental sets. Mental routines or sets are established ways of thinking about things and internalizing control. Flex Flex is short for cognitive flexibility. Flex is impulse stimulation combined with emotions, reflex actions, and feelings. Flex, at the developmental age of the neonate, occurs as a response to sensory-motor stimuli and reflex actions which are initiated from internal basic needs, such as the need for food, water, and breathing. Likewise, flex is a response to impulses generated by stimuli from the external environment. Flexibility occurs when trying to overcome obstacles to achieve goal attainment imposed by external or internal sources. Flex is the cognitive action of escaping external and internal control or obstacles and thus contributes to goal attainment or problem-solving. Flex occurs with intentionality when escaping internal control. If the internal impulse is to get food because of hunger, then flex is the cognitive action of eliminating obstacles in the environment to achieve the goal. Flex does not involve planning as cognitive and emotional impulses may only be a spur of the moment, and sometimes completely irrational. When responding to a goal, flex is the process of using cognitive and emotionally generated ideas creatively or differently as a way to achieve the goal. A neonate lying in a prone position in a crib is hungry. A bottle is placed in the hands in such a way that the hands must be lifted to the mouth to find the nipple on the bottle. The reflex action is to bring the nipple to the mouth to suck the nipple. Repetitive actions increase memory traces. At a later time, the bottle is dropped. The goal is the same and the actions to solve the problem require a series of steps to retrieve the bottle and bring the nipple to the mouth. Flex can be the adaptive cognitive thinking process (trying out different methods on how to retrieve the bottle). The goal may never be achieved because reacting to the impulse (hungry-find bottle) with imagination may be insufficient. Flex contributes to creative behavior as flex along with control and conceptualization allows the 170 | P a g e 171 Prepublication Copy problem to be solved. That is, through the flexible and adaptive thinking process involving the inner world of words, numbers, and spatial entities, problems can be solved. Flex does not occur in isolation. As conceptualization and ideation increase, so may flex. If conceptualization or imaginative ways of achieving goals are unregulated (without control), then the dreamer or divergent thinker may not be grounded in the reality of objects and emotions. Flex mediated by emotion without the intervention of analysis as one method of control can lead to many different interesting conclusions, depending on circumstances. There are not many studies on cognitive flexibility at this age as most people are interested in the child establishing and maintaining control while he or she increases self-regulation. The studies on creative thinking occur later when the child engages in goal-directed behavior, imaginative activities, manual tasks, and reading. Differences in Types of Problems Solved Word problems solving For the neonate, word problem-solving begins with nonverbal behavior. Gestures are a common means of communicating by 7 months. Gestures require intentionality. In the early months, language develops. Language consists of babbling or saying familiar words like “dada” or “mama.” This may result in a long series of syllables which, in turn, might produce sounds that appear to be a conversation (birth to 8 months). Sometime around 10-12 months, a few recognizable words are spoken. By 13-15 months the average vocabulary is 4-10 words. By 18 months, the number has increased to 20. Even words, such as “please” and “thank you” are part of the vocabulary. Two-word phrases are evident at 24 months. In our model, we assume that everything that the child feels, hears, and sees is encoded simultaneously but in different parts of the brain. Every action that a child makes before birth (fetus) and later in the early years constitutes the experience of the child. We used the term "picture memory" to refer to the encoding of what the child sees visually. Thus, the image of a tree is encoded as a picture memory. Whether it is stored as a picture memory is a matter of contention. Later, when the child sees a visual representation of a tree in a book, better discrimination occurs when there is corrective feedback simultaneously with the event. In common terms, a parent says the word "tree" as the child sees the picture in 171 | P a g e 172 Prepublication Copy the book. This process, when coupled with a non-judgmental tone, reinforces and modifies the association in memory. Exposure without corrective feedback has limited value. A child can see and encode many things in their picture memory based on experience but only the references verified over time by corrective feedback, either by person or actions in the environment, determine the individual orientation and perspective of the child. Many children from birth to 2 are exposed to numerous experiential situations, but in some cases, the child only receives corrective feedback based on their behavioral response-bad behavior, good behavior, etc. Many children learn to control behavior but do not receive corrective feedback on cognitive information associated with the “why” of the situation. We use the term "printrich environment" to denote a child who is brought up from birth to 18 months with both behavioral and corrective cognitive feedback about words, numbers, and spatial activities. Corrective feedback is especially useful during reading sessions with print matters such as books or pictures. As noted earlier, children from a print-rich environment, respond differently to problem-solving in the latter years of adolescence. Many parents increase the cognitive experience of the child by providing books with pictures such as Richard Scarry's Best Word Book Ever. This book, written in 1963, is still available on Amazon. Again, a child who is exposed to numerous picture books with corrective feedback differs substantially in academic achievement from a child who is exposed to pictures without corrective feedback. Numerical problem solving All type of theories exists about the neonate and his or her ability to use numbers. Some are nativist, that is, researchers suggest that children are born with an inherent understanding of quantity such as bigger and smaller. Others suggest that number and quantity problems are associated with everyday learning and experience such as having portions of food on a plate. Studies in neuroscience have demonstrated that neonates can comprehend relative size by estimation. The area of the intraparietal sulcus is involved when neonates show surprise about changes that occur in the length of rows of M & Ms at 3 months old. These studies conducted by Dehaene in the 1990s led to the hypothesis that children are born with an innate ability to estimate. Her later work suggested that impaired functioning of this numerical estimation system resulted in lower grades on standardized math tests. She called the impairment “dyscalculia” (the computational equivalent of dyslexia). In her article in Science, “They earn less, spend less, are more likely to be sick, are more likely to be in trouble with the law, and need more help in school.” (Dehaene, 2010). 172 | P a g e 173 Prepublication Copy Controversial studies by Wynn (1992) and Wynn, Bloom, and Chiang (2002) suggest that children as early as five months can discriminate differences in quantities and use that knowledge to add and subtract simple numbers up to 3. They reached their conclusions based on experiments that manipulated the number of objects placed behind a screen. By adding and subtracting objects and measuring the time intervals that children watched the objects (violation of expectation method), they deduced that children could discriminate differences in quantities. Very young children at (14-16) months repeat numbers in their daily languages, such as one, two, three, and jump, however, this may only indicate partial comprehension or memory. Spatial problem solving Newborns organize the objects in their perceptual field according to the relationships in space. According to Piaget (1954), the newborn’s knowledge of space is based on the activities within that space. A search for space is based on an egocentric frame of reference if environmental cues are missing. Researchers have generally agreed with this position. In the absence of cues from the environment, the position of their bodies is used to find an object and make decisions about location. Bremner and Bryant (1977) hid objects to the right or left of 9-month-old subjects. After exposing them to training sessions where they learn how to find the objects, the children were rotated 180 degrees. The children were unable to find the objects since they appeared, they were still using the bodies as a frame of reference. As the child matures and develops, the use of cues or landmarks to specify a physical location is more evident. The ability to reproduce the visual-spatial world accurately and to recreate relevant objects in the absence of relevant stimuli is one of the hallmarks of spatial processing (Gardener, 2000). At this point, this ability does not appear to be in the neonate from birth to 18 months. Chapter summary According to Piaget, almost all children can be correctly classified as predominately Motor Problem Solvers at this age. Motor problem solvers exhibit simple reflexes, and intentional movement through the use of hands and arms by age 7 months. Children can stand and walk upright between 9 to 16 months. In the early months, the neonate has little sense of a separate self. Perceptual problem-solving occurs when children are extremely alert to changes in their environment. Children, by 3 to 4 months, have depth perception, and perceptual scanning ability (Nañez, 1987 b.150). Individual differences in visual activity are evident in children, especially during the period of 12 to 18 months. Children develop a minimal capacity to analyze early as they can discriminate or differentiate between the properties of visual objects. Their social nature is evident in smiles as well as sensory behaviors such as touch. 173 | P a g e 174 Prepublication Copy Although it is difficult to identify with any certainty, problems solving styles exist. We can ascribe general categories, based on behaviors observed in the environment. One group of differential problem solvers is developmentally behind in normal actions, such as speaking, standing, or crawling. A second group is restricted in certain types of exposure to words, numbers, or spatial problems. Restrictive implies limited exposure to certain types of activities but not others. For example, a child is allowed to play but has limited contact with language as few people talk or initiate talking with him or her in the environment. A third group is general problem solvers as they have exposure to a varied environment of numbers, words, and spatial activities. Children from a print-rich and experiential environment that provides for imagination, play, and motor activities are more likely to be general problem solvers. Almost all children ages (0-18 months) are assumed to have less controlled cognitive and emotional systems. Each child shows, anger, joy, happiness, and mood changes. Behavioral control is related, in part, to parental control. Many children focus perceptually, and have an association in memory, but do not follow through with goalrelated actions at less than 18 months. Self-initiation is related to goal-related actions. When children start to have some control over simple things like choosing toys from a group of toys, self-initiation begins. Self-initiation and success in goal-related activities engender success and a feeling of self-confidence. From ages (0-2), children are less likely to exhibit flexibility in thinking as options and alternatives are not available. However, the more times a child is engaged in interactive responses, the more likely energy utilization and the more memory storage response to be developed for later usage. Chapter references: Ames, E. (1997). The development of Romanian orphanage children adopted to Canada. Final Report to National Welfare Grants Program) Burnaby, British Columbia: Simon Fraser University. Ball, W., and Tronick, E. 1971; W. (1971). Infant responses to impending collision: Optical and real. Science, 171, pp. 818–820. Berthanthal, B. I. and Bai, D. L. (1989). Infants sensitivity to optical flow for controlling posture. Developmental Psychology, 25, 936-945. 174 | P a g e 175 Prepublication Copy Bremner, J. G. & Bryant, P. E (1977). Place versus response as the basis of spatial errors made by young infants. Experimental Child Psychology 23(1),162-71 Butterworth, G., Jarrett, N., & Hicks, L. (1982). Spatio-temporal identity in infancy: Perceptual competence or cognitive deficit? Developmental Psychology, 18, 435–449. Collard, R. (1971). Exploratory and playful behaviors of infants reared in an institution and in lower and middle-class homes. Child Development, 42, 1003-1015. Dekaban, A.S. and Sadowsky, D., (1978). Changes in brain weights during the span of human life: relation of brain weights to body heights and body weights, Ann. Neurology, 4,345-356. Dehaene S1, Pegado F, Braga L. W., Ventura P, Nunes Filho, G., Jobert A, DehaeneLambertz G, Kolinsky R, Morais J, Cohen L. (2010). How learning to read changes the cortical networks for vision and language. Science. 330(6009):1359-64. doi: 10.1126/science.1194140. Epub 2010 Nov 11. Dennis, W. & Narjarian, P. (1957) Infant development under environmental handicap. Psychological Monographs, 71, 1-13. Fox, N. A., & Davidson, R. J. (1986). Taste-elicited changes in facial signs of emotion and the asymmetry of brain electrical activity in human newborns. Neuropsychologia, 24, 417422. Gibson, E. J. (1969). Principles of perceptual learning and development. Englewood Cliffs, NJ: Prentice-Hall. Galler, J. R, Ramsey, F. & Solimano, G. (1985). A follow up study of the effects of early malnutrition on subsequent development: Physical grown and sexual maturation during adolescence. Pediactric Research, 19, 524-527. Gardner, H. (1999) Intelligence reframed: Multiple intelligences for the 21st century. New York: Basic Books. Hotz, R. L. (1996). Deciphering the Miracles of the Mind: Los Angeles Times, Los Angeles, CA. Johnson, D. E. (2000) Medical and development sequel of early childhood institutionalization in Eastern European adoptees. In C.A. Nelson (Ed.) Minnesota symposia on child psychology, 32,113-162, Mahwah, NJ, Erlbaum. Kopp, C. W. (1987). The grow of self-regulation: Caregivers and children in N. Eisenberg (Ed.). Contemporary topics in developmental psychology. New York Wiley, 35-53 175 | P a g e 176 Prepublication Copy Lee, D. N. & Aronson, E. (1974). Visual proprioceptive control of standing in human infants. Perception and Psychophysics, 15, 529-532. Lewis, M. (1994). Myself and Me. In S. T. Parker, R. W. Mitchell, & M. L. Boccia (Eds.), Selfawareness in animals and humans: Developmental perspectives (pp. 20–34). New York: Cambridge University Press. Lewis, M. & Brooks-Gunn, J. (1979). Social cognition and the acquisition of self. New York: Plenum Press. Liston, C. & Kagan, J. (2002). Brain development: Memory enhancement in early childhood. Nature 419, 896. Maccoby, E. E. (1984) Socialization and Developmental Change. Child Development, 55, 317-328. T Nañez, J. (1987). Perception of impending collision in 3- to 6-week-old infants. Infant Behavior and Development, 11, 447–463. Neisser, U. (2003). Cognitive psychology. In, The history of psychology: Fundamental questions (pp. 447–466). New York, NY US: Oxford University Press. ISBN 9780195151541 Nüsslein-Volhard. C. (1996). A few crucial molecular signals give rise to chemical gradients that organize the developing embryo Scientific American Piaget, J. (1954). The construction of reality in the child. New York: Ballantine. Rochat, P., & Morgan, R. (1995). Spatial determinants in the perception of self- produced leg movements by 3- to 5-month-old infants. Developmental Psychology, 31, 626–636. Rochat, P. (1995). Early objectification of the self. In P. Rochat (Ed.), The self in infancy: Theory and research (pp. 53–71). Amsterdam: North Holland/Elsevier Science. Robart, M. K. (1989). Temperament and development. In G. A. Kohnstamm, J. E. Bates, and M. K. Robart (Eds.) Temperament in childhood. New York, John Wiley, and Sons, 182-247. Scarry, R. (1963). Best Word Book Ever Giant Goldbooks Schmuckler, M. A. (1995). Self-knowledge of body position: Integration of perceptual and action system information. In P. Rochat (Ed.), The self in infancy: Theory and research Amsterdam: Elsevier Science Publisher, 221–241). 176 | P a g e 177 Prepublication Copy Stevenson, J., M J Thompson, M. J., & Sonuga-Barke, E. (1996). Mental health of preschool children and their mothers in a mixed urban/rural population. III. Latent variable models. The British Journal of Psychiatry, 168 (1) 26-32; DOI: 10.1192/bjp.168.1.26 Van der Meer, A. L. H., Van der Weel, F. R. & Lee, D. N. (1995). The Functional Significance of Arm Movements in Neonates. Science, 267, 693-695. 9. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749-50. Wynn K. (1), Bloom, P., & Chiang WC. (2002) Enumeration of collective entities by 5-monthold infants. Cognition, 83(3), B55-62. Yonas, Albert; Pettersen, Linda; Lockman, Jeffrey J. Young (1979) Infants' sensitivity to optical information for collision. Canadienne de Psychologie, 33(4), 268-276. Younger, B. A. (1985). The segregation of items into categories by ten-month-old infants, Child Development, 57, 1574-1583. Further reading Fox, Nathan A.; & Davidson, Richard J. (1988). Patterns of brain electrical activity during facial signs of emotion in 10-month-old infants. Developmental Psychology, 24(2), 230-236. Research: Hotz, R. L, (1996). Deciphering the Miracles of the Mind: Los Angeles Times, Los Angeles, CA. 177 | P a g e 178 Prepublication Copy Chapter 12 Infancy and Early Childhood: 24 months to 7.9 years Introduction Information in this chapter, as well as part of the previous chapter, is based on theory as well as formal and informal observations. We have not measured children at ages 2, 3, and 4 years old with formal research studies. Most of our studies in this book came either from children in schools (ages 5-17) and/or people in a work situation (18-70). The 70-month period from neonate to middle childhood is extremely important for the development of problem-solving skills. This is the basic stage of development. Compensations and modifications begin to occur when youngsters do not live up to the expectations of parents or when comparisons between other children are made. Later, this compensation leads to differences in how each person solves problems. Filters are amplified as layers are developed. Layers inhibit problem-solving as layers siphon energy to deal with emotionally laden feelings thus slowing the problem-solving process. Fewer layers increase problem-solving skills and focus. During this period, the child develops more memory and thinking skills. Prior to 24 months, sensory-motor development is centered on crawling, walking, and finally running. Gross motor control is evident. As time progresses, the ability to utilize associations and abstractions changes everything. Children start to solve everyday concrete problems—how to get what they want! Notice the emphasis on concrete problems or problems involving touch, feeling, or realistic objects because what the child perceives is the child’s reality. Concrete problems manifest themselves around real objects in the environment-chairs, beds, trees, clothes, and real feelings such as anger, joy, and embarrassment. Brain and energy The brain undergoes tremendous growth between the ages of 24 months and 7. During this period, the brain increases from 70 to 90 percent of its adult weight. Neuron development is prolific as the brain reshapes and refines. Synaptic growth and myelination of neural fibers require a lot of energy. There is an overproduction of neurons in the cortex. A large number of neurons support brain plasticity, a process that ensures that regions of the brain remain active even in face of adversity. Overproduction of neurons leads to synaptic pruning; some neurons die. 178 | P a g e 179 Prepublication Copy Fibers linking the cerebral cortex to the cerebellum are complete at about age 4. This contributes to dramatic gains in motor control. The frontal lobes experience rapid growth from 3 through 6 years of age. Energy as an activity level It is not always possible to determine the exact amount of energy used during an activity level. Therefore, a rough measure of energy and activity was developed. The measure was based on the assumption that the more time spent doing an activity, the more energy expended Activity level, in our system, measures active (playing sports) vs. passive activities (watching TV). Many activities from the age of two are controlled by parents and only some by the child. This is especially true of selected activities such as music, dance, art, and sports. In our model, activity requires energy. For example, the more time spent playing a musical instrument, the more energy is used. This includes time spent practicing and interacting. Diagram 3: The Cognitive Model (Infancy) Cognitive Model: Infancy and Early Childhood In the last chapter, the cognitive model for the newborn was shown in Diagram 2. Compare that model with the model for infancy and early childhood illustrated above in Diagram 3. The cognitive model for toddlers and older children differs from the neonate by three 179 | P a g e 180 Prepublication Copy factors: working memory, analysis, and logical thinking. The addition of these 3 processes does not necessarily mean that children will use any higher-order thinking processes, but some cognitively advanced children show evidence of both. Evaluation probably occurs but depends on the child. Depth of processing is missing. Synthesis in the form of imagination and play could be listed but how and where is the issue. Working memory is often measured by digit span. Digit span or the ability to remember a specific number of digits increases from 2 years of age. At 2, the average number of digits remembered is about 2.5 while at 7, the average number is 5 (Dempster, 1992). Problem Solving Categories (Ages 24 months-7 years) Based on our formal observation of children, some measurement distinctions are evident according to the amount of time spent on different kinds of tasks. For instance, a very young child spends different amounts of time, perhaps a minute or even up to more than 10 minutes handling different kinds of toys. The time that a child spends with 1) concrete objects (toys, objects in the room, etc.), 2) academic activities such as reading or learning, 3) methods of play (social, with others versus individual play) 4) daydreaming and 5) watching TV or other passive activities is very significant. Very few of the children that were studied participated in just one or two activities. Most children's actions were dependent initially upon parents’ or caregivers’ initiative, with fewer being engaged in reading. Problem-solving categories are lumped rather than split at this age as cerebral differentiation is still occurring. That is, the child might be classified as social (S) but not have any other letters (Analytic or Control) to denote a more specific problem-solving orientation. Children (over 5) responded to preferences on a written instrument (putting strikes in letters or circling figures) or were observed by a trained observer (graduate student) who recorded behaviors at home or school. In addition to our instruments, standardized test data, where and when available, was used to indicate strengths in verbal, numerical, and spatial problem-solving. The data from the children help identify the descriptive tendencies for most categories, with many children having one dominant orientation as opposed to mixing styles with several areas of strength. Thus, the Category Framework given earlier in Chapter 2 helped identified developmental differences. Next, we present general descriptions for some of the ten problem-solving categories. Again, can all individual children be identified at this young age? No! But the characteristics can! With teachers, observation is key. We observe, hypothesize, identify and study. 180 | P a g e 181 Prepublication Copy Descriptive Problem-Solving Categories General problem solvers The general problem solver often is driven by individual initiative, social reward, and the desire not to fail. These attributes are acquired very early from 2 to 5 years of age. Teachers and parents reward children who take initiative and complete tasks responsibly. Likewise, children respond with an initiative to obtain social rewards from parents, caregivers, significant others, and teachers. The general problem solver, again is not the brightest child in the class but instead works responsibly to complete tasks on time, shows motivation to do more than the average, and is willing to spend the time necessary to undertake more complex problems in all classes. What matters most is how the child responds not only to success but to failure in handling tasks well. Children often learn attitudes and behaviors in pre-school education which is based on games, having fun, and enjoying the learning process. Later the child enters kindergarten, first and second grade. The average classroom has reading, writing, and arithmetic so problem-solving tasks are more often academic than not. Occasionally, projects in the classroom are less focused on academic skills and utilize general problem-solving behaviors. Children have little homework but are still required to complete some simple class projects by second grade. Some children who are general problem solvers also excel in outside class activities, including music, sports, and other motor activities. In terms of our theoretical model, a lot of children at this young age, are learning through the use of memory and recognition. The input mechanisms are directions on worksheets, verbal directions from the teacher as well as stimulus activities from computers, other children, and drawings. The work of the children generally favors convergent thinking or a single correct answer. Many times, verbalization with repetition rather than reading is emphasized in test situations because the non-readers would be at a disadvantage. Most second-grade teachers do not expect a lot of comprehension and interpretation from children in the age group of 5-7 years old. Instead, their emphasis is on skill building which has memory as its basis. Since memory is necessary for most problem-solving episodes, this is understandable. In many cases, general problem solvers have prior exposure to academic problems through pre-school and/or print-rich environments at home. As a group, general problem solvers have better memories and faster reaction times in solving academic problems. 181 | P a g e 182 Prepublication Copy Differential problem solvers The majority of children are differential problem solvers. Remember that differential problem solvers can have the highest, average, or lowest grades in the class; it just depends. These children pick and choose what is important to them. They can have multiple or fewer strengths, depending on their motivation, and the kind of problems they choose to solve. Differential problem solvers have many interests which may include or exclude any particular school subject. Some like math but hate reading as they become embarrassed easily while attempting to read aloud. Others may have motor skills but lack social skills. Everything is dependent upon how each child chooses to apply their strengths and their energy. Differential problem solvers can have analytic skills but apply these skills only to their areas of interest. The category is designated as differential as one never knows what to expect. One day, the child is task-oriented but another day, the same child could demonstrate a lack of interest in anything. More often than not, a differential problem solver is still coping with individual emotions that drive them into fantasy, offtask behaviors, and occasional outbursts. Children in the differential category may be average or better learners with developed skills exhibited in certain areas such as art, music, athletics, or manual activity. The ability potential of the child may be normal, better than normal, or less than normal. In reality, the ability does not play very much of a part in problem-solving behavior at the kindergarten level since emotional needs are primary and often the child has not found a way of handling emotional situations. This differs for many first and second-graders as some are better at handling emotional and non-emotional situations. In contrast, a child that is too self-contained, too tightly controlled, and too proper can be just as worrisome as such behavior is less expected. Differential problem solvers may or may not be behind their peers in developmental behaviors. Differential problem solvers are not at the same developmental stage. Each child is different, depending on home life, interests, wants, needs, and well-being. In many areas, this group is average or excellent, below average or superior. Differences are great as early development has been unevenly resulting from a lack of exposure to any formal number, word, or spatial exercises. This unevenness in development results in less stability in academic work. Outside of academic work, especially in motor or skill areas, the child may shine. One example often cited is the ability to memorize tremendous facts in an area of interest. This is, think of the child who can name all the baseball players on different teams, their batting averages, and their position of play. Or the young lady who can name all the current pop stars on television. Neither child prefers to remember which explorer discovered the Pacific Ocean. 182 | P a g e 183 Prepublication Copy On the other hand, a differential problem solver could exhibit deficits relating to emotional regulation and/or early differences in cognitive activities. Such a child could have a problem following simple directions, sitting for any period of time in a chair, completing assigned tasks, and can be a problem child (i.e., exhibit attention deficit). Or then again perhaps the child is quiet, shy, attentive, and unassuming, but still exhibits limited previous experience or the language prerequisites to apply to conventional school problems. The teacher is aware that he or she must address the emotional needs of each child; while attempting to provide, problem-solving activities for the majority of students. Limited prerequisite skills contribute to affective and emotional responses. Those children with limited emotional control and skill differ from other children who may approach regular school work with a rigorous orientation toward academic work. Limited prerequisite skills may lead to deficits in certain areas, such as math or reading. This is not because of ability, but a lack of emotional regulation. Completion of work is a problem since the child reacts emotionally to inner impulses and has difficulty following conventional activity requirements. The problems of emotional control in the problem-solving areas of the child were probably evident before the age of two or before. Caregivers, either parents or parent substitutes, had not instituted practices that help the child develop internal control behaviors. Internal control behaviors include controlling impulses which normally are associated with instant gratification--eating, hitting others and getting one’s way every time. Whether the child becomes a successful problem solver and at what level is completely dependent upon the amount of individual exposure. Underachieving differential problem solvers Common examples of differential problem solvers who are underachieving include a) behaviors such as not being able to match colors, b) slow processing of information from parents, c) not having hand-eye coordination, and d) being slower in general activity levels. Parents notice the child fails to carry out intended actions. If given a task such as "pick up a shirt, or get a toy", the child may not complete the task. Likewise, tasks that the child initiates, are not completed. The child does not complete a drawing started earlier or leaves many tasks incomplete or partially done. The child exhibits confusion, lack of motivation, or lack of energy when completing simple tasks. The school system usually identifies developmentally delayed children for parents if they have not been identified earlier. The child may have supplementary or individualized instruction from resource teachers such as special education. The impairments can be 183 | P a g e 184 Prepublication Copy either language or physical impairments of sight, hearing, or motor disabilities. If the child is not formally identified as special education, then the teacher may notice a lack of motivation or inclination to solve problems posed at school. For the developmentally delayed, some elementary teachers either think of problemsolving as a task involving math or general living skills. A generalized living skill is the capability to comprehend simple group social action, or even to get to the bathroom and back. Their goal is to help children gain basic living skills to succeed in everyday life. In many instances, teachers are forced to teach to the middle of the class especially if they have 30 or 35 first graders. Children who already have pre-exposure to academic skills are reinforced and rewarded while those who have little or no pre-exposure are just beginning their developmental stage in problem-solving. Capability has some effect on learning outcomes but previous exposure and experience have more. Children with parents who are teachers of fundamental skills from birth to 5 have more exposure and experience. Very few teachers are going to neglect a child who needs help. However, these children may receive less attention as teaching, even in the first-grade places more emphasis on group activity, rather than individual activity. Thus, instructional worksheets, reading, learning stations, and other activities may be provided to the group as a whole group or as small group instruction. Teachers have learning stations where more individual attention is given to students while other students are engaged in small group learning tasks. By second grade, the developmental differences cumulatively generated from birth to five begin to have deleterious effects on general motivation, and "time on task" and start to filter into personal characteristics, especially if the parents and child do not value a problem-solving approach. The child approaches most tasks in school based on memory as teachers reward memorized material as it indicates effort or goal orientation. Problems are viewed as discrete, simple tasks that have a very tangible outcome. For example, write a simple sentence or paragraph; complete drawings and tasks handed out in groups, and do simple tasks for the class. In some classrooms, students complete the mental operations associated with addition, subtraction, simple division, and similar mathematical tasks. Some projects are assigned but the children who do not complete them are those children who were behind a half or full grade at the end of first grade. Often children who start kindergarten and first grade behind, have difficulty making up the developmental difference. 184 | P a g e 185 Prepublication Copy Perception (24-72 months) Attention, as indicated earlier, is the first step in perceiving. Focused attention comes from the sustained information received through the senses. Selective or focused attention increases with age. The reticular activating system, which activates arousal, is not mature until adolescence so maturation probably accounts for a lack of focus. Focused attention has been measured by Ruff and Lawson (1990). Using six different toys, they found a linear increase in the amount of attention directed toward individual toys. On average, a 1-year-old focused for 3.33 seconds. A two-year-old focused for 5.36; while a three-and-ahalf-year-old focused for 8.17 seconds. There is a world of difference between the 2, 4, 5, and the 7-year-old. Ask any child development specialist! After age 2, problems of perception usually begin with problems of attention. If a child cannot spend enough time attending to a stimulus, visual perception develops haphazardly. Hyperactive and very slow processing children have difficulty in selective attention. Children with average skills of selective attention spend differential amounts of time when scanning visual symbols in our tests. For the most part, this consists of figural symbols, letters, and symbols associated with mental operations such as simple numbers and words. Children by age 3 or 4 can pick out the features of numbers and letters which are not variable, such as those which are horizontal or vertical. They have trouble with diagonal lines (w's) or mirror images such as ‘b’ or ‘d’. Children at this very young age can usually perceive curve lines and distinguish them from straight lines (Gibson, 1970). A child at five or more is usually adept at scanning a visual field to find a number or a letter. Children whose parents have exposed them to more experiences involving letters and numbers through preschool education or home learning come prepared to master the necessary skills of kindergarten and first grade. Only at or around age 5 do most children tend to read more than 3 letter words. Before that time, children recognize, imitate, and comprehend 1 to 3-letter words (cat, dog, etc.), except when adults have established precursor behaviors for reading. Exposure to picture books and a repeated instance of problem-solving facilitate the reading of short words by 3.5 years. Perceptual development is dependent upon exposure to perceptual activities. Although some genetic predisposition is apparent, experience from activities in the environment sharpens the application of skills later defined as perceptual problem-solving. Children who like to read, play, draw, and paint, work on computers have pre-exposure experiences for problem-solving. 185 | P a g e 186 Prepublication Copy Part-whole relationships Do preschoolers see the whole or the part? For the neonate, this was not a question as vision and perception changed from birth to 24 months. Neonates see the whole not the part. In the first six months, vision is fuzzy; perceptual acuity increases from birth to 24 months. From age 2-5 some types of difficulty in discriminating perceptual objects were noted above. Development moves from gross motor to fine motor for preschoolers. Again, the answer to part-whole relationships differs from individual experiences. In the next section on perceptual speed, the data from 299 children who are 5-7 years old is presented. Less than 5 percent of five-year-olds could add and subtract 3 numbers in a sequence, or find parts embedded in a whole. These exercises were timed. Smith (1989) noted that preschoolers are influenced by the whole and have difficulty picking out the parts. He concluded that the answer to part/whole relationships was dependent upon the complexity and distinctness of the whole and the part. Our data support that conclusion. Children at the age of five have difficulty picking out the parts and doing simple 3-number addition and subtraction, especially in a distracting field. Perceptual speed Perceptual Speed may or may not be important in problem-solving depending on the type and complexity of the problem and situation. If one is processing signals associated with a missile attack, then the speed of processing is important (DeNovellis, 1984) while if one is a scientist who is solving a complex problem related to the energy development in the physical universe, speed may not be as important. Throughout these chapters several trends from our research involving perceptual speed become apparent. First, slow processing speeds of children result in lower test scores when the test or problem-solving activity is timed. Fast processing speeds of children do not always result in higher scores in untimed problem-solving situations but usually do result in higher scores when problem-solving is timed. Perceptual speed interacts with the ability to mentally transform symbols and letters as well as memory. A child---who has a faster processing speed, better short and long-term memory, and the ability to mentally manipulate letters and symbols--- usually learns faster and scores higher on reading and math standardized tests. A typical classroom in California is filled with children with many different backgrounds, speaking many different languages. When perceptual speed and problem-solving are measured, all unique differences must be taken into account. The list is overwhelming as each is important and affects the outcome of solving various kinds of problems. 186 | P a g e 187 Prepublication Copy Demographic factors include gender (G), age (A), socioeconomic background (SES), English as a second language (LED), special resource children (SED), and gifted and/or talented. In our research, SES was categorized by differences in the amount of money that parents earn. Since our database extends from 1977, figures regarding socioeconomic status have changed over the years. In the early years, those who earned less than 25000 were classified as lower SES, middle SES was between 25001 and 42000. Higher SES is above 42,000. That dollar amount changes over the years because of inflation. Ethnicity, for us, usually had five categories (Caucasian, Asian, Hispanic, African American, and Middle Eastern) which were often collapsed when the numbers in an ethnic group were small. Any child receiving extra help from a resource teacher was classified as special education development (SED). Another factor that influences the outcome of problem-solving was exposure through preschool activities so teachers and caregivers were interviewed to assess the amount of time a child spent in preschool activities. The perceptual tests involved scanning a field of curved and straight lines from an exemplar (which measures cognitive flexibility) or picking out a specific letter such as an ‘x’ or ‘e’ from a crowded field of many lines of random letters (measures the discrimination of parts). Likewise, another perceptual test requires the individual to circle an embedded figure in a group of embedded designs (measures dis-embedding of the part from the whole) or perform a simple arithmetic operation such as adding (1 + 5 -2) in a distracted field. The latter perceptual test has a lot of distractions that an individual might address rather than proceeding with simple arithmetic. A 2-minute memory test was used to judge the ability of young children to hold letters and symbols in short-term memory. To measure children in the age range from 5 to 7, teachers who were graduate students at Cal Poly administered simple tests in their classrooms. The results which follow are a summary of some of these findings. Considering the ages of children from 5 to 7 (See Appendix for other sample characteristics), older children scored higher on these short tests which emphasize time limits on perceptual accuracy and memory (Table 1). The difference in scores is probably due both to attentional difficulties as well as differences in speed of processing which is influenced by neural development. Younger children are more easily distracted than older children, especially when some of the material presented is irrelevant (Lane and Pearson, 1992, B-266). There were often trends related to SES. Children whose parents made more money usually scored higher on perceptual speed. The ethnicity of these children in our samples was primarily Caucasian and Hispanic. No differences related to ethnicity were found at this early age of 5 and 6. Children who were exposed to preschool had higher scores on arithmetic processing. However, differences in ethnicity were often found as children 187 | P a g e 188 Prepublication Copy aged. The average scores of children often were higher for Asians, Caucasians, Middle Eastern, Hispanics, and African Americans in that order--sometimes significant, sometimes not, depending upon the sample. Changes in the order were often the result of SES. As socioeconomic status increased, the order of averages for ethnicity was closer to random. When considering special characteristics such as language and the use of resource teachers, English as the second language scored higher than special education. Regular students scored the highest on our speed tests (gifted students were not separated at 5-7 years of age). When gifted students were included in the sample, they usually scored higher. There were some differences between boys and girls. In a small sample of five-year-olds (boys scored higher than girls on perceptual speed). These gender differences were not evident in the six and seven-year-old groups. In the sample listed below boys did better on the 2 simple tests of perceptual speed, i.e.; the Perceptual Flexibility Tests as well as the letter identification tests. The test scores of the girls approach the level of significance on the more complex perceptual test of finding designs embedded in a group of designs. All children were 5-7 years of age (DeNovellis, R. L. & Dehler, C., 2002). Two asterisks (** or P=.05) suggest that an event is likely to occur 5 times out of 100 while one asterisk (* or P= .01) suggests that an event is likely to occur 1 time out of 100. Table 1 Perceptual Tests Means Standard Dev Significance N Boys –Perceptual Flexibility 2.88 1.05 .05** 279 Girls --Perceptual Flexibility 1.28 1.38 Boys--Letter Identification 9.44 4.9 Girls--Letter Identification 6.14 3.85 279 Boys--Embedded Designs 1.33 1.00 279 Girls--Embedded Designs 2.85 1.95 Boys--Arithmetic Operations .22 .66 279 Girls--Arithmetic Operations .06 .04 279 279 .05** .06 279 279 **P=.05 Perceptual Speed Tests (Age 5) Examining the progression in the speed of processing from age five to seven is one method of understanding the interaction of biological systems. If development is normal, then one would expect a gradual increase in speed as the nervous system continues its development. Likewise, some restrictions might be apparent in those whose biological 188 | P a g e 189 Prepublication Copy and psychological systems are not being stimulated normally or are restricted genetically or environmentally. Children identified as special education students fit the latter category. One expects some differences between the speed of processing by special education students and regular students. This is indeed the case. In Table 2, there are differences between both groups in both speeds of processing (PF) and arithmetic operations, an achievement factor. However, in Table 2, the differences are not significant. For us, the relatively small difference in perceptual speed differences between special education and regular students is important. Table 2 Ages Grp PF Letident Emb. Des Arith 5 Sp. Ed 1.5 /2.3* 06.7 / 4.3 .2 / 3.3 .0 / .0 Reg. 2.0 /1.2 07.8 / 4.9 1.5 / 4.2 .8 / 1.7 Sp. Ed. 2.4 /1.8 09.5 /5.5 2.3 / 4.8 .3 /1.5 Reg. 3.5 /1.6 10.6 / 6.0 7.8 / 5.6 2.0 /2.0 Sp. Ed. 3.4 /1.4 10.9 / 5.5 5.2 / 4.9 1.7 / 1.5 Reg. 4.2 / 2.3 13.7 /6.5 7.9 / 6.0 3.7 /4.6 6 7 *Mean/Std. Dev. Means and Standard Deviations of Perceptual Test Data (Ages 5-7) N>200 The differences in Table 2 (which includes special education children) reflect developmental age differences and processing differences. Processing differences in special education students are a product of many things but indicate arrestment (slower response time). As expected, the central and autonomic nervous systems are more advanced in older children (linear increase in means). Some children experience developmental delays and their neurological processing systems indicate these differences by a time differential. A year (sometimes 1-3 months) of developmental delays is very apparent. Since the sample size for the data above is greater than 200; the means and standard deviation are fairly stable, i.e., less fluctuation due to sample size. Addressing the data from one classroom as representative of the trend in perceptual problem solving, the following patterns from correlational data using standardized test data. The data are from a classroom of 28 six and seven-year-old children with 15 males and 13 females. The group scores around the 58th national percentile rank for math and reading. There were nine six-year-olds and nineteen seven-year-olds. The correlations are shown below in Table 3: 189 | P a g e 190 Prepublication Copy Table 3: xx Means SD Per flex 3.5 1.8 Letid 14.89 4.34 0.37* Embed 2 2 0.21 0.22 Arith 3.43 2.7 0.38* 0.19 -0.23 Memlet 4.5 3.63 0.23 0.35 -0.19 0.28 Memsymbols 3.29 2.8 0.03 0.1 0.2 -0.1 -0.54 TotR 76.04 19.39 0.3 -0.17 -0.07 0.43* 0.15 -0.16 TotM 49.07 10.95 0.43 0.07 -0.01 0.55** 0.23 -0.08 N=28 Ages= 6-7 P **.05=.37 Perflex Letid P*=.01=.479 Two tailed Embed Arith Memlet Memfig TotR 0.79 TotR=reading standardized; TotM=math standardized Correlation of Perceptual Speed and Memory tests with Math and Reading Standardized Tests Table 3 lists the mean, standard deviation, as well as the correlation of the perceptual speed tests, memory tests, and standardized tests for six and seven-year-old children. Significance using the two-tailed test at a .05 level for N=28 is .37. The eight tests are perceptual flexibility (Per flex), letter identification (Letid), embedded designs (Embed), arithmetic distraction (Arith), memory test for letters (Memlet), memory tests for symbols (Memsymbols), Total reading (TotR) and total score on math (Totmath). Math and reading are correlated at .79 which is not a surprise as both are reliable and valid standardized tests and almost all research suggests math and reading are highly related. The next highest correlation is the perceptual speed test with arithmetic distraction (.55). Again, not a surprise as the same relationship is found for almost all standardized tests with older children also. Perceptual flexibility is related to the total math score but is more highly correlated with computational procedures (.53 not shown here). “Computational procedures” is a subtest of total reading. Letter identification is negatively related to total reading. This test is related to clerical accuracy in older adults and represents a convergent activity. What is obvious from both Tables in the samples above is that most children at age 5 do not find Embedded Designs. The average number of embedded designs for non-special education children found is 1.5 at age 5 (total possible designs = 22) in a time limit of two minutes. However, at ages 6 and 7 Table 2, children do find more embedded designs (7.85 mean/5.8 standard deviations), and the children who find embedded designs also do well on tests using letters and numbers. In contrast, the line drawing (symbols) is negatively related to memory for letters (-.54). At least, in this sample, children remember 190 | P a g e 191 Prepublication Copy letters better since they have more exposure. The average mean for 5-7-year-old children on the embedded designs test is only 2. Also important is the fact that children who come from homes with greater income do much better on the letter, number, and spatial problems. Later, the data suggest that embedded designs (perceptual spatial data) change as children mature. Conception At this age, conceptual problem solving differs, but is integrated with and develops concurrently with memory and motor problem solving because of the interaction with developing biological systems. Conceptual infers generating ideas and concepts. Conceptual problem solving involves generating ideas to apply to a problem-solving activity. Being able to apply a concept to a situation speeds up the problem-solving process. Children generate concepts by being exposed to experiences required by many different kinds of mental and physical activities. Children who are exposed to motor activities, such as sports, dancing, and gymnastics, stimulate the neurological and physical motor system which increases control and brain development. Likewise, memory is especially important as a lack of it is called a production deficiency (Flavell, 1963). Ratner’s (1984) study showed a positive relationship between 3-year-old memory performance and the mother’s questions about past events. At the heart of conceptual development for this age group is the “separation of self”; i.e. the capacity to realize that events are outside of oneself. In Piagetian terms, this is the movement in the child’s thinking from an egocentric state to a realization that other people’s feelings and ideas are important. In the egocentric stage, everything revolves around the child’s thoughts, actions, and ideas. As separation occurs, children use phrases such as “I don’t like carrots but daddy likes carrots.” This separation is seen also in the affective systems of social behavior like learner perception and self-concept. Concept development is enhanced by make-believe play and fantasy. Children engage in role-playing and idea generation during play. During imaginative play, children assume the identity of fantasy heroes, sports persons, or TV characters (Harris & Leevers, 2000). Conceptual development is limited by growth and maturation in three and four-yearolds. In their minds, all events must be observed to be known. They do not infer. For example, at ages 3 and 4, youngsters believe that mental activity ceases when a person stops talking. According to Favell (1963), in general, children are also less aware of their thinking processes. 191 | P a g e 192 Prepublication Copy Concept development is enhanced by spoken language. Change in conceptual thinking occurs when the child begins to read and attends school. Schooling and teachers help the child create reality components for many of the concepts learned in preschool and by picture books. Later when discussing pattern processors vs. object processors, the reference is to a conceptually driven child vs. a motor-driven child. Motor Those children who spend the maximum time inside and outside of the house in physical play continue to be Motor dominant. These children are active at most times, using their hands, legs, feet, and mind to encounter their environment. Even interactions with other children show physical dominance. Motor-oriented children spend a lot of their time just doing things in their area of interest. A large number of children, both boys, and girls are motor dominant. The motordominant child learns by physical interaction and activity since so much of their early activity is involved in this manner. The child develops internal discipline by regulating their physical actions to obtain success in their goals. Think of the children who learn dance, ballet, athletics, and play music as motor-controlled actions. The mental actions and sensory-motor reflexes are combined to obtain short-term and long-term goals. Motor dominance and physical play may produce personality traits that can result in leadership qualities, vocational excellence, and academic scholarship. Initially, some Motor dominant children may struggle in the educational system since schools are developmentally in lockstep from K-3. Everything depends on the circumstance. Observe the child who goes from task to task, toy to toy, activity to activity, without any guidance. Free play is often the name given to this kind of activity. Children, who have had little external structure imposed or internal structure developed, display difficulty with tasks requiring long attention spans. For motor-dominant children, they can become extremely good problem solvers. Their mastery depends on the development sequence of internal and external control as well as their motivation to apply print materials to their area of interest. Teachers are conscientious and feel a responsibility to have children learn what the curriculum dictates by the end of the first (5-6 years) or second grade (6-7 years). Some motor-dominant children lack the structure, attention span, and routine to learn basic skills. Even though teachers emphasize the "whole child" and put as much time into 192 | P a g e 193 Prepublication Copy teaching values, habits, routines, attitudes, and behaviors, some motor-dominant children require more time for academic problem-solving. Analysis In the previous age group of neonates, there was an emphasis on discrimination, sorting by perceptual similarities, and some simple deciphering of properties by similarity. In this 2-7 age group, new tendencies appear. A common cognitive analytic property found in two or three years old is called seriation. This is a process of putting objects in serial order, such as 1, 2, 3, or from biggest to smallest. The capability to perform more complex seriation occurs with maturation from 4-7. Compared to the neonate, the ability of 2-year-olds to discriminate between comparative lengths has increased substantially. A greater number of children can tell that A is greater than B when a series of sticks are used. Previously the neonate could make discriminations when differences were very large; now, infants, toddlers, and those older can distinguish differences that require finer discrimination. Analytic tendencies, or the capability of breaking things into parts or rotating objects spatially, are often incomplete in many children in this age group (ages 2-7). Children use concrete analysis, such as figuring out the steps of how to get to the desired object such as a doll. Abstract analysis varies with different kinds of early exposures. When a story is analyzed in kindergarten, only some children cannot identify some main characters, the main storyline, and the general meaning of a simple story. These tasks are possible for many 6 and 7-year-old. Notice that analytic tendencies are different from logical tendencies. Logical as used in IPS is to denote operations that can be verified by others. A logical arithmetic operation is 2 + 2 if the child can show or demonstrate how or "why" 2 + 2 is four. A memory response is four. A logical response could involve putting 2 marbles down on the ground, adding two marbles to those marbles which are already there, and having the child give a response of 4 because all the marbles are grouped in a circle where they can be counted. In our definition of logical, the child must understand why 2 + 2 is four (verifiable by having a 2-marble set added to a 2-marble set) and be able to explain or give an answer verifiable by others, even if the response is made after counting each object to obtain 4. A logical verbal response for this age group is that sugar could be added to cereal to make it taste sweeter "not to make it taste better." In contrast to Piaget’s theory, there is some evidence of formal reasoning in children as early as 4 years old (Bryant and Trabassco, 1970). 193 | P a g e 194 Prepublication Copy As noted in the model, at the age of 6 and 7, responses that approximate logic are more realistic than actual logical responses. Logical approximations to the verbal response about sugar would be: adding something, such as favoring, to make it taste better. Social Social behaviors are very evident in children in this age group. Emotions and socialness are generated from within and externally. In children during early childhood, the term “socio-emotional” is often used as emotions are intertwined with social cognition. In the neonate, the development of all kinds of emotions, -crying, fear, happiness, anger, and sadness occurs from birth. The neonate was a morass of emotions trying to understand all the environmental cues from faces, and feelings. The neonate’s feelings were all over the place--up, down, and sideways. Unbridled anger from not getting the desired object was common. Friendships were just beginning. Smiles were often. Now with the development of cognition, language, and memory, there is more understanding, more separation from self, and better recognition of the needs of others. Socialness is more common as peer relationships increase and interactions with others occur. The child from 2-7 develops a host of behaviors related to self-concept, self-esteem, and self-understanding. As rules and control structures are continued and elaborated by parents, the child continues to develop a conscience. Violation of the rules set out by a caregiver leads to emotions of guilt. Increased emotional self-regulation is related to social recognition and social-referencing. Complex emotional behavior–jealousy, shame, guilt, envy-are the product of increased cognition and recognition of behaviors involving others. Attachment is the common bond between caregiver and infant. Attachment results from dependency engendered by constant interactions for important caretaking functions such as feeding, warmth, sleeping, and security. Some theories give credence to non-verbal and verbal signals, engendered over time and transferred between the caregiver and infant. Control and structure Control, as used here for this age group, is a broad construct, typified by exhibiting control over knowledge, emotions, and feelings so that problems can be encountered and solved. It is also the ability to structure external events. Earlier, the distinction was between 194 | P a g e 195 Prepublication Copy behavioral control and structuring as well as mental control and self-regulation. Each is intertwined with the functions of cognition and emoting. Behavioral control is subdued by the actions of adults as they institute a control system that children must follow. In psychological terms, actions and dictums from the adult are in the form of doing and don’t, threats, and consequences. Behavioral controls are instituted by adults through the process of structuring events around the child. In psychoanalytic terms, these dictums about moral behavior, do’s and don’ts become the conscience of the child. Again, for most children, the constant repetitive structuring, as well as the rewards and consequences, increase the external control system During this period of development, children are continuing to develop internal or external "locus of control." Internal locus of control is important as the child feels that he or she has control of their environment. Active cognition applied to the environment in the successful resolution of problems results in an internal locus of control. This is as opposed to an external locus of control where a child is constantly being driven or reacting to the emotions of external events placed on them. Self-regulation results from mental control. The child actively controls his or her behavior and thought processes to the degree that each is a conscious thought as opposed to subconscious thought. Self-regulation is important in this age group as behavioral control is integrated with general cognitive control. The self-perceptions of the child are facilitators or inhibitors of problem-solving, especially around ages 5-7. Flex Flex is a measure of the strength of preference for the activity level of make-believe, impulse generation, role-playing, and allowed idea generation during the years 2 -7. In short, flex is also related to controlling as too much control and structure inhibit flex. In the literature, the construct is cognitive flexibility. The basis of cognitive flexibility is increased or decreased through long and short-term memory, analytic behavior, associations, and conceptual development. Because cognitive flexibility is filtered by memory and associations, emotion and cognition are mixed which is why emotional impulse generation is part of idea generation. It is also why it is so difficult to measure and such an elusive concept. To better understand it, think of watching a movie scene and having the feelings of a warm sensation sweep across your neck. At the same time, the feelings stir ideas associated with an event in your childhood or with your parents. All of these cognitive processes influence the control or lack of it in multi-tasking and multiple idea generations. Sociodramatic play affects conceptual development and mental representation. From 5 through 7, children display minimal awareness that make195 | P a g e 196 Prepublication Copy believe is a cognitive activity separate from reality. During this same period, there is the beginning of ego-separation from a child’s centric viewpoint. Children are exposed to many ideas, some important to them, some not. Their flexibility of thinking is related to how often they use their ideas and are rewarded for their use. A child who sees, hears, and touches many new things increases memory representation. Such a process requires time and the use of different ideas that utilize a lot of energy. Constant energy utilization results in more flex. When flex is too great, it may be the result of random and uncontrolled thinking, a response to inner impulses and emotions. For example, a child who is constantly talking and generating ideas from within, unable to control his or her thought processes would score higher on the construct of flex. At the same time, a very bright child who is constantly generating ideas with control and analytic thought can also score high on flex (See example data in later chapters). Likewise, a truly emotional impulse when grounded in a faulty conceptual notion and not mediated by either analysis or structure can result in harm or injury to others. There is a difference in the constructs of control and flex as they share both similar and different neural pathways. The control of behavior is for controlling impulses and implies the use of thinking or cognition to help in control. Flex is the allowed utilization of ideational generation (cognitive) and the free flow of impulses (emotional) combined. At this age, the differences are so integrated that the distinctions are few. Differences become apparent later in the classroom as is evident in our data for adolescents. Flex, as a semi-cognitive component, is also related to algorithms and problem-solving procedures as both of these methods involve flexible thinking. For example, in children in the second grade, the correlation between our perceptual test for perceptual flexibility and standardized test on problem-solving procedures is .54. One can ask. Why do the two variables correlate so highly for this age group if not related to a common antecedent? In the first grade, a typical example of flex problem solving is illustrated by the following scenario: Bobby the cat was joined by two birds and then by 3 dogs. How many animals are in the group and how do you know? One verbal response by a first grader: “I draw pictures of all the animals and counted them.” Another better and more complex response was, “I added the two birds to bobby and got 3 animals and then added the 3 dogs and counted six animals. 196 | P a g e 197 Prepublication Copy Differences in Types of Problems Solved Word problem solving Many conceptual academic problems are based on learning facts that require memory. The learning of numbers, and letters, as well as other basic learning skills, such as listening and following directions, can be introduced by age 3. By age four or five the children, who were introduced to academic learning early, have read stories or seen many different learning programs on TV. Other children have sporadic or little exposure to verbal or numerical skills. They may spend time in daycare or have only minimal guidance during their daily activities while their parents are working. Exposure to academic reading, without the pressure to succeed at an early age (3-5), is crucial since a child exposed to reading differs considerably in later skill development from a child who is not exposed to reading. For children in the age group from 2 to 7, very early development in solving word problems is based on mastery of letter identification. In almost all of our samples, letter identification is highly correlated with memory for letters. Both letter identification and memory for letters are significantly correlated with scores on the running record, a system used by teachers to keep track of students’ ability to read. There are many differences between children who are not exposed to reading and those who are coaxed to read or listen to stories. There is also a difference between children who have adults read to them and those who, by themselves, make letters to form small words. When reading is activated by the child rather than the adult, the child is actively processing the information. Even a simple activity such as having alphabetic letters on an ice box at age two, three, and four, and having the child interact with two or three simple letter words such as 'to, dog, or cat' leads to the child increasing conceptual development. Likewise, having children arrange words or letters to form a thought such as the --dog runs—affects memory and encoding. (We put alphabetic letters with magnets on the refrigerator so 2 of our children ages 3 and 4, could display words that they had learned.) Reading or exposure to a medium of abstract symbolization is the energy stimulation that creates the basis of different kinds of problem-solving modes. Abstract symbolization can be in the form of verbal and pictorial expressions coming from the caregiver, a mobile hanging over the child's head, books with pictures, and programs provided by television. Consider an adult in the age range from 45 to 55, who, as a child, never learned to read or has restricted reading ability. Our study of these adults in 1995 confirms they are 197 | P a g e 198 Prepublication Copy generally restricted to jobs involving manual tasks or labor, or vocations dependent upon verbal learning or imitation. A homeless worker who works as an extra in a movie production spends a lot of time standing around waiting for verbal directions on how to play her or his part. Illiterate homeless adults make up a small extreme of a normal distribution of all those with problem-solving skills. The reality is that individuals with different kinds of problem-solving skills are unevenly distributed over the entire population. This book is an attempt to identify this amorphous group and bring some sort of understanding of how those differences in problem-solving are amplified throughout life. Numerical problem solving Do children understand conservation, cardinality, and ordinality? These are fundamental concepts involved in numeric operations. Cardinality is the total number in a set while ordinality is simply the order in which a number appears in a set. Conservation relies on spatial ability and perception. Objects have size and shape. If objects have the same size and shape, regardless of how each is positioned or divided by groups, the shape remains constant. Therefore, size and shape are independent of positioning. Children, at an early age, have difficulty keeping the two ideas separate and may indicate that size and shape are different as an object is repositioned. Again, numerical operations, similar to reading operations, are developed over time. Name and object associations such as pictures of one apple and two apples can be learned (memorized) by the association at age 2. Concept development involving the operations of addition, subtraction, and transformations must await later development. Children, ages 3 and 4, can learn simple numerical processing in the same manner that they learn to read simple words. The use of picture books at ages 2 and 3 are ways to accelerate the number and word processing. A “picture” book that shows two apples and removing one apple may result in learning of operational significance if the process of using picture books and corrective language has been introduced earlier. With current technology, interactive computers, laptops, or tablets provide early exposure and experience. Academic games are fun. What are the two most important factors? Not surprisingly, time and readiness to learn are at the top of the list. If a child receives selective attention, interest, and encouragement then early learning can occur. In our research, time tests that require adding and subtracting single digits in a series of three (2+4-20) provide a quick example of a numerical facility. Children at the age of five have difficulty with adding 2 digits. Numerical calculations with three digits are even more difficult for most children. In a minute or two, one can assess memory and the 198 | P a g e 199 Prepublication Copy ability to do simple calculations. This simple exercise of adding and subtraction three numerical digits is highly related to scores on standardized math tests suggesting some overlap with later problem-solving and procedures. The exercises also help identify developmentally delayed children! Standardized tests are not usually given to five-yearolds but six and seven-year-old children may have the end-of-the-year achievement tests; a few children take standardized tests. Our research suggests that the same children who are ahead of their classmates in primary school tend to be ahead of their classmates in secondary school. Early learning of letters and numerical operations provides immense opportunities. By the ages of five, six, and seven, if early learning of numerical processing has occurred in the ages two, three, and four, then reinforcement of the same numerical concepts occurs in a school setting. Spatial problem solving At a very young age of a few months, the newborn has limited spatial perception. The salient perceptual characteristics of objects govern the newborn’s thinking. Children cannot yet manipulate objects abstractly. What one sees is somewhat what one gets. When a cat is given to the newborn, the child does not see the detailed aspects such as the hair follicles; the child sees only the large areas such as the cat's head, body, and tail. A child scans the environment globally and incompletely. What is stored as a memory or a group of neurons is an iconic representation associated with visual input and the chemical energy units of several thousand neurons associated with the haptic and linguistic store of a cat. Later that memory has many thousands of associations so that the visual object of a cat may be linked to the word "Persian or Angora" as a kind of cat. Only at age two and above do some children have the capability of mentally manipulating an object in the brain (Spatial tendency). Note the difference between mentally manipulating objects versus the child’s use of plain space perception where objects are not manipulated mentally. Children in the 2-4 age group have better spatial processing than children less than 2. Mentally turning an object such as the head of a hammer with its claws from the right over to the left side becomes easier. If that seems difficult to you, think about rotating a key from one side to the other. Both of these feats are generally less available to the average child between 2 and 4. Only a few exceptional children with some innate abilities or children whose parents have exposed them to music or activities which engender these capabilities can rotate objects before a normal developmental sequence period. Many teachers are aware that most educational skills are developmental. The teacher must wait until the time arrives (readiness); however, many parents do not. Coax but do not push or coerce and do not get frustrated if readiness has not occurred. 199 | P a g e 200 Prepublication Copy What is readiness? Readiness is developmental maturation-dependent upon exposure and experience. If a child does not have all those early (birth to 5) experiences in number, word, and spatial activities or if the child is physically limited by neural maturation, then the child is not ready to solve verbal, numerical, and spatial problems. Father and Mother Time level the playing field for all children. Some children just need more time to mature. In our research, the perceptual speed tests, particularly cognitive flexibility, and the embedded designs represent spatial processing. The Perceptual Flexibility Tests (PF) provide us with a baseline for spatial processing. The children have 2 minutes to look at a figure on the top of the page, scan the field and find a matching figure which may or may not be rotated. There are 13 figures. At best, cognitive flexibility is an encoding process or it is a search and finds process. If the figure is encoded in working memory then during the scanning process, mental representation is matched to each figure in the field. If the process is a search and find, then the child looks back and forth at the figure and the field until a match is found. The second method is very slow and the first process is faster. The embedded design test is very different. A single example of a figure is found in the first frame; this is followed by similar figures embedded in the background. Finding a rotated figure which is matched well to the background in four different examples requires convergent detail scanning as well as the ability to represent the figure in various rotated positions. Children at the age of five have difficulty with this type of spatial processing as many different levels of developmental maturity exist. However, from five to seven, children perform much better as shown earlier in the section on perceptual speed. Siegel, Kirasic, & Kail (1978) developed a theory about route mapping based on the assumption that distinct locations or cues in the environment (landmarks) are necessary for processing a spatial environment. In their theory, 5 and 6-year-old children had to acquire more than mental knowledge (memorizing a map) about a sequential route through a model town. The experience was required to successfully negotiate a path through space (top-down processing combined with bottom-up). Following a defined pathway through the town helped the kindergarteners and provided that experience. Increasing familiarity with the physical space helped children produce accurate maps of the town. Temperament Emotions tend to stabilize between years 3 and 4. Irritability decreases, attention span increases, and socialness is evident. Social tendencies are often labeled as temperament. 200 | P a g e 201 Prepublication Copy However, most research suggests that tendencies change over time, especially with most children. Those who were initially shy become more outgoing, and children who were very outgoing regress slightly. Experience modifies initial inhibition as self-confidence increases. Cognition and problem-solving development Notice that simple differences in problem-solving are promulgated by organized institutions such as the school and church systems. Our tasks of identifying different problem-solving tendencies are inherently associated with the activities learned at play or in school, church, and the home. Initial problem-solving tendencies often begin in the home but are crystallized by the daily activities of the school, home, and church. Supervised and unsupervised play is very important in children ages 2-4. Problem-solving, from the perspective of the school system, begins in kindergarten (preschool) and first grade. Teachers emphasize abstract symbolization (letter and number recognition, shapes, simple exposure to reading, and verbal thinking). Special schools recognize that most children learn from concrete to abstract. Recognizing that there can be deleterious effects from pushing children too hard or too fast, the following statements assume a normal exposure to a print environment with nonjudgmental feedback occurring when engaged in cognitive tasks. The children who have less exposure to abstract symbolization during the 0 to the 5 years soon find themselves behind, as they must proceed, in a developmental sense, through stages, with the biological clock regulating part of the cognitive growth. Even parents who emphasize the cognitive skills process approach recognized that practice is necessary to move through a developmental stage. For many children that practice is distributed in small amounts over the 5 years before first grade. What are the chances of making up missed practice time devoted to problem-solving in kindergarten and first grade? The answer varies with the individual child. But if the past is any indication, those children who have behavioral habits which interfere with learning, are not going to develop attention, listening skills, and direction-following before midyear of kindergarten or first grade. Therefore, expect at least one-half grade difference in the academic skills of these children. Add language differences, especially in an ethnically diverse area that cannot deal with individual differences, and that one-half grade difference may escalate to one grade difference by the beginning of second grade. 201 | P a g e 202 Prepublication Copy Problem Solving Summary The following provides a global descriptive summary of four simple problem-solving styles in the class system. The styles for this age group were observed and charted by teachers. We denote each as C, S, M, A, G, and D as differentiation in the biological systems is still occurring. Later as less differentiation and more stability occur, the letters are combined (MA) to illustrate differences in problem-solving behavior. At these early ages, nothing is written in “stone.” There are lots of experiences ahead. Conceptually (C) Our research summary suggests that conceptually dominant problem solvers spend more time generating ideas; occasionally, this relates to academic tasks (reading, writing, and arithmetic) but most of the time, it does not. When the ideas relate to schooling, the parents are generally well-educated, have higher SES, and want their children to succeed in school. These parents use their extra money to expose their children to preschool and educationally stimulated activities. The behaviors and skills learned in preschool are reinforced when they arrive home. There is a lot of verbal conversation and an interest in what the child does. When the environment at home is less conducive to academic learning at home, the child is stimulated by other mechanisms--TV, other children, significant others, or their desire to read. Idea generation and stimulation must come from somewhere. Conceptual problem-solving children are exposed to a variety of different environments, regardless of whether it is academically oriented or not. Analytic (A) problem solvers are also physically active but spend more time discerning differences encounter in the environment. The parents buy the children objects such as trucks, bulldozers, and electrical or sewing kits. Their physical play is aggressive with inherent hierarchies of authority. Parents continually help analytic children by asking them questions that make them discriminate against the differences in objects in the environment. Parents or caregivers ask questions and more questions. Children’s responses are not reprimanded for inaccurate or incomplete answers. In response to the children’s questions, adults give more complete educationally responsible answers. Motor (M) Earlier we described this group as children who spend the maximum time inside and outside of the house in physical play or activity. These children are active at most times, using their hands, legs, feet, and mind to encounter their environment. Children spend a lot of their time just doing things, some randomly, some with purpose. Play is guided by the desire to get what they want. Even interactions with other children show physical dominance. Motor children differ considerably along the continuum, some ahead, some behind, and some in between. Analytic behaviors of motor children are evident in figuring out their 202 | P a g e 203 Prepublication Copy immediate goal which could be getting affection and attention. However, their facility with numbers, letters, and spatial processing may be delayed by a lack of exposure. This is also evident in the spoken language. Their spoken language may be less descriptive (get that thing over there). Their ability to solve problems associated with physical play is great. They want to do well i.e.; “best” on the team. In the classroom, in some instances not as well, some motor children find it difficult to sit long enough to read. They do not understand why others do better at schoolwork. On the other hand, motor children may be the best learner and students in the class. Many children who participate in organized sports (male and female) learn to control, teamwork, and social behaviors. Motor dominance can lead to the world’s best soccer or tennis player. Many parents put their children in problem-solving situations at home that include manual and motor tasks such as drawing, art, and shop work. The difference between children who excel in motor activities comes from experience and exposure, readiness, and control of emotions. Social (S) This group of children is more easily identified by teachers and they constitute the largest group. Maternal and caregiver attachments are very noticeable. Some children are just more sociable and seek identification with the teacher, just as each did with their parents. The one characteristic that separates this group at this age is their “emotions are worn on their sleeves.” Never a doubt. Are they happy, sad, or sensitive? The emotion is expressed on their faces and in their body language. How do emotions affect their problem-solving? It is difficult to solve a problem when one is sad or not attentive. On the other hand, happy and content children join in, solve the problem in groups, and find solutions based on experience? General (G) Can one identify a general problem solver at age 5-7. No! However, it is possible to identify the child with the characteristics of a general problem solver. Picture the child in kindergarten, first or second grade who came to school with a thirst for knowledge, always asking questions about this or that. Think about the child who was taught to read at three and four or was exposed to picture books that identified objects, names, letters, and numbers. These children are confident, more social, and physically active. Did you ever wonder about the young person who is socially controlled, listens, and tries to anticipate the necessary parts of the lesson? Differential (D) Everyone who is not a general problem solver is a differential problem solver? Not really! Some differential problem solvers morph into general problem solvers over time. Others do not. Many do not want to be general problem solvers. Many children are happy doing what each prefers; just as many adults prefer doing what they like not what others want them to do. Success in classroom activities varies as teachers provide 203 | P a g e 204 Prepublication Copy many avenues of success for all children. Many children succeed in many different ways in classroom activities. Solving different kinds of problems, not just academic problems, is the basis of many activities that adults face in a lifetime. Chapter summary Information in this chapter identifies the foundations of solving problems that are part of the repertoire of very young children. Every child is exposed to many words, numbers, and spatial kinds of problems during daily activities. Exposure to relevant feedback is key to development. Exposure without feedback to the child may or may not be useful. All children have different experiences during this important period but adult supervision and direction can aid and assist children as they move toward motor and academic readiness. Chapter references Bryant, P. E., & Trabasso, T. (1970). Transitive inference and memory in young children. Nature, 1971, 232, 456-458. Dempster, F. N. (1992). The rise and fall of the inhibitory mechanism: Toward a uniﬁed theory of cognitive development and aging. Developmental Review, 12, 45–75. DeNovellis, R. L. (1984). Manuel for the Learning Inventory. AHP Electronic Publications, Claremont, CA. DeNovellis, R. L. & Dehler, C. (2002). Speed, Ability, Achievement, and Student Growth Scores. Paper (Division C). American Educational Research Association, New Orleans, LA. Flavell, J. H. (1963). The developmental psychology of Jean Piaget. New York: D. Van Nostrand. Gibson, E. J. (1970). The development of perception as an adaptive process. American Scientist, 58, 98-107. Harris, Paul L., and Hilary J. Leevers. 2000. “Reasoning from False Premises.” In Children’s Reasoning and the Mind, edited by Peter Mitchell and Kevin J. Riggs, 67–86. 204 | P a g e 205 Prepublication Copy Ratner, H.H. (1984). Memory demands and the development of young children's memory. Child Development, 55(6), 2173-91. Ruff, H. A., & Lawson, K. R. (1990). Development of sustained focused attention in young children during free play. Developmental Psychology,26, 85-93. Siegel, A. W., Kirasic, K. C., Kail, R. V. (1978). Stalking the elusive cognitive map: The development of children's representations of geographic space. In J. F. Wolhwill and L. Altman (1972). Human behavior and the environment, 3, New York: Plenum. Smith, L. B. (1989). From global similarities to kinds of similarities: The construction of dimensions in development. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 146–178). New York, NY: Cambridge University Press Further reading Ruff, H. A., Lawson, K. R., Parrinello, R., and Weissberg, R. (1990). Long-term stability of individual differences in sustained attention in the early years. Child Development, 61, 60–75 Ruff, H. A. (1984). Infants' manipulative exploration of objects: effects of age and object characteristics. Developmental Psychology,20, 9-20. Ruff, H. A. (1986). Components of attention during infant's manipulative exploration. Child Development,57, 105±114. Ruff, H. A., Saltarelli, L. M., Capozzoli, M., & Dubiner, K. (1992). The differentiation of activity in infants' exploration of objects. Developmental Psychology, 28, 851-861. Ruff, H. A., Capozzoli, M., & Saltarelli, L. M. (1996). Focused visual attention and distractibility in 10-month old d infants. Infant Behavior and Development 19 281±293. Smith, L. B. (1983). Development of classification: The use of similarity and dimensional relations. Journal of Experimental Child Psychology,36, 150–178. doi:10.1016/00220965(83)90064-4 Smith, L. B. (1984). Young children’s understanding of attributes and dimensions: A comparison of conceptual and linguistic measures. Child Development, 55,363– 380.doi:10.2307/1129949 Smith, L. B. (1985). Young children’s attention to global magnitude: Evidence from classification tasks. Journal of Experimental Child Psychology, 39, 472–491. doi:10.1016/0022-0965 (85)90052-9 205 | P a g e 206 Prepublication Copy Chapter 13 Late Childhood: The Child from 8 until 9 Introduction Previously, the problem-solving stages of children less than 8 were rather arbitrary and occasionally elusive. Now, with developmental differences occurring more rapidly, definitive changes in thinking and a personal approach are taking place. Third, fourth, and some fifth graders are just "becoming their person." There is some semblance of identity and a growing awareness of, but not necessarily respect for, individual differences. Children’s responses to various written instruments are more consistent and reliable, although many responses still have elements of fantasy. The use of abstractions for solving school-related problems changes from associational thought to occasional higher analytic and spatial thought. True, some children in the third grade are already functioning at a higher level of thinking, however, the percentage is quite varied. Early analytic and conceptual thinkers are stimulated in home environments by significant others whose constant attention to the child’s intellectual development is of great interest. Children between the ages of four to eight who have early exposure to enhanced “print-rich” home environments are more adept at processing abstract information later on. Children who enter the schooling process at first grade ahead of other children often stay ahead of those same children for the entire 12 years of education and sometimes into adult life. For other children, the process differs. At age eight, the vast majority of children have their thinking tied to concrete things-chairs, beds, trees, clothes, feelings, touch, and embarrassment. They are capable of abstract thinking, but that thinking is tied to objects which are familiar since that is the level of exposure. Abstract thinking which is related to a concrete object or feeling referenced to daily experiences is more likely to bring comprehension and understanding. Even though teachers do an excellent job of trying to compensate for the difference in learning by accentuating the strengths of each child, children notice comparisons. They are very aware of those other children who score better on exams than they do! The result is social differences in self-perception and self-concept--a trend very evident in the research data. 206 | P a g e 207 Prepublication Copy Brain and energy Remember, energy is present at every stage of physical and emotional development. The consequences of a lack of food are obvious. Less obvious is the energy needed at the cellular level to sustain a physically maturing child. Brain growth is almost finished by this stage of development, less than 5 percent of growth remains. With the brain’s physical growth coming to completion, other factors such as neurotransmitters and hormones show their effects on physical maturation. For boys, the male hormone, androgen increases significantly and affects the boy’s higher activity level. This contributes to social dominance and “play” fights (Maccoby, 1998;1974;1987). The lack of neurotransmitters in proper amounts may contribute to serious developmental problems such as inattention, over-activity, and emotional disturbances (Steven, et al., 1996). Cognitive differences, social differences, and physical differences contribute to individual differences. Diagram 4: Cognitive model (Late Childhood) The Cognitive Model for Children 8-9 Years of Age 207 | P a g e 208 Prepublication Copy The cognitive model for the 8-9-year-old illustrated in Diagram 4 is similar to the 2-7-yearold, only the concept of synthesis has been added. Some children, at this age and earlier, synthesize ideas using written papers, drawings, and creative objects. Again, not all children use cognitive processes with the same degree of regularity which, of course, accounts for individual differences. Can you hear your mother saying “What? You did not think? You have a brain; why don’t you use it?” “Signifying nothing” as Shakespeare might say. At this age, children show a lot of variation in their preferences and cognitive thinking. Only a few children show definitive preference patterns and use logical thinking. This leads to mixed and sometimes contradictory results in measurement. Category System The Category System suggests that dominant preferences are integrated and form identifiable categories that exemplify differences. Thus, a child who is a general problem solver and who is dominant in the one mode of Conceptual (GC) differs considerably from a child who is a differential problem solver and dominant in Motor skills (DM). Rather than using a single bipolar scale with a cut line for general and differential problem solvers, we devised one scale for the general problem solver and calculated the scores for the second scale (differential problem solvers.) The second subscale was easier for teachers to interpret as it was inversely proportional to the first. Therefore, any significant differences in the first automatically occur in the second. Again, the Problem solving (Ps) subscale for young children less than 11 or sometimes 12 years of age is not cognitive but a combination of scores on the perception of ability to solve problems based on cognitive independence, the capability to learn, and self-concept. Some differences are apparent in measurement. We generate raw score means and standard deviations based on the children’s responses. A typical example using 256 elementary students was collected by two graduate students (Hvidson, 1992) and (Yates, 2000) as part of their Master’s Thesis as well as by a group of graduate students who were studying the children in their classrooms. They, as well as many other graduate students, used different measuring instruments that were converted to the present problem-solving scales. The groups of children ranged in age from 8-9 and had significant differences in their scores on standardized achievement tests for math and reading. For comparison, older children (10-11) with academic delays in math and reading were used. That is, we compared the scores on the problem-solving subscale of those who were in the normal academic range (8-9) to those who were slightly delayed (10-11) but at the same grade level. We expected that there should be some difference, at least, on the problem-solving scale. The problemsolving scales are: Ps- (general problem-solving skills); Df- (differential problem solver); Cn-(conceptual) problem solvers; Per-(perceptual); Mt-(motor); An-(analysis); Sc-(social); 208 | P a g e 209 Prepublication Copy Ct-(control); Fx-(flex); and EI-(extraversion/introversion). Differences are noted at the .05** level. We expected that the 8 and 9 years-old children would have better problemsolving capability than the delayed group of 10 to 11 years old as measured by our instruments and this difference would be reflected in a higher score on the problemsolving subscale. Table 4 Name Age N Mean SD Std. Err Min Max Ps* 8-9 104 11.12 3.04 .30 4.00 18 10-11 44 10.19 4.21 .63 .00 18 Total 148 10.66 3.48 .29 .00 18 8-9 104 10.67 3.04 .30 7.00 21 10-11 44 11.39 4.21 .63 7.00 25 Total 148 11.03 3.48 .29 7.00 25 8-9 104 28.92 9.15 .90 .00 48 10-11 44 25.91 12.31 1.86 .00 48 Total 148 28.03 10.24 .84 .00 48 8-9 104 30.88 8.79 .86 12.00 48 10-11 44 26.64 10.67 1.61 .00 44 Total 148 29.62 9.55 .78 .00 48 8-9 104 26.77 8.27 .81 8.00 48 10-11 44 27.82 12.08 1.82 .00 48 Total 148 27.08 9.53 .78 .00 48 8-9 104 40.48 10.91 1.07 16.00 64 10-11 44 41.27 14.20 2.14 .00 60 Total 148 40.72 11.93 .98 .00 64 8-9 104 41.77 10.65 1.04 12.00 60 10-11 44 33.91 13.71 2.07 .00 60 Total 148 39.43 12.14 1.00 .00 60 8-9 104 40.69 11.96 1.17 4.00 60 Df* Per Cn* Mt An Sc* Ct* 209 | P a g e 210 Prepublication Copy Fx* EI 10-11 44 34.82 13.85 2.09 .00 56 Total 148 38.95 12.79 1.05 .00 60 8-9 104 35.50 3.45 .34 25.00 43 10-11 44 37.11 4.92 .74 29.00 50 Total 148 35.98 4.00 .33 25.00 50 8-9 104 16.62 5.03 .49 4 28 10-11 44 16.36 6.00 .90 0 24 Total 148 16.54 5.32 .44 0 28 ** P=.05 Raw Score Means and Standard Deviations Age Group 8-9 N=104 and Age Group 10-11 N=42 Examining the means, standard deviations, and spread between the minimum and maximum, there is quite a bit of numerical separation. In some cases, the range of scores is around 50 (subtract the maximum score from the minimum score). The average standard deviation on the motor subscale, for example, is as large as 10 or above. This separation is necessary to achieve the kind of classification that is desired in our category system. However, there is a trade-off as internal reliability (Cronbach Alpha) suffers. The subscales variation increases as item variability increases. Thus, statistics measuring internal consistency decrease as there is a need to increase variation for classification. However, test-retest reliability is good (usually .72-.88). Our goal is to be able to classify and describe children and adults based on combinations of subscale scores. To do this, there must be a mean separation between the classifications of problem solvers (general vs. differential) as well as some of the subscales (motor, perceptual, etc.). These differences provide a solid foundation for classifying. In this case, the subscales which are significantly different (**) at the .05 level are Ps, Dif, Soc, Control, and Flex. Since the older children are slightly behind in academic problemsolving (non-cognitive) related to math and reading, one expects to find differences in the PS. Of course, since Df is a calculated inverse scale of Ps30, any difference in Ps30 is also on Df. The difference in the So is also expected as children at this age level who fall behind academically are prone to select fewer social items. Likewise, the 8-9-year-old children are higher on control and structure while the delayed children on higher on Flex. Children who are very young and behind academically are more likely to have a more negative self-perception and perception about learning which ultimately affects their achievement and socialization. Our model simulates processes found in brain functioning. The model is interdependent as all of the brain functions occur almost simultaneously or in juxtaposition with each 210 | P a g e 211 Prepublication Copy other. There is not a measure of correctness on non-cognitive measures however, for math and reading standardized tests, the outcome is the right answer. According to our model, there are many different subscales on which a person may show strengths or high scores. Based on many research studies including our review of the literature, the expectations are that girls mature faster than boys in this age group but reversals occur in later age groups. Theoretically, girls should score higher on some scales such as conceptualization, and boys higher on subscales related to motor activity. However, at this age, because of sampling error, a child’s scores do not always correspond to the literature or our expectations. Demographic Factors Demographic factors for late childhood included such varied factors as age, gender, socioeconomic status (SES), ethnicity, giftedness, and special resource students. Many different kinds of data using demographic factors were analyzed. In short, for this age group, SES was not significant but there were gender and other related differences. As expected, gifted children scored better than other students; special education did not score as well. Of the four major ethnic groups tested, samples contained a greater number of Caucasians and Hispanics with the sequential order of Caucasians first. Examples of gender and educational differences are illustrated below. According to theory, gender differences occur from early infancy, not only because each is perpetuated by parents and actions from significant others, but because of individual choice. In Table 5 below, the average means (M) and standard deviations (SD) from multiple studies with male and female 8-9-year-olds are listed. Usually, these gender differences persist into adulthood. On average, on over 50 different studies using large sample sizes, females score higher on the conceptual, social, and control scales and extraversion while males score higher on Analysis, Motor, and Flex. Differences in the subscale mean often provide clues to the sample characteristics. The scores below are from a sample of 260 students who are in the second and third grades. Table 5 displays gender differences while Table 6 displays developmental differences. An asterisk suggests significant differences in subscales. Sample sizes in Table 6 are very small so the variation in standard deviations is large; true differences are not indicated. Resource Dependent Students are those who have special tutors in some subjects such as math or reading. 211 | P a g e 212 Prepublication Copy Table 5 Males Ps Dif Per Cn Mt* An* So Ct Fx EI M 10.94 10.82 31.03 28.86 27.08 38.48 38.66 38.84 34.92 16.58 SD 2.62 2.02 9.45 9.84 9.00 11.56 11.66 12.50 3.59 4.82 Females Ps Dif Per Cn* Mt An So* Ct* Fx EI M 11.02 10.75 30.23 34.36 22.95 33.55 43.93 41.68 35.19 16.66 SD 2.83 2.18 9.84 7.29 6.45 9.84 8.93 11.26 3.49 4.96 Males N=134 Females N=126 P=.05* Non-cognitive elementary instrument Gender Differences Exhibited by 8-9-Year-Olds Males and Females On 10 Different Problem-Solving Scales Although the sample sizes are small for the RSP and Gifted groups, the data in Table 6 illustrates that differences in the subscales are in the expected directions except for the analytic subscale. Generally, RSP has less preference for analytic items and a greater preference for social items. Table 6 Subscale Group N Mean Std. D Subscale Group N Mean Std. D Ps RSP 6 10.20 3.94 An RSP 6 45.33 9.35 Regular 54 11.05 3.06 Regular 54 41.93 9.35 Gifted 9 13.42 4.78 Gifted 9 45.33 14.97 Total 69 12.13 3.35 Total 69 42.67 10.14 RSP 6 11.38 3.94 RSP 6 39.33 8.91 Regular 54 10.73 3.06 Regular 54 42.15 10.59 Gifted 9 8.91 4.78 Gifted 9 46.22 10.79 Total 69 12.87 3.35 Total 69 42.43 10.48 RSP 6 27.33 9.93 RSP 6 36.00 11.87 Regular 54 28.67 7.76 Regular 54 42.30 11.03 Gifted 9 25.78 10.79 Gifted 9 40.44 16.79 Total 69 28.17 8.30 Total 69 41.51 11.90 RSP 6 25.33 7.87 RSP 6 37.67 4.55 Dif Per Conc Sc Ct Flex 212 | P a g e 213 Prepublication Copy Mot Regular 54 31.19 8.77 Regular 54 35.33 3.55 Gifted 9 28.44 7.60 Gifted 9 36.22 3.15 Total 69 30.32 8.63 Total 69 35.65 3.60 RSP 6 28.00 7.16 RSP 6 15.00 5.02 Regular 54 26.52 8.52 Regular 54 17.74 4.82 Gifted 9 29.78 7.77 Gifted 9 15.11 6.25 Total 69 27.07 8.29 Total 69 17.16 5.08 Ex RSP (Resource Dependent Students) Developmental Differences Exhibited by 8-9-Year-Olds On 10 Different Problem-Solving Scales Problem Solving Categories (Ages 8-9) In the IPS model and from our point of view, a high IQ is not needed to solve many career and project problems; however, learning capability is extremely helpful. Remember any person can do well with different kinds of problems; results depend on the kind of problem involved (everyday living, interest-related, projects, and academic problems) and the person. Therefore, at the age of 8 or 9, many different kinds of problem solvers are very evident. Our experience and data suggest that in any group of thirty-five 8-9-year-old children, we can classify accurately at least two categories, such as DS (Differential and Social). The categories, such as motor problem solver, are useful for understanding global differences but specific differences are only evident when a child's natural inclination is indicated by greater preferences and performance on subscales. This also provides a more accurate classification. Remember any descriptive process, especially at this age, is incomplete. The control systems of children often are not developed; however, the two systems of control and flex and their interplay influence how problems are addressed. It is like identifying a tall building in a skyline. The streets, small buildings, and contour of the city remain nondescript but the tall buildings are apparent. Nine different illustrative examples are presented for understanding the global difference in the measurement subscales. We start with a descriptive characterization of imaginary children called ’Erin’ and ‘Britt.’ 213 | P a g e 214 Prepublication Copy General academic problem solvers Erin and Britt Erin and Britt do well when given different kinds of problems. Their scores on standardized tests are above grade level. When given any type of problem, they comprehend the characteristics of the problem quickly and have efficient strategies for attempting a solution. They both use flexible ways of attempting to find a solution. Both were exposed to academic concepts in numbers, words, and spatial activities since they were 3 years old. Erin and Britt, two academically talented youngsters, are continually being exposed to new ideas, and different experiences at home. Their parents have a wide variety of interests and an interest in all kinds of problem-solving. They come from a print-rich environment and a higher socio-economic level. The energy of Erin and Britt is continuously channeled into controlled experiences requiring skill development. Brit has taken piano since the age of three and practices often. Erin is in a variety of organizational activities outside of school which require completion of proposed activities--boy scouts, church, and interest activities. Seldom do Erin or Britt just lay around except to read! They are very active and energized by encounters with new situations. Both like to learn and compete. Both read profusely and yet both are motor driven; sports, school activities, and competition allow them to demonstrate their skills. Brit is an extrovert while Erin is an introvert and each differs in social relationships. Differential problem solvers Differential problem solvers constitute a large group of children in this age group. They differ considerably in the kinds of problems that they can solve. Some are good at numbers, some are good with words, and others have the spatial ability as illustrated by their drawings. Many children have some interest in various kinds of problems encountered in the classroom. Classrooms that are filled with all kinds of interesting objects (fish tanks, paintings, plants) stimulate this group. Differential problem solvers can be great at solving problems! The problem is identifying which kinds of problems each prefers. Some children like academic problems, and others like non-academic problems. Some children prefer interest areas such as science but not 214 | P a g e 215 Prepublication Copy math or perhaps math but not science. A differential problem solver at this age can become a general problem solver in later life or vice versa. There are not any barriers; only the kinds of exposure to life and its many facets of problems. Differential problem solvers do not necessarily like solving all kinds of problems, just those which they like. If there are problems in an area outside of their interest, most of them are likely to question the real need for a certain activity or course of study. They do not prefer things unless it relates to their area of interest. Many Differential problem solvers who are low on control and high on flex learn well in their area of interest but may fail miserably in subjects or work which they do not prefer or spend time on. When the match between their interest and task is made, few things can hold them back. They are extremely motivated to solve any problems within their demonstrated areas of expertise. A child may be good at sports but not as good at some classroom skills. Alice: Alice is very bright. She is dedicated, hardworking, earnest, and conscientious. Her grades are good. She is an A and B student. She scores as a Differential problem solver but is on the cusp between a differential and general problem solver. She is the typical student who as she matures might hold leadership positions requiring a general knowledge of problems. In the future in many different real-world situations, Alice may be a better problem solver than students who are characterized as general problem solvers. Wait and see! Mary Mary is a differential problem solver. She scores well academically but has some trouble with math. She does not like or want to understand math and feels poorly when she does not do well. But Mary excels at many things, especially reading. She is methodical in her approach to life and to the things which she loves to do. Mary’s behavioral scores, based on her conduct in classes, are high. 215 | P a g e 216 Prepublication Copy Mike: Some children have basic difficulty finding solutions to general problems because of behavioral or attentional difficulties (Resource Students). Mike has problems with attention, he listens sometimes, but not often. Mike often does things in the classroom which are difficult for teachers to understand. Responding to internal stimuli, Mike may get up out of his seat, go to the back of the room, and muse to himself. This is not unusual behavior for Mike. When asked to solve different kinds of problems, Mike cannot focus long enough to understand the simplicity or complexity of the problem. Mike can repeat from memory his name and other common kinds of information such as a chair, dog, and cat, but has difficulty reading at grade level. Mike needs individual attention, special learning resources, and controlled problem-solving situations. Scotty: Scotty has energy but it has often been redirected or inhibited by others. When his energy is redirected from the environment by a control mechanism imposed by others, he turns his energy inward to what he likes. The meanings, developed in his world, are not necessarily socially understood by everyone. The meaning is not shared by others. His wolf calls are important and meaningful to Scotty but not to others. Turning energy inward often results in having less in common with the external environment. When his energy is continually inhibited by others, the energy often manifests itself in normative behaviors that can be regarded as anti-social, aggressive, and inappropriate. Perceptual problem solvers Livesley and Bromley (1973) traced perceptions of a group of 320 children ranging in age between seven and sixteen. Their results suggested that the number of dimensions of perceptual accuracy grew developmentally. The greatest increase in perceptual accuracy was in the seven and eight-year-olds. Attention to detail in the environment is a prerequisite for being a perceptual problem solver. Some children can draw, and some cannot. At this age, drawing is not a 216 | P a g e 217 Prepublication Copy prerequisite to being a perceptual problem solver; however, children who are good at drawing and graphics have better than average perceptual accuracy and tend to develop skills in perceptual problem-solving. Charlene is a great example of a perceptual problem solver. Charlene: Charlene is average academically, she has adequate memory, her attention span is average, and she listens well but her forte is replicating with speed the things that she can see. She can taste the food and find subtle distinctions in flavors. She reads and types well, especially being accurate and fast at visually extracting words from a printed page. She has the skills often used in offices and banks. Charlene likes the computer since she can use it to copy pictures and do her work. She uses her energy to produce products, pictures, and images that others enjoy. Her energy is evident in activities requiring basic perceptual speed. She uses her perceptual energy to reproduce objects accurately and with great detail. Perceptual Speed In the previous chapter, when discussing the ages of 5 through 7, differences in perceptual speed were evident via the 6 simple scanning tests that were used with children. Usually, older children scored higher on these timed tests than younger children. Our data showed solid relationships between perceptual speed, transformations, and math scores. Remember that perceptual speed is can be independent of transformations and learning. Our benchmarks are letter identification for perceptual speed, embedded figures and cognitive flex for transformations, and arithmetic as representative of learning. Perceptual speed is sometimes related to memory. Again, the significance of this information becomes apparent as children age and become adults. Does the pattern of increased perceptual accuracy continue for our data at the ages of 810? How do the scores differ? Looking at the progression of the scores from age eight to nine is one method of understanding the interaction of biological systems. If development is normal, then one expects a gradual increase in speed as the nervous system continues its development. Likewise, some restrictions in speed might be apparent in those whose biological and psychological systems are not being stimulated normally or are restricted genetically or environmentally. Children identified as special education students fit the latter category so one expects some differences between the speed of processing by special 217 | P a g e 218 Prepublication Copy education students and regular students. This is indeed the case. In Table 7 below, these differences are apparent in both speeds of processing (perceptual tests) and arithmetic operations, an achievement factor. For example, in Table 7 the differences by age (from 8-9: 9-10, etc.) are not significantly different, except for arithmetic which involves a logical operation. Table 7 Ages Type PF/ SD LI /SD ED / SD AR** /SD 8 Sp. Ed 4.6 /1.6 13.5/6.5 9.0 / 6,4 2.9 / 1.7 Reg. 5.5/ 2.3 17.5/6.6 9.0 /4.2 5.5 /3,2 Sp. Ed. 5.3/ 2.0 16.5/8.3 13,8 / 9.5 3.9 / 2.5 Reg. 5.6 /2.6 21.5/ 8.2 13.7 /5.6 6.4 / 4.9 Sp. Ed. 5.6/ 2.3 18.6 /5.5 12.8 / 7.1 3.1 / 2.7 Reg. 5.7 /2.6 23.2 /7.2 16.4 / 7.8 8.2 / 4.4 9 10 CF (cognitive flexibility); LI (letter identification); ED (Embedded designs); AR (Arithmetic Distraction) Sp. Ed=Special Education; Reg.=Regular Education, SD=Standard Deviation Differences in Perceptual Tests based on Ages 8-10 The overall difference across the age span in Table 7 reflects basic developmental differences. The almost linear increase in speed has been well documented by Kail (1991) and DeNovellis and Dehler (2002). Again, most of the sample sizes listed for the studies are large so the means are fairly stable, with fewer fluctuations in the averages associated with the sample. Conceptual problem solvers Many children in this age group prefer using associations, although they can process conceptual and abstract information. A few children conceptualize very well and display their creativity in writing, and oral stories. Identification of children who use associations 218 | P a g e 219 Prepublication Copy can be heard in their responses to verbal questions. If you ask a child of eight, "What happens if you put your hand in the fire?" Most can give a reasonable response such as ‘it will burn.” If the next question is "How do you know that?" Most children rely on their memory of previous experiences (such as being near a fire, seeing a paper burn, or feeling the heat from a fire). The response is associational, i.e., associated with previous feelings or previous information stored in memory. The relationship is fire: burn. Piaget's (1954) word for this stage is concrete operational, with the word 'concrete' relating to tangible objects which are in the child's experiences. Operational denotes limited ability to carry out mental operations except for those with concrete experiences. From the previous sections, it was evident that association, concepts, and simple operations can be taught from age two and one half through seven. However, if a child’s primary way of thinking is via associations then one must start helping them from where there are currently conceptualizing. To teach a child about abstractions, one must start with the concrete and move toward the abstract. For instance, for a child to understand the concept of the universe, have the children build the planet and stars in a 4-foot by 3-foot box or use a diorama. Have the children get inside the structure and construct different objects such as planets, galaxies, and stars; then have them answer questions about the relationships of the different objects which they can see and touch. Around eight years of age, children increase their ability to conceptualize people. Their phrases are more specific. In the results from standardized tests, generally, those who are classified as conceptual also score higher on reading and math. Sammy is an excellent example of a conceptual problem solver. Sammy: Sammy (age 8) is artistic, funny, and likes to be the center of attention. She is always making quips, coming up with unusual ideas, and entertaining. Sammy likes to read, watch TV, and sing with her guitar. When given essays to write, Sammy can write and write and write. She tells you about her experiences, her thoughts, and the way she understands the world. When given a problem, Sammy is one of the first to verbalize an idea about how to solve it. Her ideas are often "off the wall." Sometimes her ideas are useful, sometimes not, but no matter what, the ideas are hers. Sammy can overwhelm any other student with her ideas, often competing for "air time." Other students like Sammy but many do not understand her. Sammy's energy comes from her ideas. She likes the response from others as she quips. Her energy is internally generated. Even at home, she gets excited by the ideas that she generates and her parents listen to her, encourage her, and stimulate her. 219 | P a g e 220 Prepublication Copy The child who is continually stimulated by ideas and manifests these ideas in creative outcomes is more likely to be called Conceptually Dominant Problem Solver. Motor problem solvers The student who does well in the motor, hand-eye coordination, and manual skills often chooses items on the Motor problem-solving subscale. These children have spent a good part of their previous 7 years involved in events or activities that require the use of hands, legs, arms, and mind. Physical dominance is a hallmark of their out-of-school activities. They become environmental problem solvers. That is, what is encountered in their environment is to be mastered and solved. These lead to an interpretation of the motor problem solver as being very practical, hands-on, and realistic. What one sees is what exists. Reality is what is felt, touched, seen, or abstracted from the environment. Objects are perceived as real and are the focus of attention. Motor skills and hand-eye coordination entail a host of activities from cooking, cleaning, and drawing, as well as the use of tools, instruments, and utensils. Males and females are equally equipped to handle a wide array of motor activities. Along with the motor control comes the control of the objects in the environment. Arranging or sequencing events to control environmental activities is part of maturation. Organized and directed physical activities to increase internal control. Boys in the age group of 8-10 tend to score higher on Motor problem solving while girls often score higher on the social scale. Girls who score higher on this scale are usually oriented toward athletic activities, such as dance, gymnastics, and basketball. Kyle: Kyle, a third grader at a local elementary school is a great example of a motor problem solver. How does one know that Kyle is a motor problem solver? For Kyle, almost everything must start with things that can be touched. Kyle does not listen very well because his attention span wavers. When Kyle approaches problems, he likes to handle things--pick them up, turn them over. Kyle is likely to be distracted quickly when anything is presented too abstractly. Kyle prefers to play outside at recess and is usually the last one off the playing field. Kyle is always playing sports, occasionally competing with other children. When a project involves hammering a nail, putting boards together, or carpentry, Kyle leads the pack. His interest is intense. His work is more efficient, more exact, and more productive. Kyle enjoys leading since his skills are more advanced in the area as his father 220 | P a g e 221 Prepublication Copy is in construction. Kyle's father has been helping him learn applied skills since he was born. Almost all of Kyle's energy goes into his body. Even at home, while watching TV, Kyle is constantly in action, moving, fiddling, talking, and being active. Sitting in a chair, Kyle's legs move up and down shaking like they are motor driven. While he is working on projects at school, Kyle continually fidgets Kyrie: Kyrie, also a child in a local elementary school, is also good at manual skills as she has been helping the family since she was five. She cleans the house, makes dinner with her mother, and participates in almost all family activities. She has a good eye and can put things in order very quickly. She is also very attentive and responsible. Kyrie has learned life-related problem-solving skills early as must help the family. She has gross motor skills and is keen on finding the proper solution to any existing problems. She is quite aural, listening intently for instructions from her mother and father about how to go about helping the family. Kyrie does not have time to read much as she is tired after working so hard when she gets home from school. Kyrie does not fidget, is not distracted easily, and is never disrespectful to her parents. Motor-driven children can be very good at abstract problem solving, especially those related to objects or things that can touch, seen, or smelled in later years. They tend to excel at a solving problem which has a tangible solution. For example, athletes, forest rangers, and firefighters are well-known motor-dominant professions. Many motordominant individuals are accountants, banking employees, and business workers. Again, exposure, past experience, and motivation are key to the development of motor-dominant children. Analytic problem solvers Thinking in this stage is different from the previous stage as objects in the environment are not “as they appear.” In the previous stage of development, the characteristics of perceptual objects were described by the child as real. For example, assume that a row of six pennies was spread over 6 inches while below it a row of six paper clips was spread over 7 inches. If a child of 5 were asked which had a greater number of --the row of six pennies--or the row of six paper clips, the response would be the paper clips. In that sense, the child’s analytic outcomes are limited to what he or she perceptually observes or sees. 221 | P a g e 222 Prepublication Copy In the eight to 9 age group, the ability to make a mental representation of objects which are turned or compared differs considerably. Objects appear greater, or smaller, longer, or shorter than other objects-- even if they are not physically handled. Perceptual capacity differs. Many different kinds of problems require a kind of spatial thinking. If a child of 10 is given an object that has three dimensions, he or she might successfully use an abstract formula such as the volume of a cylinder is equal to length times the width times the height but may not understand the same problem presented spatially. More complex levels of seriation--ordering or placing things in a sequence that makes sense--can occur, although the number of problems requiring seriation is usually limited to textbooks that pose problems. Analytic approaches to problem-solving occur more often but are still not apparent in many children. Many eight and nine-year-old and only some ten-year-old children cannot give a satisfactory answer to the following scenario: If you stand at the top of a staircase and dropped a penny, a pin, and a pencil at the same time, which of the objects fall to the ground faster. The answer to this question is not in the experience of children, although most children are familiar with the objects of penny, pin, and pencil. They are less familiar with concepts of mass and acceleration. The children who use an analytic approach are more likely to have parents who emphasized an analytic approach at home (the parent’s style of interaction requires justification or reason for behavior or action “tell me why you hit Johnny.” Likewise, these children are more likely to receive an explanation for actions at home such as “You are staying home because….”. “Explain the consequences of your decisions? Generally, in our samples for this age group, the average preference scores of males were higher than females on the analytic subscale. Females scored higher on control and socialness. Averages are averages. When a child or group of children receives a score that is not consonant with expectations, then further exploration is warranted. Children at this age can verbalize a type of comparison and contrast; the hallmark of analytic thinking. Around eight years of age, children are more likely to separate things into concrete categories but show separation by naming objects with incompatible characteristics. “She is nice but she can be mean sometimes then nice again.” 222 | P a g e 223 Prepublication Copy Travis: Travis, another local child, is good at analyzing things, even his teachers listen to him. His analysis is not always right but insightful. Travis scores well on some tests and not as well on others. He is considered a good B student according to his teachers. Even at home, Travis's parents listen to him when he offers explanations. It seems that Travis’ mind just starts working whenever he encounters anything in his environment. He is always asking questions, wanting to know how things work. He has been that way from an early age. Now his curiosity, and desire to learn, translate into a verbal approach to explaining his version of events. Not always correct, but thoughtful. Travis has a lot of emotional and physical energy. He is always tinkering, seldom watching TV, unless it is about a subject or cartoon that he likes. Travis' energy travels inward, often leading him to take things apart –to see how they work. He enjoys going to museums or discovering new things. Like most analytic problem solvers, Travis does well at giving a verbal analysis of problems encountered in the environment and may do better with problems in some areas of science, geometry, or arithmetic. When reading in areas of English, history, or literature, sometimes he gets bored. Analytic problem solvers, like Travis, may have difficulty writing sentences that embellish an idea. Analytic students tend to write terse sentences without embellishments. The written analysis becomes easier with practice. Social problem solvers As a group, most elementary students have a higher score on social problem-solving. The scores which predict reading and math standardized testing are mainly extraversion and introversion, socialness, independence in thought, self-concept, and learner perception. Theory suggests that the need for independence is increasing all through elementary school. Independence, in this sense, is cognitive independence as well as social independence. Cognitive independence, as described earlier, is the ability to differentiate one own feelings, beliefs, and thoughts from those of other people. Social independence is the development of social distance between mothers and fathers. Academic emphasis on social behaviors by teachers, church, and societal institutions often leads to higher scores on social behaviors as well as on math and reading The Social problem solver recalls information and content dealing with people--history, social studies, and language arts. He or she prefers to interact with others while solving different kinds of problems. On the other hand, those whose emotions are still evolving 223 | P a g e 224 Prepublication Copy and not under control have difficulty interacting with other students. Occasionally they may respond to problem-solving situations with anger, passivity, or withdrawal instead of solutions. Melissa: Melissa is a social problem solver. She is a master of most of her own emotions. Melissa likes to resolve conflicts with others as she is attuned to the social world and feels the emotions of others. She works well in groups. Melissa responds to happy situations, touching others, and to” kind” words. When she solves problems, it is with people who help each other. Melissa likes to work in groups, especially those in which people have fun. When Melissa is asked to solve a problem, she usually asks a lot of questions. She asks a question from the context that she uses to apply to the constraints of the problem. If the teacher is not available to answer her questions, she asks other students. Often when she gets home, she asks her mother questions about her homework. Melissa has a close relationship with her family who have helped her often in solving problems related to general living. While at school, she likes the variety in the elementary classroom as she can encounter many different kinds of problems and is less likely to get bored. With an average memory and average problem-solving skills, Melissa can do the work required in any third to fifth-grade classroom. Melissa's energy often travels outward toward others. She is energized by social approval, social reward, and social recognition. Melissa directs her energy into the kind of activities which will win her approval and accolades from others. Controlled problem solvers In the children’s age group (2-7), there are two types of control, internal structuring of one’s behaviors and external structuring of other behaviors. External structuring is the most obvious as the child directs others on how to solve a problem. External structuring is often the result of internal feelings, sometimes anxiety or fear of failure; other times, a sincere desire to help others. In contrast, deep internal structuring often reflects the behavioral control learned from parents, the church, teachers, and other significant figures. 224 | P a g e 225 Prepublication Copy How are these control systems displayed as the child ages? Usually, they are just extensions of behaviors and ideas learned earlier. When they are not, the new control systems are extensions of independent thinking designed to obtain immediate goals. The control systems are learned through repetition, in regularized, controlled environments. That is, day after day, the children follow a consistent routine and internalize habits, rules, and procedures. The reward of internal and external structuring comes from the solving of academic problems or the satisfaction gained from learning to solve problems in the day-to-day world. Both mental operations result in a condition often called “internal locus of control.” Our research suggests how control and structure are related to higher academic standardized test scores and favorable treatment from others. As most people are aware, children can be in control sometimes and out of control at other times. Many children do not show the extremes of identifiable attributes but instead display behaviors that are characterized by the normal process of maturing. That is, children sometimes make mistakes but try hard to overcome any adverse conditions related to them. When the control systems are not internalized or operational, then children’s behaviors are well documented. The lack of a control system often results in self or other-directed destructive behaviors. Not so for Jennifer who is characterized next as she has learned to control her behavior: Jennifer: Jennifer likes to solve problems. She is quiet, conscientious, and detailed. She has a good self-concept and perceives herself as capable of handling diverse kinds of activities. Jennifer is often chosen as a leader since she often finishes what she starts. Jennifer is the firstborn child of a mother who works as a professional architect. Her grades are slightly above average and her teachers like her since she follows the rules. Jennifer works diligently and has a very traditional work ethic. Jennifer likes to get things accomplished quickly. She often tells others how what to do and how to do it. Others look to Jennifer for advice as she is so conscientious. Jennifer is quite a leader so she is chosen to organize activities in school. Jennifer hates to fail at anything and appears driven at times. Regardless, Jennifer is a model student Are structuring, planning, and controlling, learned behaviors? The academic literature suggests that control and structure are associated with cognitive flexibility. That means that the people who control and structure external events a lot, also have a lower score on 225 | P a g e 226 Prepublication Copy cognitive flexibility as solving a problem occurs in the same manner and the same way each time it is presented. Remembering how it was solved before helps in solving it again. Or then again, maybe not! As is shown in the next section as children mature and are rewarded for solving problems, a child can have both a high score on control and a high score on flex. This type of response pattern is associated with solving many different kinds of problems. Whereas the first pattern (high control and less flexibility) often comes from the repetitive solving of the same kinds of problems in the same type of environment. Doing the same thing over and over forms a mental set or cognitive boundary? Being exposed to different events over and over again breaks those boundaries. The need to survive can be an impetus to learning new ways of solving an old problem. Flex problem solvers Flex is based mechanism based on cognitive and affective impulse control. Impulses are generated quickly depending on the sensory-motor and reflex systems of people. Children are quick to notice perceptual differences such as changes that occur in the expressions, emotions, or moods of others. This is particularly true if a threatening situation occurs. If there is any kind of threat, energy emanates from the neural layers as part of the flight or fight of the autonomic system. The manifestation of the energy impulse as it moves through the cognitive system is imaginary, creative, or ideational. When an obstacle or problem is posed, energy in the cognitive and affective systems interacts with memory representations in the neurons to form the basis of imaginary or creative content. There are distinct differences in children who score high on flex. These differences may or may not be mediated by control. When control is low and conception is high, flex is manifested in many different ways. Sometimes flex is cognitive flexibility that is unbounded, a wild imagination, ideas gushing from everywhere. At other times, flex allows “one to think outside the box” and or even how to destroy the box. When a high score on flex represents a lack of impulse control, the results are obvious to everyone. Danger can occur from an impulsive action. Below, the characterization of a student named Jackson helps to personify how emotions and feelings interact with cognition in the process of defining Flex. 226 | P a g e 227 Prepublication Copy Jackson: Jackson is a very creative but undisciplined young man. Being full of emotion, he is likely to “fly off the handle.” He does not think his parents understand him and they probably do not. His actions are “off the wall” at times. Jackson is liked by his classmates and teachers but has a very difficult time finishing anything on time. He is the world’s greatest procrastinator. Jackson always has an excuse for anything which he goes wrong. Being imaginative, Jackson can always think of a reason why he did not get his homework finished or why he is in the back of the room bothering other people rather than doing his work. Jackson is quite ingenious when he wants to be. His original jokes, witty saying, and cavalier attitude make him the envy of many. He can do many things that others cannot. He has a host of hobbies, such as electronics. Give him a problem in his area of interest and he can elaborate for hours on possible solutions. Jackson does not study very much, there are too many other things that he would rather do. Liking music and having the ability to play an instrument, Jackson often entertains the other kids by playing the guitar. When he is not entertaining, he is getting in trouble. Trouble for Jackson is anything new or different. His curiosity is overwhelming. He will take anything apart but is highly unlikely to reassemble it or learn from it. Having fun is dismantling things. His room looks like many garages with clothes, boxes, and junk strewn in every direction. Jackson is a study “unto himself.” Finally, although many flex problem solvers who have low scores on the control subscale are creative and imaginative, many are not. At this age, flex problem solvers who are less creative are great at following the lead of others and getting into various kinds of trouble by letting their emotions run unchecked. Role of interest on career paths and selection Children at very young ages have not solidified their career choices. By age 8, some have progressed beyond the age of fantasy; all of them do not want to be policemen or firemen. However, their career choices are not based on any practical experience. Most children are familiar with work based on their mother’s or father’s occupation. The influence of parents is often very influential in a career choice as children mature. Career choice is not a high priority at the ages of 8-9. Even when speakers are brought to schools to extol the merits of certain occupations, the children are more likely to pay 227 | P a g e 228 Prepublication Copy attention to the entertainment value of the presentation not the emphasis on a vocational opportunity. The result is that children's choices are immature and transitory. Only a few indicate the desire to be a professional. Since interests are related to personal goals, at this age, there is a lot of instability in trying to assess career problem-solving categories. Differences in Types of Problems Solved Word problems solving In many of the earlier chapters, groups of children scored differently on problem-solving words, numbers, and spatial activities. In this section, the differences in the problemsolving scales are based on the separation of scores into the group by the median or the 50 percentiles. The strategy is to use the categories of words, numbers, and spatial activities as a method of separating and identifying individual differences. This is illustrated when choosing a median split at the 50th percentile as a method to divide scores of reading (word), math (numbers), and spatial activities (our spatial tests). With that split, there is a high group and a low group, i.e., a group average below the 50th percentile and a group average above the 50th percentile. Significant cognitive and affective results should appear on the problem-solving subscales. Two classrooms of children who were 9 and 10 years old answered items on the instrument. Their problem-solving skills were assessed by standardized tests and they responded to their activities via a questionnaire. This is the same data collected by Hvidson (1992), Yeates (2001), and others. The subscales are the same as noted earlier. As an example, using the reading standardized test score, low indicates an average of all who scored below 50 percent on the reading standardized tests and high indicates an average of all who scored 50 percent or more. An asterisk (**) indicates a significant difference at the .05* or .01** level in mean scores for a particular subscale. If the mean scores for those scoring higher on reading standardized tests are significantly higher than the scores for the low group, this is consonant with the expected direction. In Table 8 below, Psa and Df scales are non-cognitive and composite scales that show the significant mean difference between the scores for the Low and High groups respectively (10.2 vs. 11.41). The composite scale is artificially compressed which is why the standard deviation is so small. The same compression can occur by dividing a total for a group by a large number such as one hundred. The other subscale which demonstrates significance was Control (The low group average score was 38 while the high group average was 44.56. The interpretation of this difference is: Children who score in the top 50 percent on verbal 228 | P a g e 229 Prepublication Copy achievement tests also had higher scores on the General Problem Solving/Diff subscale. This same group of children was more likely to select items of control and structure. In essence, over the years, there were differences in the subscales for many different age groups on much different math, reading, and spatial standardized tests. Many of the same differences were also found in many groups of adults, managers, and workers in various Fortune Five Hundred Companies. Selected examples are shown in different chapters. Table 8 Subscale Grp N Mean Std. Subscale Grp N Mean Std. Psa** Low 57 10.76 2.61 An Low 57 42.74 10.40 High 52 11.96 4.33 High 52 42.92 12.43 Total 109 11.33 3.57 Total 109 42.83 11.36 Low 57 14.24 2.61 Low 57 38.18 11.64 High 52 13.04 4.33 High 52 40.69 13.20 Total 109 13.67 3.57 Total 109 39.38 12.41 Low 57 25.40 8.67 Low 57 37.33 10.62 High 52 26.46 10.54 High 52 39.77 15.02 Total 109 25.91 9.58 Total 109 38.50 12.90 Low 57 29.61 8.81 Low 57 36.32 3.69 High 52 28.85 9.90 High 52 36.06 4.43 Total 109 29.25 9.31 Total 109 36.19 4.04 Low 57 27.65 8.92 Low 57 16.14 4.41 High 52 27.15 9.90 High 52 17.50 5.87 Total 109 27.41 9.36 Total 109 16.79 5.18 Df** Per Cn Mt So Ct* Fx EI **P=.05; *P=.01 Difference between high and low groups on reading standardized tests There were other differences found in the questionnaires. That is those children who scored higher on items (such as ‘learning better with visual cues than auditory cues’) perform much better in reading comprehension. Likewise, this same group of children liked to see and read examples rather than have someone give them oral examples. Word problem solving is based on the total score of reading comprehension, spelling, and grammar. 229 | P a g e 230 Prepublication Copy Numerical problem solving The question is—what are the differences in average scores on the math standardized (number) testing if the total group was separated at the 50th percentile into a high group (scores above the 50th percentile) and low group (all scores below the 50th percentile)? As noted in Table 9 below, the average score for the general problem solver high group (11.54) is greater than the average score for the low group (10.24). Just as important are the higher scores on the other subscales. Table 9 Subscale Grp N Mean Std. D Subscale Grp N Mean Std. D Psa** Low 61 10.43 2.80 An* Low 61 41.64 11.11 High 47 12.43 4.15 High 47 44.17 11.68 Total 108 11.30 3.58 Total 108 42.74 11.37 Low 61 14.57 2.80 Low 61 37.51 11.50 High 47 12.57 4.15 High 47 41.36 13.09 Total 108 13.70 3.58 Total 108 39.19 12.31 Low 61 24.92 8.78 Low 61 37.64 11.20 High 47 27.66 10.71 High 47 39.32 14.88 Total 108 26.11 9.71 Total 108 38.37 12.90 Low 61 29.31 9.32 Low 61 36.57 3.81 High 47 28.94 9.18 High 47 35.74 4.36 Total 108 29.15 9.22 Total 108 36.21 4.06 Low 61 27.34 9.30 Low 61 16.30 4.96 High 47 27.57 9.59 High 47 17.53 5.18 Total 108 27.44 9.38 Total 108 16.83 5.07 Df** Per** Cn Mt So Ct Fx EI **P=.05; *P=.01 Difference between high and low groups on math standardized tests 230 | P a g e 231 Prepublication Copy As is true in almost all cases, as young people develop and gain maturity, math tends to provide a slightly greater separation on the Ps scales than reading, but less separation than spatial, depending on the criteria used. Many times, the 8-9-year-old children had a higher score on Flex. Using non-cognitive scores suggested that children had less impulse control and therefore were more impulsive. The Flex subscale was artificially compressed as is evident by the small standard deviations. Spatial problem solving At this age, spatial tendencies are more evident in children who do well in math or who play the piano, or other musical instruments. Most of the spatial tendencies involve the perception of distance; i.e. what is the distance between two objects, lines, or geometric figures? Children are exposed to concepts of shape early–putting blocks, circles, or hexagonal figures through a hole. However, children spend less time building objects such as tinker toys. Some limited rotation of spatial objects occurs during out-of-school activities. However spatial tendencies are more likely learned as a part of early drawing experience and projects where objects are made and placed in dioramas. In grade levels two and three, many spatial activities are presented as games or fun things to do. The perceptual speed tests have spatial properties of embedding and rotation as well as the restriction of time. As seen in Table 10 below, when the group of children was divided by the 50th percentile using the perceptual speed tests, the children in the lower group did not have lower average scores. In other words, at this age (8-9) and with perceptual spatial problems, there was not the separation that was expected. Separation of the means on the spatial tests occurs with greater task complexity using blocks and rotated figures. Speed and low task complexity did not show a significant average difference. Table 10 Instrument Grp N Mean Std. D Std. Min Max Cogflex* Low 40 5.5 3.08 0.49 1 12 High 41 5.07 2.55 0.4 1 10 Total 81 5.28 2.82 0.31 1 12 Low 40 22.8 13.01 2.06 4 47 High 41 15.59 8.99 1.4 0 43 Total 81 19.15 11.67 1.3 0 47 Letiden* 231 | P a g e 232 Prepublication Copy Emb* Arith Low 40 8.95 9.93 1.57 0 32 High 41 6.59 7.24 1.13 0 32 Total 81 7.75 8.7 0.97 0 32 Low 40 4.22 3.59 0.57 0 13 High 41 4.63 3.89 0.61 0 16 Total 81 4.43 3.73 0.41 0 16 **P=.05 Age 8-9 Difference between high and low groups on perceptual speed tests at 8-9 years old Measurable differences? At this age, most complex categories of problem solvers are not measurably distinct, but jumble because of the stage of development. Only some groups of problem solvers, who excel at very specific kinds of problems, are measurably distinct. However, differences in problem-solving characteristics become more distinct with age. Other methods of understanding the responses on the problems solving subscales were also used. The ratings of students by teachers provided one separate measure. Often there are differences in the averages given by the teacher and the averages from the self-report of 8-9-year-old. This suggests that children's responses at an age younger than 10 are not always reliable. Elementary teachers attend to and consider most students holistically, that is, not focusing on their specific differences but praising their strengths to bolster their weaknesses. In any fifth-grade classroom, the teacher can identify some students who exemplify the different categories of problem solvers; however, many students are such a mixture that, solely by teacher observation, the result is not clear either. The use of instruments that identify self-reports of students combined with the observations of teachers is the most reliable, but again occasionally arbitrary. In general, teachers can identify students who are having trouble academically but excel in physical activities on the playground. Likewise, they are aware of children who must have special attention from a resource teacher in areas such as reading, or math or need emotional support to finish their lessons. Informal observation by teachers helps identify the cadre of kids who a) were social, b) asked teachers for help, c) worked well in groups, and d) did well academically. Do these children exemplify our groups of problem 232 | P a g e 233 Prepublication Copy solvers? Not really! The only way that you can differentiate problem-solving categories is when the child is presented with different kinds of problems. That difference is paramount in the IPS model. Since Social Problem Solvers solve problems better in groups or teams, social skills are necessary, but also necessary is the capacity to utilize information from other people to solve the problem at hand. As one expects, gender differences are evident at this age. Girls successfully solve some kinds of problems significantly better in groups than boys. The problems solved are found more often in subjects such as language arts, or history. Gender differences are not as distinct as they are later but do play a part in how problems are solved. Girls excel at verbal activities and in some cases, spatial and mathematical. This changes around ten or eleven as boys begin to mature faster during the late eight to ten-year period. Differences are not very great but have an overall gender effect. When presented with problems, boys and girls exhibit the same tendency of trying to solve complex problems -----simply. Using the Problem-Solving Model The working problem-solving model is appropriate for understanding certain actions of the 8-9 age group in current classrooms. The model is effective in understanding cognitive operations such as memory, speed of comprehension, and various ways that children can become arrested or adept in different stages of problem-solving. Memory From third through fifth grade, a lot of emphases is placed on the ability to memorize important information. There is nothing wrong with memorization since the basis of more complex problem-solving is, in part, based on memory storage. The downside is that students who do not do well at recall may be given lower grades simply because they are not good memorizers or because they do not spend time memorizing. The latter is more likely to be true as most teachers know. Students are exposed to a vast amount of information in the areas of history, language arts, math, and science as well as the home environment. Theoretically, achievement testing which occurs at the end of the year reflects the amount of material remembered or sometimes learned. Some students can learn the material (memorize and answer questions) in school and not have the slightest idea of how the material relates to a problem of society or mankind in general. To get to a level of understanding or comprehension, a question of "why" is 233 | P a g e 234 Prepublication Copy necessary. Associational thinking based on memory does not truly require any understanding or the ability to answer "why?" One of my daughters, at age 9, could answer a question from science that involved an environmental change from man-made or natural causes. But she sometimes answered without any real understanding of "why?” My son, at age 10, was learning about bones in science but when asked "why" he is studying this material he responded that it was part of the 5th-grade curriculum. Only with extensive questioning did both children elicit a satisfactory response of why they were learning certain concepts in the curriculum. Comprehension Questions often elicit some indications of comprehension and understanding. In response to the question, "Why did explorers come to the new world?" Children who do not spend much time studying history might answer: "To get better food?” or the conventional “I don’t know.” An associational memory response from the lesson which suggests some comprehension is "Queen Isabella gave them money and fame to explore the New World for Spain." An analytic response is that "Queen Isabella and King Ferdinand recognized the need for more territory and riches for the Spanish people and sent explorers to the new world. A divergent response is "There are many different reasons depending on which explorer you are talking about. The reasons for Columbus coming to the New World are different from the reasons for Ponce de Leon. I cannot answer the question until you specify which explorer." A convergent response would be "If you are talking about Ponce de Leon, he was seeking the Fountain of Youth in the new world after visiting with a woman from Guadeloupe, an island off the coast of Florida." None of these responses is actually from third graders since any third-grade teacher knows that they are far too sophisticated for an eight-year-old or even a ten-year-old. The responses illustrate the point that understanding and comprehension are more important than just memorizing. The average eight and nine-year-old child gave very short incomplete answers or statements that required additional questions to get to any degree of complexity or sophistication. Remember, for many 8 to 10-year-olds, their developmental level is still associational, not analytic, so this is not unusual. Arrestment in problem-solving at 8-9. One of the advantages of the problem-solving model is recognizing the different stages in that children and adults can be arrested or delayed. For example, many special education children are stymied from solving problems simply because of a lack of memory or the ability to control emotions. Some third-grade children cannot convey information with 234 | P a g e 235 Prepublication Copy comprehension since they fail to spend enough time on tasks and cannot relate to associations. By not spending time, the level of processing is shallow, and the response indicates incomplete associations. The problem-solving model suggests some students are good at diverging or coming up with a multitude of different answers for a potential problem. These divergent problem solvers are generally less structured externally but can be structured internally (have knowledge storage compartmentalized for easy recall). This kind of internal structure comes from hours of thinking about different kinds of answers or the way that material is structured in various books that they have read. These divergent problem solvers have a terrible time converging to a single correct answer. Because of their relational or associative thinking patterns, many possibilities are conjured up. This inability to converge either rapidly or to a single answer causes them to score lower on many different kinds of standardized tests. In other words, standardized tests may not be the best measurement of their knowledge. They display the richness of their understanding by writing. They think less in a convergent analytic manner; therefore, some multiple-choice questions are too ambiguous for them. In problem-solving situations later in life, these individuals excel since the richness of the alternatives which they propose is often transferred to a suitable career. Again, they have the same problem, converging to a single right answer; however, later in life, time is on their side and many times they do not have to reach a single problem outcome in a defined period. Likewise, arrest in a problem-solving mode in this age group occurs because of subgroup differences due to culture, gender, ethnicity, religion, or personality characteristics. Earlier, two important personality characteristics exhibited by subgroups were based on a preference for either analytic or social problem-solving. Children are extremely aware of individual differences. In the classroom, children who are social problem solvers are very aware of differences exhibited by analytic problem solvers, especially during oral questioning, as well as history, math, or science-related classes. The social problem-solver hides his or her analytic capabilities behind a social veneer, increasing their capabilities by emphasizing social characteristics in everyday ordinary problem situations involving group conflicts and individual social situations. During a problem-solving situation, this can result in a deferment (arrestment) to others who might have a better answer. Other well-known situations are based on gender and cultural characteristics. That is, certain Asian and other cultures place emphasized that groups of people (females, religions, and ethnicity) should not be too forward or brazen when encountering problems involving verbal solutions. Teachers in classrooms of children who are eight and nine emphasize memory and convergent solutions as state curriculums require it. In our problem-solving model, children are at different stages in their problems solving capability. Developmentally, many brain functions (frontal lobes) which represent our problem-solving categories are 235 | P a g e 236 Prepublication Copy the last to develop in young people. As stated earlier, sensory-motor functions are the first developed therefore the integrated categories of the motor, social, and flex are the first to develop. Preferences that allow selection of categories such as control, analysis, and conceptual develop later with exposure, experiences, and many varied examples of problems. In our view, the child who has success in problem-solving chooses categories of items that reflect that success. The integrated categories of control, analysis, and more accentuate convergent thinking. The problem solvers who can reach a convergent solution fairly rapidly excel at most activities in the third, fourth and fifth grades since the teacher’s often stressed convergent kinds of activities. Current practices in many classrooms are at odds with an educational theory that suggests that material such as the Internet, books, and encyclopedias should be used as an aid to remembering (Look it up when necessary! Not memorize everything!). This approach requires less knowledge content to be learned but requires a greater level of comprehension by students since a deeper level of processing is necessary to obtain more complex answers and outcomes. At the same time, when using such a method, a student may understand the material better but not score as well on standardized tests which emphasize memory and convergent solutions. At some time in the future, standardized tests may change their format to have students find information on the Internet and then provide solutions to real problems in academia. Chapter summary Late childhood is a developmental period of physical, social, and cognitive changes. Everything is important as biological changes such as androgens for boys and estrogen for girls define a transitory period. The greatest changes are social as both boys and girls learn to control emotions and adjust to a fast-paced society. This Chapter presents many concrete descriptions of what constitutes a general and differential problem solver as well as how the other constructs can be dominant for some children. Illustrated are the examples of analytic vs social; conceptual vs motor and flex vs control. All different types of children find ways to solve number, word, and spatial problems by moving from concrete objects which are touched to abstract attributes which are defined by them. Gender differences are more evident at this young age as boys mature slower than girls. Emphasis is on the memory of ideas and less on the application of ideas. Examples of arrest occur as individual differences are accentuated. 236 | P a g e 237 Prepublication Copy Chapter references DeNovellis, R. L. & Dehler, C. (2002). Speed, Ability, Achievement, and Student Growth Scores. Paper (Division C) American Educational Research Association, New Orleans, LA. Hvidson, C. H. (1992). Out of school activities and classroom learning. Unpublished master’s thesis, California State Polytechnic University, Pomona California Kail, R. (1991). Developmental change in speed of processing during childhood and adolescence. Psychological Bulletin,109, 490-5. Maccoby, E., & Jacklin, C. N. (1974). The psychology of sex differences. Palo Alto, CA: Stanford University Press. Maccoby, E. (1987). Gender segregation in childhood. In Hayne W. Reese (Ed.) Advances in Child Development and Behavior, 20, 239–87 Maccoby, E. (1998). The two sexes: Growing up apart, coming together. Harvard University Press, Cambridge, MA, 1998. Piaget, J. (1954). The construction of reality in the child. New York: Ballantine. Steven R. Pliszka, M.D., James T. McCracken, N, M.D., James W. Maas, M.D. (1996). Catecholamines in Attention-Deficit Hyperactivity Disorder: Current Perspectives Journal American Academy. Child Adolescent. Psychiatry, 35(3),264–272. Yates, C. E. (2000). Integrating new technologies into the seventh-grade mathematics classroom, Unpublished master’s, thesis, California State Polytechnic University, Pomona, California. Further reading Kail, R. (1986). Sources of age diﬀerences in speed of processing. Child Development, 57, 969–987. Kail, R. (1988). Developmental functions for speeds of cognitive processes. Journal of Experimental Child Psychology, 45, 339-364. 237 | P a g e 238 Prepublication Copy Chapter 14 Early Adolescence 10-13 Years of Age (Middle School Years) Introduction One should call this stage “the age of crystallization”; because so many of the problemsolving modes and behaviors are now more identifiable, although the variation between individual children is still large. About 2 or 3 percent of 10 and 11-year-olds have complex problem-solving behaviors. A majority, about 55 percent of children in our data banks, can solve some type of complex problems in a consistent manner; however, this occurs closer to 13 years of age. Early adolescence is a period of change, but not necessarily traumatic change. For this age group, there is a change in self-concept, self-esteem, identity, and psychological wellbeing. The changes in problem-solving behaviors are more obvious since the concepts of behavioral and conceptual independence are emergent. Children are becoming independent thinkers and independent learners (conceptual independence). Adolescent children want to be more independent of parental influence (Behavioral independence). Both types of independence, independence of thought and independence of behavior, lead to academic and social problem-solving behaviors. This is an important stage as Piaget has noted, children are just now showing the ability to manipulate abstractions better. Although the process differs for each individual, somewhere between 10 and 15 years of age, surface characteristics are more identifiable. The surface characteristics of the individual’s personality, cognition, and interests are constantly being modified by an environmental press that comes from the interaction of parents, significant others, and now more than ever, peers or friends. This is an important chapter as age differences are enumerated in the problem-solving approach. A lot of numbers are used in this chapter to illustrate individual and group differences in the solving of problems. At the ages of 12-14 and adults, some of the problem-solving scales are cognitive rather than non-cognitive. For children less than 13, a non-cognitive scale is denoted by Psa. In contrast, the cognitive Ps scale is divided into three groups (spatial, logical analytic with abbreviations of Ps30; Pssp; Pslap). Ps30 represents a combination of scores from spatial (Pssp), as well as the sequence, and analogical problems (Pslap). Both cognitive and non-cognitive are scaled similarly for comparison but the comparison is not exact and varies by sample size. Quantification is 238 | P a g e 239 Prepublication Copy necessary as many development differences are evident. If numbers are not useful to you, then skip to Chapter 18. Biological and motor development Motor development was important to socio-emotional maturation in the earlier stages of infancy and early childhood. Now, the expression of motor development in adolescence is even more crucial. Motor development continues in importance as body changes are developing at a rapid differential rate. Adolescence brings the most dramatic physical changes seen in the body since the first year of life. Puberty is accompanied by changes in growth rate, an increase in body size and rate, and a significant change in the body shape and composition; a condition usually associated with the development of secondary sexual characteristics (De Waal, Van Coeverden, and Rotteveel, 2001) During middle childhood and early adolescence, the weight of the brain increases by about 10 percent. fMRI reveals that myelinated nerve fibers and grey matter in the areas of frontal lobes, parietal lobes, and corpus callosum are contributing factors (Durston et al., 2001). Reduction in the grey matter due to synaptic pruning is taking place simultaneously. According to Dammerman and Kriegstein (2000), neurotransmitters at this age are extremely important. A lack of neurotransmitters causes serious developmental problems such as inattention and over-activity, emotional disturbance, and epilepsy. The presence of neurotransmitters allows neurons to be selective in responding to certain chemical messages that aid in efficient and flexible thinking as well as general cognitive performance. Brain functioning also changes because of hormones, particularly androgens and estrogens. In many animal species, androgens affect brain organization (Hines & Green, 1991). Initially, children’s social, emotional, and cognitive development is heavily reliant upon central nervous system development; now, at this age, cognition and emotion are primarily influenced by practice and exposure. For the developmentally normal child, the central nervous system can act as a constraint or a boost to solving problems, not a deterrent, except, of course, through traumatic accidents. Energy and physical development Energy has been important to the total physical and problem-solving developmental process since birth and has been evident in both intellectual and social growth. Overall, energy is just as important in this stage of adolescence, as changes begin to manifest themselves in many different behaviors. As adulthood approaches, there are expectations of a change in children's behavior. Children are expected to do more physically and mentally. 239 | P a g e 240 Prepublication Copy Consider how much energy is necessary just to maintain the schedule of a single day. Some people have a lot of high energy; while others have average or low energy. Based on IPS criteria, the person with greater physical energy is involved with many different kinds of activities during the day while the person with average energy does less. The low-energy person spends more time sitting and watching. The high-energy adolescents have a rigorous schedule, getting up in the morning, and off to school where they show their energy in the classroom and out-of-school activities. High-energy children are often the "doers,” leading other children or being an active participants in classroom situations. When the time for recess occurs, very seldom do these children stay indoors or watch other children play; instead, they are usually the first out the door to engage in more play or social activities. The low-energy child is not lethargic but less active overall. Less active does not infer timidity, shyness, lethargic behavior, or inferiority, only less overall activity due to less biological energy. Consider yourself for a moment, how much energy do you have on any given day? How many different kinds of things must you do; how much rest do you require? Are there days when you have less energy, want to relax more, or just sit and release stress by not doing too much? Did you ever decide not to go shopping or to go outside to do chores such as mowing the grass or cleaning up? Probably you are just a person with a normal amount of energy. Consider the child who just does not have as much energy or must be prodded to be involved in activities. Certainly, a lack of motivation or willpower can be responsible for not doing something, but these internal forces can be modified. Less biological energy should be distinguished from less psychological energy, if and when, motivation or endurance, is involved. In our thesis, those who have expended energy and have been involved in physical and mental activities at earlier ages reach puberty faster and solve problems better than those who do not. The classic research of the California Growth Studies and others (Weatherly,1975) supports the fundamental differences between boys who mature early and those who mature late. Early maturing boys are usually bigger, taller, better coordinated, and have some leadership characteristics. Often some people mistake size as a sign of maturity and thus expect more and give more responsibility to larger children. Late maturing boys who 'act out' in rebellious rather than constructive ways are often more dependent on others. Gross motor physical attributes are three/quarters developed by adolescence. This makes them extremely difficult to modify. School activities, especially physical education, are valuable for helping children increase general hand/eye coordination, but on average across all US schools, only about 30 percent of children are required to take PE classes. 240 | P a g e 241 Prepublication Copy The gross motor areas which require practice and skill building include hand/eye coordination and manual use of the hands. Fine motor skills increase during the lifetime as many adults can testify. Fine motor activities involve anything from assembling small pieces, such as models, to painting detailed figures. Fine motor skills develop later for some children, especially those at this stage of age development. A lack of energy comes from malnutrition which is evident in many poverty-stricken children and those who eat inappropriately. There is a direct impact on learning and behavior when malnutrition accumulates over many years through early and middle childhood. Growth-stunted children are more likely to respond with greater fear with an increase in heart rate and cortisol in saliva (Fernald & Grantham-McGregor, 1998). They do not solve everyday or academic problems well. Energy and cognitive development Up to this point, many responses given by children to our measurements are constrained by immediate experience. Responses by many children represent minimal operational thought except for those who have reached mental maturity early. In early adolescence, children are moving from concrete operations to formal operations (Piaget, 1954). Formal operations, according to Piaget, is the ability to use mental operations that can solve complex problems. The developmental process takes place at various times for different individuals with some individuals not reaching formal operations at all. Likewise, some children may reach formal operations in some areas but not in others. A recent study found that 40-60 percent of college students could not pass Piaget’s formal operations tests. For adults, this is particularly obvious. How many adults are good with spatial plumbing problems? What percentage of adults would rather be involved with social activities rather than solve a Rubric’s cube problem? Uneven development and lack of exposure and practice lead to differences in problemsolving approaches and skills. For example, one group of children who have social problem-solving skills as their predominant mode may not reach formal operations in answering mathematical problems while another group who are motor-dominant problem solving may not reach formal operations in areas such as literature or social reading. This uneven development begins in the years from birth to five!!! Do children ever catch up? It is difficult. However, problem-solving activities in life and work are often different from problem-solving activities in the world of academia (math, history, and English skills). Many children who do not score well in academic work often become far more successful and richer in the world of real-life practical problem-solving. For others, as one matures, problems found in work or on the job which required the academic skills of reading, writing, and arithmetic, are learned through necessity, practice, and repetition. 241 | P a g e 242 Prepublication Copy Parents have to help children practice and focused on problem-solving situations and expose them to as many variegated situations as possible. Exposure without corrective, nonjudgmental feedback is less useful in problem-solving situations. Since problems come in all sizes and different forms, the key to finding a solution is often exposure to corrective feedback. Exposure helps the individual recognize the facets and limits of the problem situation. But, as is patently evident for many children, exposure must be accompanied by feedback as to “why” a solution could or could not be found. Often the feedback is given as reasons or explanations. And then again, the feedback may come in the form of a question? Asking a child to explain “why” things occur in a certain way helps him or her differentiate between solutions to the social situation and practical problems encountered daily. Feedback about behavior is given to correct an improper response in social situations; while feedback on solutions to problems is given to approximate immediate or evolving change in problems encountered daily. Regardless of the form, reasons provide cognitive support for situations that are encountered as part of the problem. Diagram 5: Cognitive Model (Late Adolescence) Cognitive Model: Adolescence 10-13 242 | P a g e 243 Prepublication Copy The cognitive model for the 10-13-year-old does not change from the cognitive model of the 8-9 as children are just using more of their cognitive and affective systems. Late starters and late bloomers are now able to solve problems that were previously out of their cognitive range because of the “readiness” factor. Just about every child has strengths in one or more subject matter areas; if they do not, then this becomes the time when children often think about dropping out of school. Sometimes, during this development period, depending on the child is where a preference for certain types of problem-solving styles begins to crystallize. This crystallization allows measurements using self-report and independent measures of performance. The goal is to predict within error which child is more likely to perform better on different kinds of problems—verbal, numerical, and spatial. The independent measures, at least, to begin with, are teacher-made tests, standardized tests, and problem-solving exercises. An example of a teacher-made test is a simple test for doing fractions, an exercise with which many children of this age group have difficulty. Teachers administer these low-level mathematical tests at the end of a teaching unit. Many teachers find these unit tests already developed in booklets by the publisher of the curriculum that they are using. Standardized tests are more formal and rigorous and generally administered at the end of the academic year. Other independent measures included projects or written class assignments by the teacher. If the goal of prediction is successful, then those children in the 10-13 age group who score higher on our preference subscales will also score higher on the independent performance tests, similar to the children in the 8-9 age group. This is a process of validating our problem-solving instruments as well as understanding individual differences. Our longterm thesis is to identify children and their strengths. For example, the child who has a higher score on the General Problem-Solving subscales should do better on an academic standardized test while a child whose scores are higher on the Differentiation subscale should do better on academic and project-oriented tests which are in their area of interest. Of course, the assumption of doing better is based on averages. In a class of 40 students, comparing the scores of the top half of the class to the bottom half on the independent measures can identify differences related to the problem-solving scales. Remember problem-solving styles are not defined by precise categories. Instead, they are arranged by the strongest preference pattern. For example, a student with a preference for motor problem solving (M), may have perceptual (P) as a second preference and social (S) as a third (designated as MPS based on the order of use). Our experience is that the top one or two dominant subscales are most important and that the order of dominance is not final but tends to shift with age. The greatest volatility in age shift is from ages 817, with some stability from ages 18 - 24, and generally, after 25 years of age, dominance remains fairly constant, with a minimum of the shift, except with traumatic life events 243 | P a g e 244 Prepublication Copy (psychosis, neurosis, brain injury, etc.). Again, we have established fairly complex empirical definitions, which take into account the diagnostic criteria associated with interests, personal characteristics, perceptual orientation, and a preference for spatial and analogic problems as a method of designating the category of problem-solving with which an adult or student is more aligned. These categories can be useful in helping a youngster determine potential work and career paths. The Measurement System for the Early Adolescent In this section, we begin to show data that confirms the thesis that some children are slower in the process of solving academic problems while others are becoming more adept. Children who are classified as regular education but suffer from a low academic self-concept, a problem with timed tests, and a host of other problems which include difficulty in making logical and spatial decisions score lower in academic problemsolving. This group of students is, by definition, a differential problem solver. Cumulative factors lead to a lower grade point average (GPA) and low academic achievement on both teacher-made and standardized tests. Anne Holbrook (1989) examined some of the family background and parental behavioral practices which led to the conclusion that children who come from a “print-rich” family are more likely to have faster processing speeds and better academic problem-solving. Anne, as part of her Master’s Thesis, collected data on 100 randomly selected students with high GPAs (greater than 3.3) and 100 randomly selected students with a lower GPA (less than 2; less than C average). The students with high GPAs consisted of both differential and general problem solvers. With the parent’s permission, she tested 147 eighth-grade students from multiple schools. She sent home questionnaires. The parents of thirty-one of the low achieving students (Group A) and fifty-one of the high achieving students (Group B) returned the questionnaires; with a 54 percent return rate. Using data from instruments developed by the author, Ann determined the home and parental factors which separated the high and low achievement groups. She concluded that parents of high achievers stress the importance of a high school and college diploma, kept in close contact with the school and teachers and stress academic work as a priority in the home. The data from that study was statistically re-analyzed in terms of the present thesis. The average scores of both groups on problem-solving as well as the speed of processing instruments are presented below in Table 11a and 11b 244 | P a g e 245 Prepublication Copy Table 11a: Psa 9.18 2.46 Ps30 11.99 1.48 An 35.05 10.1 Pslap 13.26 2.93 Pssp 13.11 2.12 Df 11.96 1.11 Per 28.59 7.73 Cn 35.49 7.96 So Ct Fx 34.41 46.63 40.56 9.24 15.52 3.31 Scores of 13-year-olds on the Problem-Solving Instrument Mt 34.39 7.38 EI 17.99 9.34 Table 11b AGE PF Letid Emb Arith N Mean 13 11.52 27.22 29.98 15.48 82 SD .05 1.89 6.69 2.96 5.73 PF=Perceptual Flexibility LD=Letter identification, Emb=Embed Figures, Arith=Arithmetic Distraction Average scores for 13-year-olds on Speed of Processing The scores for the problem solving are unremarkable while the scores on the speed of processing are higher than average for the age group, scores bolstered by the number of high achieving students. If the scores in the two groups are divided into Group A (Grade Point Average less than 2) and Group B (GPA greater than 3.3) then the average differences are very remarkable. Table 11c and Table 11d present the scores on problemsolving and Table 11e presents the scores on the speed of processing instruments. Table 11c Group A Psa Ps30 Mean 7.27 10.93 SD 2.28 1.35 Group B Psa* Ps30* Mean 10.33 12.64 SD 1.46 1.13 Group A N=31; Group B N=51 P=.01* Pslap 10.89 2.73 Pslap* 14.70 1.45 Pssp 12.16 2.05 Pssp* 13.69 1.89 Df** 12.69 1.17 Df 11.51 0.65 Per 28.90 7.50 Per 28.39 7.80 Cn 31.03 7.12 Cn* 38.20 6.79 Scores for 13-Year-olds (Groups A & B) on the PS Instrument 245 | P a g e 246 Prepublication Copy Scores in Tables 11c and 11d illustrate the large differences between the low-achieving group and the high-achieving group. Scores on both types of instruments Psa and Ps30; Pslap; & Pssp are illustrated. From Table 11c, the high achieving group (Group B) has significantly higher mean scores on Conceptual and all general problem-solving scales (Ps30, Pslap, Pssp). The low achieving group, which has an average GPA of less than 2, is significantly higher on the Differential subscale as well as two other subscales that appear in 11d. Table 11d Group A Mt* An* So Ct Fx* EI Mean 36.40 37.67 30.20 37.87 41.32 16.13 SD 6.75 11.91 10.50 17.25 2.96 9.35 Group B Mt An So** Ct** Fx EI** Mean 33.49 33.69 36.90 52.00 40.10 19.20 SD 7.32 8.71 7.48 11.70 3.41 9.36 Group A N=31; Group B N=51 + Levine statistic (heterogeneity of variance) Scores for 13-Year-olds (Groups A & B) on the PS Instrument From Table 11d, Group A, the lower achieving group, has higher means on Motor, Analysis, and Flexibility while Group B, the group with higher GPA has significantly higher means on a total of 8 subscales including- Socialization, Structure /Control, and Extraversion. Now addressing the speed of processing scores in Table 11e below, the group with a higher GPA has significantly higher means on almost all speed of processing tests. Table 11e Group Name CF** Letid** Emb** Arith* Group Mean 10.83 25.27 28.63 14.20 2.60 7.94 4.75 6.77 12.22** 29.16** 31.33** 16.76* 1.17 5.44 1.18 4.69 A Group A Std. dev. Group Mean B Group B Std dev. Group A N=31; Group B N=51 **=.01 *=.06 Scores for 13-Year-olds (Groups A & B) on Speed of Processing 246 | P a g e 247 Prepublication Copy In conclusion, these Tables support the notion that high achieving students as indicated by a higher-Grade Point Average (GPA) have faster processing speeds and a propensity to solve academic problems with less difficulty. Tables 11c and 11d also indicate the non-cognitive Psa and the cognitive scores (Ps30; Pslap; & Pssp, as a measurement of academic problem solving, move in a similar direction with a large average difference. For example, Psa, Ps30; Pslap, & Pssp, as representative of cognitive and noncognitive variables, have large average differences between Group A and Group B. This next section shows data that verifies how perceptual speed increases developmentally for the age group of 10 through 13. Perceptual speed (10-13) Perceptual speed, which includes a component called attention span, is still increasing at 11 and 12-year old but stabilizes at about 13 years of age. As noted in an earlier chapter, the Perceptual Flexibility Test (PF) has 13 stimulus items. The perceptual field contains about 26 rotated and non-rotated similar items. The students have two minutes to match as many items in the stimulus field to the perceptual field. Table 12 Age Male (M) S.D. Female (M) SD. Range Max N. Sp. Ed SD. N 7 4.2 2.3 4.6 2.24 0 11 185 3.40 1.4 42 8 5.5 2.3 6.0 2.54 0 12 324 4.65 1.36 15 9 5.6 2.8 6.1 2.60 0 12 135 5.33 2.0 47 10 5.7 2.7 6.6 2.78 0 13 142 5.6 2.3 41 11 7.1 3.0 6.7 3.31 0 13 188 6.15 2.5 25 12 7.5 3.2 8.5 3.25 1 13 94 6.6 2.4 92 13 8.3 3.1 9.3 5.3 0 13 125 7.0 2.56 32 Male and Female (Means and S.D.) for Perceptual Flexibility Tests for Ages 7-13 247 | P a g e 248 Prepublication Copy Notice in Table 12 above, the Perceptual flexibility test, that the seven-year-old male has an average score of 4.2 and a standard deviation of 2.3. A female of the same age (seven)) has a mean of 4.6 (SD-2.24). Compare this with an eight-year-old male scoring 5.5, a nineyear-old scoring, 5.6 (2.8), a ten-year-old 5.7 (2.7), and an eleven-year-old male scoring 7.1 (3.0). Females, who were eight, nine, ten, eleven and twelve-year-olds had average scores / (standard deviation) 6.0/ (2.54), 6.1/ (2.6), 6.6/ (2.8), 6.7/ (3.31), and 8.5 / (3.25) respectively. In other words, the averages for perceptual speed tests have been increasing steadily, along with brain and body development since about 5. The increments, taking into account socioeconomic status, ethnicity, and gender, are fairly stable and predictable. This pattern follows the work of Epstein (1978) and Toepfer (1980) on brain growth. Accordingly, Epstein and Toepfer suggested that brain growth occurs in spurts, with defined periods of no growth. The 3 periods in which the brain does not show cognitive growth are 4 to 6 years of age, 8 to 10, and 12 to 14. Based on Epstein and Toepfer, one expects the averages of the Speed of Processing Tests at different ages in perceptual development to follow similar patterns with spurts at 7-8, and 11-12. Although the pattern is not exact, the average increase is 5.7 to 7.1 (males) and 6.7 from 8.5 (females) around 11 to 12 years of age. Differences in means are large for males and females but are not statistically significant. Is the same pattern evident in the other tests involving perceptual speed? Table 13 below shows the average correct scores on letter identification, embedded designs, arithmetic, and memory show identical patterns. Table 13 PF Letid Emb Arith N Mean 5.34 21.36 13.56 6.55 162 SD 2.87 9.72 9.91 4.94 Mean 6.25 22.81 15.60 7.60 SD 2.85 8.00 8.28 4.94 Mean 6.71 25.50 16.05 9.66 SD 3.09 8.67 8.53 5.40 Mean 7.69 28.61 17.31 11.12 SD 3.00 8.69 8.67 5.47 Mean 7.80 29.43 16.83 10.38 SD 3.31 8.90 9.46 5.27 AGE 9 10 11 12 13 178 219 275 178 +includes special education averages differ from the previous table due to sample size 248 | P a g e 249 Prepublication Copy Scores on the Perceptual Speed Tests for Ages 9-13 Note: Table 13 demonstrates that all means for the perceptual tests increase almost linearly with age, i.e., memory and perception are dependent upon sequential growth in the brain and central nervous system. Table 14 below shows the average scores and standard deviations on two timed perceptual memory tests for regular and special education students (5-13). The students were given a sheet with a field of 26 letters in a normal or rotated status. The task was to remember as many of the letters as they could. They studied the field for 2 minutes. The sheet was turned over. The students were shown another field of letters and told to identify any figure present in the first field by circling. The same procedure was used for symbols. A correct score was the correct number memorized as indicated by placing a circle around the figures that were present in the field. Table 14 Age Regular S.D. Min Max N Sp. Ed Mean SD Range N 5 0.00 0.0 0 00 00 0.00 0.0 0.0 0.0 6 00.00 0.00 0 00 00 02.79 1.93 0-05 14 7 06.23 3.92 0 14 24 03.64 3.00 0-10 14 8 07.68 3.48 0 16 47 04.64 4.94 0-14 14 9 08.39 5.08 0 16 60 04.20 3.66 0-12 15 10 09.65 5.09 0 23 54 05.27 3.73 0-12 15 11 10.60 5.23 0 26 187 08.13 6.46 0-22 22 12 10.45 5.25 0 26 45 13 10.58 5.60 0 26 25 Average Scores on Memory for Regular and Special Education Students The sample did not include any regular-age students at ages 5-6. However, we did measure a small group of 14 special education students at age 6. At age 13 the regular students remembered an average of 10.58 letters or symbols. The pattern is: the older the child the greater the number correct until about age 11-13 then the average, for young students, remains consistent at about 10.55. Special education and regular students did better with letters memorized and circled than with symbols. Regular students were able 249 | P a g e 250 Prepublication Copy to correctly retrieve from memory more correct symbols and letters. Notice the number correct also increased with age. From our perspective, the increase in memory and perceptual accuracy with age is important. Memory and perception are the basic building blocks of problem-solving. Again, in the IPS model, the input process is perceptual and the process factor is a memory. Before problem-solving can take place, an individual must take in the information (attention/perceptual) and store the basic building blocks in memory. Children's thinking patterns, up to this point, have been mainly associated, with some analytical thought. Only some children display logical approximation, inference, and logical analytic thought. Usually, students who are 11 or 12 years of age are in the sixth or seventh grade. Teachers who have a classroom filled with sixth-grade students can testify about the limited number of children who use logical thought or logical approximation. There is also some evidence that a few children understand the complexity of life's decision-making and can approximate better decision-making. Average or belowaverage 7th graders who can make better life decision-making (deciding what clothes to wear to school) may still have problems with abstractions in specialized areas such as math. For this group of 12-year-old, there is generally a less statistical correlation between standardized test data and skills requiring more complex operations (spatial analysis and sequence identification). From seventh grade, onward, children solve more complex academic problems using logical and spatial thinking. The basic elements of the problem-solving model apply differently to each age group (1113, 14-17, etc.). Developmental perspectives and maturation play an important part in understanding how the individual approaches each problem. The problems solving categories were somewhat conceptually distinct, but not necessarily always mathematically distinct at 8-9 years of age--are they mathematically distinct at 1013? Five different Master’s Theses (from Kristen Shand, Erwin Odbam, Jim Cox, Anne Holbrook, and Mike Ellis) give us an insight into both the problem-solving categories of youngsters at this age and into differences due to development. These 362 children represented by the five studies provide a good look at a cross-section of youngsters in the California school system. Scores on their standardized tests generally followed a normal distribution. Most of these children were 12 years old, a few were 10 and 11. For the first time, one can derive a measurement of an age group in which confidence can be placed. The test-retest reliability for these scales varies from .84 to .92. Below are the numerical averages and standard deviations of the scales. The sample variation in average scores of 3 of the five groups is evident on the subscales. Table 15a shows the means and standard deviation across the 10 subscales for the elementary non-cognitive assessment. 250 | P a g e 251 Prepublication Copy Table 15a Name Age Psa Df Per Cn Mt An So Ct* Fx EI Erwin 12 12.11 11.48 39.44 43.86 35.30 46.32 46.95 53.12 27.49 22.79 2.43 0.93 9.61 10.77 10.39 9.47 11.38 13.90 3.34 4.82 9.18 11.96 28.59 35.49 34.39 35.05 34.41 46.63 40.56 17.99 2.46 1.11 7.73 7.96 7.38 10.10 9.24 15.52 3.31 9.34 12.03 10.93 37.47 36.33 33.07 34.33 42.27 63.87 26.44 22.63 N=62 2.69 1.33 10.97 8.49 7.54 7.90 8.58 18.98 4.29 5.14 Average Mean 11.75 11.77 36.31 37.00 36.82 38.37 41.83 49.91 30.40 20.87 Std. 1.37 1.11 10.13 9.94 9.35 10.71 10.56 15.79 6.18 6.51 Psa Dif Per Cn Mt An So Ct* Fx EI N=114 Ann 12 N=82 Mike 12 Means and Standard Deviation on Non-Cognitive PS Subscales Scores For 262 Twelve-Year-Old Students A factor analysis of the ten subscales suggests that at least two groups exist: the first group is conceptual, analytical, and social while the second is general/differential, perceptual, and motor. The first factor is dubbed internal representations and the latter scale is called performance. The first set of scales is related more to creative endeavors such as music, drawings, and artistic development while the latter is associated with academic indicators, doing well on academic tests, and performance with hands. These relationships are somewhat expected. However, one might question why perceptual motor also occurs with differential and general problem-solving. For now, suffice it to say that academic performance, the second factor, is significantly correlated with memory while conceptual, analytical, and social are not. What other tests are significantly associated with the second factor? From the same study, standardized pretests, posttests, regress gain scores on arithmetic as well as memory are all significantly related (r=.36 to .52, mean correlation .45; p=.05). This establishes the second factor as an academic factor related more to math problem-solving. From the results of another study, the first factor dubbed Internal Representation is significantly correlated with Structure, Achievement, Learning Perception, and SelfConcept (r=.40 to .56; average mean=.46 p=.001) All of these subscales are indirectly related to achievement tests. 251 | P a g e 252 Prepublication Copy Gender differences Gender differences are shown in Table 15b below. The means for the Psa scale is almost 1 point higher than the means for the 8-9 years old students who were presented in the previous chapter. Females score higher on the Conceptual, Social, Control scales and Extraversion while males score higher on Analysis and Motor. Notice that the Flex scores are comparable but Control is much higher than Flex. Males scored significantly higher on the Perceptual Scale. Table 15b Males Psa Df Per** Cn Mt An* So Ct Fx EI Mean 11.49 11.67 34.13 34.08 34.61 38.44 34.95 52.03 28.61 19 SD 1.54 1.25 7.52 8.43 7.38 8.79 9.06 17.49 3.68 7.48 Females Psa Df Per Cn* Mt An So* Ct* Fx EI** Mean 11.54 11.3 32.14 60 32.99 32.04 40.71 57.39 28.13 21.17 SD 1.45 1.14 10.53+ 7.9 7.43 7.99 7.68+ 16.34 3.79 6.88 N=485 **P=.05 *P=.01 +logarithmic correction for heterogeneity-Levine’s statistic Elementary Non-cognitive (Psa), PS instrument Gender Differences for 12 Year- old Male and Females Combined Means From Five Different Studies of 12-year-old on Adolescent and Elementary Instruments In this next section, we examine each of the PS subscale scores more closely to determine how each subscale compares to normative data of 10-13-year olds. The presentation starts with those subscales which identify the general and differential problem solver and then examines the means and standard deviations of the rest of the problem-solving scales for the early adolescent. The measurement system includes cognitive and affective data from many different studies conducted from 1994 and sometimes earlier. 252 | P a g e 253 Prepublication Copy Problems Solving Scales General problem solving The demographic characteristics of the children in the five studies, generated by the graduate students working on their Master’s Thesis, are as follows: In the first study, Michael (Ellis, 1994), there were 62 twelve-year-old, 29 males and 33 females. Students came from a moderate SES background. The group consisted of 23 Caucasians, 3 Asians, 5 Afro-Americans, and 29 of Hispanic origin. The average Stanine score (goes from 1-9) on the California Standardized Achievement Test (CSAT) was 4.53 with the math percentile being 41.2 percent. Overall, this group was below average academically in math. The scores on perceptual speed tests were generally average for their age group. Three other studies, Shand (1999), Obdam (1994), and Cox (1995) were similar in that the students were predominantly Caucasian and Hispanic with a small number of Asians and Afro-Americans. Obdam’s group of 114 people and Cox’s group of 174 people consisted of mostly twelve-year-old and a very small group of 11 years old. Erwin’s and Jim’s groups had a greater number of lower and middle social-economic classes. The latter three groups of Jim, Kirsten, and Erwin had higher average scores on the academic achievement tests. Kirsten’s group, which had more advanced students, had an average proficiency score in the 64th percentile in reading and math. The goal is to predict and classify children and adults based on their performance and preferences. If one could find a set of predictors that separated children’s performance based on their preferences, this could be quite helpful in understanding individual differences. The non-cognitive general problem-solving scale (Psa) is based on the premise that those children who are developing emotional stability, social insight, independent thinking, and achievement orientation are more likely to perform and learn better than those who do not. These non-cognitive characteristics come from instruments measuring children 12 and younger. That premise related to non-cognitive factors is likely to be most evident in younger children rather than adults. What do we find in this age group? Four (Erwin, Ann, Jim, and Mike) of the five studies are compared on all subscales next. We first examine the scores on general problem-solving in Table 16. 253 | P a g e 254 Prepublication Copy Table 16 General Problem Solving Elementary Noncognitive Psa Name Sample Size Age Statistics Erwin 114 12 12.11 S.D. 2.43 Mike 62 12 S.D. 12.03 2.69 Jim 104 12 S.D. 11.45 2.41 Ann 82 12 9.18 S.D. 2 Ave of 4 studies 11.19 Ave. SD 2.38 Average all 12yrs N=629 250 12 1.71 S. D. Mean 8-9 11.61 Psa* Total 148 8&9 11.03 3.48 S.D. Comparison of Averages for Different Groups on The Elementary (non-cognitive) PS Instruments Erwin’s group scored the highest while Mike’s group, which was selected for remedial work in math, had the second highest Psa or General Non-Cognitive Problem-Solving score (12.03). The other scores, including the average of all 12-year-olds, were generally comparable. Without going into a lot of detail, 3 of 4 studies with 12-year-olds showed good mean separation using both non-cognitive and cognitive for the ten measurement subscales. The following examples show one study of the cognitive subscales (Table 16a and Table 16b) with normal differences in the mean separation and one study (Table 17) that is reversed from expectations. Table 16a below presents the data from Kirsten’s Group. Kristen’s group used the cognitive adolescent PS instrument (Ps30; Pssp; Pslap). A very large percentage of students were higher in academic achievement and therefore the separation between the 254 | P a g e 255 Prepublication Copy means on the Problem-Solving subscales was very good. Although the samples are disparate in numbers, the differences are illustrative. Table 16a: Kirsten’s 12-year-old Group Ps30* Pslap* Dif Pssp* Per Cn Low High Low High Low High Low High Low High Low High N 29 99 29 99 29 99 29 99 29 99 29 99 Mean 10.97 11.80 11.36 12.48 10.95 12.65 13.79 12.85 41.6 40.66 36.64 33.28 SD 1.46 1.74 2.08 2.6 2.18 2.52 1.82 2.32 10.33 11.53 8.62 12.05 Mt An Soc Ct Fx EI Low High Low High Low High Low High Low High Low High N 29 99 29 99 29 99 29 99 29 99 29 99 Mean 45.28 44.27 37.12 39.38 48.32 43.81 41.92 36.58 35.52 39.22 19.28 20.25 SD 9.5 11.09 10.43 15.32 11.71 11.37 11.32 14.49 13.23 12.42 6.11 6.49 P=.01* Averages of students on the PS subscales using the Math Standardized Tests as a Division at the 50th percentile Table 16b below gives a normative comparison for older age groups (16-50) on the same instrument. The normative comparison age groups, listed in 16b, were based on 300 children (ages 16-17) and 447 adults who are greater than 23 years of age. Note the increase in means for the problems solving subscales for older age groups 16-17 and 23+ (Averages of 12.31 & 13.25) as well as the other differences in the subscales. Table 16b Ps30 Pslap Pssp Dif Per Cn Mt An So Ct Fx EI 16-17 12.31 13.91 13.42 11.33 33.31 30.46 33.26 40.69 37.66 38.86 33.89 18.69 SD 1.42 1.81 2.43 1.72 9.08 11.68 10.61 13.20 11.26 12.43 9.77 6.04 23+ 13.25 14.72 14.89 10.19 42.61 15.26 19.88 20.04 38.97 32.14 24.49 12.35 SD 1.64 2.42 2.63 2.09 11.79 5.53 5.70 6.38 14.49 13.23 7.25 11.51 For 23+ age group N=448; 23+ group had more college educated in sample for 16-17 N=70 Comparison Scores for 2 Age Groups (ages 16-17; 23-60) 255 | P a g e 256 Prepublication Copy Next, Table 17 shows a group with the non-cognitive Psa that did not have a good separation of the mean scores based on high and low scores on reading. Best results are obtained when groups are similar in age, i.e., 10-11; 11-12, or 12-13, with a maximum variation in the group reading, math, or spatial scores. Michael’s group in Table 17 did not show as much differentiation on the reading standardized tests as they were below average and much more difficult to separate. For Michael’s group, there was also a single cognitive score on Pslap. The cognitive and non-cognitive problem-solving scores could be compared for these select groups. The average scores for Michael’s Pslap were 11.07 with a standard deviation of 1.54. Using Tables 16a and 16b compare this average of 11.07 with the averages for Kirsten’s, the age group of 16-17, and the adults 23+ who were academically superior. In Michael’s group, a greater number of students scored between 0 and 33 percentiles on standardized tests. There is a lot of homogeneity in the scores of individual students who comprise the lowest one-third of a standardized test group. Our theory is that the group was so homogeneous, that the means on the general problem-solving scale were in almost the same proportion for both groups of high and low. The Psa for Michael’s group was 12.03/2.69. This average suggests that although the very low students did not score well on math tests, they possessed greater self-esteem and learning identity which is one reason that they were selected for special math training. These results are reflected in the non-cognitive Psa score in Table 17. Table 17: Michael’s Group Df Psa Cn Per Mt Low High Low High Low High Low High Low High N 38 22 38 22 38 22 38 22 38 22 Mean 11.17 10.89 10.76 11.24 36.63 38.91 36.68 35.73 33.21 32.82 SD 1.6 1.44 1.21 1.49 12.07 8.83 8.15 9.2 6.79 8.85 Table An So Ct** Fx EI Low High Low High Low High Low High N 38 22 38 22 38 22 38 22 38 22 Mean 34.26 34.45 42.63 41.64 66.32 59.64 25.9 27.36 22.53 22.82 SD 8.53 6.87 8.1 9.53 17.14 21.56 3.86 4.9 5.5 4.56 P=.05** 256 | P a g e 257 Prepublication Copy Averages of Students on the PS subscales using the Math Standardized Tests as a Division at the 50th percentile Michael’s group had means which were comparable across subscales with only the Structure and Control preference scale showing significance. In the next section, compare the mean separation on all different problem-solving scales across the different studies. Differential problem solver The majority of students are differential problem solvers based on this calculated subscale. The foundational characteristics, ideas, and work habits of the differential problem solver are formed in early life. This is evident in the studies below. Kirsten’s group (not shown) was the highest academically and scored the lowest on the Dif scale as this scale is almost the inverse of the Ps scale. Interestingly enough in Table 18 below, Mike’s group scored comparatively higher on this subscale i.e. they did not perceive themselves as general problem solvers. As noted earlier, Mike’s students did not score well on academic achievement. Originally, Michael’s students were selected based on the need to improve their performance on math fractions. Table 18 Differential Sample Size Age Elementary Mike 62 12 12.06 S.D. Erwin 1.74 114 12 S.D. Jim 1.75 104 12 S.D. Ann 11.27 11.13 2.31 82 12 10.74 S.D. 1.89 Mean of 4 studies 11.30 SD of 4 studies 1.92 10.24 257 | P a g e 258 Prepublication Copy Ave. all 12 yrs. S. D. Mean yrs. 1.95 8-9 Dif* S.D. Adult 148 8&9 11.03 3.48 Scores of 12-year-old Students on the Differential Problem-Solving Subscale Perceptual problem solver Perception relates to what a child sees and hears when addressing a problem situation. The amount of time that a child focuses on a problem is inherently related to problemsolving effectiveness. A child who cannot focus his or her attention for any length of time has difficulty solving complex problems. Attention span for average youngsters at age 12 is about 15 minutes—about 5 minutes at the short end and 25 minutes for those with the longest attention spans. Most of all, children who have longer attention spans tend to spend more time with printed materials or reading. Attending is the first step in the conceptualization of the external environment. Children who have a very short attention span also have trouble attending to the spoken word. They turn their attention to their interests--feelings, mind wanderings, objects, or thoughts of the day. For children with short attention spans, individual directions and explanations are necessary since many children with short attention spans do not attend except when given individual attention. In Table 19 below, notice the various mean scores and standard deviations for the 12year-olds on the Perceptual subscale. The average score range is 28.59 for Ann’s group to 39.77 for Jim. 258 | P a g e 259 Prepublication Copy Table 19 Perceptual Sample Size Age Elementary Jim 104 12 39.77 S.D. 12.23 Erwin 114 12 S.D. 39.44 9.61 Mike 62 12 S.D. 37.47 10.97 Ann 82 12 28.59 S.D. 7.73 Mean of 4 studies 36.32 Ave. SD 10.14 Ave. all 12 yrs. 40.84 S. D. 11.28 Mean 8-9 S.D. 148 8&9 28.03 10.24 Scores of 12-year-old Students on the Perceptual Problem-Solving Subscale Conceptual The operational definition used in research for conception is using and/or displaying a preference for ideas. Children in this age group who are high on ideation are generally voracious readers (or come from homes where the parents display behaviors such as liking verbal word games or creating verbal images. Some authors substitute words like creative or imaginative to describe conceptual thinking. In our studies, various operational definitions of conceptual have produced comparable results. 259 | P a g e 260 Prepublication Copy Studying the problem-solving behaviors of 450 children in the age range of 11-13 gives some indication of the number of children who identified themselves as having a greater preference for ideas. These two constructs of ideation and conceptual, by themselves, are more important in developing problem-solving behaviors which become important in later career pathways. At an early age, relationships are significant in one study but not in another. In Table 20 below, the average scores on the conceptual subscale differ considerably for the 4 groups of 12-year-olds. Erwin’s group was the highest (43.86) while the other three averaged around 35. Table 20 Conceptual Erwin a b Sample Size Age Elementary 114 12 43.86 S.D. Mike 10.77 62 12 S.D. Ann 8.49 82 12 S.D. Jim 36.33 35.49 7.96 104 12 32.31 S.D. 12.56 Mean of 4 studies 37.00 Ave. SD 9.95 Ave. all 12 yrs. 34.15 S. D. 8.03 Mean 8-9 148 8&9 S.D. Adult 29.62 9.55 Scores of 12-year-old Students on the Conceptual Subscale 260 | P a g e 261 Prepublication Copy What are academic problem-solving behaviors? Children are presented with various school academic problems and must take some active steps to solve the problem. Children who seemed to solve different kinds of academic problems well are generally inquisitive, asking questions to gain more information, structured in a sense of planning the problem out, analytical in the sense of evaluating different kinds of outcomes, and motivated, willing to try and find some kind of outcome. The outcomes of problems differ widely in that some problems are well defined and others are less defined. The undefined problems require the individual to put boundaries or constraints on the problems. The solutions may have multiple outcomes, rather than a single right answer. For example, a group of 6 students with whom I was working recently wanted to make a vehicle, similar to a go-kart. The students were sent out to look at various kinds of gokarts and design a vehicle. When their drawings were analyzed, 5 out of the 6 drew pictures based on what they had seen. The sixth person draws a vehicle that had no relation to the existing pictures of go-karts. The last person also scored higher on the conceptualization subscale. Based on his pattern of scores, he was designated as an “image pattern processor” as he was also higher on flex and average on control and structure. The image pattern process seems to rely more on top-down processing (explained in an earlier chapter). As indicated earlier, all people receive information perceptually through their senses but many take that information and form ideas which are considerably different from the information taken in. These students use ideation more and generally choose adjectives associated with constructs that they have conjured. Younger age students (10-11) in this group choose self-descriptive adjectives which are very aligned with the existing concept of ideation, especially girls. They have a preference for words such as creative, rather than realistic. This is not unusual for many are transitioning from a fanciful world of dragons, elves, and other mythical figures. The 11year-old still possesses a sense of fantasy about the world in which he or she lives. Motor problem solver In this age group, another dimension is added to the characteristics of the motor problem solver. Previously the uniqueness of this problem solver as a person who is good at motor, hand-eye coordination, and manual skills was emphasized. This uniqueness also contributed to their ability to apply simple direct solutions to problems, usually in a form or method which can be incorporated by others. The scores in Table 21 reflect their preference patterns for motor activities. 261 | P a g e 262 Prepublication Copy Table 21 Motor Sample Size Age Elementary Jim 104 12 44.5 S.D. Erwin 12.1 114 12 S.D. Ann 10.39 82 12 S.D. Mike 35.3 34.39 7.38 62 12 33.07 S.D. 7.54 Mean of 4 studies 36.82 Ave. SD 9.35 Ave. all 12 yrs. 44.47 S. D. 10.77 Mean 8-9 148 8&9 S.D. 27.08 9.53 Scores of 12-year-old Students on the Motor Subscale In the example in the previous section, children design a go-kart. Five of the six children showed designs of a go-kart that each had seen. Four of these five children chose “practical” as a self-descriptive adjective on our instruments. They preferred to solve problems based on their images similar to those derived from their senses. They see an object and modify it. The process was called “applied creativity” and we designated them “object processors”, similar to those who rely on bottom-up processing. All individuals receive information from the environment in some form for problemsolving. Some of this information comes through the five senses and some are generated from thinking and emotions. Individuals who perceive information through the senses or generate information internally from previous experiences and thoughts apply the information in a number of different ways. As a trivial example, suppose the problem is 262 | P a g e 263 Prepublication Copy to put a cap on a bottle of milk. The solution is to pick the cap with the hand, place it on the top of the bottle, and press it. Simple, yes? This is what the motor problem solver does. A motor problem solver is usually one who has abundant common experience with the problems found in his or her environment. He or she seeks solutions to those problems in a simple direct manner. If the characteristic of a motor problem solver is defined in this manner, is not everyone a motor problem solver? The answer is probably yes to some degree. But again, can you think of people who do not seek a simple solution to common problems? Instead of a simple solution, the solution is unique, too complex, or even inane? Often this characteristic separates the conceptual problem solver from the motor problem solver as maturation occurs. Can not a person be both, perhaps shifting back and forth between the two systems? Sure, in that case, if both orientations are differentiated by age, then the classification of CM occurs. However, most older people have more of a preference for one or the other when one uses a cut point at the 50th percentile. Motor choices occur with greater frequency than conceptual choices in the 12-14-year-old age group. Analysis There is a distinct difference in the preference for a certain activity and the capability to solve problems in that area. Having a preference for analyzing things does not mean that one actively spends time analyzing things but that is our assumption as the data collected over many years suggests a stronger significant relationship. Table 22 Analysis Erwin Sample Size Age Elementary 114 12 46.32 S.D. Jim 9.47 104 12 S.D. Ann 10.35 82 12 S.D. Mike 37.79 35.05 10.1 62 12 34.33 S.D. 7.9 Mean of 4 studies 38.37 263 | P a g e 264 Prepublication Copy Ave. SD 10.71 Ave. all 12 yrs. 38.94 S. D. 14.48 Mean 8-9 148 8&9 S.D. Adult 40.72 11.93 Scores of 12-year-old Students on the Analysis Subscale In Table 22 above, Erwin’s group had the highest average score while the 12-year-olds, in general, had the greatest variety of scores (SD=14.48). Why? Erwin’s group of students used computer technology as an aid in solving problems. Does this present some sample bias? Probably? Is there a difference in the preference responses of males and females on the subscale measuring analysis in 12 different studies involving children of different ages? The results of these studies show expected gender differences, with males scoring significantly higher on preference for problems involving both analytical as well as logical thought processes but these differences are slight in comparison to the total group. Remember these data are based on preferences for items reflecting problem-solving in the age group 11-13, not ability. Logical analysis elements Once again, there is a difference in our definition of analytical thought versus logical analytical thought. Logical analysis elements are based on correct responses versus preferences. Previously children who were less than age 10 had difficulty with logical thinking, especially problems involving seriation, transitive interference, and reversibility, Children in early adolescence can answer the following question with a degree of assurance: Jane is shorter than Mary. Mary is shorter than Susan. Who is taller- Jane or Susan? Our tests incorporate some fluid ability items which are in the form of analogies, series, and sequential items. All three types of items have years of precedents in the measure of intelligent behavior. Spearman (1923) used the terminology of “nongenetic thinking” to describe the process of solving analogies. The experience was emphasized by his first 264 | P a g e 265 Prepublication Copy principle: “the apprehension of experience” while his second and third principles “emphasized the power of inferences and education of correlates.”. A series is defined as being able to induce what number or figure in a series comes next. A typical series might be 1, 2, 4, 8, and 16, __ where an individual is required to circle the number 32 from possible alternatives such as 25, 9, 32, or 18. Likewise a figural series might look like: + + + + -- ++ -; whereas the answer of +would be circled from possible answers such as +, -, 0, or /. (sequence is 4+, 2+ 1+; 2-,1-,0-). These different kinds of items can be examined in the various kinds of tests in the appendix. Analogies, in contrast, can be in the form of words and/or numbers. A simple number analogy is “4” is to “12” as “?” is to “36.” The possible answers are 12, 15, 16, and 4. The respondent must choose which is correct. The verbal analogies are like "hot" is to “cold” as “?” is to “night.” The possible alternatives are day, evening, morning, and afternoon. The last analogy is very simple and 98 percent of the people in the 11-89 age group can answer it correctly. Table 23 and Table 24 below show the mean and standard deviations as well as percentages on analogies and sequential problems for the current age group (10-13) as well as a comparison of special education students in grades 4-8. Table 23 illustrates the scores of children in special education. Table 23 Mean S.D. N. Grade Age 0.96 0.36 45 4 9 1.07 0.76 35 5 10 1.43 0.98 59 6 11 2.32 1.43 41 7 12 2.45 1.11 34 8 13 Means and Standard Deviations on Analogies and Sequential Items for Special Education Students in Grades 4-8 265 | P a g e 266 Prepublication Copy Special education students had difficulty answering any of the logical problems but notice that their means still increase linearly with age. A 12-year special education student who was developmentally delayed in grade 7 could only answer about 2 out of the twelve items. Compare the mean scores of males and females at the same age and grade level in Table 24. For example, as noted in Table 24 below, a 12-year regular student could answer about 5 items (mean-5.12) or 44 percent correct. Table 24 Age Grade N Males S.D. Females S. D. Min Max Percentage 9 4 143 2.34 2.9 1.85 2.9 0 4 40 10 5 156 3.61 2.11 3.51 2.03 0 5 44 11 6 178 4.63 2.63 4.22 2.08 0 6 55 12 7 195 5.12 2.42 4.42 2.32. 0 6 44 13 8 221 6.48 2.53 5.92 2.35 0 9 47 *** Adjusted by versions of the test Means and Standard Deviations of Analogies, Sequential Items for Ages 9-13*** Notice the mean scores increase with age as expected. The same kind of sequential and series problems are used at all different age levels. The number of possible points changed with different versions as noted in the chart. Version 1.5 had 10 possible points; while, Versions 1.0 and 2.0 had 14 possible points. When comparisons between or among various groups are made in this document, standard scores can be used. The conversion is simple; just use the average means and standard deviations. Standard scores lessen the effect of sample variation. What is the difference in average scores among a 12-year-old, a 13-year-old, a 17-year-old, and a 25-year-old? An average 12.6-year-old scores 4.4 out of a possible 10 while the 14, 17, and 25-year-old have a mean score on the logical block and folded spatial problems of 5.5, 7.5, and 7.56 respectively. For measurement specialists, the standard deviations are comparable with large samples. The scores of older children and adults on these subscales are higher and start to level out after age 23 or so. Social 266 | P a g e 267 Prepublication Copy Social problem solving, in general, is important for all ages. Social problem solving, as defined here, not only refers to the ability to get along with other people in social or group situations but also more specifically the capacity to interact in a manner that facilitates solving social problems. The idea of socialness is different for a child of 10 compared to an adult who is eighteen. Our data suggest that children are less engaged in “socialness” than adults. Socialness for this age child is based on selecting any of the following types of items: a) playing together, b) being able to interact in a group, c) engaging other children, and d) working on problems as a teammate e) liking to solve the problem with other children. Table 25 illustrates the average scores for this age group. Table 25 Social Sample Size Age Elementary Erwin 114 12 46.95 S.D. Jim 11.38 104 12 S.D. Mike 13.05 62 12 S.D. Ann 43.69 42.27 8.58 82 12 34.41 S.D. 9.24 Mean of 4 studies 41.83 Ave. SD 10.56 Ave. all 12 yrs. 44.69 S. D. 11.54 Mean 8-9 148 8&9 S.D. Adult 39.43 12.14 Scores of 12-year-old Students on the Social Subscale Those who are shy, isolated from their peers or family, or who have a personal orientation that focuses more on the internal world of ideas, are more likely to be perceived as less social. However, since social behaviors occur during social or group problem-solving, the introvert can be just as good at social problem-solving as the extrovert. At the age of 10267 | P a g e 268 Prepublication Copy 13, some children are still learning how to become “social.” Other children have the benefit of being brought up in homes where social etiquette and socialness are valued at an early age. Latchkey children who have less external control as both parents work often attach a different meaning to the term “social.” Socialness to many of these “ghetto” children infers survival on a day-to-day basis as socialness is finding a group or other people who will protect them. Teachers who work with children in the previous age groups (5-10) usually placed more emphasis on socialization and social behaviors as it is a prerequisite to learning. Teachers in grades 1 to 5 are much more likely to control behavior and place emphasis on social interaction as a key to “getting along” inside and out of the classroom. Control and structure Control and structure at this age are very much an extension of co-regulation that was discussed earlier. Children are not independent; therefore, learning to be self-regulated and developing emotional and cognitive control is a constant learning process. In many cases, control for young children is related to either delayed self-gratification or goal attainment. The first is internal and the latter is both internal and external. Delayed selfgratification according to Freud (1922) comes from cognition and perception (ego) which is attempting to regulate individual needs and desires. Skinner, on the other hand, suggested control was a learning process that originated from regulating internal impulses and inappropriate behavior. In goal attainment, control is sequencing the appropriate steps (structuring) to achieve the desired end as many environmental obstacles are circumvented. With these definitions in mind, the scores on the Control subscale for a group of 12-yearolds are quite interesting. Since control and internal structure are usually associated with greater academic achievement, the expectation is that the higher the score, the better. However, since control (as an internal mechanism), when considered with flex, is so important, this is not the case for some groups or individuals. In Table 26 below, the highest score on control was Mike’s group. Table 26 Control/Structure Mike d N Sample Elementary 62 12 63.87 S.D. Erwin 18.98 114 12 53.12 268 | P a g e 269 Prepublication Copy S.D. 13.9 Ann 82 12 S.D. 46.63 15.52 Jim 104 12 36 S.D. 14.77 Mean of 4 studies 49.91 Ave. SD 15.79 Ave. all 12 yrs. 55.46 S. D. 16.54 Mean 8-9 148 S.D. Adult 8&9 38.95 12.79 Scores of 12-year-old Students on the Control Subscale yet, as explained earlier in the chapter, Mike’s group is the lowest academically. A large percentage of students scored below 33 percentiles on standardized testing. Mike’s group was targeted for extra instruction on solving math problems involving fractions. Flex problem solver Flex is part of an internal control mechanism that filters impulses from the external and internal environment. Cognitive flexibility is built over an extended period and results from being put in a myriad of different circumstances and having to quickly adapt to changes. Being related to the control system, the individual learns quickly that their reactions, actions, emotions, and behaviors cause changes in the emotions and physical behavior of others. Control is often manifested at both a subconscious and a conscious level. One simple control mechanism is the suppression of an emotional impulse at a conscious level but not necessarily at the subconscious level. Children have learned by this age that certain emotional impulses are either not socially acceptable or should these impulses be expressed overtly. There is only one thing to do, let the emotional impulses, through suppression, wander creatively in the brain and find expression in another acceptable form. Suppression of impulses leads to imagination and fantasy which can take many different acceptable forms when an outlet is found for their expression. Later in life, art, 269 | P a g e 270 Prepublication Copy sculpture, painting, stand-up comedy, and verbal quips are just a few modes of conscious expression. Children are quick to notice perceptual differences such as a change in the expression, emotion, or mood. Their reactions are controlled or not controlled. Uncontrolled impulses result in all kinds of emotional responses from anger to joy. Controlled reactions are manifested in diverse ways depending on the individual. In Table 27, Mike’s and Erwin’s group had low flex scores while Jim’s group had the highest. Jim’s group was selected for more independent thinking. Table 27 Flex Sample Size Age Elementary Ann 82 12 40.56 S.D. Jim 3.31 104 12 S.D. Erwin 13.82 114 12 S.D. Mike 37.48 27.49 3.34 62 12 26.44 S.D. 4.29 Mean of 4 studies 30.4 Ave. SD 6.18 Ave. all 12 yrs. 38.5 S. D. 12.62 Mean 8-9 148 S.D. Adult 8&9 35.98 4 Scores of 12-year-old Students on the Flex Subscale 270 | P a g e 271 Prepublication Copy Extraversion/introversion Energy utilization and focus are different for males and females. Energy is more likely to flow outward to the environment for females, primarily because of the differences in socialization processes at earlier ages. Is that difference still present from ages 11-13? For the answer, inspect Table 28 below. Table 28 Extraversion/Introversion Erwin a b Sample Size Age Elementary 114 12 22.79 S.D. 4.82 Mike 62 12 S.D. 22.63 5.14 Jim 104 12 S.D. 20.08 6.76 Ann 82 12 17.99 S.D. 9.34 Mean of 4 studies 20.87 Ave. SD 6.52 Ave. all 12 yrs. 19.54 S. D. 7.80 Mean 8-9 S.D. Adult 148 8&9 16.54 5.32 Scores of 12-year-old Students on the Introversion/Extraversion Subscale Addressing the scores from 4 of our samples of 12-year-olds, Mike’s group along with Erwin’s scored the highest for extraversion, while Ann’s group scored the lowest on the Extraversion. 271 | P a g e 272 Prepublication Copy Based on twelve other samples at this age, females score higher on extraversion or the flow of energy into the environment. This is manifested in many different problemsolving preference patterns. But most importantly it is significantly correlated with selfconcept. Children whose energy flows into the environment in the different forms of mental and physical play perceive themselves as having a better self-concept. The correlation coefficient (.26) at p=.001 at n=245 undergirds one of the basic principles in this book as the relationship persists from early childhood until cognitive development matures into the latter stages of formal operations. However, as seen in later data, there is not one but a group of tendencies that influence behavior. Inspecting the means from the 6 different studies for males and females, females tend to score higher on extraversion. Differences in Types of Problems Solved As the scores in this next section are examined, the question becomes: “Using words, numbers, and spatial factors, which problem-solving subscales have greater separation when dividing into high and low achievement groups? For example, do you think a group of students who scored above the 50th percentile on reading (word contextual meaning) have a significantly higher average score on extraversion? Perception? Flexibility? Problem-solving? Word problem solving Addressing the problem-solving characteristics of Erwin’s group when dichotomized into a low and high reading achieving (California Achievement Test, CAT/6) based on a median split, significant mean differences are apparent. There are 58 people in the low group (below the 50th percentile) and 49 people in the high group. In Table 29, there is a major difference in the Motor subscale. The high-scoring group had a mean of 33.00 when compared to the low-scoring group (36.74). Significant differences were also found on the Ps subscale as well as extraversion/introversion, flex, and Control. Notice also that Flex is high for the low group (58.37 vs.52.91); however, there is a distinct variation in the standard deviation. Again, the extraversion/introversion subscale reflects socialness, a factor of which this age group is very aware. 272 | P a g e 273 Prepublication Copy Table 29 Dif Ps30** Per Con Motor* Low High Low High Low High Low High Low High N 58 49 58 49 58 49 58 49 58 49 M 11.55 13.01 9.91 8.20 38.23 41.36 43.37 44.64 36.74 33.00 SD 2.55 1.95 1.31 1.86 10.21 8.32 11.41 9.76 10.51 9.88 Soc An** Ct** Flex** Exit** Low High Low High Low High Low High Low High N 58 49 58 49 58 49 58 49 58 49 M 43.77 47.76 45.31 49.55 51.8 55.73 58.37 52.91 21.7 23.23 SD 8.53 9.29 12.41 9.04 14.3 11.97 11.76 9.34 4.27 4.81 P=.05** P=.01* Average Differences between High and Low Reading Standardized Test Groups on the 10 Subscales Again, every sample is different, so let's now examine a study by Jim Cox to determine if there is a better mean separation on the PS subscales. Using the standardized test scores based on communication skills and a random selection process, the subscales should have equal averages. As noted, next in Table 30, there is a separation on Psa and Df as well as Extraversion/ Introversion but not on the other scales. Table 30 Dif Psa** Per Cn Mt Low High Low High Low High Low High Low High N 39 97 39 97 39 97 39 97 39 97 Mean 11.76 12.39 10.19 9.70 40.82 42.98 35.79 35.92 30.51 31.12 Std. Dev 3.74 3.49 2.87 2.69 13.59 13.11 7.56 10.06 6.44 9.60 An Low Soc High Low Fx Ct** High Low High Low EI High Low High 273 | P a g e 274 Prepublication Copy N 39 97 39 97 39 97 39 97 39 97 Mean 31.44 30.45 42.59 42.57 55.69 59.31 41.26 39.92 17.49 16.71 Std. Dev 9.19 9.14 9.39 10.65 21.11 16.31 2.67 2.92 10.11 9.15 ** P=.05 Average Differences between High and Low Communication Skills Standardized Test Groups on the 10 Subscales Data on specific age groups Because of the vast development differences in these age groups of 10-13, using defined age groupings of 10-11 and 12-13 always provides better insights. The high and low scores on reading show differences in the expected direction for the problem-solving subscales as well as the memory, speed, transformation, and learning measurements. What is expected is that the mean for speed, transformations, and learning increases as academic achievement increases. That is, the group of children who have high means of Ps subscales also have high means on the other cognitive scales. Ps30 represents the combined scales (Pslap and Pssp) for problem-solving. Pslap is problem-solving on analogies and sequence items while Pssp represents spatial and block counting items. Ages 10-11 Table 31 Name Ps30 Pslap Pssp Dif Conc Grp Low High Low High Low High Low High Low High Low High N 53 50 28 32 28 32 53 50 53 50 53 50 Mean 12.16 12.15 11.54 10.88 12.41 12.19 11.76 11.74 37.36 41.28 35.85 37.16 Std. D 2.5 2.55 2.4 2.01 2.78 2.41 2.29 2.27 10.43 13.02 8.25 8.79 Per** 274 | P a g e 275 Prepublication Copy Name Mot An Ct Grp Low High Low High Low High Low High Low High Low High N 53 50 53 50 53 50 53 50 53 50 53 50 Mean 31.66 32.52 32.79 32.32 41.62 44.52 64.23 60.8 31.43 31.1 19.13 20.72 Std. D 6.76 7.86 8.15 7.48 9.21 8.2 18.32 19.16 4.4 4.55 9.26 7.44 Soc** Flex Exint Average Differences for 10-11-year-olds on High and Low Reading Standardized Test Scores As noted in Table 31 above, only two subscales for the age grouping of 10-11 years old indicated a difference: Perceptual and Social. That is, when children are separated into high and low groups based on their reading achievement on standardized tests, there is a difference between Perceptual and Social Problem-solving scores. Social is expected, especially for this age group. The problem-solving subscales (Ps30; Pslap; &Pssp) were not diagnostic for reading but were diagnostic when separated by math standardized test scores as indicated in another study (Yates, 2000). Table 32 Name Mem Grp Low High Low High Low High Low High Low High N 47 45 53 50 53 50 53 50 53 50 Mean 11.43 11.76 6.23 7.86 27.57 30.68 19.55 22.04 10.02 13.04 Std. D 5.56 4.63 2.45 1.91 7.39 6.97 7.21 6.42 4.01 4.3 CF* Let* Emb* Arith* Comparative Differences for the same 10-11-year-olds on Memory, Speed, Transformations, and Learning According to Table 32 above, based on differences in high and low groups when using reading standardized tests, speed and transformations for the perceptual tests (CF, LD, Emb, Arith) were significantly different but the memory was not. Would the same subscales show differences for the older age groups? The sample size was increased, and the results are found in Tables 33 and 34. According to Table 33 below, the general problem-solving subscale (Ps30) and structure/control (Ct) subscale, for the age grouping of 12-13, indicate a significant difference. 275 | P a g e 276 Prepublication Copy Ages 12-13 Table 33 Name Ps30** Pslap Pssp Grp Low High Low High Low High Low High Low High Low High N 161 149 92 75 28 32 161 149 161 149 161 149 Mean 12.57 13.44 12.59 13.02 12.41 12.19 11.71 10.58 39.06 42.6 38.87 39.3 Std. D 1.99 2.65 1.84 2.69 2.78 2.41 1.97 2.49 10.34 12.08 10.23 9.58 Name Mot Grp Low High Low High Low High Low High Low High Low High N 161 149 161 149 161 149 161 149 161 149 161 149 Mean 33.54 32.35 36.66 37.32 43.57 44.5 57.22 59.06 31.93 30.74 19.94 20.82 Std. D 8.95 9.13 10.15 11.46 10.45 9.35 16.92 17 4.2 4.49 7.41 7.17 An Dif Soc Cn Per* Flex Ct** Exit P=.05** P=.01* N=310 Average Differences between High and Low Reading Standardized Test Scores on the 10 Ps Subscales In Table 34 below, for the age grouping of 10-11, all the speed of processing tests except the clerical scale of letter identification are significant. Speed and transformation are significantly different in the expected direction. Those children who score higher on reading achievement also have faster speeds of transformation and better memory speed 276 | P a g e 277 Prepublication Copy Ages 10-11 Table 34 Name Mem** PF** Letid Emb** Arith* Grp Low High Low High Low High Low High Low High N 151 136 160 149 161 149 161 149 160 147 Mean 10.85 12.28 5.74 7.15 25.61 26.87 15.24 19.24 8.77 11.46 Std. D 5.18 5.12 2.7 2.68 6.83 7.72 9.19 8.04 3.85 4.04 P=.05** P=.01* Comparative Differences for the same 10-11-year-olds on Memory, Speed, Transformations, and Learning Numerical Problem Solving There were some differences in the Problem-Solving subscales using words. Will numbers show related results? If the children in the 12-13 years old age group are divided at the 50th percentile on the California Achievement Test, this results in 77 people being in the low group and 67 people in the high group. The means and standard deviation are going to be slightly different because of the difference in the split but equivalent results to the previous examples are expected. According to the information in Table 35, the average separation between groups is very apparent on a number of variables. The General Problem-Solving high group had a score of 14.8 compared to the low group with a mean score of 13.91. The low group had a higher score on Differential of 11.5 compared to the high group with a score of 10.76. Table 35 Df Psa** Cn Per** Mt Low High Low High Low High Low High Low High N 77 67 77 67 77 67 77 67 77 67 M 13.91 14.8 11.5 10.76 41.3 45.79 35.48 37.9 31.48 30.15 SD 2.87 2.44 1.38 1.05 11.69 12.21 8.2 8.26 7.44 8.26 277 | P a g e 278 Prepublication Copy An Soc Ct** EI Fx** Low High Low High Low High low High Low High N 77 67 77 67 77 67 77 67 77 67 M 30.26 32 43.6 42.12 56.31 63.1 28.57 26.9 16.56 18.96 SD 7.96 7.05 9.38 8.19 18.36 14.77 3.97 3.32 8.67 8.36 ** P=.05 Average Differences Between High and Low Math Standardized Test Groups on the 10 Subscales On the Perceptual Scale, the high score mean was 45.79 which was significantly higher than 41.3. Compared to the Control scale, where the high group had a mean of 63.1. The group with the lowest math scores had the highest mean on Flex (28.57 vs. 26.9). To summarize, significant differences between the means for 12-13 years of age were found on the following subscales: Problem-solving, Perceptual, Control, and flex. The structure /control scale was remarkably high compared to the Flex scale which was quite low. Specific age groups Results for separation by math standardized test scores are like the results for reading. Because of the vast development differences, the age groupings of 10-11 and 12-13 provides the best insights into the problem-solving subscales. Using high and low scores on math standardized tests, Tables 36-39 show differences in the expected direction for the problem-solving subscales as well as memory, speed, transformation, and learning. Table 36 presents the differences between the 10 and 11-year-olds. Perceptual, Conceptual, and Social are significantly different. 278 | P a g e 279 Prepublication Copy Ages 10-11 Table 36 Name PS30 Pslap Pssp Grp Low High Low High Low High Low High Low High Low High N 53 50 28 32 28 32 53 50 53 50 53 50 Mean 12.16 12.15 11.54 10.88 12.41 12.19 11.76 11.74 37.36 41.28 35.85 37.16 Std. D 2.5 2.55 2.4 2.01 2.78 2.41 2.29 2.27 10.43 13.02 8.25 8.79 Name Mot Grp Low High Low High Low High Low High Low High Low High N 53 50 53 50 53 50 53 50 53 50 53 50 Mean 31.66 32.52 32.79 32.32 41.62 44.52 64.23 60.8 31.43 31.1 19.13 20.72 Std. D 6.76 7.86 8.15 7.48 9.21 8.2 18.32 19.16 4.4 4.55 9.26 7.44 An Dif Per* Ct Soc* Conc** Flex Exint P=.05** P=.01* Average Differences for 10-11-year-olds Based on High and Low Separation by Math Standardized Table 37 indicates all speed perceptual tests, except memory, are significant for the 11-12 age group. Ages 11-12 Table 37 Name Mem Grp Low High Low High Low High Low High Low High N 47 45 53 50 53 50 53 50 53 50 Mean 11.43 11.76 6.23 7.86 27.57 30.68 19.55 22.04 10.02 13.04 Std. D 5.56 4.63 2.45 1.91 7.39 6.97 7.21 6.42 4.01 4.3 PF** Letid** Emb** Arith** P=.05** Comparative Differences for the same 10-11-year-olds on Memory, Speed, Transformations, and Learning 279 | P a g e 280 Prepublication Copy Table 38 presents data indicating that Problems-Solving total (Ps30); Problem-Solving analogies (Pslap) and Structure/Control (Ct) are significant for the 12-13-year-olds age group. Ages 12-13 Table 38 Name PS30 Pssp Grp Low High Low High Low High Low High Low N 161 149 92 75 28 32 161 149 Mean 12.57 13.44 12.59 13.02 12.41 12.19 11.71 Std. D 1.99 2.65 1.84 2.69 2.78 2.41 1.97 Name Mot Grp Low High Low High Low High Low High Low N 161 149 161 149 161 149 161 149 Mean 33.54 32.35 36.66 37.32 43.57 44.5 57.22 Std. D 8.95 9.13 10.15 11.46 10.45 9.35 16.92 Pslap An Dif Soc Conc Grp High Low High 161 149 161 149 10.58 39.06 42.6 38.87 39.3 2.49 10.34 12.08 10.23 9.58 Exint Grp High Low High 161 149 161 149 59.06 31.93 30.74 19.94 20.82 17 4.2 4.49 7.41 7.17 Per Flex Ct Average Differences for 12-13-year-olds between High and Low Math Standardized Test Scores 280 | P a g e 281 Prepublication Copy In Table 39 below, one can see that all perceptual speed tests and memory are significant for the 10-11 age group. Table 39 Name Mem* Grp Low High Low High Low High Low High Low High N 151 136 160 149 161 149 161 149 160 147 Mean 10.85 12.28 5.74 7.15 25.61 26.87 15.24 19.24 8.77 11.46 Std. D 5.18 5.12 2.7 2.68 6.83 7.72 9.19 8.04 3.85 4.04 CF* Let* Emb* Arith* P=.01* Comparative Differences for the same 10-11-year-olds on Memory, Speed, Transformations, and Learning Spatial problem solving Blocks and folded figures have been used in the past as one measure of fluid intelligence (See Chapter 20 for example). When blocks and folded figures are combined with the speed of processing, a baseline is established for understanding how children solve spatial problems. In our view, spatial problem-solving can improve if sufficient practice is available. Teachers need sufficient diagnostic tools to help students who want to improve in an area that is contrary to their preferred or usual method of solving problems. Assuming at least average intelligence, most students can learn how to sufficiently master spatial and analogic thinking if they can maintain their motivation. But a large number of students, at this early age, indicate that they have less desire to learn these kinds of problems as they involve abstract manipulation of figures. They are less interested unless exercises are presented in a game-like form. Since children are now beginning to reach a stage of formal thinking, they can manipulate simple and less difficult spatial figures. Obviously, for some children, the capacity to manipulate spatially has been present since birth while other children have enhanced spatial thinking and activity by experience (using tools such as saws or hammers, and/ or playing the piano, sewing). The only question here is how well and how easily some children can use spatial thinking. 281 | P a g e 282 Prepublication Copy Three distinct kinds of spatial designs measure the basics of problem-solving--blocks, embedded designs, and folded figures. Blocks problems are interesting in that the visual perspective of the individual must consider blocks that are not seen but are assumed to be there. Examples are found in Chapter 20. In the first diagram, the block is lifted, and another is right under it. If asked to count the blocks the student must assume that there is a block under the one on the top and answer 3 blocks. This activity does not require minimum spatial manipulation since from a concrete perspective, 3 blocks are seen in total. Only a few children fail to answer the question correctly. In the second example, the child who is still operating in the concrete operational stage is likely to be unsure about the total number of blocks since all the blocks cannot be fully seen. As the number of unseen blocks increases, the activity is based on counting what one can see and then estimating the total number of unseen blocks. The folded and unfolded design problems are different. The person must mentally fold and unfold different sides to match the stimulus figure. This activity requires a level of thought which is more than recognition and memory. A type of analysis, which involves manipulating images, is required. Embedded designs (as described in Chapter 5) are confounded by perception but since depth perspectives are involved, there is an aspect of spatial thinking. When embedded designs are combined with a time constraint, this provides a solid measure of processing speed and the process of dis-embedding. Children in this age group are not as adept as adults or even older children (ages 14-17) at answering questions on blocks and folded figures accurately. On quite simple block problems, this age group (11-13) scores from an average of 5 to 13 percent behind those at the high school and college levels. On more difficult block problems, this difference increases to as much as 18 percent. For example, according to Table 40, an average 12.6month year old obtains 43.16 percent of the total points possible on these blocks and folded figures compared to an average 25-year-old adult who gets 57.18 percent of the total possible pts. Table 40 282 | P a g e 283 Prepublication Copy Ages Total Spatial Score Total Standard Deviation 12 9.10 4.83 Percentage Correct 43% 13 9.46 Percentage Correct 45% 14 10.49 Percentage Correct 49% 4.83 4.83 Spatial Scores of 12, 13, and 14-year-olds Another way to examine spatial characteristics is to inspect perceptual speed scores when dividing the group by a median split using standardized math scores. The sample from Jim consists mainly of 12 years old. Jim’s data can be compared to norms for the 12-yearolds age group. Scores for the age group come from twelve studies which provide a normative standard (N=546): Cogflex - 7.4 (2.8); Letid- 27 (8.1); ED-15.8 (8.2); Arith-8.9 (5.4); and Mem 10.6 (5.23). The average mean score is followed by the standard deviation in parenthesis. Tables 41 and Table 42 provides a comparison of a high and low group separated according to spatial scores. Table 41 CF** LD** Emb** Low High Total Low High Total Low High N 73 69 142 74 69 143 74 69 Mean 6.12 7.55 6.82 27.61 26.94 27.29 19.31 21.17 2.95 2.96 3.03 6.1 7.38 6.73 10.06 8.66 ** P=.05 Table 42 283 | P a g e 284 Prepublication Copy Arith** Mem** Letters and Symbols Low High Total Low High Total 73 67 140 63 57 120 9.52 11.61 10.52 9.76 11.82 10.74 4.01 3.98 4.12 5.17 5.1 5.22 ** P=.05 Average Differences Between High and Low Math Standardized Tests Group on the 5 Perceptual Speed Tests Since there is a significant difference in all means on all perceptual tests when dividing between high and low standardized math test scores, the conclusion is that students with lower scores on math tests also had lower scores on the perceptual speed tests. All tests except arithmetic distraction are considered non-academic. In our nomenclature, they are called semi-cognitive tests as they are certainly involved with cognition but mixed with perception. In the summary of other age groups, the perceptual tests provide additional information about the problem-solving scales. When students are exposed to spatial problems in tiny amounts with a hands-on approach in earlier grades, a larger number of students increase their motivation for learning. However, by this age group (11-13), the students are beginning to sort themselves into categories, by their confidence level. Many students wonder if they wish to master spatial problem-solving. One variable which emulates this propensity is learning self-concept. Students who have excellent learning self-concept are willing to try new things. Those children who have a lower self-concept score display behaviors in the classroom which indicate their unwillingness to try or sustain problem-solving behaviors. Our studies and others have shown numerous times that learning self-concept is related significantly to academic grades. Chapter summary 284 | P a g e 285 Prepublication Copy The early adolescent is in the throes of physical changes. Puberty affects many significant bodily changes. Children differ in the amount of energy that can be devoted to problemsolving. Children with greater amounts of energy tend to do more things, some good, some not so good. Particularly important during this period is learning self-concept, motivation, and improvement in cognition, as each affects the types of problems that are solved. Many late bloomers are beginning to show cognitive advances and if they do not, then some consider alternative schools or dropping out. Academic differences in problem-solving with words, numbers, and spatial processing are evident. Groups tend to separate on the problem-solving scales. Those who were academically proficient in the earlier grades continued to be academically proficient during this period. Many distinctive characteristics of cognition, personality, and interests are solidified. Perceptual speed is magnified and tends to separate individual learners. Structure and organization and other personal tendencies are evident and the effect of the environmental press, as well as the multitude of neural layers, are showing their effects on the emotions of young adults. Modifications and challenges from significant others affect lifelong career paths. This stage tends to separate problem solvers into many different subgroups. Chapter references: Cox, J. E. (1995). Student led conferences and self-concept. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Dammerman, R. S. & Kreigstein, A. R. (2000). Limited Transient actions of neurotransmitters during neocortical development. Epilepsia 41, 1080-1081. De Waal, H. A.; van Coeverden, S.C.; & Rotteveel, J. (2001) Hormonal determinants of pubertal growth. Journal of Pediatric Endocrinology and Metabolism, 14, 1521-1526. Durston, S. Hulshoff, P. H., Casey, B. J., Giedd, J. N. Buitelaar, J. K. & van Engeland, H. (2001) Anatomical MRI of the developing human brain: What have we learned? Journal of the Academy of Child and Adolescent Psychiatry, 40, 1012-1020. Ellis, M. (1994). Improving seventh-grade math scores on fractions. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Epstein, H. T. (1978). Growth spurts during brain development: Implications for educational policy. Yearbook of the National Society for Study of Education. Chicago: University of Chicago. 285 | P a g e 286 Prepublication Copy Fernald, L.C. (1), & Grantham-McGregor, S. M. (1998). Stress response in school-age children who have been growth retarded since early childhood. National Center for Biotechnology Information, 68(3),691-8. Freud, Sigmund (1922). Beyond the Pleasure Principle; Translation by C. J. M. Hubback. London, Vienna: International Psycho-Analytical, Bartleby.com, 2010. Holbrook, Ann (1989). Academic achievement and the home environment. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Hines, M. & Greene, R. (1991). Human hormonal and neural correlates of sex-types behaviors. Review of Psychiatry, 10, 536-555. Piaget, J. (1954). The construction of reality in the child. New York: Ballantine. Rhoades. L. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Shand, K. (1999). The effects of eight weeks of daily practice on standardized test scores. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Smiles, E. (1994) Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Toepfer, C. F. (1980) Brain growth periodization data: Some suggestions for rethinking middle grades education High School Journal, 63(6), 222-227. Weatherly, D. (1975) Self perceived rate of physical maturation and personality in late adolescence. In R. E. Grinder (ed.) Studies of Adolescence. New York: Macmillan. 286 | P a g e 287 Prepublication Copy Chapter 15 Late Adolescence (14-17) Problem Solving During High School Years This chapter provides a broad understanding of the mathematical and conceptual properties of the different problem-solving subscales used in the Category system. As such, the examples are somewhat trivial but designed to illustrate measurement and theoretical properties. In the previous chapters, the characteristics of the age group--10-13-were sometimes mathematically distinct, depending on cognitive maturation. Now with children's increased intellectual capacity per memory and brain processing, more measurement distinctions are possible. The age group 14-17 differs widely on the ten problem-solving subscales. The differences are as vast as the number of people encountered. Individual differences noted here, are based on typical demographic factors--age, gender, socioeconomic status, school and church environments, and ethnicity. In the 14-17 age group, there is an increased in the number and kinds of complex assessments as the reading and understanding level of children has increased. The total number of students assessed ranged from 1400 -1800, depending on the instruments used. Learning, problem-solving, and energy Energy is just as important at this age level (14-17) as any other. Students often complain of having too little energy to complete certain activities. Coaches who are familiar with athletes know that it is almost impossible to sustain an elevated level of activity and energy for any length of time. Those who watch athletic events often watch the energy effects of “Mo” or momentum. Momentum or energy during a game goes back and forth as one team attempts to push back against the other. Slumps by players in various sports are often the result of a lack of sustained attention or energy. Some students study late at night or early in the afternoon since they have more energy at various times of the day. Biorhythms are good examples of changes in energy cycles. 287 | P a g e 288 Prepublication Copy Diagram 6: Cognitive model (Adulthood) Cognitive Model: Late Adolescence (14-17) The cognitive model in Diagram 6 is similar to the model for earlier age groups. The reason, as noted earlier, is the same. Young adults in the age group of 14-17, the high school years, are using the same cognitive and affective pathways but with greater frequency. Accordingly, more youngsters use the thought process of logical analysis to solve analytical problems. Either early exposure or learned experience has promoted it and/or certain curricular subjects require it. Category Subscales Throughout this age group (14-17), an experiential method of solving problems is beginning to solidify. Because of age, each of the methods of solving problems is represented as mode states, not necessarily traits or types. A state is a behavioral condition that is defined by a transitory period that changes under different kinds of external or internal impetus, such as motivation or threat. For example, think of a ‘state of mind’ as a transitory period. One can be angry one moment and happy the next. Trait or type 288 | P a g e 289 Prepublication Copy exemplifies group and individual characteristics viewed as more enduring, and less transitory. The trait is a quality that persists in the behavioral repertoire of the person over a long period. Type represents a composite of all traits and states of a person. Traits, states, and types are usually related to personality dimensions and increase with maturation and result in a style. As used here, style refers to predispositions and resulting actions based on repeated use of all three conditions. Our experience has shown that each of the problem-solving characteristics is used intermittently depending on the situation. The categories, motor, perceptual and conceptual may be dominant in a child who prefers playing a soccer game as entertainment while perceptual, conceptual, and motor might be the order of dominance in a child who likes doing arithmetic problems for fun. Each of the styles is biologically interdependent. Is it possible to identify different problem-solving styles since a person may utilize different pathways with distinct kinds of problems? The answer is yes. Biologically, through the process of description, scientists have succeeded in identifying and describing the actions of many different biological systems and the impacts of environmental stimuli. The field of medicine is the study of how agents (bacteria, parasites, fungi, or environmental toxins) affect biological systems. Through the process of systemization, and taxonomic classification, the effects of problem-solving styles can become more explicit and group characteristics of trait and type are more measurable. During the latter years of this developmental period, analytic, spatial, and perceptual tendencies begin to coalesce and act in concert with motivation to form the basic skills necessary for life and career development. An eleventh-grade student who works on the school yearbook, generally, has an integrated skill set that facilitates the work of editing, copying, sequencing, and imaging. In the same manner, a lack of a coalition of skills indicates whether the individual is arrested in a particular stage of cognitive development or not. Those who have taught high school are painfully aware of the individuals who have a minimum or delayed skill development in a particular area, especially reading math, and writing. If a lack of skill development occurs in a school subject such as science or history, it directly affects performance and achievement. Any lack of skills could extend to later vocational areas where hand and eye coordination are needed. A lack of analytical skills is obvious to teachers and students alike. By high school, many students identify themselves as being academically oriented or not! It is an erroneous type of self-selection where, sadly enough, many students dropped out of school to pursue other avenues (see our drop rate in high schools). In contrast to other countries such as Germany, most of our schools are not equipped to handle those children who excel at vocational educational skills and trades. Between fourteen and seventeen is 289 | P a g e 290 Prepublication Copy also the time that students attend special schools designed for their specific skills—schools for creative arts, or schools for alternative students. Children are more likely to perceive their worth or value in areas of strength such as sports, academics, or project skills. Also, the perceptions of others are important. For many children, it is others who identify and define the talents of their worth. Gender differences Differences between boys and girls are very evident at this age and those gender differences are apparent on some of the ten subscales. Below, there are two Tables reflecting differences between males and females. Each table differs as the first represents a culturally diverse group (Hispanic, Asian, and Middle Eastern countries) of one hundred and fifty 14-15-year-old; while the second Table represents an Honor group of students who are 16-17 years of age. Examining the scores in Table 43 for 14 and 15-yearolds indicated that males scored higher on the analysis subscale and females scored higher on Motor and Social. The usual pattern of males scoring higher on the Motor, Analysis, and Flex was not apparent. In contrast to our expectations from adult data, females scored significantly higher on the Motor subscale. This is significant as it represents a sample characteristic that requires further analysis for demographic and background characteristics. Table 43 Males- Ps Df Per Cn Mt An* So Ct Fx EI Mean 11.818 12.53 32 30.37 31.32 38.712 36.41 35.593 31.59 17.66 SD 1.4472 0.848 9.1275 10.89 10.05 8.9038 11.81 9.4743 10.15 6.161 Females Ps Df Per Cn Mt** An So** Ct Fx EI Mean 11.624 12.58 33.538 28.79 34.68 35.253 42.46 36.264 32 20 SD 1.2951 0.903 10.082 10.76 9.876 8.4565 10.38 9.6036 10.18 6.216 *=.05 **=.01 N=150 Gender Differences in Male and Females 14-15-Year-Old In Table 44 below, which represents a small sample of 47, the Male Honor Students are more extroverted, score significantly higher on Analysis, and only slightly higher on the Problem-Solving subscale (Ps). Females are significantly higher on Control, Social, as well 290 | P a g e 291 Prepublication Copy as Perception, and Flex. Again, Control has a larger mean score than Flex but both Flex and Control have average scores. The scales found in Table 44 for the 16 and 17-year-olds were in the expected Table 44 Male Ps* Df Per Cn Mt An* So Ct Fx EI Mean 14.11 10.53 42.00 29.23 42.08 40.15 40.23 51.38 49.23 16.00 SD 1.33 1.84 13.25 9.99 9.81 12.70 15.61 20.34 14.03 13.34 Female Ps Df Per* Cn Mt An So* Ct* Fx* EI Mean 13.34 9.57 45.14 28.43 42.00 35.14 44.11 59.43 54.86 14.57 SD 0.99 1.53 15.49 10.26 10.29 12.74 10.21 12.64 12.69 9.91 *=.05 **=.01 N=47 Gender Differences in Male and Females Age 16-17 (Honor Students) direction as males were significantly higher on Analysis while females scored higher on the Social scale. This does not mean that males perform better at analytic thought. Instead, it just represents that male select more analytical items, while females select items more social in nature. Both genders can be analytical and social as actual performance differs from preference. Table 44b shows the means and standard deviations for the 12-year-olds in the previous chapter. As problem-solving scores increase (Ps subscale) so do the scores on Flex and Control Table 44b Males Pslap Pssp Df Per Cn** Mt* An** So Ct Fx** EI Mean 12.30 11.85 12.92 41.00 35.47 43.41 42.41 41.94 37.41 39.24 18.76 SD 2.60 2.79 2.40 11.24 10.57 8.39 11.57 11.37 13.00 11.98 5.87 Females Pslap Pssp Df Per Cn Mt An So** Ct Fx EI** Mean 12.21 11.47 13.16 40.67 32.20 45.67 35.00 47.80 37.87 37.67 21.53 SD 2.49 2.39 2.10 11.41 12.35 12.93 16.43 11.01 15.26 13.36 6.70 N=129 **P=.01 *P=.05 instrument +logarithmic correction for heterogeneity-Levine’s statistic Adolescence, Cognitive PS Gender Differences in Male and Females Age 12 regular students 291 | P a g e 292 Prepublication Copy A teaching example using the IPS Model In 1984, Bill (Clingwald, 1986), one my graduate students, as a preliminary to doing his Master's Thesis collected data on 32 people: five graduate students (group 1); five practicing teachers in the school system (group 2); five 15-year-old students who were behind academically (group 3), eight 15-year-old students who had learning disabilities (group 4), and five 15-year-old categorized as special education students (group 5). A learning disability suggests that the student needs help in a specific area such as math or reading. Bill gave all groups the problem-solving instrument, hypothesizing that even though it was a small select non-random sample, the substantive ability and the educational difference in the groups would show separation via the various problemsolving subscales. One of his reasons for gathering the data was to assess whether he wanted to use the problem-solving instrument in his master’s thesis. He also administered semi-cognitive tests. He was interested in two things: a) how the means of the problemsolving scale might differ by groups and b) how the means for each subscale might differ from each other. He suspected the special education students would score lower than the athletes who had a college degree, but he was uncertain how large the actual mean separation would be. The actual amount of mean separation was important for him as he was a special education teacher. He also hypothesized that adults would score differently than 14-15-year-old regular students. Later after examining the preliminary data, he and another graduate student collected data on a group of 70 sophomores in a nearby high school. Let’s examine the problem-solving results of Bill’s preliminary group by addressing the scores on the ten different subscales. After addressing the first five groups in Table 45 below, compare the results of the two randomly selected groups collected by 2 graduate students. These results are listed as G1 and G2 in the last rows in Table 45. There were 84 high school students in group 1 (G1-ages 14-15) and 71 adults in Group 2 (G2-ages 2655). Again, this is more of a teaching exercise to illustrate how the theory coincides with the dimensions of the subscales and to exhibit the properties of the instruments. One expects tremendous variability in the scores for the small preliminary sample due to the non-random nature of the groups. Likewise, adults are more likely to perceive the social connotations of the subscales. Differences between adults' and children's responses help quantify the social desirability of items on subscales. 292 | P a g e 293 Prepublication Copy Table 45 Names-Means Psa** Df Per Cn Mt An So Ct Fx EI Teachers 12.87 11.15 42.34 33.50 29.93 44.19 31.07 41.18 27.30 16.38 SD. 0.90 3.35 12.94 11.33 12.61 17.24 13.75 17.95 8.52 6.49 Athletes 12.20 11.84 46.40 32.80 32.80 37.60 38.40 48.00 29.60 15.20 SD. 2.74 1.04 9.63 5.22 18.42 16.64 10.43 10.20 3.36 5.40 Regular 7.53 13.85 19.20 25.60 20.00 32.00 22.40 27.20 34.84 16.40 SD. 1.83 1.27 4.38 6.07 10.95 4.90 6.69 15.85 3.31 2.61 Learning Disability 7.45 13.78 25.41 25.41 23.06 31.29 27.76 28.47 34.64 11.18 SD. 1.54 1.09 9.48 8.48 9.54 9.19 9.43 14.34 3.14 3.68 Sp. Ed. M 7.19 13.12 24.68 24.54 22.23 30.21 26.97 28.00 33.00 10.73 SD. 1.94 3.01 9.58 8.98 9.61 10.43 9.56 13.70 7.62 3.92 Comparisons Ps30** Df Per Cn Mt An So Ct Fx EI G1: Age 15-16 12.14 12.35 35.14 30.74 34.17 40.14 36.81 36.42 31.81 18.86 SD 01.42 0.91 09.6 11.01 10.22 12.93 10.97 13.1 10.51 07.13 G2: Age 26+ 12.60 11.37 40.86 34.89 35.89 30.6 41.83 54.17 52.23 19.60 SD 01.20 01.23 9.56 9.85 10.16 11.05 11.24 18.33 12.72 10.91 ** Means ordered highest to lowest on the PS scales for Bill 5 groups; N=84 for ages 15-16 and 70 for ages 26+; SD is the standard deviation Means and Standard Deviation of Bill’s 5 distinct groups Note: The problem-solving scale in Bill’s five groups and many of the previous age groups in prior chapters are non-cognitive (Psa). That is, the scale is based on a selection of items indicating perceptions of learning ability, independence of thought, and academic achievement. This contrasts with the cognitive problem-solving scales (Ps30; Pslap; or Pssp) used to measure problem-solving in the 155 people in the 2 comparison groups. Both cognitive and non-cognitive are scaled similarly for comparison. For adults and older age children with better reading ability and maturity, the problem-solving scales incorporate semicognitive and cognitive items that define the general and differential problem solvers. Other scales used basic and extended scores to classify and illustrate the integrated nature of solving problems. 293 | P a g e 294 Prepublication Copy To highlight the differences in the ten subscales, the problem-solving subscale (PS) in Bill’s five groups is ordered from the highest to the lowest, i.e., 12.87 (teachers) is the high score and 7.19 (special education students) is the low score. Again, special education students consist of two groups, those who have a learning disability (L.D.) but are average students or those who require special academic assistance (Sp.Ed.). In summary, considering all the problem-solving subscales as a group, Special Education (Learning Disability & Sp.Ed.) and Regular 15-year-old students have the lowest scores on the Psa subscale, and the Athletes and Teachers have the highest. The highest average score on the motor subscale was made by the Athletes while the lowest score was made by Regular students. The highest average Flex score was made by the students (regular students, students with learning disabilities, and special education). Further clarification for each of the subscales, starting with General Problem Solving, is given below. General problem solving Our studies of the general problem scale suggest that education is a moderating variable. That is, the level of education may influence the scores on problem-solving. The teachers had a small standard deviation on this scale. As noted in Table 46 below, the adults (G2); teachers, and athletes scored higher on this scale than the 15-year-old. The 15-year-old comparison group of high school students (G1) had slightly greater variability when considering standard deviation as well as the minimum and maximum. Table 46 Subscale Group N Mean-Psa Std. Dev. Psa Teachers 5 12.87 Athletes 5 Regular 5 Learning Disability 8 Sp. Ed. Ps30 Std. Error Lower Bound Upper Bound Min Max 0.9 0.4 11.75 13.99 12 14 12.2 2.74 1.23 8.79 15.61 7.67 14.67 7.53 1.84 0.82 5.25 9.81 4.33 8.67 7.75 1.87 0.66 6.19 9.31 5.33 10.67 9 7.19 1.24 0.41 6.23 8.14 5.33 9 Total group 32 9.05 2.91 0.51 8 10.1 4.33 14.67 Ages 15-16 84 12.14 1.42 .15 11.83 12.45 8.50 14.75 Ages 26+ 70 12.60 1.20 .14 12.31 12.89 9.00 14.50 Total 154 12.35 1.34 .11 12.13 12.56 8.50 14.75 294 | P a g e 295 Prepublication Copy ** N=84 for ages 15-16 and n= 70 for 26+; SD is standard deviation Comparison of the Mean Scores of the 5 selected Non-Random Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the Problem-Solving Scale Differential PS The differential problem-solving subscale, as identified by Dif, is a calculated scale for teachers. Rather than have teachers interpret the low score on the PS subscale as being a differential problem solver, the scale is inversely generated. The scale represents a student who performs well on things that interest them as well as areas in which their skills are strong. Given that information, the scores of the adults, (Group 2), teachers, and athletes were lower than the 15-year-old groups (Group 1 and others) were calculated to be. Table 47 presents data on the Differential PS subscale. Table 47 Subscale Group N Mean Std. Dev. Std. Error Lower Bound Upper Bound Min Max Regular 5 13.85 1.27 0.57 12.27 15.42 12.84 15.56 Sp. Ed 9 13.84 0.7 0.23 13.3 14.38 12.98 15.11 Learning Disability 8 13.7 1.46 0.52 12.48 14.92 11.51 15.73 Total 32 13.26 1.36 0.24 12.77 13.75 10.98 15.73 Teachers 5 12.34 1.32 0.59 10.7 13.98 11.07 14.04 Df Athletes 5 11.84 1.04 0.46 10.55 13.13 10.98 13.51 Differential Ages 15-16 84 12.35 .91 .10 12.15 12.55 7.88 14.20 Comparison Ages 26+ 70 11.37 1.23 .15 11.08 11.67 8.87 14.77 Total 154 11.91 1.17 .09 11.72 12.09 7.88 14.77 Comparison Mean Scores of 5 selected Non-Random Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the Differential Problem-Solving Subscale 295 | P a g e 296 Prepublication Copy Perceptual Perceptual skills are accentuated in exercises such as drawings, vocational curricula, or skills found in shop courses. The senses of taste, observation, feeling, and touch provide group separations by individual preferences. A person of fourteen years is less likely to be aware of her or his inclinations to use perceptual motor skills in different vocations as she or he is less mature. However, a seventeen-year-old student might have decided upon a vocation in which perceptual skills are accentuated, i.e., a chef, artist, photographer, and/or a connoisseur of wine and fine arts. Perceptual senses are refined in many groups of problem solvers. How can one identify perceptual problem solvers if perceptual skills are so ubiquitous? Is it by sheer numbers? Is there a greater proportion of people with refined perceptions found in the high school yearbook classes where mistakes on the printed page seemed to be magnified? Or perhaps there are a greater number of people with perceptual skills in the chemistry lab, that is, using their senses to identify smells and chemical compositions? Our category system suggests those who score high on the Perceptual scale are everywhere. A group or a person cannot be classified accurately by just perceptual skills or any single subscale. The ubiquitous nature of generalized scoring tendencies requires multiple subscales to be interpreted! Groups and individuals can be compared descriptively on the subscale of perception when nonrandom groups are involved. Because the biological systems of people are integrated, different combinations of performance skills, thinking patterns, and personality contribute to the solving of everyday problems. Below in Table 48 are the average statistics for the different groups on the perceptual scale. Notice that athletes and adults, in general, scored higher on the perceptual scale. Table 48 Subscale Group N Means Std. Dev Std. Err. Lower Bd. High Bd. Min Max Per Athletes 5 46.4 9.63 4.31 34.44 58.36 36 56 Teachers 5 44 8.49 3.79 33.46 54.54 32 52 Learning Disability. 8 26.5 10.46 3.7 17.75 35.25 12 40 Sp. Ed. 9 24.44 9.04 3.01 17.49 31.4 12 36 Regular 5 19.2 4.38 1.96 13.76 24.64 12 24 Total 32 30.62 13.23 2.34 25.85 35.4 12 56 296 | P a g e 297 Prepublication Copy Perceptual Ages 15-16 84 35.14 9.60 1.05 33.06 37.23 16.00 56 Ages 26+ 70 40.86 9.56 1.14 38.58 43.14 20.00 60 Total 154 37.74 9.97 .80 36.15 39.33 16.00 60 Comparison Mean Scores of the 5 selected Non-Random Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the Perceptual Scale Table 48 shows the range on the Perceptual subscale for each of the groups as well as the range of the standard error of the mean. The maximum and minimum scores on the subscales are listed also. The ability to classify requires the separation of groups on numerical dimensions. The numerical differences are important in understanding how people, respond to items on subscales. For example, the range for the total (groups) was a low score of 12 and a high score of 56. Given the nature of the groups, an 18-22 points separation is probably the minimum separation needed to classify individuals by subgroups. Notice the same properties on other subscales. In Table 48 above, the means of the older adults were considerably higher than the 15year-old students suggesting that items had some social desirability as well as item content that was preferred. Again, most of the items which define this subscale are quite straightforward. That is: Are you more attentive to events that mirror your own ideas? Are you more likely to notice, sounds or pictures? When one looks at an object, which is seen more clearly the whole object or the details of the object? Are you attentive to details in your daily life or do you prefer just looking at the big picture? Do you learn better by handling objects or by watching a movie? Do you prefer pictures or reading handouts to learn new things? If an item of perception is selected (pictures; watching a movie, etc.), the item is scored with a weight of one or two depending on their rank of first or second Conception This subscale measures the preferences of people who select items representing innovative and creative ideas. Therefore, a high score on this subscale is related to reading, literature, writing papers, and unique ideas. In your high school days, some people were just better at making creative quips (witty and unique statements) about everything. That sums up the gist of the subscale and its meaning for 14-17-year-old. So how did Bill’s 5 diverse groups score on this subscale? How do those average scores in Table 49 compare to the average random sets below? 297 | P a g e 298 Prepublication Copy Table 49 Subscale Cn Group N Means Std. Dev Std. Err. Lower Bd. Teachers 5 40 8.49 3.79 29.46 50.54 28 48 Athletes 5 32.8 5.22 2.33 26.32 39.28 24 36 Learning Disability 8 26.5 7.69 2.72 20.07 32.93 20 40 Regular 5 25.6 6.07 2.71 18.07 33.13 16 32 Sp. Ed 9 24.44 9.48 3.16 17.16 31.73 4 36 Total 32 28.88 9.24 1.63 25.54 32.21 4 48 84 30.74 11.01 1.20 28.35 33.13 8.00 56 Ages 26+ 70 34.89 9.85 1.18 32.54 37.24 14.00 52 Total 154 32.62 10.67 .86 30.92 34.32 8.00 56 Conceptual Ages 15-16 High Bd. Min Max Comparison Mean Scores of the 5 selected Non-Random Groups & 2 Randomly selected groups of 15 years- old (G1) and Adults (G2) on the Conceptual Scale In our model, the Cn scale represents those who like and think through different kinds of concepts where concepts relate to ideas. Recently, one of my more creative friends responded to my lamenting about bad luck on the tennis court with the statement “There is no good luck or bad luck. There is only luck.” The highest score on the subscale ‘conceptual’ was by the 5 teachers. The lowest average scores were by special education students. There was not a lot of difference in any of the means for the small group of five 15-year-old regular students, Learning Disability students, and Special Education students; however, the means of 15-year-olds were more comparable to the means of adults (Group 2). A trend that is evident in many studies is that students who are less achieving tend to have more depressed scales as their preference patterns are in the middle and cancel out differences on the subscales. 298 | P a g e 299 Prepublication Copy Motor Students who have a high score on this subscale are a diverse lot. In Chapter 13, the newborn was a morass of emotions and sensory-motor movements. The refinement of sensory-motor functions leads to those children whose life is dominated by realistic perceptions relating to the senses. They choose items reflecting their practical, concrete approach to everyday life as well as items heavily reliant upon processing objects in the environment. How will the distinct groups score on this subscale? See Table 50. Table 50 Subscale Group N Means Std. Dev. Std. Err. Lower Bd. High Bd. Min. Max. Mt Athletes 5 32.8 18.42 8.24 9.93 55.67 12 52 Teachers 5 29.93 12.61 3.2 19.92 37.68 24 40 Learning Disability 8 23.06 9.54 2.93 15.08 28.92 12 36 Sp. Ed 9 22.23 9.61 3.65 15.58 32.42 12 44 Regular 5 20 10.95 4.9 6.4 33.6 4 32 Total 32 25 11.45 2.02 20.87 29.13 4 52 Ages 15-16 84 34.17 10.22 1.11 31.95 36.38 12 60 Ages 26+ 70 35.89 10.16 1.21 33.46 38.31 18 68 Total 154 34.95 10.20 .82 33.32 36.57 12 68 Motor Average Mean Scores of the 5 selected Non-Random Groups & 2 Randomly selected groups of 15 years- old (G1) and Adults (G2) on the Motor Scale Observations by my graduate students in their master’s thesis characterized Motor students as down-to-earth, efficient, practical, and highly reliant upon a sensory-motor orientation. In the primary grades, this group was idealized as “performing”, being involved, action-oriented, playing sports, and having constant movement. In later grades, as an internal control of emotions is refined, their activities become more diverse, encompassing a wide variety of skill-based actions. Although this characterization is a singular representation, the interaction from scores on flex and control provides further classification and illumination for interpretation. The athletes did have a comparable mean score to the randomly selected groups, but the large standard deviation reflects the very small sample size. The highest mean score was the adults (ages 26+ =35.89) with a randomly selected group of 15-year-olds close behind. 299 | P a g e 300 Prepublication Copy Analytical This subscale measures a preference for using the thinking process to dissect issues. Analysis, as noted earlier, reflects the orientation to take things apart, and ferret out the underlying meaning. Some people use analysis so much that the phrase “paralysis by analysis” evolved. In this 14-17 age group, a person who uses his or her analytic ability is evident to his or her classmates. In some cases, these individuals are sought out for their expertise. In other cases, unwarranted stereotypes are frequently applied. Our goal is to use this subscale as part of the identification process in solving different kinds of problems. Is there a difference in the solving of problems for those whose major categories are ACS compared to those whose categories are MAS or MPA? Is there a difference between those who may analyze a lot but have a definitive preference for social problem solving-- for example, a priest? In any case, the results in Table 51 for the five different subgroups provide some insight. Table 51 Subscale Group N Means Std. Dev. Std. Err. Lower Bd. Analysis Athletes 5 37.6 16.64 7.44 16.94 58.26 20 56 Teachers 5 57.6 7.8 3.49 47.92 67.28 48 68 Regular 5 32 4.9 2.19 25.92 38.08 28 40 Learning Disability 8 35.5 6.57 2.32 30.01 40.99 28 44 Sp. Ed 9 27.56 9.89 3.3 19.95 35.16 12 40 Total 32 36.5 13.43 2.37 31.66 41.34 12 68 Ages 15-16 84 40.14 12.93 1.41 37.34 42.95 16.00 80 Ages 26+ 70 30.60 11.05 1.32 27.96 33.24 8.00 60 Total 154 35.81 12.98 1.05 33.74 37.87 8.00 80 Analysis High Bd. Min. Max. Comparison of Mean Scores of the 5 selected Nonrandom Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the Analytical Scale The small group of 5 teachers has higher analytic scores, more so than any of the other groups. The group of athletes scored in a comparable range with the G1 (ages 15-16) students on this subscale. 300 | P a g e 301 Prepublication Copy Social Social problems abound as people live and work together in society. Individuals who have a penchant for helping others are often called upon to aid other people, either individually or collectively. Most individuals who work as trainers, teachers, social workers, or counselors fall into this category. Almost everyone has some propensity for solving or working with some type of social problems; however, only some people prefer a career or job which is predominantly social, such as cruise director on a ship or a team leader from Human Resources in a Fortune 500 company. Some people prefer solving social problems, more than others. As a group, the people who choose social items are energized by doing things where the intent is to help others. Does this evolve into a preference for social problem solving--- certainly, not right away--only when career and vocational opportunities become the focal point? A youngster may be oriented to social activities, but the transition to helping others solve problems is a long journey. Teachers, by the nature of the profession, are usually social problem solvers. Wonder how they score- high or low? See Table 52. Table 52 Subscale Group N Means Std. Dev. Std. Err. Lower Bd. Social Athletes 5 38.4 10.43 4.66 25.45 51.35 28 52 Learning Disability 8 28 12.47 4.41 17.58 38.42 12 44 Sp. Ed 9 27.56 6.46 2.15 22.59 32.52 16 36 Teachers 5 26.4 14.03 6.27 8.98 43.82 12 40 Regular 5 22.4 6.69 2.99 14.09 30.71 12 28 Total 32 28.38 10.67 1.89 24.53 32.22 12 52 Ages 15-16 84 36.81 10.97 1.20 34.43 39.19 12 60 Ages 26+ 70 41.83 11.24 1.34 39.15 44.51 14 64 Total 154 39.09 11.34 .91 37.29 40.90 12 64 Social High Bd. Min. Max. Comparison of Mean Scores of the 5 selected Non-Random Groups & 2 Randomly selected groups of 15 years- old (G1) and Adults (G2) on the Social Scale The athletes that Bill selected were very social, more so than the teachers, who tend to be more analytic and less social as a group. Perhaps one needs to be social to teach young people in the school system but the athletes who volunteer their time to be part of the 301 | P a g e 302 Prepublication Copy study were even more social. Will this difference hold for a larger sample? The answer is given in given when comparing the results from the 2 random samples. Control/structure & flex Based on earlier studies, control/structure and flex are moderating variables that interact with other subscales. The need to have everything in its place as well as to control things that might interfere with goal orientation is quite strong for individuals who score high on this subscale. When social problem solvers choose responses that reflect a high score on flex and control, the conceptual subscale score is increased. This suggests a moderate amount of control is necessary with the capacity to let one’s mind be creative. Control/structure is related to the process of structuring things in the internal and external environment. Impulse control related to emotions and feelings is also a societal requirement as children mature. Table 53 Subscale Group N Means Std. Dev. Std. Err. Lower Bd. High Bd. Min. Max. Control Athletes 5 48 10.2 4.56 35.34 60.66 32 56 Teachers 5 39.2 21.61 9.67 12.36 66.04 12 60 L.D. 8 29 19.09 6.75 13.04 44.96 0 56 Sp. Ed 9 28 9.59 3.2 20.63 35.37 12 40 Regular 5 27.2 15.85 7.09 7.52 46.88 8 40 Total 32 33 16.48 2.91 27.06 38.94 0 60 Ages 15-16 84 36.42 13.10 1.43 33.57 39.26 12.00 60.00 Ages 26+ 70 54.17 18.33 2.19 49.80 58.54 4.00 92.00 Total 154 44.49 17.98 1.45 41.62 47.35 4.00 92.00 Control Comparison of Mean Scores for the 5 selected Non-Random Groups & 2 Randomly selected groups of 15 years- old (G1) and Adults (G2) on the Control Scale In Table 53, the group who had the highest means on the Flex subscale were the 70 adults-- aged 26 and older; the lowest means were the children with learning disabilities and those classified as special education. Again, the continual high scores by adults suggest 302 | P a g e 303 Prepublication Copy some degree of item content and social desirability---an understanding that certain items could be chosen for perceived social value. Flex Theoretically, flex and control are part of a check and balance system. When one goes up, the other goes down. The two constructs seem to be inversely related to many people. However, often the averages in groups represented by certain vocations (nurses, doctors, lawyers), are both high and average but seldom are both subscales low, except in unique low achieving populations. Table 54 Subscale Flex Flex Group N Means Std. Dev. Std. Err. Lower Bd. High Bd. Min. Max. Sp. Ed. 9 35.16 2.25 0.75 33.43 36.89 31.56 37.78 Regular 5 34.84 3.31 1.48 30.74 38.95 32 38.67 L.D. 8 34.06 4 1.41 30.72 37.4 28.89 39.56 Athletes 5 29.6 3.36 1.5 25.42 33.78 26.67 35.11 Teachers 5 29.33 5.64 2.52 22.33 36.33 23.56 36.44 Total 32 33.06 4.25 0.75 31.52 34.59 23.56 39.56 Ages15-16 84 31.81 10.51 1.15 29.53 34.09 10.00 60.00 Ages 26+ 70 52.23 12.72 1.52 49.20 55.26 20.00 76.00 Total 154 41.09 15.39 1.24 38.64 43.54 10.00 76.00 Comparison of Mean Scores for the 5 selected Non-Random Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the Flex Scale In, Table 54, Group 2, the 26 years old+ adults were highest on flex. The teachers, and athletes, in group 1, 15-16-year-olds had the lower means. Special education scored lower on control but higher on flex. There was not a great deal of variability among the groups. Flex and control interaction There are many ways that structure and cognitive flexibility (Flex) can interact during a person’s decision-making, depending on how each function is displayed in behavior. 303 | P a g e 304 Prepublication Copy Remember, that Flex is changing one’s plan or structuring of events, by responding to an inner impulse or emotional feeling or just reacting to the impulse. The action results in changing an ongoing situation by rapidly imagining and projecting another series of events. As any coach or administrator can tell you, the use of structure is a form of control. The two concepts of control and structure are often used interchangeably. Why? A person organizes and structures external events to gain control and avoids chaos or chance. Sometimes the need for this control is due to anxiety, fear of failure, but then again, structure and organization, as a form of planning, increase the chance of success. A person succeeds by having control over each step in the plan needed to reach the desired goal. The need to structure can change as events in the environment require more flexibility. This causes different patterns in different subgroups. For example, one group organizes, plans, and structures events but does not necessarily follow through with the plan (high structure and high flexibility). In that instance, plans are tentative and change as events unfold. Structure and flexibility are valued. There is a second subgroup of people who keep their plan regardless of environmental changes. Once a plan or structure is conceived, it is not to be abandoned. Everything is to go as planned never changing (high structure, low flexibility). And then, there still is a third group that does not plan and responds flexibly to any situation. They change directions on a whim or impulse (low structure or control, high flexibility). Which of these patterns are evident? In Table 55 below, athletes have the highest scores on structure/control and the lowest on Flex, similar to the pattern of juvenile delinquents in the next chapter. Teachers are above average in structure and lowest in flex while special education students’ scores are lowest in structure and highest on Flex. When comparing all groups, adults in graduate school above the age of 26 (G2) are more likely to be both structured and flexible. Table 55 Subscale Group N Means Std. Dev. Subscale Group Control Athletes 5 48 10.2 Flex Athletes Teachers 5 39.2 21.61 Regular 5 27.2 L.D. 8 Sp. Ed 9 N Means Std. Dev. 5 29.6 3.36 Teachers 5 29.33 5.64 15.85 Regular 5 34.84 3.31 29 19.09 L.D. 8 34.06 4 28 9.59 Sp. Ed 9 35.16 2.25 304 | P a g e 305 Prepublication Copy Total 32 33 16.48 Subscale Group N Means Std. Dev. Control Ages15-16 84 36.42 13.1 Ages 26+ 70 54.17 18.33 Total 32 33.06 4.25 Subscale Group N Means Std. Dev. Flex G1 84 31.81 10.51 G2 70 52.23 12.72 Comparison of Mean Scores for the 5 selected Non-Random Groups & 2 randomly selected groups of 15 years- old (G1) and Adults (G2) on the structure and flex subscales Extraversion /introversion In Table 56, below, the average scores of the teachers, regular students, and athletes are higher on extraversion than the children classified with a learning disability or special education. An average score of 10.75 is quite a low score, especially for children who are 15 years old. An average mean for males and females is about 18 or 19; however, as a group, females are generally higher on extraversion with an average of 20-21. The teacher group was predominantly female. Table 56 Subscale Exint Exint Group N Mean Std. Dev. Std. Error Lower Bound Upper Bound Minimum Maximum Teachers 5 20 6.16 2.76 12.35 27.65 16 30 Regular 5 16.4 2.61 1.17 13.16 19.64 14 20 Athletes 5 15.2 5.4 2.42 8.49 21.91 10 22 Sp. Ed 9 11.56 4.22 1.41 8.31 14.8 6 18 L.D. 8 10.75 3.2 1.13 8.08 13.42 6 16 Total 32 14 5.28 0.93 12.1 15.9 6 30 Ages 15-16 84 18.86 7.13 .78 17.31 20.40 -8.00 36.00 Ages 26+ 70 19.60 10.91 1.30 17.00 22.20 -6.00 38.00 Total 154 19.19 9.02 .73 17.76 20.63 -8.00 38.00 Comparison of the Mean Scores for 5 selected Nonrandom Groups & 2 Randomly selected groups of 15 years- old (G1) and Adults (G2) on the E/I Scale 305 | P a g e 306 Prepublication Copy Differences in Types of Problems Solved Word problem solving In earlier chapters, the speed of perception for different age groups (5-13) increased with age and maturation. Does the linear development of speed in perception continue to increase with the 14-17 years old group? The answer is a definitive “yes” and the skills which are dubbed semi-cognitive can discriminate many characteristics between certain known groups. Semi-cognitive skills, known also by the label of perceptual speed, have been isolated by factor analysis and other multivariate methods as noted earlier in the Chapter 24 review. In Chapter 4, the topics of crystallized vs. fluid ability were discussed. Crystallized ability, according to Cattell, was learned, while fluid ability was more innate. So, three of our speed tests measure fluid ability while one, arithmetic distraction is learned knowledge. Other tests of fluid ability included in our assessments are spatial figures, analogies, and sequential problems. If the two categories of fluid and crystallized ability are valid indicators of cognitive functioning, then the assessments can serve as methods of separating and illustrating the meaning implied by the problem-solving scales in the same manner as standardized tests. For the category involving ‘word problem-solving, instead of the academic standardized test, the semi-cognitive or perceptual speed tests are used to separate the problem-solving scale. The characteristic common to both the standardized and perceptual is a time limit. The random sample of 155 people includes 71 adults 26 years and older and 84 15-yearolds divided into 2 groups around the 50th percentile. The results are found in Table 57. 306 | P a g e 307 Prepublication Copy Table 57 N Mean Std. Deviation Std. Error Minimum Maximum Sign Low 69 12.03 1.49 0.18 8.5 14.8 0.009 High 85 12.6 1.15 0.13 9.3 14.8 Low 69 11.96 1.12 0.13 7.88 14.77 High 85 11.87 1.22 0.13 8.87 14.2 Low 69 38.84 9.1 1.1 16 56 High 85 36.85 10.58 1.15 16 60 Low 69 32 10.81 1.3 8 56 High 85 33.13 10.6 1.15 8 52 Low 69 35.68 9.65 1.16 12 60 High 85 34.35 10.64 1.15 12 68 Low 69 36.2 13.77 1.66 12 80 High 85 35.48 12.38 1.34 8 76 Low 69 37.1 11.23 1.35 12 60 High 85 40.71 11.23 1.22 14 64 Low 69 41.9 16.99 2.05 4 76 High 85 46.59 18.59 2.02 12 92 Low 69 38.43 15.29 1.84 10 76 High 85 43.25 15.23 1.65 12 72 Low 69 18.36 8.32 1 -8 36 High 85 19.87 9.54 1.04 -6 38 Name Status Ps30 Dif Per Cn Mt An Soc Ct Fx Ex 0.643 0.218 0.516 0.423 0.733+ 0.049** 0.108 0.053** 0.304 **P=.05 *P=.01 +lacks homogeneity of variance Separation of Means on the Problem-Solving Scales Using Letters Strike Tests Results: When using standardized tests, dividing the group into low and high by the median or mean shows little difference. The commonality is the speed of processing as the test is timed. Again, compare the results from this chapter after you have read the next chapter. As expected, in Table 57 above, there is a significant difference in means on the problem-solving subscale (the high group is 12.60 with a standard deviation of 1.15, corrected for homogeneity). The striking outcome, as it is meant to demonstrate, is the 307 | P a g e 308 Prepublication Copy mean separation across most subscales. Flex and social are significantly different at the .05 level. The goal of this exercise was to determine which problem-solving subscales show the largest mean separation. Likewise, an important question is whether any of the subscales indicate a reversal based on separation by academic standardized tests. With such a wide variation in education and ability in the sample, the maximum separation of the means should be found on one or more subscales. When significant differences are found, this information provides insight into what the subscale is measuring. Would you expect the subscale on social problem-solving to show the same mean separation as a perceptual speed subscale? Usually if it is found, it is just a chance or sample-related finding? Remember what perceptual speed tests measure? One of the tests is called the letters strike or cancellation test. In a large field on a piece of paper, 1500 letters are crowded together; the individual must put a slash through all a’s, i’s, and e’s found in a total of two minutes. The type and construction of this test are common and are most often used to assess clerical accuracy. Many examples exist in the literature which show that women excel in clerical accuracy when compared to men. Numerical problem solving If one attempts to understand what the subscales are truly measuring, then differences in the perception of letters, numbers, and spatial figures help in the clarification process. Table 58 indicates the differences in the PS subscales for the high and low groups. 308 | P a g e 309 Prepublication Copy Table 58 Ps30 Df Per Cn Mt An So Ct*** Fx EI N Mean Std. Deviation Std. Error Minimum Maximum Sign Low 45 11.98 1.53 0.23 8.5 14.8 0.028 High 109 12.5 1.23 0.12 9 14.5 Low 45 11.88 1.32 0.2 7.88 14.77 High 109 11.92 1.12 0.11 8.87 14.2 Low 45 39.73 10.56 1.57 16 60 High 109 36.92 9.64 0.92 16 60 Low 45 32.67 8.73 1.3 12 50 High 109 32.61 11.42 1.09 8 56 Low 45 36.27 8.01 1.19 20 52 High 109 34.4 10.96 1.05 12 68 Low 45 37.64 11.28 1.68 16 64 High 109 35.05 13.6 1.3 8 80 Low 45 37.29 10.58 1.58 12 56 High 109 39.83 11.6 1.11 18 64 Low 45 40.24 20.43 3.05 4 88 High 109 46.24 16.66 1.6 12 92 Low 45 33.78 13.05 1.94 10 72 High 109 44.11 15.32 1.47 12 76 Low 45 19.11 9 1.34 -8 36 High 109 19.23 9.07 0.87 -4 38 0.875 0.111 0.974 0.304 0.26 0.206 0.06 0.0** 0.941 ***approaches significance Mean Separation for the 2 Randomly Selected groups On the Problem-Solving Scales Using Arithmetic Distraction In Table 58, problem-solving (ps) is assessed by an arithmetic perceptual speed test. As expected, problem-solving (ps) is significant as is Flex. Control, at the .06 level, approaches significance. Since arithmetic is a learned skill and involves some abstract manipulation and speed of processing, which of the 12 subscales is most likely to show 309 | P a g e 310 Prepublication Copy significance? In summary, as indicated in Tables 58 and 59, letters and numbers affect mean differences in the problem-solving subscale as well as control/cognitive flexibility and social problem-solving when the speed of processing is used to separate two groups of low and high. Spatial problem solving For spatial problem solving, two perceptual tests called embedded designs and cognitive flexibility were selected. Each of these tests required perceptual recognition and speed of processing as well as mental rotation of symbols. Embedded Designs: With a two-minute time limit, the embedded designs test contains 13 sets of 3 groups of symbols which must be matched and separated from their background by visual rotation. The use of embedded designs is usually associated with the concept of field independence and field independence (explained in Chapters 2, 23, and 25). Below, in Table 59, are the results from the analysis of a random sample of 155 people divided into 2 groups, high and low (above and below the 50th percentile). For this age group, the PS scale was significant as expected, but none of the other scales approached significance. Table 59 Name Status N Mean Std. Deviation Std. Error Minimum Maximum Sign Ps30 Low 75 11.96 1.36 0.16 9 14.3 0.001 High 79 12.72 1.22 0.14 8.5 14.8 Low 75 11.89 1.19 0.14 7.88 14.77 High 79 11.92 1.17 0.13 9 14.03 Low 75 38.51 10.1 1.17 16 60 High 79 37.01 9.85 1.11 16 60 Low 75 31.87 10.75 1.24 8 52 High 79 33.34 10.62 1.19 8 56 Low 75 34.77 10.27 1.19 12 60 High 79 35.11 10.19 1.15 12 68 Low 75 34.27 11.42 1.32 8 64 High 79 37.27 14.23 1.6 12 80 Low 75 38.19 10.69 1.23 12 60 High 79 39.95 11.92 1.34 14 64 Low 75 43.19 18.6 2.15 4 92 Df Per Cn Mt An So Ct 0.872 0.354 0.393 0.837 0.153 0.336 0.384 310 | P a g e 311 Prepublication Copy Fx EI High 79 45.72 17.41 1.96 12 88 Low 75 39.47 17.27 1.99 10 76 High 79 42.63 13.3 1.5 12 68 Low 75 18.43 9.49 1.1 -8 38 High 79 19.92 8.55 0.96 -6 36 0.203 0.305 **P=.05 *P=.01 +lacks homogeneity of variance Separation of the Problem-Solving Scales Using Randomized Group Scores from the Embedded Designs Tests What the results suggest based on this random sample as well as many others in our data bank is that speed of disembedding is a major contributor to problem-solving using fluid intelligence measures. The reason why Field Independence/Field Dependence test show these differences is that test like Witkin’s increase spatial complexity under time conditions which separate people into subgroups Cogflex: For the second spatial example, the test called cogflex required a perceptual search of a rectangular spatial area containing 40 different symbols and line figures. The task was to find designs in the spatial area which matched the 13 stimulus figures found in a box below the spatial area. The stimulus figures could be rotated; thus, requiring mental manipulation for the match. The results are found in Table 60. Table 60 Name Status N Mean Std. Deviation Std. Error Minimum Maximum Sig. PS Low 77 12.06 1.46 0.17 8.5 14.5 0.007** High 77 12.64 1.16 0.13 9.3 14.8 Low 77 11.81 1.25 0.14 7.88 14.03 High 77 12 1.1 0.12 9.3 14.77 Low 77 37.04 8.91 1.02 20 56 High 77 38.44 10.94 1.25 16 60 Low 77 31.01 10.33 1.18 8 50 High 77 34.23 10.83 1.23 8 56 Low 77 36.62 9.87 1.12 12 68 High 77 33.27 10.31 1.17 12 56 Dif Per Cn Mt 0.315 0.384 0.061 0.041* 311 | P a g e 312 Prepublication Copy An So Ct Fx EI Low 77 35.92 12.72 1.45 8 64 High 77 35.69 13.32 1.52 12 80 Low 77 39.69 12.11 1.38 12 64 High 77 38.49 10.55 1.2 20 60 Low 77 44.74 19.41 2.21 12 92 High 77 44.23 16.56 1.89 4 84 Low 77 40.29 15.99 1.82 10 72 High 77 41.9 14.83 1.69 12 76 Low 77 18.96 10.03 1.14 -8 38 High 77 19.43 7.94 0.9 0 34 0.911 0.515 0.862 0.518 0.749 **P=.05 *P=.01 +lacks homogeneity of variance Separation of Means of the Problem-Solving Scale Using Cognitive Flex and Random Groups Notice in Table 60 above, the conceptual scale approached significance. Motor, for the low group and problem-solving for the high group, were significant. Chapter summary The ten different subscales are examined by using five very disparate groups with small sample sizes and two randomly selected groups of 155 people, one half of the sample are 15-year-old while the others are adults in graduate school. Since the scores of the five groups are very biased, variegated, and diverse, differences are exaggerated. The mean scores and standard deviation show large differences. Because of generalizations found in the literature review, the differences provide one method to conceptualize what is measured by each subscale and each perceptual test. For example, one obvious expectation is that adults should be better at solving problems than children designated in special education. The amount of separation by mean difference in the subscale is just one way of displaying the mathematical and theoretical descriptive properties. Therefore, the examples of the subscale properties in this chapter are trivial, descriptive, and not generalizable, but illustrative. Using high and low groups separated by the 50th percentile, there are differences in the subscales which are evident in the solving of numbers, words, and spatial activities? The problem-solving subscale exhibits mean separation as expected. Other subscales, Social, Control, and Flex indicate differences in letters and numbers. Results in this Chapter 312 | P a g e 313 Prepublication Copy confirm the well-known observation that the speed of processing is associated with problem-solving. But what about situations in the real world where no one is keeping time and problems have to be solved. Will the differences in the subscales be maintained when large samples, older adults, managers, and different vocational groups are used? The next chapter and our paper presented to the American Educational Research Association in 2002 provide possible answers. Chapter reference Clingwald, B. (1986). Ideation, field independence, and right brain thinking. Unpublished Master’s thesis, California State Polytechnic University, Pomona, California 313 | P a g e 314 Prepublication Copy Chapter 16 Late Adolescence and Adulthood Data for Problem Solving in Older Age Groups Introduction The period of late adolescence and adulthood is the beginning of complex and compound problem-solving. No longer are simple solutions expected. Instead, problems involve a multitude of steps, with many different potential outcomes. Likewise, a single problem can be extremely difficult without an apparent solution. Older adolescents are exposed to many different types of academic problems; but many prefer to solve vocational problems that have simple, practical solutions. Many people want to concentrate on the kinds of problems associated with daily living or their area of interest. Others have already thought about a profession and want to take the courses necessary for their life-long vocational quest. Complex and compound problem solving is difficult and can require teamwork. A single problem such as “what is the irrational root of the derivative of the diameter of the circle with a radius of 6” is a complex problem. It is unlikely that an ordinary adolescent or older person has been exposed to the necessary skills to solve such a complex problem. Usually, an individual, either goes to the literature or works with a team to derive a solution. Likewise, as can be expected, few people are exposed to the compound problems or skills required to solve problems in a specific trade area such as house building. Once someone builds a house, it is easier to build another house. However, think of the myriad of skills necessary to complete the task. Decisions require planning. Resources must be obtained and used. Compound problem solving requires many resources to be coordinated before any problem can be solved. The housing industry has a skilled labor force requiring exceptional skills such as carpentry, plumbing, or masonry. The building and trades industry has performance specifications for each job. A standard of quality must be obtained before a house is sold. In essence, each tradesperson has a series of problems that must be solved. Builders know that tradespersons are valuable and necessary since each has an individual skill that meets the total specification process. A tradesperson without skills is seldom asked to work again. Building a house requires compound problem solving performed to a maximum standard. In contrast to real-life problem-solving skills, the complexity of problems solved in high schools usually involves three or four steps at the most. Probably 75 percent of the problems in the initial years (freshman and sophomore) are based on either memory retrieval or the use of a combination of memory plus two or three steps of processing 314 | P a g e 315 Prepublication Copy information. Problem-solving is not a generic model since there is not a general methodology of problem-solving which is followed in every academic area. The closest thing to the problem-solving model is found in science and math—i.e., problems following the scientific method. Most every high school student knows the sequence-define the problem, collect information on practical solutions, generate a hypothesis, apply different methods of solutions, determine the best solution, evaluate the results, and if necessary, apply a new solution. This methodology is usually presented in a beginning high school science course, such as physical science. The current chapter is data-oriented and compares the complex and compound problemsolving performance found in different samples--adolescents, college students, managers, and graduate students. By using various diverse groups such as juvenile delinquents and normal academic students as well as those selected for academics or the lack thereof, the dimensions of the problem-solving scales are further clarified. In the discussion below, the general problem-solving scale and selected samples illustrate important attributes. The purpose is to present normative data to understand how group differences are operating in late adolescence and early adulthood. As always, the question is “Are there subgroup differences in the problem-solving approach toward verbal, numerical, and spatial problems?” This question is addressed in the last part of the chapter. Gender differences In Table 61 below are gender differences for 466 people (average age = 31.26). These gender differences mirror the differences found in early age groups. That is, males (n=262) tend to prefer analytic items while females (n=204) prefer social items. Females, on average, are more extroverted than males and select items containing value content related to control and structure, a tendency prevalent in the earliest years of schooling. 315 | P a g e 316 Prepublication Copy Table 61 Males Ps30 Df Per Cn Mt An** So Ct Fx EI Mean 12.14 11.76 38.42 30.16 39.03 43.2 41.8 60.97 51.81 14.62 SD 1.39 1.86 11.95 10.21 9.45 13.08 12.65 20.52 14.02 11.44 Females Ps30 Df Per Cn Mt An So** Ct** Fx EI** Mean 12.08 11.78 38.78 30.95 39.36 32.73 47.11 63.16 49.94 17.22 SD 1.51 2.06 15.29 9.45 9.88 11.65 12.85 25.23 15.14 10.79 N=466 P=.01** P=.05* +logarithmic correction for heterogeneity-Levine’s statistic Gender Differences for Adults on the PS subscales Samples Below in Table 62, there are nine different comparison groups representing 1312 people. The table is constructed with the nine-different subscales across the top with the last row representing introversion and extraversion scores. The total statistics for all scores are listed either in the Appendix or in the manual for each instrument. Means or averages in this chapter may not be directly comparable to other samples in other chapters as the instruments and items may differ. The means and standard deviations are close, however. Table 62 No Name N Ps30 Pslap Pssp Df Per Cn Mt An So Ct Fx EI 1 Graduate Students 89.00 14.10 16.89 15.82 9.87 33.41 37.25 48.82 40.41 36.27 43.86 46.68 15.29 2 Gifted 32.00 13.94 16.53 15.37 9.05 32.55 37.48 33.35 44.16 33.42 41.68 50.06 15.39 3 Managers 64.00 13.20 14.48 14.92 10.30 35.01 29.33 32.33 34.21 39.25 39.02 39.15 18.07 4 College 279.00 13.16 15.05 14.55 10.20 42.67 29.60 40.20 38.01 40.48 73.52 47.02 9.32 5 Adults 305.00 12.74 14.69 13.89 10.71 32.75 36.37 39.86 38.19 37.56 51.60 51.12 15.23 6 Hs (16-17) 70.00 12.34 13.91 13.42 11.33 35.64 33.45 32.87 38.12 37.48 36.78 33.97 18.61 7 Hs (14-15) 150.00 11.70 12.54 12.75 14.87 35.92 32.39 33.36 36.61 39.12 36.00 31.84 19.08 8 Juv. Del. 68.00 10.98 8.98 11.74 14.64 39.86 32.19 37.02 34.86 35.69 49.72 38.15 15.14 9 Alternative 113.00 10.82 14.06 29.43 32.64 34.57 32.29 36.04 36.35 48.14 15.45 Averages 145.78 12.55 14.14 14.06 12.23 35.25 33.41 36.93 37.43 37.26 45.39 42.90 15.73 1.19 2.50 1.38 1.91 4.00 3.05 5.36 3.53 2.17 11.99 7.21 2.90 SD Hs=High School; Juv. Del =Juvenile Delinquents; Alternative-=Alternative High School. 316 | P a g e 317 Prepublication Copy Comparison of Scores for 9 Different Groups On the 10 Problem Solving Scales Rather than using the raw scores, the scores could be presented as normalized T scores with a mean of 50 and a standard deviation of 10. Anyone who prefers the T scores can simply convert using the data shown in Table 100 in Appendix B. The instruments for measuring these 10 groups produce two sets of scores--- base and extended. The base scores found in Table 62 are ordered by the average problem-solving scores (Ps30beginning at 14.10 and ending at 10.82). The base scores represent the separate and distinct personality and cognitive measurement scales. These problems solving cognitive scores use analogies and spatial drawing and reflect fluid intelligence. The base scores on the problem-solving scales have been explained throughout the various chapters. The extended scores, not shown, here, are based on the composites (integration) of career, semicognitive, cognitive, and personality and are used for predicting subgroups. The first of the nine comparison groups are graduate students from two different universities. These self-selected students volunteered for a testing session over four days during the 1990s (DeNovellis and Shand, 2004). The second sample (Gifted) consisted of high achieving high school students (n=32) who were selected for a summer institute at Mississippi State University (Carskadon, 1986). The criteria for selection was a national percentile ranking on a standardized test for math and reading as well as problem-solving ability. The third sample (Hitt, 1987) was a group of Extension Agricultural Managers (ages 30-64) who were judged for their managerial effectiveness in a dissertation study in 1985; while the fourth group was College students who were part of a career testing program at California Polytechnic University (1983-1989). The fifth group were high school students (16-17) who participated in a master’s Thesis study (Clingwald, 1986) and were 16-17 years of age. The Adult data came from the studies conducted by the Personality and Research Institute for Business and Education (DeNovellis, 1984-1995). The seventh sample (Hunt, 1987) was composed of 150 students ranging in age from 14-15 (91 females and 59 males, Hs 14-15). This sample, generated as part of the master’s Thesis, was selected for its ethnic diversity and included 49 Caucasians, 23 Asians, 26 Hispanics, and 43 African Americans. Samples eight and nine were also part of different master’s Thesis studies. Sample eight was from a pilot study for a master’s Thesis using sixteen to eighteen-year-old juvenile delinquents. The male juveniles were incarcerated by the California Youth Authority for criminal offenses (Juveniles); many offenses were drug-related. The average reading and math level was 6th grade (Bernal, 1989). 317 | P a g e 318 Prepublication Copy The ninth comparison group (Alternative High School) consisted of 89 alternative high school students. Of the 89 alternative high school students (Wooley, 1988), 41 males and 48 females attended the alternative school because of their low achievement, the potential to drop out, or simply as an alternate route through high school. Based on the previous literature reviews, certain differences related to the subscale scores are expected. Without going into all possibilities, the most obvious are listed next. Since the problem-solving scale (Ps30; Pslap; Pssp) is a more academic scale that separates groups of problem solvers, the expectations are that both the alternative high school and juvenile delinquents would score lower on the Ps scale, therefore, higher on the differential scale (Df), a calculated scale. The students selected for a summer (gifted) program are expected to score higher on the academic Ps scale than other college or high school students. Based on the IPS theory, one expects those people with higher levels of education to have higher conceptual scores. Which group would you expect to score higher on the subscale for motor skills—alternative high school or delinquents? Problem Solving Categories General and differential problem solving For the 9 groups in Table 63 below, the problem-solving scale (Ps30) along with the differentiation scale (Df) can be compared concurrently. Both problems solving scales measure some degree of seriation, pattern recognition, and logical thought. The subscale has items that include spatial orientation and analogies which require mental transformation and mental rotation of objects. The overall mean for the Ps30 is 12.42, while the mean for DF is 12.19. 318 | P a g e 319 Prepublication Copy Table 63 Ps30 Std. Dev. Df Std. Dev. 89 14.10 1.73 9.87 3.17 Gifted 32 13.94 1.09 11.79 6.54 3 Managers 64 13.20 1.48 12.58 3.19 4 College 279 12.68 1.48 11.58 5.13 5 Hs (16-17) 70 12.34 1.42 13.84 2.57 6 Adults 447 12.05 1.48 12.20 5.13 7 Hs (14-15) 150 11.70 1.36 14.87 2.87 8 Juveniles 68 10.98 1.31 12.36 3.17 9 Alternative 113 10.82 1.49 14.06 2.77 No. Name Sample 1 Graduate 2 Grand Average Grand Std. Dev. 12.42 12.19 1.43 3.84 Average Scores of the Nine Groups on Ps and Dif The patterns for these two subscales are self-evident. The gifted and graduate students scored highest on the Ps30 scale while the Juveniles and students attending alternative schools scored the lowest. The lowest average score on the Df scale was the Graduate Students while the highest score belongs to the high school students. The Df scale is an inverted calculated scale that is for the benefit of teachers interpreting the information on problem-solving and as such is not used in any of the research calculations. Do these groups show a difference in word, number, or spatial problems? The answer comes later! 319 | P a g e 320 Prepublication Copy Perceptual The base scale for the perceptual scale measures a person’s orientation toward the environment as well as the ability to attend to the details of elements in the environment. Selective attention increases from birth. We assume that people attend to various environmental objects when those objects become the focus of attention. Those who score higher on the perceptual scale are more likely to attend to the details of objects than those who score lower. The extended scales, not shown here, are a composite scale that is composed of a combination of scores from different perceptual tests as well as responses to subscale items. The extended scales are highly influenced by scores from the speed of processing tests. Table 64 below shows the nine groups' averages and standard deviations for the Perceptual Scale. Table 64 No. Name Sample Perceptual Std. Dev. 8 Juveniles 68 39.86 5.07 7 Hs (14-15) 150 35.92 3.2 5 Hs (16-17) 70 35.64 3.01 3 Managers 64 35.01 3.74 1 Graduate Students 89 33.41 4.21 4 College 279 33.25 5.41 6 Adults 447 32.75 5.41 2 Gifted 32 32.55 7.02 9 Alternative 113 29.43 12.47 Grand Average 33.40 Grand Std. Dev. 5.51 Note: Different Instrument used for adults, do not compare averages with young adults (8-13) Average Scores of the Nine Groups on Perceptual The average score of all nine groups is 33.40. average standard deviation is 5.51 Juvenile delinquents had the highest average score of 39.86 on the Perceptual Scale. Interpret this score to a group of people who spend a lot of time on the streets where awareness of the environment is important. The next highest average scores come from high school students and agriculture managers. The mean of the HS (14-15) was 35.92 while the mean 320 | P a g e 321 Prepublication Copy for HS (16-17) was 35.64. In general, managers (mean=35.01) are a very select group, noted for solving a variety of problems. Their overall means of problem-solving scales are usually higher. The lowest average mean (29.43) on the perceptual test is made by the students attending the alternative high school. Interesting! The standard deviation of the grand mean (33.40) for perceptual is 1.98 so about two-thirds of the mean scores fall between 31.40 and 35.40. Conception No longer are young people dependent upon just memory for conceptualization. Idea generation results in many creative and unique ideas or perhaps, ideas that are practical and useful. IPS assumes that conceptualization is increased by an achievement orientation. Top-down processing occurs continuously as one strives to obtain a goal. All of the hours of fantasy and thinking about new things, which began in elementary school, reach fruition in object and mind creations. Table 65 below shows the average scores for the nine groups. Table 65 No. Name Sample Conceptual Std. Dev. 2 Gifted 32 37.48 14.76 1 Graduate Students 89 37.25 9.25 6 Adults 447 36.37 8.26 4 College 279 35.85 8.26 5 Hs (16-17) 70 33.45 8 9 Alternative 113 32.64 8.71 7 Hs (14-15) 150 32.39 8.37 8 Juveniles 68 32.19 7.13 3 Managers 64 29.33 9.72 Grand Average Grand Std. Dev. 35.56 9.16 Average Scores of the Nine Groups on Conceptual So, which group scores the highest on the conceptual scale? Not surprisingly, the gifted and graduate students have the highest average mean score. Which group scores the lowest? -managers, especially middle managers in our data. Graduate students and 321 | P a g e 322 Prepublication Copy gifted students score a little over one standard deviation higher than the students who are in high school. In our data banks, the only other subgroup that scores higher than gifted and graduate is a group of 100 youngsters chosen as part of a talent program emphasizing music, dancing, and other creative endeavors. Their average scores were 37.87 on the adult problem-solving instrument. Motor The physical and mental discipline required to master motor skills causes a concomitant increase in the development of the central nervous system as students mature from birth to high school. The more activity to which the CNS is exposed; the earlier that the development occurs. The neuron rate increases dramatically in the first years of life and is stimulated by hands-on experience. One outcome is a group of people who are practical, and realistic, rely heavily on motor skills, and use bottom-up processing. Remember that bottom-up pathways in the brain increase attention to object processing. The samples below in Table 66 did not include career groups such as construction workers, athletes, or firefighters -–people who generally score higher on motor development. So, who did you choose to be high on the motor subscale? It probably was not the graduate students. However, since 45 of the graduate students were from the College of Business and Accounting, this finding is not unusual. Business students are usually quite practical and grounded in the reality of what goes on in the world around them and thus score higher on the motor subscale. In Table 66, the average score for most of the adults in the sample was 36.86 with college students having a mean of 39.60. The lowest scores on the motor scale were managers at 32.33 and the gifted group had the next lowest score with an average of 33.35. Middle Managers in Fortune Five Hundred companies usually score high on the Motor Scale. These managers, in contrast, were University Agricultural Extension Managers. 322 | P a g e 323 Prepublication Copy Table 66 No. Name Sample Motor Std. Dev. 1 Graduate Students 89 48.82 11.78 6 Adults 447 39.86 9.52 4 College 279 39.6 9.52 8 Juveniles 68 37.02 7.65 9 Alternative 113 34.57 10.02 7 Hs (14-15) 150 33.36 10.09 2 Gifted 32 33.35 15.7 5 Hs (16-17) 70 32.87 10.61 3 Managers 64 32.33 11.53 Grand Average 36.86 Grand Std. Dev. 10.71 Average Scores of the Nine Groups on Motor Subscale The expectation is for those individuals who score high on the motor problem-solving scale to contrast significantly with those who score high on the conceptual subscale. Go back and look at all the scores for the different groups and compare motor and conceptual. Analysis Analytic tendencies or the capability of mentally decomposing concepts into parts or rotating objects spatially is a performance action that often results in a product or verbal outcome. Analytic problem solvers can be convergent or divergent. The majority of people use both processes simultaneously every nanosecond and over time have a preference for a combination of processes that operate in conjunction with motor/conceptual, flex/structure, or social-emotional/analytical. The key to the process is the type of problem presented as well as the energy flow inward and outward. Analytic tendencies when combined with motor and structure/control lead to greater object processing while social/emotional tendencies when combined with conceptual and flex lead to greater pattern tendencies. 323 | P a g e 324 Prepublication Copy Convergent analytic thinkers break the whole into the sum of its parts and then elaborate on each of the parts. Divergent analytic problem solvers generate many alternatives to a problem solution prior to convergence or they diverge a long time then converge then diverge again. All people, as expected, are combinations of different processes—convergent, divergent, or even analytic. Certainly, it is difficult to follow the mental processes of convergent or divergent thinking. A few examples might help. Convergent analytic Those who are convergent analytic combine the convergent process with an emphasis on logic (depending on age) or associations. A convergent problem solver converges to a single solution, after analysis. For instance, consider a simple example in solving a math problem, the problem solver might answer the following problem from memory-100-50 = 50. A more complex math problem involving a series of steps is as follows: (300-50) + 2(10 -5) = 260. The analytical process requires an analysis of all the constraints and limits of each part of the problem, first (300-50) or 250, then (10-5) or 5, then 2 times 5 or 10 then finally 250 + 10 or 260. The solution is a compilation of the operations, perhaps memory analysis and then memory analysis again. However, each process involves convergence. Another example of convergent problem-solving using words is illustrative by the following example. Find the letter from the following list (a; e; r; o; u) which defines the word "b_t" which means "to wager." Note that the characteristics of the problem given can cause the problem solver to be convergent. Divergent Divergent analytic problem solvers do not converge easily or often to a single solution. The divergent analytic problem solver often is intrigued by an array of symbols and images (scenes in the environment, pictures in a magazine). Their analytic tendencies tend to extract similarities and differences in the symbols, or words. Principles are often extracted by generalizing from symbol systems. Often the pronouncements from divergent alternatives are only logical approximations. The intermediate problem solutions do not necessarily fulfill the requirements elicited by the problem. Instead, logical approximation puts the solution in the ballpark. The divergent person’s interest in generalizations often causes problems or controversy, especially among those looking for a single solution and a singlecase scenario. Analytic problem solvers who use both divergent and convergent thinking processes equally can consider multiple alternatives and select the best representation of that alternative as a 324 | P a g e 325 Prepublication Copy convergent response. These individuals excel at social, technical, scientific, and mathematical problems. Many people find the process of analyzing things enjoyable which is why they select items that are analytic in content. Having a preference does not mean that one is analytic, but for many people, which is what occurs. Simple discrimination, numerical and verbal comparison, and mental rotations are second nature to many in this group. So, which group in Table 67 below prefers items that are deemed analytic? As suspected, the gifted group, aged sixteen and seventeen, win first prize. So, which group is the lowest on the scale? Why do you think that the alternative high school student scored the lowest? Table 67 No. Name Sample Analysis Std. Dev. 2 Gifted 32 44.16 12.2 1 Graduate Students 89 40.41 10.15 4 College 279 38.44 10.19 6 Adults 447 38.19 10.19 5 Hs (16-17) 70 38.12 9.01 7 Hs (14-15) 150 36.61 8.74 8 Juveniles 68 34.86 8.24 3 Managers 64 34.21 11.87 9 Alternative 113 32.29 9.69 Grand Average 37.82 Grand Std. Dev. 10.03 Average Scores of the Nine Groups on Analysis Social From birth through adolescence, children score high on the social subscale, usually much higher than the Analytic scale. Socialization is primary in our society and continues as part of our school curriculum, especially in the elementary grades as teachers emphasize social conduct. At each age level from 5 until early adolescence, items from the social subscale are the items of choice. With that in mind, the high scores on the social scale for youngsters in the 14-15 age are not unusual. But what about the managers, why are their 325 | P a g e 326 Prepublication Copy social scores so high? In data from almost 2500 people selected for management positions ranging from technical management to senior management, the average scores on the Social problem-solving subscale are generally higher (37.24). As managers progress up the management ladder, one of the attributes that are part of the selection process is the capability of solving the problem with different kinds of people. Their problem-solving scores differ, however, according to levels of management and the duties required (See Chapter 18). The general trend for scores on the social scale is to increase with education, i.e. the more education, the greater the awareness of social situations. In our nine comparison groups below, the incarcerated group and those going to alternative schools have lower social scores. Also, students in the gifted group were less likely to select social items, which is not surprising based on literature reviews. So, what exactly is social problem-solving? Examples of items that measure social problem solving include Liking other people, being comfortable in a group when solving problems, expressing one's feelings or ideas orally, and knowing when and how to contribute to the solution of an ongoing problem. All behaviors are examples that contribute to solving the problem individually or in a team or group. The adult who likes to work in groups with other people to solve problems generally is interested in a myriad of distinct kinds of social problems, from the delinquency of minors to the place of religion in the workplace. Again, the scores for the nine groups in Table 68 are basic (not integrated with other subscales). When extended scores are used, a different picture is painted. For example, when integrating interest scores, the mean scores on the social scale are increased by vocational preference (whether a person prefers to be a Human Resource manager or a scientist). That is why both base and extended scores are used for analysis and are the reason for the integration of subscales (extended scales). 326 | P a g e 327 Prepublication Copy Table 68 No. Name Sample Social Std. Dev. 3 Managers 64 39.25 12.2 7 Hs (14-15) 150 39.12 9.78 6 Adults 447 37.56 14.86 4 College 279 37.55 14.86 5 Hs (16-17) 70 37.48 9.1 1 Graduate Students 89 36.27 11.4 9 Alternative 113 33.47 13.42 2 Gifted 32 33.42 18.81 8 Juveniles 68 32.98 12.35 Grand Average 36.34 Grand Std. Dev. 12.93 Average Scores of the Nine Groups on Social Control and structure The definition of control and structure, as well as its use in problem-solving, has been thoroughly discussed throughout this book. As described earlier, the need for structure is a process learned from birth. Control becomes a system used to structure internal and external events, usually by planning. Control reduces chaos and increases the chances of success in reaching a goal. Layers of memory imbibed with parental and society’s “do this” and “do not do this” are embedded from early childhood and result in various forms of self-regulation and methods of dealing with other people. Many academics argue profusely over the exact relationship between control and structure which is why we developed another subscale for the analysis of the phenomenon. In Chapter 12, the definition of control was expanded for adults and older children as the need to deal with complexity increases as people age. Two additional bipolar subscales of preceptivity and receptivity were developed to assess how adults interacted with stored and layered knowledge, preconceived ideas, and the structuring of information. In 327 | P a g e 328 Prepublication Copy the IPS theory, scores on external structuring are added to scores on internal structuring to derive a final score in the extended subscales. Control of information and emotions is paramount as problems are encountered in the environment. Which of the nine groups in Table 69 will score higher on control and structure and the subsequent subscale of Flex, i.e. control’s counterpart? Table 69 No. Name Sample Control Std. Dev. 4 College 279 52.12 14.81 6 Adults 447 51.6 14.81 8 Juveniles 68 49.72 7.13 1 Graduate Students 89 43.86 11.84 2 Gifted 32 41.68 19.86 3 Managers 64 39.02 10.98 5 Hs (16-17) 70 36.78 9.63 9 Alternative 113 36.35 14.34 7 Hs (14-15) 150 36 9.51 Grand Average 41.66 Grand Std. Dev. 12.55 Average Scores of the Nine Groups on Control In general, most college-educated students and adults score higher on control while the students attending alternative schools as well as young high school students have lower control scores. The score of the juvenile group is 49.72. Why? See the answer in the section on Flex and Control below. The group of managers in the agricultural extension system at the university has slightly lower than average scores while the graduate and gifted students have moderate control systems. 328 | P a g e 329 Prepublication Copy Flex The second control system, the counterpart of control, is Flex. As explained earlier, in an integrated system, different subscales interact or act in concert, sometimes. The sometimes is based on tendencies from introversion, extraversion, and analytic suppression but not explained here. Addressing the Flex subscale found in Table 70 in isolation, several things are evident. The lowest scoring group is the 150 (age 14-15) youngsters in high school. The highest scoring groups are gifted, college and adults. Managers score less than a standard deviation below the mean. In other words, managers as a group (see Chapter 19 for actual differences between managers) tend to have less flexibility. This is especially true of middle managers who use past experience, rules, regulations, and organizational structure to manage Table 70 No. Name Sample Flex Std. Dev. 6 Adults 447 51.12 14.52 4 College 279 50.98 14.52 2 Gifted 32 50.06 13.66 9 Alternative 113 48.14 5.85 1 Graduate Students 89 46.68 14.59 3 Managers 64 39.15 10.25 8 Juveniles 68 38.15 10.37 5 Hs (16-17) 70 33.97 9.77 7 Hs (14-15) 150 31.84 10.15 Grand Average 43.34 Grand Std. Dev. 11.52 Average Scores of the Nine Groups on Flex 329 | P a g e 330 Prepublication Copy Flex and control patterns Patterns become more explicit when both control scales are addressed simultaneously. Addressing Table 71 below, examine both the control and flex means for the groups scoring the lowest on the general problem-solving scale; that is, students attending the alternative school. The students attending alternative schools have low control and high flexibility. In other words, they are less likely to control and structure events in their environment. They are flexible in response to impulses of thinking and emotions and score the lowest on the PS subscale. The juvenile group scored high in control and low in flex. This suggests more control of external events in the environment and less flexibility in thinking and emotions. Compare this to the Gifted group of students who have average scores in control and higher scores on Flex. In contrast, managers, college students, high school students, and adults are relatively balanced in their control and flex systems. Table 71 No. Name Sample Control Flex 1 Graduate Students 89 43.86 46.68 2 Gifted 32 41.68 50.06 3 Managers 64 39.02 39.15 4 College 279 52.12 50.98 5 Hs (16-17) 70 36.78 33.97 6 Adults 447 51.6 51.12 7 Hs (14-15) 150 36 31.84 8 Juveniles 68 49.72 38.15 9 Alternative 113 36.35 48.14 Grand Average 41.66 43.34 Grand Std. Dev. 12.55 9.05 Average Scores of the Nine Groups on Flex and Control 330 | P a g e 331 Prepublication Copy Category and profile analysis Using the data above, the category system is used to paint a clinical picture; but first, the following caveats are warranted. In the following scenario, the grand average is used; however, realistically when we are profiling individuals and groups, it is better to use averages that are based on many small groups of similar ages, ethnicity, gender, socioeconomic status, occupational status, and instrument subscales. As one expects, these groups are small based on divisions and subdivisions. By using the grand averages for the groups above, the spectrum for comparison is highly exaggerated (gifted and graduate students vs. juveniles and alternative high school students). But again, this is designed to show the methodology and process of our categorization system. For the general problem solvers (Ps), the groups above the grand mean are the graduate, gifted, and college students and managers. The other groups are designated as differential problem solvers. The highest scores on Perceptual are juveniles, high school students, and managers. Whether the P is assigned as the second letter of description is based on the total profile. So, for the managers the two highest relative scores are GPS-s. Managers, who are general problem solvers, score higher on the subscales--- perceptual, social, and control. (GPS-s). For the gifted students: There are higher scores on general problem solving (G), conceptualization (C), control (s), and flex (u). The order was GC-us. The statement describing the gifted student is that of a general problem solver who prefers to conceptualize with flexible thinking and control. The first question relates to a group of students who scores low on a conceptualization: “What are their scores on control, problem-solving, and flex?” For the group of students attending an alternative school, consider that their highest scale above the grand mean was Flex. Putting this information together with their low problem-solving scores and high Diff (D), the pattern becomes u with low control and high flex. Our descriptive summary of the scores with such a pattern (D-u) is as follows: The students attending alternative high schools are differential problem solvers with lower scores on control and high scores on flexible thinking. Juvenile delinquents also are differential problem solvers (D). They show a pattern of high control and less flexibility in how the ideas are implemented (D-s). Their orientation is less social with a greater emphasis on analyzing events. Now, let us try to determine which group prefers which kind of problems-word, spatial, or numerical. There are many mixed patterns. 331 | P a g e 332 Prepublication Copy Differences in Types of Problems Solved Word problem solving Again, standardized test scores are used as one measure of solving verbal or word problems. The sample group contains 40 high school students; ages 15-18, some of the students in this sample were honor students. The sample was selected as it is representative. The criterion was splitting the single group into two groups at the 50th percentile, with the designation of “low” for those below the 50th percentile on the verbal section and “high” for those scores above the 50th percentile. This same strategy was used with many examples as it provides insight into the mean differences between high and low groups on various subscales. The question of interest is “Do those students who have higher scores on the verbal section of the standardized tests (labeled as high in Table 72) have significantly higher scores on the Problem-Solving scales? The answer is given in the Sign (significance) column. Two scales, Problem Solving and Motor have a significant difference at the .05 level. On the general Problem-Solving scale, the high group has a mean of 14.18, and the low group at a mean of 13.42 with a significance level of .055. The other scale which shows a significant difference is the Motor subscale. The high group has a mean of 31.91 while the low group has a mean of 25.33. Also, look at the scores on the conceptual scale. Our data suggest that the greatest number of young children have higher scores on motor (66 percent) with only about (33 percent) having higher scores on conceptual. As the propensity for reading and the level of education increases, there is a greater increase in those both males and females who mark items related to the conceptual scale). Table 72 Ps Df Per Cn N Mean Std. Dev Std.Err. Min Max Sign Low 18 13.42 1.17 0.27 11.25 15.5 0.055* High 22 14.18 1.26 0.27 12 16.25 Low 18 10.2 1.67 0.39 7.53 13.8 High 22 10.19 1.9 0.41 7.17 14.07 Low 18 33.47 5.99 1.41 20 44.35 High 22 30.67 6.86 1.46 20.87 43.48 Low 18 45.11 9.36 2.21 30 58 High 22 39.55 9.72 2.07 22 62 0.998 0.183 0.075+ 332 | P a g e 333 Prepublication Copy Mt An So Ct Fx EI Low 18 25.33 9.46 2.23 12 42 High 22 31.91 9.57 2.04 10 48 Low 18 35.33 13.56 3.2 14 66 High 22 40.91 11.82 2.52 16 60 Low 18 45.56 15.52 3.66 12 66 High 22 39.55 13.03 2.78 18 68 Low 18 70.22 25.64 6.04 16 112 High 22 68.73 28.89 6.16 8 116 Low 18 49.11 12.93 3.05 28 68 High 22 52.91 14.34 3.06 28 72 Low 18 19.44 10.47 2.47 -2 34 High 22 12.27 12.67 2.7 -4 36 P*= .05 0.036* 0.173 0.191 0.865 0.389 0.062+ +approaches significance High and Low Groups Split at the 50 Percentile on a Reading Standardized Test Numerical and logical analytic During the high school years, there is a direct increase in analytic and spatial tendencies which vary with age and education. Each year older brings about a greater variety of cognitive experiences which affects one’s capability to do various kinds of analytical and spatial types of problems. Table 73 represents Analogies and Serial Scores based on differences associated with age. Table 73 Age Possible Percent Mean SD 13.9 yrs. 12 ** 47 6.5 2.80 14.9 yrs. 12 ** 49 7.01 2.80 15.9 yrs. 12 53 7.50 2.43 16.9 yrs. 12 58 8.2 2.2 **Adjusted by versions of test N=250 *** Excludes gifted and special students Analogies and Serial Scores based on Age Ranges 333 | P a g e 334 Prepublication Copy Spatial problem solving Table 74 shows the averages for spatial scores for children between the ages of 14-17. As noted in both Tables, the mean and percentage correct for analytic and spatial problems increase with each age group; the sample size is 250. Table 74 Age Possible pts Male Mean Male Std. Dev Female Mean Female SD 13.9 25 12.4 4.93 9.34 4.02 14.9 25** 13.3 4.83 11.1 4.95 15.9 25 14.50 4.89 12.21 4.86 16.9 25 14.9 4.64 12.3 4.93 **Adjusted by versions of test N=250 *** Excludes gifted and special students Spatial Norms based on Age Ranges 14-17 For spatial problem solving, two groups of students at different universities (Breeding,1990) consented to engage in a problem-solving activity on a Saturday during the 1990s. The students were given a computer activity in which 13 different targets with R’s rotated in various spatial positions (0 degrees, 60 degrees, 90 degrees, 270 degrees, etc.). In some instances, the R was reflected as well as rotated. The activity was timed. Students were to identify both the degree of rotation as well as the reflection. In general, the time of choosing the correct answer was a function of the degree of rotation and reflection, i.e. the greater the amount of rotation and reflection, then the more time was required to make a correct decision. In essence, as complexity increased, time increased. The demographic factors of the 2 groups were quite a diverse-sample size: 85 students; age: 31.25, gender: slightly more females; ethnicity was predominantly Caucasian with a few Hispanics and a few African Americans. When there was missing data, the subject was dropped from the analysis. The most complex situations generally require both speed and accuracy of spatial processing. The spatial score was the difference between the initial time required for assessing the targets (R) under normal conditions subtracted from the amount of time required to assess the target in both reflected and rotated positions. Those who had faster times and more accurate assessments were assigned to the high group 334 | P a g e 335 Prepublication Copy while those who had long times and less accurate assessments were assigned to the low group. The criterion was separation at the 50th percentile. Examining Table 75 below, the only subscale which is significant is the general problemsolving scale. The other scales did not show any significant mean difference when students were divided into high and low spatial groups. Table 75 Name Status N Mean Std. Deviation Std. Error Minimum Maximum Sig. Ps Low 32 13.88 1.44 0.25 10.5 16.5 0.01* High 41 14.63 1.19 0.19 12 17 Low 32 11.28 1.06 0.19 9.93 13.73 High 41 10.96 0.96 0.15 9.47 13.3 Low 32 35.13 10.1 1.78 16 60 High 41 38.34 11.66 1.82 12 60 Low 32 33.5 12.68 2.24 4 60 High 41 31.02 14.96 2.34 4 72 Low 32 47 11.54 2.04 16 72 High 41 51.02 11.79 1.84 24 72 Low 32 37.88 12.11 2.14 16 64 High 41 38.54 13.29 2.08 20 68 Low 32 42 14.15 2.5 12 76 High 41 45.37 13.52 2.11 24 68 Low 32 53 16.13 2.85 16 72 High 41 56.39 14.77 2.31 20 76 Low 32 47 15.24 2.69 12 72 High 41 47.02 14.22 2.22 12 76 Low 32 16.12 7.45 1.32 4 28 High 41 14.44 7.13 1.11 4 30 Dif PC Cn Mt An So Ct Fx EI 0.17 0.21 0.45 0.14 0.82 0.30 0.35 0.99 0.32 **P=.05 P=.01* High and Low Ps Groups Split at the 50 Percentile for Spatial 335 | P a g e 336 Prepublication Copy Other important variables Without going into a lot of numerical tables, over the years, many different variables related to adults were studied with the problem-solving scales. Some of the more important ones included: divergent thinking, intelligence, word skills, creativity, and math skills. A summary of the results follows: Divergent thinking and creativity. Divergent thinking is a concept associated with creativity, thinking out of- the-box, verbal quips as well as the use of unique and different ideas. The subscales most mediated by those concepts on the problem-solving instrument were Conceptual, Flex, and Control. For both divergent thinking and creativity, the conceptual subscale was elevated and concomitantly so was control and structure for those individuals who have a higher educational level. When the educational level was less, the control/structure subscale tends to decrease, and flex elevates. When the scores on the Motor subscale are elevated, divergent thinking and creativity are more applied. Intelligence: When IQ tests are used with the problem-solving subscales, the higher the IQ the less the differences in the PS subscale. Although the Ps30 scale is elevated (Mean= 12.80-13.90), only the subscales for Control and Flex are affected. Vocabulary and Math: Higher vocabulary and math scores are mostly associated with higher structure and control in older adults. Chapter summary In this Chapter, a tremendous number of numbers was used to illustrate how different groups of people scored on the problem-solving subscales. The problem-solving scale for these groups was a cognitive scale that used the person’s correct responses to various forms of cognitive items involving spatial figures, analogies, serial patterns, block counting as well as rotational exercises. The sample groups were diverse and selected to illustrate patterns. Older groups of students and people responsible for solving the everyday complex problem have quite different kinds of scores on the problems solving instrument. Data from this chapter illustrates many different important trends. As usual, gender differences are evident, not on the problem-solving scale but on the preference scale. When sampling either in a school, classroom, workplace, or unit, any differences from the usual pattern should be examined. One important trend, evident and expected, is that the number of Ps subscales that show significantly decreased with age. That is, younger children with developmental attributes 336 | P a g e 337 Prepublication Copy show greater variation in mean differences on the ps subscales. In older age groups, other subscales are influenced (structure/control; Pslap, Ps30; Pssp). Chapter references: Bernal, N. (1989). Learning styles of the juvenile delinquents Unpublished master’s thesis. California State Polytechnic University. Pomona, CA. Breeding, B. (1990). Data submitted to the Psychological Research Institute for Business and Education, Murray State University, Murray, Kentucky. Carskadon, T. (1986). Data submitted to Psychological Research Institute for Business and Education, (summer’s research program for gifted students), Mississippi State University, Starkville, Mississippi. Clingwald, B. (1986). Ideation, field independence, and right brain thinking. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. DeNovellis, R. L. & Shand, K. (2004). Speed and Accuracy in Cognitive Processes. Unpublished paper. Associates for Human Perspectives, Claremont, California. DeNovellis, R. (1984-1995). Data submitted to the Psychological Research Institute for Business and Education. Claremont, California. Hitt, W. (1987). Data submitted to the Psychological Research Institute for Business and Education, North Texas State, Denton Texas. Hunt, M. (1987). Learning styles and ethnic groups. Unpublished master’s thesis. California State Polytechnic University. Pomona, CA. Wooley, R. (1988). Learning styles in secondary education. Unpublished master’s thesis, California State Polytechnic University, Pomona, California. Further reading Obdam, E. (1994). Fifth grader’s cognition of navigation icons. Unpublished master’s thesis. California State Polytechnic University. Pomona, CA. 337 | P a g e 338 Prepublication Copy Chapter 17 The Career Subscales Introduction In IPS theory, the foundation of generalized problem solving is learned within the first five years with skills, attitudes, and behaviors honed, sharpened, and developed over a lifetime. Generalized problem solving is based on early exposure to a wide variety of problems that required logical thought, spatial reasoning, and social awareness. In early life, as children gain motor skills, each child comes in contact with a multitude of everyday problems such as how to eat with a spoon, ride a bike, get dressed in the morning, tie one’s shoelaces, and how to get along with other children in play situations. Social awareness is increased by being exposed to diverse kinds of social situations while logical thought and spatial reasoning come from the use of motor activities that extend hand-eye coordination and fine motor skills such as activities involving riding a bike, throwing and catching a baseball, sewing and cooking, dancing, and applying keyboard related skills. All distinct kinds of activities increase individual decision-making and motor skills. Decision-making and choices during problem exposure lead to goal-related activities which result in increased individual self-efficacy and belief in one’s ability to solve situational social and task-related problems. Self-confidence built from generalized problem-solving carries over to task and domain-specific problem-solving in math, English, science, and history when children enter schools. When young people are sure of their identity and desire to succeed, each is more likely to choose experiences that mirror their occupational interests. Interests are amplified by being able to solve problems in any area, particularly where success is found. Initially, problems, especially during the younger years, are generalized to activities occurring within the immediate environment. Does the child read, engage actively, and find solutions to everyday problems? Puzzles, games, motor activities, media, taking things apart, and youthful exuberances help to establish patterns of interest. Interests are formed at an early age but are amplified by home, school, people, church, and exploration of the outdoors as well as individual activities and engagements selected by parents. Interests are not formalized until much later in life when self-efficacy, self-confidence, and true identity become a part of everyday life. Identity is a monumental key to the establishment of interests. Social awareness and social conformity increase when children enter schools. Children are expected to follow the rules, display order, and make decisions under adult supervision. Interests become a motivating factor, especially when children become 338 | P a g e 339 Prepublication Copy young adults and are allowed to be curious, ask questions, and explore. According to Holland (1956), when students and adults are comfortable with objects and things in their environment, they are more likely to investigate. Interests in the solution of problems can take many forms, some young adults like the challenge of trade skills while others want to be entrepreneurs, scientists, homebodies, or athletes. Regardless of the individual’s current occupational interest, the interactions of personality, cognition, and speed of processing form patterns found in Holland’s six categories are used as one cornerstone for classifying subgroups of people. Holland’s career patterns Holland (1997) used the 6 areas which, in his writings, were characterized as personality rather than interests but have been used extensively as the basis for career exploration. These six areas are often designated as the RIASEC (i.e., Realistic, Investigative, Artistic, Social, Enterprise, and Conventional) model. In many ways, the six types of personality reflect gender differences and preferences which are promulgated in real-life situations as expressions of interest. For example, according to Holland, a “Realistic” person likes to work with objects perhaps machines, cooking utensils, cutting tools, or cars, and enter career opportunities as a carpenter, an engineer, or a construction worker; while an “Investigative” person likes to take things apart, search out solutions in laboratory work or solve problems in medical areas. In contrast, a “Social” person” enjoys working on problems having social significance such as working in social services (family, church, or home). An “Enterprising” young man or woman prefers career patterns that influence others such as politics, business, or selling. An “Artistic” person, as the name implies, might display creative endeavors in fashion design, while a more “Conventional” person likes structure and order in their daily lives and could choose jobs involving clerical work, math, or accounting. In research, the RIASEC circumplex model proposed that the six types of personality/interests are arranged in a circular (hexagonal) structure based on the relative similarities/differences among them (Holland, 1997). According to Holland (1997), the model of RIASEC was operationalized as a rank order structure following a circumplex (hexagonal) model pattern. He surmised the structure from patterns of correlations found by correlating the different subscales. Thus, in his structural model, adjacent subscales (e.g. Realistic and Investigative) are more strongly related than alternate subscales (Realistic and Artistic). Likewise, the differences on opposite sides of the circumplex model show greater individual differences than those which are adjacent. In Holland’s studies (1959), natural patterns result from the development of strong interest patterns over weaker patterns. 339 | P a g e 340 Prepublication Copy Our Career and Interests Inventory As described in Chapter Two, a career/interest assessment was developed and tested with Cal Poly students during the years 1984-1989. The students came from all different kinds of populations, but a considerable number were students who were undecided about a major (career indecisive). We were allowed the opportunity to test them since most of them could not decide on a major in college. From our data, the primary career subscales which provided the greatest average separation in means scores for females were called literary, social, outdoors, and conventional. In contrast, the primary subscales for males were investigative, mechanical/realistic, and outdoors. These subscales can be more diagnostic for either males or females when the scores are reversed based on gender. For example, when a male has a higher score on literary and a lower on mechanical/realistic, this provides diagnostic information about the subject as the response pattern reflects a reversal from the normative pattern. Occupations can be divided into many groups based on subscale information. Holland’s category system, which divided occupations based on an individual’s three highest scores (i.e., RIE for realistic, investigative, and enterprising) was the most accurate for occupational classification. According to Holland, when groups of people in a similar occupation were tested, their scores were closest to the theoretical prediction made by the scores using the 3-letter acronym. For us, Holland’s categories were expanded to include auxiliary and other supplementary scales. For example, our subscale of Realistic included mechanical; while our subscale of Investigative included literary. Aligning Holland’s scales with the Problem-Solving subscales (Realistic-Motor); (Artistic-Conceptual); (Investigative-thinking); (Social-social), and (Conventional-control), only Enterprising does not have a counterpart. Holland’s Enterprising subscale mirrors one’s ability to influence others; so, similar information is found using the career and interest inventory. The data from our instrument were modeled to determine the best fit. The results were different from those found using Holland’s instrument. Our results mirrored a Circumflex (hexagonal) model as shown in Picture 4 below. The acronym for the subscales becomes RIEASC as noted in the principle components analysis below. Notice the pattern of the major categories corresponding to Holland’s subscales. Realistic is in the lower right quadrant, upper right is Investigative and Enterprising. In the upper left quadrant is Artistic. Going from right to left the pattern is RIEASC. In this analysis, Realistic is the opposite of Artistic and closer to Investigative moving from right to left. Enterprising is more opposite of Social and Conventional. As the subgroups (1-36) become more familiar, there is a relationship between the subgroups and Holland’s convention (RIEASC). This is easily seen in Appendix B. 340 | P a g e 341 Prepublication Copy Picture 4 Circumflex RIASCE Career Model around the 36 Subgroup Career and Interests (CR1-CR6) R=CR1; I=CR2; A=CR3; S=CR4; E=CR5; C=CR6 In the following Picture 5, the speed of processing factors has been added to the career subscales. Notice that subgroups and subscales tend to remain in the same position, but the axis is rotated depending upon the addition of variables. When the speed of processing becomes part of Picture 7, notice the following. Arithmetic and Cogflex are closer to Investigation and Artistic while letter identification and embedded figures are close to Social and Conventional. In general, the speed of figural processing (PF) is associated more often with Artistic, while the speed of processing cognitive (arithmetic numbers) is more often associated with Investigative. These scores for picture 7 have a greater number of females in the sample. 341 | P a g e 342 Prepublication Copy Picture 5 Circumflex Career Model & Speed of Processing Around the 36 Subgroups Career and Interests (CR1-CR6) R=CR1; I=CR2; A=CR3; S=CR4; E=CR5; C=CR6 Speed of Processing (S1=PF; S2=LD; S3=Emb; S4=Arith) According to vocational theory (Osipow, 1983; Rohlﬁng, Nota, Ferrari, Soresi, & Tracey, 2012 ), early adolescents become more aware of social cues, and social expectations in the movement from early adolescence to late adolescence (Betz, 1994; Gottfredson, 1981; Harmon, 1989). Social awareness, parental attitudes, and cultural expectations create a basic preference pattern that mimics gender stereotyping along a continuum of men preferring tasks and opportunities involving things and women preferring tasks involving people (Tracey et al., 2005; Tracey & Robbins, 2005). These interest patterns are evident in meta-analytic studies which indicate that men had higher scores in Realistic and Investigative job-related interests while women had higher interest scores in Social and Artistic subscales (Su, Rounds, and Armstrong, 2009). Meta-analytic studies tend to show gender-related differences in the career standard scores of men and women; therefore, diagnostic differences appear by examining each gender separately. (Tracey & Robbins, 2005). 342 | P a g e 343 Prepublication Copy Analysis of gender and demographic response patterns Gender differences Experiences, personal choices, and interests often lead to a selection of a particular item on a subscale. This constitutes a predilection or bias which is reflected on a measuring instrument as a more socially desirable, error, or correct response. This is particularly true for children at a particular age, and for adults who represent different demographic, cultural, and gender subgroups. When a female around age 8 is given two choices of a preference for either a firetruck or pink baby blanket, most young females choose in an average frequency pattern (such as 70 percent for pink baby blankets and 30 percent for firetruck). The statistic may change from 80:20 or 60:40 when a culture or other demographics are considered. These item biases are then reflected in the subscale scores when each subscale is normalized. Many authors have developed theoretical or empirical positions to account for gender selections of certain items resulting in a higher score for a particular sex. This bias is corrected in measuring instruments by mathematical adjustments as well as item equating. In classification, these biases help place a person more accurately in a particular subgroup. Controlling for gender bias When classifying people into different subgroups, the sample for the profile can be equally distributed for all potential biases related to demographic variables. Thus, a sample contains an equal number of distinct cultural groups (Asians, Hispanics, etc.) as well as an equal number of males and females of similar ages. The career sample with an even distribution is then correlated with the problem-solving subscales and then deconstructed. The resulting deconstructed correlation matrix is assumed to be different from a correlation matrix that contains a distribution of only male Asians or a correlation matrix of only female Hispanics. The next series of correlation matrices demonstrate these differences. The first of the three correlation matrices as shown in Table 76 is balanced for different demographic influences, i.e., reflects the item choices of a sample containing an equal number of males and females of similar ages as well as diverse cultural groups. Table 76 is a correlation matrix of Holland’s categories with our problem-solving instrument which includes cognitive and non-cognitive items. Table 76 can be compared to the 343 | P a g e 344 Prepublication Copy following Tables 77 and 78 respectively containing just Caucasian males ages 22-42 and Caucasian females 22-42. Notice that Ps30 is dropped from the analysis (redundancy!). Table 76: Controlling Response Bias R I A -0.29 0.30 S E c R 0.52 I A -0.38 S E 0.41 C Pslap 0.27 Ps-p -0.35 Per Cn 0.37 0.43 Mt -0.40 -0.40 -0.21 An 0.37 0.53 So -0.30 -0.51 -0.44 0.56 Ct Fx Ex -0.29 0.49* 0.39* N= Means from 52 studies * P (.05) =.279 **P (01) =.361* Correlation of the means from 52 studies involving Male and Female Career Subscales with the Problem-Solving Subscales As noted above, many of the correlations are quite strong, i.e. social on the career instrument is correlated .56 with social on the problem-solving instrument. Investigative is positively correlated with analysis (.53) and only slightly with problem-solving logical analysis performance (.27); while Conventional is weakly related to control (not shown). Extraversion is positively related to Social on the career instrument As explained in Chapter 19, the correlation matrix from above was deconstructed. The standard scores for the 36 subgroups were developed as a result of the deconstruction. As one becomes more familiar with the subgroups, the numbers assigned to each subgroup reflect patterns and sub-patterns within subgroups. For example, notice that subgroups 25 and 28 almost always are in the same quadrant in almost all pictures even when the 344 | P a g e 345 Prepublication Copy quadrant may be rotated. The same is true for subgroups 1 and 4. Also, understanding that some correlations (i.e., extraversion and social concern (.37); logical analysis and spatial analysis (.54)) appear with regularity with a large sample of data allows the deconstruction into standard scores. Compare the previous Table 76 with Table 77 below which contains only responses from Male Caucasians. The Tables should be similar in many ways but reflect a stronger bias toward the male. For example, Investigative is correlated only .46 with Realistic and there is a strong negative correlation of Artistic between the performance scales (-.33 with Pslap and -.32 with Spatial) Table 77: Male Caucasian Responses R R 1.00 I 0.46 I A S C 1.00 A 1.00 S -0.08 1.00 E 1.00 C -0.53 Pslap -0.33 Pssp -0.32 Per -0.34 Cn 0.40 Mt E 0.44 0.24 1.00 0.33 0.45 -0.56 0.33 0.30 An 0.41 -0.31 Sc -0.47 0.43 Ct 0.49 0.35 0.36 Fx Ex 0.54 N= Means from 52 studies *P (.05) =.279 -0.34 **P (01) =.361 Correlation of Means from 52 studies of Male Career and Interest subscales with the Problem-Solving Subscales 345 | P a g e 346 Prepublication Copy Summarizing the stronger associations of correlations from Table 77 of Male Caucasians above: Investigative on the career subscale appears to be positively related to the preference for Analysis (.41) and Conceptual (.40) on the problem-solving subscales. The Realistic subscale on the career is more related to a preference for Motor (.33). The Artistic scale is strongly related to Conceptual thinking (.45) while the Conventional scale is more related to Social (.49) and Control (36). The Social scale on the problem-solving instrument is also associated with Social (.43) on the interest scale. The career subscale Enterprising for males was correlated more with the Motor (.30) and Control (.35) subscale, while the problem-solving subscale of Control was correlated with both Enterprising and Conventional. In Holland’s original studies, the Conventional subscale was correlated with the need for structure and order. Now compare both of the former Tables (76 and 77) with the next Table 78 containing the responses patterns of females who are Caucasians. Notice there is a weaker correlation between Realistic and Investigative and almost no correlation between the career scales and performance items. Social on the career instrument is correlated (.46) with social on the problem-solving scales. Extraversion is correlated (.51) with Social on the career instrument. These results suggest that in classifying a respondent the profiles for each gender are important. Knowing how a balance correlation matrix of demographic attributes differs from each gender profile provides information about the degree of bias in the response patterns. Table 78: Female Caucasian Response Bias R R 1.00 I 0.29 I E C 1.00 1.00 -0.40 E C S 1.00 A S A 1.00 0.44 0.41 -0.35 0.34 1.00 Pslap Pssp Per 0.50 Cn Mot Ana 0.41 -0.43 0.40 0.31 0.44 0.42 0.24 346 | P a g e 347 Prepublication Copy Sc Ct -0.30 0.46 0.41 0.42 Fx Ex 0.33 0.43 -0.45 0.51 N= Means from 52 studies * P (.05) =.279 -0.52 **P (01) =.361 Correlation of Female Career and Interest subscales with the Problem-Solving Subscales Summarizing Career Trends: In an integrative system, a single person chooses both preference and performance items in the areas of cognition, personality, and interests. All choices are often a reflection of both peripheral and core values. Individual actions are outcomes related to strongly held beliefs, values, and individual biases. The question remains as to whether a composite score, representing core values and selection, increases the separation of IPS means more than any single scale by itself. Below is a summary of research results from our subscales which reflect Holland’s six subscales and the basic problem-solving scores of personalities and cognition. As noted, only some subscales are separated in the expected direction that the theory suggests. Others do not separate well. Only those subscales that separate people in the direction of classification trends are used. Without going into a lot of different tables and numbers, the following paragraphs summarize the major findings related to the career subscales. Education The career scales, by themselves, are not very diagnostic for young people in 7th grade through high school unless the students are exceptional, either in problem-solving or maturity. For college-age students who have not decided on a major course of study (career or program indecisive), the career subscales often were not very useful. However, when the career scores are integrated with the personality, cognition, and semi-cognitive subscales, the group of scores becomes more diagnostic. For men and women, (college or graduate school), mean scores on interests, cognition, and semi-cognition subscales increase with education. The results are generally the same through graduate school. The average scores on the Investigative and Literary subscales may increase as much as 5 points as individuals gain more education. 347 | P a g e 348 Prepublication Copy Age As people age, the scores in different occupational groups (engineer, medical, etc.) increase. That is, individuals, identify well with certain kinds of work. As a simple example, individuals from a fortune five hundred company who were building airplanes had noticeably higher scores in motor and perceptual accuracy. In general, people of all ages become more social with age. Likewise, achievement and independence tend to remain high while structure and control increase with age and experience in most occupations. The tendency to investigate and read is also more prevalent as people age. For cognition and speed of processing, the increase in average scores is in the 21-28 age group with varying results coming during the 30s-50. As expected, this suggests people have greater facility with logical analytic thought and think faster than younger age groups (7-15 years). Generally, performance and career scores decline in the 60-80-yearold groups. Likewise, flex increases in some occupational groups with age. Culture Over the decades, two large world service organizations used the instruments in the US and many overseas countries. Data collected from individuals who were native to their countries and English-speaking helped determine the cultural bias inherent in the measuring outcomes. Many of the participants were in quasi-management positions as their positions did not fit the US traditional conception of the first line, second line, or executive management. However, each of the positions was responsible for the administration of financial and employment decisions There are trends regarding problem-solving skills for both men and women indicated on the career instruments. In various countries around the world, some career preference subscales reflect only a passing interest. Other subscales are categorically strong and reflect both work performance and work preference. This strength of the relationship was determined by a correlation with performance indicators of work. The computational subscale for men is one such scale. For example, a person might choose a preference for subject matter courses in algebra, geometry, and calculus and also score higher on performance items of logical analysis, simple fast computational skills, and the ability to rotate objects spatially. Such performance skills are related to both experience and familiarity. When dividing people into high and low groups around the 50th percentile, the two subgroups repeatedly similarly separate the means. That is, a strong interest in computation is strongly correlated with computational skills. 348 | P a g e 349 Prepublication Copy Chapter summary Career subscales are useful in career exploration for certain individuals in certain situations. In many instances, for individuals who are career indecisive, the subscales reflect indecisiveness. That is, many of the subscales are not elevated enough to reflect a pattern that is useful for helping people. When information from the career scales is combined with additional information from personality and cognition, the combined information is more diagnostic and more useful. Interests are theoretically and tangentially associated with solving everyday problems. The response bias associated with demographic differences and gender can be used to effectively in clarifying one’s approach to problem-solving. The career subscales, by themselves, are predicted in specific situations and with very specific people who have established a work identity. Holland’s career patterns appear to be useful when considering work patterns associated with existing jobs. Combining information from various instruments is more diagnostic than using a single instrument. Chapter references: Betz, N.E., & Fitzgerald, L. E. (1987). The career psychology of women. New York: Academic Press. Gottfredson, L. S. (1981). Circumscription and compromise: A developmental theory of occupational aspirations. Journal of Counseling Psychology, 28, 545–579. Harmon, L. W. (1989). Longitudinal changes in women's career aspirations: Developmental or historical? Journal of Vocational Behavior, 35, 46–63. Holland, J. L. (1959). A theory of vocational choice. Journal of Counseling Psychology, 6, 35–45. Holland, J. L., 1965 Holland, J. L. (1965). Holland Vocational Preference Inventory: Manual. Palo Alto, CA: Consulting Psychologists Press. Holland, J. L. (1976). The virtues of the SDS and its associated typology: A second response to Prediger and Hanson. Journal of Vocational Behavior, 8, 349–358. Holland, J. L. (1997). Making vocational choices: A theory of vocational personalities and work environments (3rd ed.). Odessa, FL: Psychological Assessment Resources. Osipow, S. H. (1983). Theories of career development (3rd ed.). Englewood Cliffs, NJ: Prentice-Hall. 349 | P a g e 350 Prepublication Copy Rohlfing, J. E., Nota, L., Ferrari, L., Soresi, S., & Tracey, T.J. (2012). Relation of occupational knowledge to career interests and competence perceptions in Italian children. Journal of Vocational Behavior, 81, 330–337. http://dx.doi.org/10.1016/j.jvb.2012.08.001. Su, R., Rounds, J., & Armstrong, P. I. (2009). Men and things, women and people: A meta -analysis of sex differences in interests. Psychological Bulletin, 135, 859–884. Tracey, T. J. G., & Robbins, S. B. (2005). Stability of interests across ethnicity and gender: A longitudinal examination of Grades 8 through 12. Journal of Vocational Behavior, 67, 335–364. Tracey, T.J., & Rounds, J. (1993). Evaluating Holland's and Gati's vocational interest models: A structural meta-analysis. Psychological Bulletin, 113, 229–246. Tracey, T. J. G., & Rounds, J. (1996). Spherical representation of vocational interests. (Monograph) Journal of Vocational Behavior, 48, 3–41. Further reading Hubert, L., & Arabie, P. (1987). Evaluating order hypotheses within proximity matrices. Psychological Bulletin, 102, 172–178. Liben, L. S., Bigler, R. S., & Krogh, H.R. (2001). Pink and blue-collar jobs: Children's judgments of job status and job aspirations in relation to sex of worker. Journal of Experimental Child Psychology, 79, 346–363. Osipow, S. H. (1999). Assessing career indecision. Journal of Vocational Behavior, 55, 147– 154. Tracey, T. J. G., & Ward, C.C. (1998). The structure of children's interests and competence perceptions. Journal of Counseling Psychology, 45, 290–303. Watt, H. M. G., & Eccles, J. S. (2008). Gender and occupational outcomes: Longitudinal assessments of individual, social, and cultural influences. Washington, DC: American Psychological Association. Wightwick, M. Irene. (1945). Vocational interest patterns: A developmental study of a group of college women., (pp. 69-82). New York, NY, US: Teachers College Bureau of Publications, vi, 231 pp. McClelland, D. C. (1961 The Achieving Society. Princeton, N. J.: Van Nostrand Co. 350 | P a g e 351 Prepublication Copy Atkinson, R. C., &: Crothers, E. J. (1964). A comparison of paired-associate learning models having different acquisition and retention axioms. Journal of Mathematical Psychology, 1, 285-315. 351 | P a g e 352 Prepublication Copy Chapter 18 Vocational Problem Solving Introduction The theory is not particularly useful unless one can see the results in everyday situations. Therefore, the validity of the IPS theory was tested with technical and non-technical managers, as managers are excellent vocational problem solvers. The sample consisted of 1500 general and differential problem solvers in different levels of management in many different kinds of fortune five hundred companies. The group was composed of prospective managers, non-managers, seasoned senior and middle-level managers, displaced managers as well as those who managed “mom and pop” organizations. The first part of this chapter provides information about interest theory as interests are the foundation of vocational problem solving, especially when managers are involved. Interest theory helps to identify general and differential problem solvers and the subgroup to which each belongs, thereby providing accurate feedback to increase problem-solving skills. Managers, as a subgroup of individuals who are generalized problem solvers, manifest their skills in various kinds of verbal, numerical, and spatial problems. The middle part of the chapter describes our instruments, methodology, and definitions for managers. The latter part of the chapter addresses substantive information about the validity of our theory and our measuring instruments and how the theory can be applied to managers. Again, this is a data-oriented validation chapter that provides a lot of tables illustrating vocational problem-solving. This chapter begins by summarizing the main points about interest patterns found in separate places in the book. IPS-interest theory IPS theory suggests that people use their energy in various activities in the environment and this process helps establish “interest” patterns. An “interest” pattern is the sustained activity with objects, thinking processes, or general goal-related actions. Interest patterns are the result of daily living and social interaction which generate energy reactions in neural pathways contributing to readiness characteristics that are satisfying and rewarding to the individual. Theoretically, personality (an affective state) and cognition (a cognitive state) use separate neural pathways but are constantly interacting in the brain and eventually lead to actions and outcomes in the environment called interest patterns. Interests are a measure of sustained activity with different kinds of problems. The problems in an area of interest 352 | P a g e 353 Prepublication Copy are solved by the individual over time and are the result of energy devoted to the activity as a result of wish and goal fulfillment. The cutting of new neural pathways for complex problems is often rewarding and enhances the associated activities with a particular kind of problem. Many people prefer to spend their time in vocations where often-used neural pathways result in quick solutions to everyday problems. Once a neural pathway is cut and used over and over, the individual derives satisfaction and reward in the use of a particular skill and displays an interesting pattern. This results in satisfaction with different kinds of problem activities. A reluctance to learn new skills or develop new interests can result from the “comfort” of using the same neural pathways over and over. An “interest pattern” is a series of actions that occur frequently and are identified in the daily activities of a person. For example, some people might say “Joe likes helping children play basketball. Interest patterns become specialized through neural differentiation, motivation, the reward for experiential activities, and the reward for solving problems in a particular area. The reward comes from the direct action of neurotransmitters such as serotonin and dopamine at neural synapses as the activity increases exhilaration and satisfaction when the goal is accomplished, and problems are solved. Constant reward and success increase skill development associated with a particular problem. Interest patterns and skill development often coincide. Interest patterns Interest patterns in young people (less than age 10) are not well-formed but a function more of “wish fulfillment” --for example: “I want to be a nurse, policeman, or fireman.” In younger adults, interest patterns are usually broad rather than narrow and become more specialized with time, reading, and experience. Interest patterns become outcomes associated with the temperament and cognition of the individual as the time of engagement with various kinds of problems increases. As the person spends more time and engages in problem-solving. this results in a greater identification with objects, thinking patterns, and goals. This can lead to expert performance, even at an incredibly early age. Expert performance in problem-solving is just one kind of outcome related to interest patterns. There are many other kinds. Many interest patterns are transitory and/or trait-like depending on many factors that vary specifically with the daily patterns of the individual. Although the amount of time varies with the individual, interests change substantially over time. Some people change their interest patterns more often than others. With a very versatile young person, the only way to ascertain their interests is by daily observations. 353 | P a g e 354 Prepublication Copy The specialization associated with interest patterns requires more than just experiential activity; therefore, there is a limit to the complexity of the problem that can be solved based on experience alone (skill development). The complexity of problems solved is increased as a sufficient amount of time is devoted to reading or studying problems in a particular area of interest. Reading and understanding contribute to skill and experiential development, vocations, and career, especially management skills. One of the most difficult interest patterns to develop is the management of groups of people and things since it requires social acumen, knowledge requirements, and experience. These next two sections provide validation data for our interest theory related to management and its application to real-world settings. The next section defines the diverse levels of managers and their measurements. Defining and Assessing Managers Which group of people are more likely to use their interests, personality, and ability in the solving of general and specialized problems (DeNovellis, 1992)? We selected managers as representatives of “general and differential problem solvers” who solve complex problems. Senior Managers and Middle Managers in large complex fortune five hundred companies met our criteria of general problem solvers in the real-world setting. The first line and technical managers, at least in our data, are more likely to be ‘differential problem solvers.” That is the essence of almost 20 years of studying managers at all levels- Mom and Pop to Fortune Five. There are quantifiable differences between the problemsolving orientation at different management levels (Technical vs. First line vs. the Second line vs. Middle vs. Senior Management. To better understand the different responsibilities in the organization, each level of management had to be operationally defined. What follows are our definitions for the management positions. Senior managers, such as CEOs, Vice Presidents, and Group Managers, represent general problem solvers as their duties, and responsibilities required knowledge of trends, forecasting, and analysis of potential problems affecting their organizations as well as a host of more complex problems relating to their products and services. In actuality, a world of difference exists even among levels of senior management positions. In many complex and Fortune Five Hundred organizations, the President’s and/or Chief Executive officer’s (CEO) duties require more leadership, vision, and trend forecasting, while the duties of the Vice President require more operational responsibilities. 354 | P a g e 355 Prepublication Copy Middle managers are different from senior management in many ways. This is mostly due to their assigned responsibilities in the day-to-day operational management, people, resources, and tasks. For the most part, the duties of middle managers are abstract since they are confined to offices where paperwork is required. Usually, middle managers are responsible for first and second-line managers and report to senior management. In our classification system, all general managers are assigned (middle, third, second line managers, first line managers, and supervisors) by the number of people who are either supervised or responsible to the manager and by their daily responsibilities. A middle manager may be responsible for 20-40 other managers, while a first-line manager may have 1 to 5 people reporting to him or her. The first line and technical managers have more technical skills and are generally ‘working’ managers, chosen from a group that performs actual tasks related to products and services. Often many first-line managers do not perceive their duties as management but prefer the term “supervisory.” As an example, a first-line manager might be responsible for the workers who provide service in the pick-up of garbage and waste at your house. Some managers are technical, and some are non-technical. Technical managers usually do technical work in companies. A technical manager uses technical knowledge related to the service or the product of the organization. A good example of a technical first-line manager is the person who attends to the computers and servers as well as the daily operations of employees who perform internet services. A technical manager could be a first-line manager or supervisor. A non-technical manager is found in general areas such as small family-owned businesses or local shops--retail stores, clothing shops, or other similar areas. In our classification system, there is also a group designated as “Managing specialists.” Managing specialists are people who help managers through the organization, clerical activities, and record keeping. A managing specialist is not a manager, per sec, but one who possesses all the skills of management and helps those people who are in management. Administrative assistants are excellent examples of Managing Specialists. Managing specialists may become managers. In defining the responsibilities of management, each level in the company or corporation is assumed first to be developmental. That is, a person moves from a supervisory or a first-level job to a second-level job after being successful and understanding the position. The problems at each level of management differ. The supervisor is usually quite good at the specialized problems that are part of the group that he or she supervises. The middle manager (2nd or third level) usually supervises other managers and oversees operational policy at the first level. Middle managers administer support functions that help firstline people do a better job. In large Fortune Five hundred companies, they often supervise, 355 | P a g e 356 Prepublication Copy evaluate, and administer to 2nd and third line managers. Senior managers have the broadest overview of the organization and understand all the component groups and their functions, usually by age and experience. A final group of our managers was defined as displaced, prospective, or in training. These three groups of managers often have response patterns on the instruments which are completely different from regular managers. The response patterns on management instruments mirror people who are not managers or those who have not developed a management identity. For example, a displaced manager is a manager who is leaving the organization because of downsizing or due to management decisions. Displaced managers’ profiles are generally more similar to regular managers than either prospective or in-training managers. Assessing managers Since the manager’s position requires an interest in the work that each must do, the scores from the career and interest tests as well as management instruments served well to identify those who select items that corresponded to our categories of problem solvers. To assess their performance, the simple process of letting those who work with the manager judge their efficiency and effectiveness was used. Except for a Senior Manager, who did not have a person above them, managers both above and below their level rated each on both effectiveness and efficiency as well as a variety of other management issues. Consultants and others who were independent of the managers provided ratings on the problem-solving capability of each assessed manager. Since the rating was independent, they were a primary source of instrument validity. Also, individuals with a background in organizational development and management experience judged each assessed manager for both efficiency and effectiveness. And finally, a measurement group hired by one of the large aircraft companies rated our measuring instruments and compared them to other well-known measuring instruments used in the field. This measurement and training group invited managers to a team-building session where the managers were given actual performance and problem-solving activities during separate weekend retreats. Based on actual data from the problem-solving situations, the managers were then assessed with 8 well-known instruments, and 4 instruments were selected for use by the aircraft company. Our set of instrumentations was one of the four. (Zimney, 1989) Applying the IPS theory in a form that was palatable and easily understood by the people in the companies necessitated the use of both basic and extended scales. As an example, to derive the extended scales, many different self-report scales were combined to assess management effectiveness, and efficiency. Additionally, independent and anonymous subordinate and supra-ordinate employees gave the rating of management effectiveness and efficiency. 356 | P a g e 357 Prepublication Copy The IPS subscales (Conceptual, Social, etc.) were the same as those used with grade school children, high school students, college students, graduate students, and adults, as defined in previous chapters. To provide continuity and comprehension, the original IPS subscales were combined into the language and terminology of the managers. Some of the extended scales included terms such as Management Effectiveness, Tasks vs. People Orientation, Management vs. Non-Management identity, Team player vs. Technical Problem solver, and Management Improvement (DeNovellis & Brush, 1986). The ratings by fellow managers and workers were given on a scale from one to five. Some of the attributes which were assessed were leadership, effectiveness, efficiency, amount of impatience, and stress. Six other areas were also assessed: 1) the manager’s need to demand or apply pressure, 2) management planning skills, 3) their willingness to improve, 4) their adaptability, 5) the amount of control and structure, and 6) the degree to which the manager was oriented to people as opposed to tasks. These ratings were integrated with scores from IPS subscales, career, and interest scales as well as the cognitive data and provided the basis of subgroups categories for classification. Measuring instruments The career and interest instruments cited in Chapters Three and Seventeen were also used with managers. These instruments were modified to provide real-world associations for the manager. In essence, the main focal point was the overlap between the position held and their current job responsibilities. In other words, the focus was on the degree that interest patterns could predict how the person perceived oneself as an effective and efficient manager who could solve problems in one’s area of responsibility. Interest patterns when combined with cognition and personality, as outcome variables, were often associated with independent ratings of others. Cognitive and semi cognitive We used the same cognitive and semi-cognitive scale that had been used with other adults and children. This included analogies, sequences items, spatial items, and speed of processing subscales. The purpose of the items and subscales was to assess the degree to which fluid intelligence and processing speed influenced the outcomes related to management responsibilities. The Problem-Solving scale was redefined to encompass the potential to solve latest problems while the Management Effectiveness and Efficiency scales became the outcomes variable associated with actual problem-solving ability. 357 | P a g e 358 Prepublication Copy Primary goal The primary goal was to assess how well each of these IPS subscales provided information about the manager’s effectiveness and efficiency in solving problems related to their management position: senior, middle, first line, and managing specialist. Our secondary goal was to categorize the IPS patterns in a manner that allowed us to analyze subgroup patterns and provide additional information back to the individual. The individual scores were compared both to their local subgroups as well as other groups of managers. For example, a person who was a middle manager and who supervised 10-20 people could compare their management scores to other middle managers in a similar organization. Validation Management consultants provided a separate measure for validating most of the IPS categories. Many of the people who used the instruments were management consultants, management trainers, and organizational development specialists. These people provided feedback on the validity of the categories when the managers were tested. In some instances, managers were displaced during the downsizing of the organization for economic reasons. In other instances, managers were being hired for a particular position. In all cases, the results of our instruments were used only for improvement and feedback, not as a tool for hiring and firing. In a few instances, the management instruments were given to those managers who were on “retreat” as a source of feedback. Results from basic scales Over 10 years many interesting results were obtained. The results would fill another book. Here, Table 79 bullets some of the more interesting results. 358 | P a g e 359 Prepublication Copy Table 79 College students N PS Dif Per Con Mot An Soc Control Flex Exint 179 12.33 11.59 37.48 29.24 39.46 44.76 43.67 53.53 50.18 14.56 0.7 1.1 10.8 11.1 10.1 15.6 16.1 16.6 14.2 11.4 12.25 12.75 27.26 35.29 27.00 37.43 46.00 36.29 54.29 16.79 0.4 1.4 13.8 18.3 14.1 15.0 16.4 20.8 21.9 12.4 12.22 11.26 36.09 28.96 40.36 46.26 44.29 58.74 55.44 14.60 0.9 1.1 8.9 10.7 9.5 13.2 13.9 16.4 11.5 10.9 12.36 11.27 35.45 31.88 36.85 44.91 46.06 60.00 57.09 14.42 1.0 1.2 12.4 10.5 9.9 15.1 12.8 15.1 13.1 9.9 12.56 11.34 31.73 31.94 34.94 43.71 42.74 56.81 54.19 14.98 0.6 1.2 11.7 13.6 13.1 16.7 17.1 18.7 15.4 12.5 12.47 11.09 30.07 34.00 35.41 46.00 40.24 60.71 56.71 16.41 0.7 1.1 8.4 10.3 10.4 9.0 12.8 16.6 12.2 12.6 S.D. Trainers 25 S.D. First 180 S.D. Second 25 S.D. Middle 35 S.D. Seniors 20 S.D. S.D.=Standard Deviations Basic Scale Scores (Means, S.D.) for Different Groups o managers and non-managers The sample of college students noted above came from two major universities in California. These students responded to the instrument to measure their interest in management as a career. The other groups, trainers, senior managers, etc. were randomly pulled from our database of managers. Most of these managers were from Fortune Five Hundred companies. As can be seen from Table 79, higher levels of management (Senior and Middle Management) had slightly higher problem-solving scale scores, but not much. Second-level Management through Senior Management scored higher on Control and Flex. Trainers and Senior Managers had lower Perceptual (Global) scores and higher scores on Conceptual Problem Solving. Senior Managers and trainers were more extroverted. Non-management and First line managers were more cognizant of the real world of objects and things (sensory-motor). Senior Managers and Trainers scored higher on analytic thought. One can compare these scores with the other data from adolescence through graduate students found in earlier chapters. 359 | P a g e 360 Prepublication Copy Results from ratings Many of the management scales evolved as the time when on. Originally all the results were based on the manager’s self-report, i.e. how each manager perceived their management effectiveness or the interpretation of perceiving their management effectiveness based on normative scores. For many, the manager’s self-report of management effectiveness and others’ perceptions of management effectiveness was quite different. For that reason, ratings from trainers, consultants, employees, and others were soon integrated into the scoring system. Then these results were compared to the manager’s scores. The integration of ratings led to overall lower effectiveness and efficiency scores on various management scales. In other words, the consultant groups were more likely to rate the manager lower than the rating that the manager gave to them. The results from some of the ratings are summarized below. Anonymous ratings • • • • • • • Anonymous ratings can be effectively used for assessing the efficiency and effectiveness of Management Problem Solving Senior Managers (because of the intense hiring practices and scrutiny received from others in the organizations before being hired) had the highest rating from other managers and independent raters. Managing Specialists and first-line managers received the lowest rating and show the greatest need to improve The most common attributes of those who received the lowest score in management effectiveness and efficiency suggested they were too demanding, too impatient, and created stressful environments Higher levels of management had more stress than lower levels. The greatest level of management stress was often self-imposed. Managers who possess better skills in working with people received better management ratings. There is a significant positive relationship between solving complex organizational problems solving and the following variables (Management identity, Management Effectiveness, Management Efficiency, and Leadership) Results from extended scales As mentioned earlier, four of the most useful extended scales include Management Identify, Team players, Management Effectiveness and Management Efficiency. We assumed that high scores on these scales indicate the ability to solve organizational problems in a manner that incorporates the concerns of employees as well as the concerns of the organization. 360 | P a g e 361 Prepublication Copy To measure this assumption, the scores of the managers’ self-report were compared to the ratings of other managers and independent observers such as a trainer or consultant who studied the organization. Obviously, if the manager’s self-report and the rating both indicated the need for improvement, this resulted in a lower score on the management effectiveness scales. However, as is often the case, one of the measurement scales, either the ratings or the instrument subscales, were at odds. The technique of discrepancy analysis was used to determine a final numerical outcome. Discrepancy analysis is a score or numerical value reflecting the difference between a manager’s self-perceptions and other people’s perceptions. As a real-life example of discrepancy analysis, one of the male middle managers in a Fortune Five hundred company gave himself a rating of 1 or “little need to improve.” When the same manager came to another item about “his or her need for improvement” he also marked a 1 (little need to improve his management skills). The manager perceived little need to improve and, in his mind, felt that his fellow employees or coworkers did not think that he needed to improve any of his management skills. On the rating scale, a five signifies the need to improve a great deal while a one denotes little need to improve. Guess what! The ratings from other managers or independent raters suggested that the manager needed to improve both management skills and technique (all 5’s) since he was rated low in leadership, high in contributing to a stressful environment, less flexibility in management decisions, and less effective and efficient in the solving of daily management problems. As a result of this large discrepancy between the manager’s self-ratings and the ratings of others, he received a low score on Management Effectiveness and Management Efficiency. Other factors contributing to a low score on the same two scales were combinations of scale scores such as a high need for control and little flexibility. His interest profile also indicated less interest in management or activities associated with his job. Management scores without ratings The results from Table 80 below indicate that in this random sample of 469 managers. There is an average difference for important management variables (motivation, management consistency, team management, and management effectiveness) when considering distinct levels of management and non-management. Yes, the small sample of trainers was dropped from the analysis when differences were calculated. 361 | P a g e 362 Prepublication Copy These average scores did not include a rating from other managers integrated into the scale. A small group of trainers was included for comparison. The scores also suggest that all levels of management can improve. There are not a lot of differences in effectiveness scores although sample size probably affects the outcome. Management Consistency suggests a large discrepancy between self-perception and other perceptions using only self-report. There was a greater need for Team Management (as perceived by lower levels of management--trainers, first line). Standard score averages used a mean of 60 rather than the usual 50. In Table X below, the sample of trainers was quite small (only 9). When these scores were deleted from the analysis, the results changed slightly Table 80 N Mean Std. Deviation Minimum Maximum Significance NonManagers 175 66.83 7.76 36 83 P=.00 Trainers 9 63.89 5.28 53 70 First line 174 69.05 6.93 47 90 Second line 34 68.85 8.73 46 86 Middle 59 69.98 7.63 47 87 Senior 18 69.78 5.99 61 79 Total 469 68.25 7.51 36 90 Mgt. Nonmanagers 175 61.95 10.04 21 100 Consistency Trainers 9 68.11 5.06 59 73 First line 174 65.05 9.9 26 100 Second line 34 64.85 13.3 39 100 Middle 59 66.12 10.65 50 100 Senior 18 62.06 6.45 50 73 Total 469 63.96 10.26 21 100 Team Nonmanagers 175 67.85 12.11 13 95 Mgt. Trainers 8 70 7.37 58 80 First line 172 60.03 11.17 27 95 Second line 33 60.33 13.47 32 95 Middle 58 61.67 11.37 37 83 Senior 18 66.56 10.14 35 75 Total 464 69.47 11.76 13 95 Mgt. Motivation P=.00 P=.00 362 | P a g e 363 Prepublication Copy Mgt. Nonmanagers 174 58.5 9.56 0 83 Effectiveness Trainers 8 63.13 5.33 55 73 First line 171 65.57 7.03 40 89 Second line 30 68.03 9.52 40 83 Middle 54 69.56 8.57 42 86 Senior 18 68.56 9.34 38 78 Total 455 59.28 8.55 0 89 P=.06 Comparison of 4 Scales of Management Effectiveness for Managers and Non-Managers In general, the scores on the 4 subscales of Management suggest that Senior and Middle Managers had higher average scores than other groups of managers. Management scores with ratings We did another random cross-comparison of 140 managers which included nonmanagers with the integrated rating scales. This sample did not include Senior Managers, however. The scores in Table 81 dropped below the mean of 60 when the ratings were added. Still, there were significant differences between the scores of diverse levels of management and non-management. In this sample of 140, management effectiveness did not show a significant difference but, in other smaller samples, there was a significant difference. Table 81 N Mean Std. Deviation Minimum Maximum Significance P=.00 Mgt. Non-mgrs. 23 52.28 9.06 34 69 Motivation First 57 54.25 7.17 40 71 Second 23 57.8 6.25 49 71 Middle 37 60.14 6.26 44 74 Total 140 56.07 7.66 34 74 Mgt. Non-mgrs. 22 53.6 11.09 34 80 Consistency First 57 51.92 8.86 33 69 Second 23 56.65 9.77 40 76 Middle 37 61.7 11.42 38 84 Total 139 55.57 10.78 33 84 P=.00 363 | P a g e 364 Prepublication Copy Team Non-mgrs. 22 58.68 6.13 49 71 Mg First 56 60.26 6.06 49 74 Second 23 63.05 6.21 51 74 Middle 37 62.47 7.09 51 76 Total 138 61.07 6.5 49 76 Mgt. Non-mgrs. 22 53.5 10.16 31 70 Effectiveness First 57 56.06 7.73 31 71 Second 23 55.09 9.66 31 69 Middle 37 57.47 8.22 36 71 Total 139 55.87 8.61 31 71 P=.05 P=.37 Comparison of Three Levels of Managers and Non-Management Chapter summary As one might expect, the problem-solving indicators which measure fluid intelligence provided only a rough estimate of the potential for solving more technical and general problems. The best measures of complex problem solving were a combination of data from diverse sources. For example, discrepancy scores which were the difference between a manager’s self-ratings of efficiency and effectiveness and the ratings of other managers (above and below the manager) when combined with additional information from the management problem-solving categories provided the best assessment. The integration of the five different measures related to cognition, personality, interests, self-ratings, and other ratings provided solid validity information about solving complex problems and the subgroup management information provided excellent feedback to the managers. Chapter references: DeNovellis, R. L. and Brush, L. (1986). Management and Personality Type Indicator Test Manual. Psychological Research Institute for Business and Education. DeNovellis, R.; (1992). Technical People, Technical Management & Successful Management-What are the Challenges? Journal of Clinical Engineering. 17,6, 429-505. Holland, J. L. (1965). Holland Vocational Preference Inventory: Manual. Palo Alto, CA: Consulting Psychologists Press. Knapp, L. Knapp, L &Knapp, R. (1974). COPS test manual. Edits, San Diego, California, 92107. 364 | P a g e 365 Prepublication Copy Simney, S. et al. & Sophisticated Data Research, Inc. (1989). A study of tests of potential values for the prediction of success in the workplace. Report for McDonnell Douglas Corporation, Atlanta, Georgia. Strong, E. K., & Campbell, D. P. (1966). Strong Vocational Interest Blanks manual. Stanford, CA: Stanford University Press. 365 | P a g e 366 Prepublication Copy Chapter 19: Research, Categorization and Integrative Models Introduction This chapter addresses research, categorization, and integrative models. A model is a way that scientists show relationships between different kinds of concepts. Models are displayed as diagrams; some involve numbers while others involve words with arrows going in all different directions. Notice, in this book, there are different kinds of models: process models, research models, and categorization models. Each model is different and has different objectives. The three-tiered cognitive process model which explains the complex process of solving problems is different from our research and categorization models. The categorization model is more clinical and explains how subgroups interact during the process of solving problems while the research model projects different mathematical solutions. Our goal in this chapter is to present our research model, the model of the research process used in analyzing problem-solving in the different areas of words, numbers, and spatial activities. First let us examine how other authors, in the areas of cognition, personality, and interest, model their work. In each of the areas of cognition, interests, and personality, researchers and armchair theorists have developed models to explain the complex relationships of their concepts. There are complex models both within and among the areas. For the models within each of the areas, a major concept such as general intelligence (“g”) or extraversion is subdivided into many different areas. For the models among the areas of cognition, personality, and interests, the researchers take a general concept such as “g” and then integrate the subcomponents into a base, usually designated as interests and personality. The latter explanatory models are called integrative. In this section, three separate well-known models are presented: 1) A cognitive model, 2) A personality model, and 3) An interest model. Finally, in the latter part of the chapter, our integrated research model is illustrated. A cognitive model The work of the 4 major theorists provided us with different ways of explaining human cognitive behavior. There is a consensus among researchers in the field about how abilities are related to each other. The most prolific theorists in the areas of cognition are Carroll 366 | P a g e 367 Prepublication Copy (1993), Horn (1965), Vernon (1950), and Cattell (1971/1987). From a measurement standpoint, most of the theorists have the general ability (“g”) as a major factor followed by broad groups of second and third levels. Carroll’s explanatory model has wide acceptance. Carroll’s intelligence model incorporates two concepts originally coined by Raymond Cattell called fluid intelligence and crystalline intelligence. Fluid intelligence is composed of sequential reasoning and inductive reasoning while crystalline intelligence includes verbal and reading comprehension. Another factor of Carroll’s is knowledge and achievement which incorporates general school achievement as well as verbal information and knowledge. Perceptual speed memory and mental reasoning are also separate factors. Finally, there are two closely related vectors named visual perception and closure. According to Carroll’s model, general intelligence is composed of seven major factors (crystallized intelligence, ideational fluency, knowledge and achievement, learning and memory, perceptual speed, visual perception, and fluid intelligence which are divided into many separate components. 367 | P a g e 368 Prepublication Copy Math Reasoning Math Reasoning, Quantitative Reasoning Fluid Intelligence (Gf) Sequential, Quantitative, Piagetian, & Inductive Reasoning Visual Perception Closure Spatial Scanning, Visualization Closure Speed, Flex Perceptual Speed Stroop, Clerical Speed, Digit/Symbol, RT General Intelligence Learning Memory-Visual, Associative, Free Recall, Span Knowledge and Achievement General School Achievement, Verbal, Information, Knowledge Ideational Fluency Word Fluency, Expression Fluency, Naming Fluency Creativity, Figural, Crystallized intelligence (Gc) Verbal Comprehension, Reading Comprehension, Spelling, Lexical Knowledge Reading Speed, “Cloze”, Communication, Oral Style, Writing, Figure 2: (Derived from Carrol, 1993): Modified Factorial Constructs 368 | P a g e 369 Prepublication Copy It is possible to group the 7 major areas as follows: Crystallized and fluid intelligence are two areas, visual and perceptual speed are another two areas, knowledge and memory coexists and finally, ideational fluency stands alone. The grouping of these areas brings the total group to 4 rather than 7. Our research has drawn heavily on Carroll’s cognitive factors (1993). Our modified model (after Carroll) is found in figure 2, Chapter 3. A newer model, recently developed by Johnson et al. (2005) is called VPR which stands for Verbal, Perceptual, and Image Rotation. In their model, the hierarchical “g” factor (general factor) of Thurstone (1938) consists of 3 broad highly correlated factors identified as verbal, perceptual, and image rotation. These are then subdivided into 8 specialized factors. Verbal consists of verbal (6 tests), scholastic (11 tests), and fluency (8 tests); perceptual becomes number (10 tests), memory (4 tests), spatial (10 tests), and perceptual (14). Imagine rotation is defined by 4 separate tests. A model of personality Ackerman and Heggestad (1997) used the works of Eysenck (1947/1970), Costa and McCrae (1994), and Tellegen (1982) to develop an integrative framework for personality. Their framework is a three-tiered model with Neuroticism, Psychoticism, and extraversion at the apex with the work of (Eysench) as the first level, the five factors (Neuroticism, Agreeableness, Extraversion, Conscientiousness, Openness) by Costa and McCrae as the second level, and the 11 constructs (Stress Reaction, Well-being, Alienation, Aggression, Social Closeness, Control, Achievement, Traditionalism, Absorption, Harm Avoidance) of Tellegen as the third level. Their integrative framework for personality is a hierarchy with three different tiers. Most personality theorists agree that broad factors encompass specific factors. A model for interests Holland’s et al. (1969) hexagonal structure is the major explanatory model in studies about vocations and interests. The other models are Roe’s (1956) circular and Gati’s (1979) hierarchical. Roe’s circular model is more theoretical, while Gati’s hierarchical model is more empirical. There are ample studies that favor Holland’s model; however, empirically Gati’s hierarchical model appears to have better predictive value. The issue, of course, is the same for the work presented here – ease of use vs. practicality. Established instruments provide a substantive theory that can be easily interpreted and explained to 369 | P a g e 370 Prepublication Copy others are more practical, and useful. Instruments with predictive value may not be used as much by the general populace. Many empirical models have scientific use but lack a simple theoretical explanation for those who use them. This is simply a part of the age-old controversy of scientific theory vs. practical use. Both kinds of instruments have their place, however, in the social science area where there is greater variability, the theory may never accurately explain the data and vice versa. Integrative models For an integrative model, the best example comes from Armstrong and Ackerman. Armstrong et al. (2004) used Holland’s interest measures as a primary starting point stating that it was a logical choice given its prominent position within vocational literature. They proceeded to use published sources as a basis for their analysis. Using property vectors as the statistical technique, they located a set of coordinates based on Rounds and Tracey, (1993) which help define a two-dimensional circumflex structure of Holland's six types at the following coordinates -R (.00, .58), I (.50, .29), A (.50, –.29), S (.00, –.58), E (–.50, –.29), C (–.50, .29). Without going into the technical aspects which are available in their papers, they found their results were consistent with previous research between Holland’s type and other personality measures. Using 31 environmental measures, they fitted the variables into the circumflex model of interest. Again, their conclusion about personality, interests, and ability was: “important connections between personality, interests, and ability when variables are integrated into a circumflex structure.” A separate study presented in the paper by Armstrong et al. (2008) used a threedimensional model of personality, ability, and interests. Again, a general conclusion was that interests were a good starting point for integrating individual difference variables and that personality can be aligned with environment and ability. In their opinion, people integrate ability and personality to adjust to environmental context. Ackerman’s integrated model is hierarchical and uses a 4-tier model with cognition as the central tenet. At the pinnacle is “Intellectence (sp)” which encompasses the 3rd tier as general intelligence; the 2nd tier as fluid intelligence, visual perception, perceptual speed, learning and memory, knowledge and achievement, ideation fluency, and crystallized intelligence, and 1st tier as math reasoning and closure. Holland’s interests are interwoven between the 1st, 2nd, and 3rd order tiers. 370 | P a g e 371 Prepublication Copy Cattel’s 16 PF Actually, the best representation of an integrative model that exists at a single level of cognition and multiple levels of personality is Cattell’s 16 Personality Factors. This instrument uses a subscale of analogies denoted as ‘B’ or Intelligence, 81 different profiles, and 6 career themes. The 81-profile pattern published by Samuel E Krug (1981) at the Institute for Personality and Ability Testing, Inc. illustrates the basic methodology of interpreting clinical patterns. Many of the 81 profile patterns are extremely rare. For example, a profile pattern denoted as 1111 occurs with an incidence percent of .1 with a rarity rank of 10 (the rank is low given 81 profiles). The rarity of many profile patterns is a real occurrence regardless of the instruments used for measurement. This is one of the primary reasons to use only 36 profiles for the IPS theory. Before addressing our research integrated model, a concise review of some of the pertinent theoretical issues is necessary. The dominance of an integrated cognitive, interest, and personality attribute comes from the use and practice of a particular function over favored, often travel neural pathways. Auxiliary or secondary cognitive, interest, and affective functions are less used. Pathways are identified in multiple areas of the brain by fMRI as a result of developmental differences, specialization, experience, and genetic heritage. Our Research Integrated Model To keep the model simple and understandable, the holistic elements are noted first and the components later. At the peak of the model is cognition (“g”) and then cognition is interwoven with personality and at the base is interests. The reason for placing cognition at its peak is based on the hierarchical organization of the brain. The hierarchical structure of the neocortex suggests that the structure above are higher-order processes that are dependent upon the structures below (integrated sensory-motor function). The brain processes cognition and affect almost simultaneously. Emotional energy generated from a sensory-motor function that gives rise to personality is tightly interspersed in neural networks which are a part of cognitive processing. The broad base representing the actions of personality and cognition is interesting. So, the triangle below represents the first way of visualizing our integrative model. “g” Cognitive Processes, Personality Cognitive Processes, Personality 371 | P a g e 372 Prepublication Copy Interests (Environmental Problem Solving) (Verbal, Numerical, and Spatial problems) A hierarchical model is best based on the literature review. For predictive purposes, the model can be rotated either left or right depending on the research objective. It now looks like this: Cognitive Processes, Personality g Interests Cognitive Processes, Personality Why rotate the ends of the model? Our three-tiered cognitive model presented in this book utilizes neural pathways that reflect how “g” or cognition is displayed in the real world of problem-solving. The process begins with our equations with different components of “g” filtered by personality and other cognitive processes to predict outcomes that are associated with vocational interests or environmental problem solving (verbal, numerical, and spatial problems). A typical regression equation or discriminant function could be used for predictive purposes. The model could be flipped in the other direction to predict how interests, filtered by personality interact with “g.” However, the data support the first view. Since models are just ways of conceptualizing strategies for doing things, another methodology emphasizes a different view. Rather than using a simple triangle as a model, let us employ a cube to emphasize how subgroups use personality and cognition to solve problems. The best way to conceptualize the measurement of subgroup solving problems is to think of personality and cognitive interactions. In Chapter 2, subgroups are displayed as a non-metric, 2-dimensional model as it is easy to comprehend. However, what if the subgroups are displayed as three or four dimensions. That is, personality 372 | P a g e 373 Prepublication Copy attributes are along the top of the cube and cognition is along the side with subgroups layered at every level of cognition. Interests are displayed in the cube as situational relationships within each subgroup. See Appendix B for all the subgroups with measures of cognition and personality integrated around interests. Wow, it sounds complicated! Not really, many studies have studied aptitude treatment and aptitude personality interactions. As more complicated statistics and forms of analysis have become available so have ways to conceptualize and analyze information. The research community has graduated from simple univariate statistics to multivariate statistics with a host of complicated experimental designs. Roughly to understand how subgroups are formed, visualize a cube with all the different subgroups at 6 distinct levels that interact with personality and cognition. Interests are found within each subgroup. Categorization model Categorization models are clinical in orientation. Clinical models are different from measurement models. Clinical models often are inferred from major differences in assessment instruments. By noting a clinical profile (the ups and downs of average scores on a measurement scale such as the number and kinds of white blood cells), clinicians make decisions about treatment and/or judgments about people. The clinician is the direct assessor of what is seen, observed, and noted in a patient or client. The clinical model is usually holistic, interpretive, and suggestive of treatment, prescriptions, or suggestions. Although the measurement models provide research answers which may eventually become part of the clinical assessment, the categorization model is short-term and immediate. Categories help people understand decisive numerical differences. The categorization model is more clinical and uses algorithms to simulate what is seen and observed in real life. The cornerstone of the categorization model is cognition, personality, and semi-cognition rather than interests as the research literature provides more substantive foundational knowledge about the categories. The term “semi-cognitive” refers to tests that measure speed and reaction time as well as dis-embedding (such as field independence and field dependence). Cognition in our model refers to the assessments based on analogies and sequences and spatial decision-making (block counting, spatial representation). Personality refers to subscales that measure personality or temperaments. Interests refer to subscales that measure interests. Standard scores are scores from each of the cognitive, semi-cognitive, personality, and interest subscales which have been developed for different age groups and are located in the Appendix. The mathematical and theoretical basis of our model is found in Chapters 20 and 21 while the clinical features are described in the chapters by age groups. 373 | P a g e 374 Prepublication Copy As is argued in the later chapter, using the current research literature and the current categorization models, human behavior is far too complex for simple categories. Categorization models are transitory, depending on many different demographic and cultural factors. At best, it is possible to take the current literature, construct a model and identify categories and significant trends that exist at any age level. Models become a snapshot in time so that at a later date we may compare the information. This snapshot can be compared to a criterion group of other people who have a similar snapshot and hopefully describe the relationship between the two. The first type of measurement is intraindividual (constructs within the person) and the second time is referred to as interindividual (constructs measured between people). Both methods are used in later chapters. Chapter References: Ackerman, P. L., & Heggestad, E. D. (1997). Intelligence, personality, and interests: Evidence for overlapping traits. Psychological Bulletin, 121, 219 –245. Armstrong, P. I., Smith, T. J., Donnay, D. A. C., & Rounds, J. (2004). The Strong ring: A basic interests model of occupational structure. Journal of Counseling Psychology, 51, 299 –313. Armstrong, P. I; Day, S.; McVay, J.P.; Rounds. (2008) J. Holland’s RIASEC Model as an Integrative Framework for Individual Differences. Journal of Counseling Psychology, 55, No. 1, 1–18. Carroll, J. B. (1993). Human cognitive abilities. A survey of factor-analytic studies. Cambridge: Cambridge University Press. Cattell, R. B. (1971). Abilities: Their structure, growth, and action. Boston: HoughtonMifflin. Cattell, R. B. (1987). Intelligence: Its structure, growth, and action. Amsterdam: NorthHolland. Costa, P. T., Jr., & McCrae R. R. (1995). Domains and facets: Hierarchical personality assessment using the Revised NEO Personality Inventory. Journal of Personality Assessment, 64, 21–50. Eysenck, H. J. (1947). Dimensions of personality. London: Routledge & Kegan Paul. Eysenck, H. J. (1970). The structure of human personality. London: Press 374 | P a g e 375 Prepublication Copy Gati, I. (1979). A hierarchical model for the structure of vocational interests. Journal of Vocational Behavior, 15(1),90-106 DOI: 10.1016/0001-8791(79)90021-6 Holland, J. L., Whitney, D. R., Cole, N. S., & Richards. M., Jr. (1969). An empirical occupational classification derived from at theory of personality and intended for practice and research (ACT Research ReportNo.29). Iowa City, IA: American College Testing Program Horn, J. L. (1965). Fluid and crystallized intelligence: A factor analytic study of the structure of primary mental abilities. Unpublished doctoral dissertation, University of Illinois. Johnson, W. & Bouchard, T.J. (2005) The structure of human intelligence: It is verbal, perceptual, and image rotation (VPR), not fluid and crystallized. Intelligence, 33, 393-416. Krug, S. (1981). Interpreting 16pf profile patterns. Institute for Personality and Ability Testing, Inc. Champaign, Illinois. Roe, A. (1956). The psychology of occupations. New York, NY: Wiley. Rounds, J., & Tracey, T. J. G. (1993). Prediger’s dimensional representation of Holland’s RIASEC circumplex. Journal of Applied Psychology, 78, 875–890. Tellegen, A. (1982). Brief manual for the Multidimensional Personality Questionnaire. Unpublished manuscript. Thurstone, L. L. (1938). Primary mental abilities. Chicago: University of Chicago Press. Vernon, P.E. (1950). The structure of human abilities. London: Methuen. Vernon, P.E. (1950). The structure of human abilities. London: Methuen. Further Reading Horn, J. L., & Cattell, R. B. (1966). Refinement and test of the theory of fluid and crystallized intelligence. Journal of Educational Psychology, 57, 253–270. Tellegen, Auke, and Niels G. Waller (2008). Exploring personality through test construction: Development of the Multidimensional Personality Questionnaire. The SAGE Handbook of Personality Theory and Assessment, 2, 261-292. 375 | P a g e 376 Prepublication Copy Chapter 20 Measuring the Problem-Solving Categories Introduction A theory is not particularly useful unless others can verify the assumptions through a series of measurements. In essence, many of the tables given in this book allow others to determine the usefulness of the theory based on the data collected. Since this system is unusual— descriptive, recursive, interdependent, and intertwined based on the individual characteristics of the problem solver and the individual characteristics of the type of problems solved--a measurement system that at least defines the ends and middle of the continuum are needed. To understand the measurement system, let us provide some background. In reality, all individual differences are interdependent and recursive. Think about it! Is your digestive system separate from your integumentary system? How can one measure something which is interdependent? That has been the question for research and medical personnel and others since the beginning of the objective measurement. The response, of course, is that our taxonomic or classification systems help to describe and understand individual differences and provide us with places to look for the major difference. Taxonomies and classifications allow one to make statements about the subgroup to which the child, student, or adult belongs. According to J. T. Lamiell (1998), Wilhelm Windelband, a Kantian philosopher, described an objective (nomothetic) and a subjective (idiographic) approach to understanding taxonomies and classification. The nomothetic is more statistically quantitative while the idiographic is more qualitative. The qualitative process (taxonomies and classifications) identifies where remediation or development is needed while the quantitative approach provides answers about groups to which people below. Idiographic measurement Since our goal is to classify a person, whose systems are interdependent, the first method of measurement must be idiographic or intra-individual. That is, the different modes (cognitive, personality, interests, and semi-cognitive) form a single standardized profile which is analyzed in the same manner as a single chromosome composed of genes. The methodology illustrates peaks and valleys in the profile which forms the base of classification. By standardizing each score of the subscales and plotting these as a profile, the assumption is that people who have like profiles are going to be characterized similarly. This methodology emphasizes that order and sequence are important, not only at the subscale level but also at the item level. 376 | P a g e 377 Prepublication Copy Base versus extended scales Since age has such a powerful demographic effect, throughout the long history of assessment, adults and children were given different measuring instruments and scales. In primary school and some secondary schools, the measuring instruments were dubbed “learning style” as that was politically and educationally acceptable. The problem-solving scales for the primary students were extended or used a combination of various base scales. Also, for secondary schools, new and different subscales were developed with age-appropriate language. For adults who worked in the industry, the scales were changed again depending on whether a group of managers or single individuals were being measured. The base scales (developed for adults and children in secondary, university, or industry) were psychometrically pure as they used simple additive scores derived from items. For very young children, extended scores were composites. What is meant by composites? Since base scales generated too much error in the classification process, the primary scales of cognition, personality and career were combined to give extended scores and increase classification accuracy. Yes, I know that combining scales decreases the reliability of the total test/items. However, if test/retest reliability is not practically affected then the gain must be weighed against the loss. The extended scales are used in the same manner as a doctor uses the clinical pathology profile in the diagnosis of a disease. The methodology and groups of subscales that were combined are given in the last part of the next chapter. Years of classifying people into different subgroups led to a classification system that had fewer errors since extended scales were used. Item level scoring The ranking was selected as the best alternative for the measurement of items. Why ranking? First, items are less likely to be selected based on social desirability. Second, ranking provides the separation in the mathematical averages that were needed to classify the existence of subgroups. What is rank? In simple terms, rank is “order” based on preference. By analogy, if there are five runners, the order of finish is important. The runner finishing first has a better time than the runner finishing second. One can rank the runners from 1-5 based on their times to the finish line or based on the order in which each person finishes. Our system of item measurement for the problems solving subscales requires that each person rank two choices out of four alternatives. Within the 4 alternatives, there are usually a pair of 377 | P a g e 378 Prepublication Copy items that measure the same construct. Therefore, most items have 4 alternatives consisting of 2 pairs. When a person is given a choice of the alternatives and chooses one item over another then this constitutes a weighted preference. A person is given an item stem and told to rank only two out of the possible 4 responses. Given these instructions, the rank order is important. When 2 responses or a pair represent the same construct, ranking two items of the same pair has more weight than ranking one or none. If the respondent chooses two items, one member of the first pair and one member of the second pair, then the first ranked response is given more weight than the second. As a concrete example, a person is given four items, two items representing nuts and two items representing fruits. The subscale is scored positively based on whether the person makes similar or mixed choices for the positive end of the subscale. The positive end of these four items is designated “preferring fruit.” A person who chooses two items for fruits versus two items for nuts is assumed to have a stronger preference for fruits than nuts. The assumption is that two similar choices represent a stronger preference than two mixed choices or two choices which do not represent the positive end of the item subscale. That is, a choice of two fruits displays a greater preference for fruit than a mixed choice of one fruit, and one nut or a response of two items for nuts. For any mixed response, the first rank is more important than the second rank. Therefore, greater weight is assigned to the first choice. The items below represent the item stem, directions, and responses below. In the example below, a person’s order of 1st choice is weighted by 2 as it is perceived to hold a higher value as the first choice over the 2nd choice. If the first response is weighted by 2, the possible set of scores becomes (6, 4, 2, and 0) which, of course, reduces to 3, 2, 1, 0. Across a set of 7 groups of item choices, the maximum score is 42 (7x 6) and the minimum score is zero. This method of ranking is often criticized by many people as it requires a forced choice. That is, the respondent must select 2 of the four choices. In reality, he or she may not like and would not select any of the choices. This is why it is called a forced-choice item selection. Forced choice items have several drawbacks so there are other items with more choices including ranking alternatives up to 10 possibilities. The analogies, sequence, and spatial items are presented as multiple-choice selections. Scale level Example: (yes, the computer does the scoring!) Which of the four things do you like best? Chose two responses: a) Apples b) Oranges c) Almonds d) Cashews 378 | P a g e 379 Prepublication Copy (Item can be scored for a preference of fruits with the assumption that a rank of “a” or “b” is a higher preference than the items scored for nuts – “c” or “d”. Theoretically, the item can be scored for nuts and/or fruits but we select the preferred alternative. In the example above, we scored the 2 items for fruit, not nuts. A person may have the following sets of item scores when 2 are assigned as a preference for fruit but not nuts. A score of zero is a lack of preference for fruits: Likewise, if the fruit is in the first position, then it receives twice as much weight as the fruit in the second position Some different combinations are listed below. a) 4, 2; The person chooses Apples and Oranges (“a” and” b”) and received a total of 6 points for a total score. Apples are in the first rank (2x2) and Oranges are a fruit in the second position (2x1). The total is 4 +2 for the item. b) 4, 0; The person chooses Apples and Almonds as the first and second rank and receives 4 points for Apples being a fruit and choosing it in the first position and 0 points for Almonds as it is a nut. The total score is 4 points. c) 4,0; The person chooses Apples and Cashews and receives 4 points for Apples and 0 points for Cashews. d) 0, 2; The person chose Cashews and Oranges for a total score of 2 points e) 4, 0 The person chooses Oranges and Cashews for a score of 4 points f)) 0,0. The person chooses Cashews and Almonds for a score of 0 points there indicating that he or she did not prefer fruits. The resulting points are treated on each subscale as interval data. With the weights, the scoring of each choice results in an item score of 6,4, 2, or 0). This reduces to 3 2, 1, 0 with weighting. The interval between 3 and 2 is not assumed to be exactly one, just as the intervals on a 1-5 rating scale (1, 2, 3, 4, 5) are not assumed to be 1. Profile selection. In the measurement, a scale score is the sum of correct items regardless of how the response is weighted. An ordinal scale score takes into account “order.” Thus, when a person chooses a response, the assumptions of order and sequence are important. For people who often score in the middle ranges on different subscales, our classification algorithm chooses the highest standardized score. In the example below, five subscales make up an overall profile 379 | P a g e 380 Prepublication Copy for each of the following areas--- personality (p), interests(I), cognition (c), learning (l), and semi-cognitive scores (sc). These scores are listed as a single profile below with the 10 normalized scale scores (mean of 50 and standard deviation of 10). The primary scales for personality are conceptual and social, for interests-science and business), for cognition-analogies and spatial; for learningvocabulary and computation standard scores, and for semi-cognitive-arithmetic and letter identification. The single profile of standardized scores is listed in Table 82. The highest scores (above 50) in each category are Social (56), Business (54), Vocabulary (56), and Arithmetic (58). The ranking of the categories is Arithmetic (58), Vocabulary (56), Social (56), and Business (52) with weights of 1 assumed for each category since none of the scores exceeded a single standard deviation of 10. Table 82 Personality Interests Mot Sci. Bus 38 54 48 Social 56 Cognition Anal 38 Learning Spat 42 Semi Cognitive Voc. Comp 56 47 Arith 58 Letter 52 Selection of Profile score to form a subgroup There is an order to these scores. The algorithm chooses semi-cognitive or perceptual speed first to classify a problem solver. The next set of scores is classified as cognitive followed by personality and finally interests. Based on these scores, the idiographic methodology is used to describe the person’s method of solving problems: good with words and numbers and can apply these talents socially in an area such as business. Our classification above begins with semi-cognitive and then cognition. Next comes social problem solving (S), the highest score, and then adds letters based on extended or basic subscale scores, a process explained elsewhere. 380 | P a g e 381 Prepublication Copy Subscales and selected examples of items General/differential problem solver As one expects, differential and general problem-solving exist on a continuum. Differential problem solvers can become general problem solvers and vice versa. A general problem solver is a person who likes to spend time solving problems in any area and engaging in social or non-social activities. Time is on their side as they enjoy solving a new problem, developing a new skill, or encountering a new and different situation. General problem solvers have strengths and weaknesses also. The greatest strength is finding the time to engage and solve complex problems that others do not want to solve. The greatest weakness is that the time to spend solving problems takes time away from other important activities, especially those involving family or loved ones. A general problem solver can solve almost any type of verbal, numerical, or spatial problem, depending on individual differences. The capacity to overcome difficulties in solving different kinds of problems helps one become a general problem solver. There are a large number of differential problem solvers for they do the majority of work in society. This group constitutes your artisans, craft people, skilled salespersons, entrepreneurs, and a host of other well-known careers people. The one common element of this group is their skill level is centered on their strengths and interests developed over time. For the purposes, here, a differential problem solver is a person who applies skills in a differential manner in the completion of daily problem-solving. This selected application of skills to solve some problems (either with words, numbers, or spatial activities) continues over a lifetime. Mastery of multiple skills comes with encounters with many different problem situations. There are many instances where being a differential problem solver is better than being a general problem solver! For example, many worlds chess champions, sports heroes, and great artists are differential problem solvers. They solve problems mainly in an area of interest. Here, we emphasize items that separate individuals into the two groups-either general or differential problem solvers. Items that are used to differentiate the general problem solver from the differential problem solver are based on scores from analogies, sequence, block counting, arithmetic, figural speed tests, and preference responses. The cognitive categories associated with this particular kind of problem solver are designated by letters such as Pslap, Pssp, Ps30, PF LD, etc. with the order and the letters depending on the results from types of cognitive assessments. In all cases, normative demographic information (gender, ethnicity, socioeconomic status, and age) and the normative tables for cognitive variables (standardized tests and others) are standardized. See normative tables in Appendix I. Some of the items are listed below. 381 | P a g e 382 Prepublication Copy Directions: Select any 3 responses in order of preference 1st, 2nd, and 3rd. I prefer: a) b) c) d) e) Solving math problems Solving chemistry problems Solving problems with people Solving problems in business Not solving academic problems but doing things I like Which type of courses did you prefer in high school? a) b) c) d) e) f) Physics Calculus Social Studies Literature Sports, non-academic classes Did not prefer school courses Would you rather? a) b) c) d) e) f) Write a book Build a house Play with a Rubric’s cube Sell cars for a living Be free, work in a job that you like Be an individual who does what he or she likes What kinds of problems do you prefer? a) b) c) d) e) Academic problems (math, English, history) Project problems (projects that I like to do) All kinds of problems; it does not make a difference Only problems in which I am interested. Do not really prefer working on problems Which do you prefer? a) b) c) d) e) f) Reading a book for fun Painting a picture Use a drawing to build a bridge Surveying for the county Using my hands to do work Using my mind to do work 382 | P a g e 383 Prepublication Copy g) None of the above I prefer: a) b) c) d) e) f) Learning lots of different skills Being a jack of all trades Performing well on a math test Building a go-kart Doing well with work that I like Working on my stuff Perceptual problem solvers Perceptual problem solvers are especially attuned to the characteristics of either real objects or images presented as real objects. Perceptual problem solvers show faster speed in the identification of images, letters, pictures, or other objects contained within complex backgrounds. They look at objects in a room or drawings and notice incorrect things, out of place, or incorrectly positioned. They strive for symmetry. They would be the first to notice the different patterns in curtains which match the form and function of other floral designs in the room. When entering a room, they are bothered by a picture that is tilted or a tablecloth that needs to be straightened. Most perceptual problem solvers are not even aware of their gifts in solving perceptual problems. They may work in a specialized field such as banking, where their attention to perceptual details is highly valued. When their unique gifts are combined with a propensity for math, many perceptual problem solvers become accountants, bank tellers, or managers. Most of the time, only after many years, do they realize that some special kinds of jobs or vocations (architectural design) match their problem-solving abilities. Some perceptual problem solvers become great artists, editors, and proofreaders, or have the capability of solving problems related to graphic design, form, and image. In many cases, their talents are accentuated by computers or design equipment which enhances their abilities. How is this assessed? By analyzing the response patterns of perceptual problem solvers and comparing these to the other groups of problem solvers. The objective is to first identify different kinds of items that this group is most likely to select. What kind of problems do you prefer? a) Modifying spatial designs b) word problems c) number problems d) Noticing design properties 383 | P a g e 384 Prepublication Copy I am: a) Quick to notice differences in design b) Attentive to changes in the environment c) Better at thinking than noticing differences and d) less attentive to changes around me. When I am walking in a crowd of people, I a) Am quick to notice any changes c) Am aware of everyone b) Am usually thinking about the day’s events d) Am usually lost in thought Conceptual problem solver The preference for dealing with ideas, either in the form of reading or verbal ideas either developed by the individual or given by other people are the foundation of this problemsolving category. Conceptual problem solvers are those children or adults who solve problems predominantly using linguistics or words. They often learn slightly better by reading rather than hearing and are often considered word smart. Conceptually dominant children who enter first grade are generally those who have families who value educational processes and have introduced their children to vocabulary words and the world of ideas by reading books, promoting creative play, talking extensively, or teaching the child to read. Notice that conceptually dominant problem solvers can be stimulated in a verbal and nonverbal manner (either by ideas read individually or by ideas learned from others who read books or speak to them). Some children in first grade cannot read well but have a great speaking vocabulary and an understanding of many different words. The amount of interaction and time given by a caregiver is paramount; that is, someone must take time to speak, interact, or read to them. One of the characteristics most evident in the conceptually dominant adults and children is their propensity for being stimulated by the ideational content found in words. They enjoy making connections with symbols or abstractions seen in the environment. For example, a conceptually dominant person gets enjoyment from manifesting a singular image of their own making (humor related to a pictorial image created in the mind by the word "joker") or the words coming from another person in a contextual manner that stimulates images that evoke humor. Often the association between words, symbols, or images is important in the stimulation process. Also, extremely important are the individual or group meanings given to words, symbols, or abstractions. Individual meanings are constructed in the person's mind based on individual experiences, while group meanings often are based on societal or standard definitions. An adult conceptually dominant person may look at the symbol "+"; i.e. (plus) and define it as "connectivity in the universe, spiritually of all mankind, or holistic 384 | P a g e 385 Prepublication Copy representation of all numbers." In other words, the person has created symbolic or abstract connotations for “+”. Because they prefer words, ideas, and reading, conceptual dominant problem solvers choose words on career and interest tests that demonstrate how their cumulative everyday experiences have influenced their interest patterns. For example, they may choose items suggesting they like to solve problems related to "acting in plays" or “doing creative writing on the job." The occupational portion of our problem-solving tests has many different items which help to define the conceptually dominant problem solver. Some of these items are: I prefer: a) Theoretical problems b) Reading problems c) Solving complex problems d) Languages e) Learning vocabulary words f) Writing for others, not myself g) none of these items Because people have many different kinds of personality characteristics, a subgroup of the conceptually dominant group wants to apply their ideas to problem situations or understand the working of different kinds of things. For example, this group chooses items such as: a) Having knowledge of special subjects b) Creating models c) Making pottery d) Creating designs for business e) Developing good photographs e) Creating motion pictures f) Applying ideas to technology My mind and brain work best: a) If I see, touch, and feel what I want to learn c) If someone draws me a picture b) If I think about it in my mind. d) If someone tells me about it first. 385 | P a g e 386 Prepublication Copy Motor problem solvers Sports, athletic events, or activities that require hand and eye coordination dominate the lives of individuals who select items representing this category. Many experiences are learned outdoors, through parent-directed activities, or during play with others. Most motor skills are learned by imitation and emulation as well as trial and error. Parents who have similar motor skills spend time teaching their children to emulate their activities (hockey players, acrobats, carpenters, etc.) Instructions are mostly verbal with a "follow me or watch what I do" type of interaction. In reality, most motor children learn from concrete to abstract, from physical activities to conceptual activities while a small minority learn vice versa. Motor activities (crawling, standing, moving the arms and hands) are the first activities that allow the child to explore the environment and find links between words (verbal conceptualization) and objects. This exploration of the environment continues until later in life when motor problem solvers try to solve problems by finding concrete links to abstractions. A motor problem solver uses their senses to handle, smell, manipulate, and measure any representation of the objects involved in a problem situation. A mechanic, when given a problem about a leak from a car, will put his finger in the residue, smell it, taste it, or feel the area from which the leak came. Some children in this group are less likely to read a book except to solve the immediate problem. Example of items for the Motor subscale: As a child, I: a) b) c) d) Preferred outdoors activities Loved anything which involved physical activity Spent most of my time inside watching TV Preferred watching others rather than doing things myself As a child, I preferred: a) b) c) d) To play sports Using my hands Using my mind Doing anything which did not involve reading On the career portion of the problem-solving instruments, adults mark items such as liking to solve problems associated with different activities such as: a) Loading trucks b) Making deliveries c) Driving big machines d) Using mechanical tools 386 | P a g e 387 Prepublication Copy e) Moving furniture f) Cleaning rooms in houses g) Using muscles for sports or actions h) Lifting heavy objects The cognitive categories associated with this particular kind of problem solver are designated by letters such MSC with the order and the letters depending on the results from types of cognitive assessments. Analytic problem solver All people use analytic thought, however, for many people, especially women, the dominant use of analytic preferences is not easily recognized as it remains hidden by social etiquette. Other analytic thinkers and problem solvers, in contrast, are quite obvious in the display of their analytic tendencies. They analyze everything; sometimes too much (paralysis by analysis!! Analytic problem solvers often use the meta-components of evaluation and generalizations as they examine each step in the analytic process. Education and time spent in the thinking process help with the recognition of different kinds of problems and problem solvers. For example, the course of study that people take in the field of engineering requires a lot of analytic exercises. Education leaves its distinctive marks on those who graduate. Recently one of the friends was describing a person whom he had just met. He quipped, “Oh, he sounded like a mechanical engineer.” Enough said! Analytic problem solvers place greater emphasis on either the logic of responses and outcomes or the degree to which something can be broken into its parts. Analytic problem solvers often have learned the rules of logic through the formal process of learning or by actual work experiences later in life. They search for definition and clarity. “What do you mean by that?” “I don’t understand your sentence.” If given a writing assignment during high school, these types of problem solvers want to know how many pages and what should be the focus (establishing the constraints on the problem). Later in life perhaps during a work situation at a military-industrial complex, a group of analytic problem solvers could spend 10 hours defining the problem, 20 hours clarifying the problem, and 30 hours writing out the problem so others can focus on it. Contrast that with a work situation in a small business, where this same type of problem solver must not only define, clarify, and write the problem autonomously, but also must have the expertise for solving it. The world, in the mind of the analytic, has no boundaries for either work or sometimes their ambitions. On the vocational part of the problem-solving instruments, adults who are already working in business, industry, or technology mark items such as: 387 | P a g e 388 Prepublication Copy I: a) Prefer logical outcomes b) Make tradeoffs in business c) Measure objects carefully d) am not very analytic e) Like being an engineer e) prefer social activities I prefer to a) b) c) d) Take things apart to see how they work See the parts and details and then fit them together See the big picture and not worry about details Take a global approach and let us fill in the details. I am: a) b) c) d) An analyzer Good at detecting issues Great at seeing differences in designs The best at helping people The cognitive categories associated with this particular kind of problem solver are designated by letters such AS with the order and the letters depending on the results from types of cognitive assessments. Social problem solver The use of the term "Social Problem Solver", once again, suggests that social interactions are basically at the forefront of the individual’s approach to problems. Therefore, the social problem solver could be motor proficient, and/or have great perceptual skills. The results are entirely dependent upon experiences. A social problem-solver usually comes from a family with caregivers who recognize the need for social interaction or social conventions. A lot of energy and time is spent developing the kinds of experiences which emphasize and value people-related activities. A social problem solver is generally cooperative and allows others an equal opportunity for engagement with the problem at hand. A social orientation does not change the need to be competitive and have standards of excellence. One of the prominent characteristics of social problem solvers is their preference for being involved with and solving socially related problems. Over a lifetime, these experiences provide social acumen, and an understanding of people and their problems. 388 | P a g e 389 Prepublication Copy Social problems can require manipulations of abstract concepts or direct experiences related to problems that people generally encounter. Social problems exist at all levels of society and can require group interactions for all perspectives of the problems to be addressed. Social problem solvers (clergy, teachers, health care professionals, social workers, politicians) often interact with large groups and their importance to society becomes evident over time On the career portion of the problem-solving instruments, adults in the age groups from 1872-mark items such as: I like solving problems that involve: a) People rather than objects or things b) Helping others c) Teaching adults d) personal disputes are involved e) Handling employment issues e) big ideas I prefer solving problems with: a) Social activities more than non-social activities b) People rather than things c) Objects that I can see d) An object that I rotate in my mind. The cognitive categories associated with this particular kind of problem solver are designated by letters such ASP with the order and the letters depending on the results from types of cognitive assessments. Control/structure Control, about problem-solving, differs with age and development. In many instances, control for young people is related to personal responsibility and conscientiousness. Control in IPS theory is related to flex and behavior. A child learns to regulate their behavioral impulses so they can function in real-life situations. Even as early as kindergarten and firstgrade classrooms, one observes a child who is well-manner, well-behaved, follows rules and regulations, listens to the teacher, and tries to follow directions given in problem-solving situations. Children with these behavioral tendencies are more likely to develop throughout life into structured problem solvers. They listen to directions and follow them explicitly, even if the directions are incorrect or misleading. In the preschool years, children do not necessarily solve school problems better but are more likely to be rewarded for effort and following the rules. Think, for example, of the young 389 | P a g e 390 Prepublication Copy child in preschool who is given a crayon to color objects, or scissors to cut objects. The child who finishes the tasks is more likely to have control. One can reach the goal, overcome the intervening obstacles, or complete the task because of their controlled focus and behavioral responses. Later in life, control is related less to behavioral responses and more to planning, thinking about the problem situations, and developing a strategy or method by which the problem is solved. Behavioral control of emotions is important, but just as important is control of the thinking process needed to solve a problem. Because of developmental changes from childhood to adulthood, there are different scales of measurement for different age groups. Our definitions are implicitly related to those subscales. For the most part, ages 8-10, 11-13, and 14 -15 encompass the definitions of control related to young people. The physical and mental changes from late high school to adulthood require the shift from behavioral control to cognitive control. In solving everyday problems, I: a) b) c) d) Want to be in control Prefer to direct others Control things so I do not make a mistake Live life freely without controls or restraints Other people think of me as: a) b) c) d) Living in the fast lane Living a quiet life Structuring my life to be efficient As a planner who decreases stress. I am a problem solver who a) b) c) d) e) Am in control most of the time Keep things structured and controlled to increase efficiency Does not worry about control Seldom needs to control situations, just let things be. Only solves problems in which I have control Flex (cognitive flexibility) Flex is related to measuring impulsivity in the thinking process. Some people must work on a single problem until it is finished. Others working on a problem of interest have difficulty breaking their preconceived conceptions about how the problem should be solved. This "set" 390 | P a g e 391 Prepublication Copy or preconceived way of solving a problem is difficult for some people to break. In general, people are more likely to solve a similar problem just like they solved it before, especially if successful. Flexible thinking processes are often related to fluency or the ability to generate multiple options or alternatives to a particular problem situation. People who exhibit flex often can work on several projects at one time. In fact, they prefer to work on many different projects, because they are bored easily. Sometimes these people are less structured in their orientation; thus, they can be flexible about how a problem is solved. People who score high in flexibility are often more creative in their orientation toward problems. In the work world, individuals in diverse kinds of job responsibilities respond differently to flex items. The items which exemplify ‘flex’ are: In solving problems, I: A) Prefer the freedom to seek alternatives b) Like the freedom to think c) Allow my mind to wander d) Do not like to be boxed in E) Feel creative, when I am allowed to think. I can solve the problem most easily: a) When it is solved in different phases sequence b) When I am allowed to solve problems as I want thinking c) When it has an identifiable d) When I can be flexible in my Which type of problems do you prefer? a) b) c) d) e) None Problems that I can see, touch, and feel A problem that is simple and easy Open-ended, without constraints Problems that I can choose the best alternative Extraversion, ambivert, and introversion When the energy is directed inward, the concept is introversion, outward, the concept is extraversion and when the preferences are equal for both, the concept is ambiversion. The extrovert is more likely to talk and seek out others. Talking and conversing is a mechanism for expressing inner thoughts about daily experiences and feelings--becoming energized. Likewise, the extrovert prefers to be engaged, and involved in social activities where emotions, feelings, and spirit can be exhibited. 391 | P a g e 392 Prepublication Copy Ambiverts, the group between the extrovert and introvert, is just as important in IPS as either extraversion or introversion. In our view, the ambiverts are a real identifiable group. This assumption holds for others who score as “the in-between groups” on our measurement subscales. Ambiverts exhibit patterns of both introversion and extraversion. The traits which are exhibited depend on the situation and circumstance. The preferences of ambiverts are just less defined in either direction. Introversion is a preference, not a condition. An introvert can be warm, affable, and have concerned for others. In contrast to stereotypes, introverts are not necessarily shy. Introverts are often problem-oriented as the problem is often a matter of puzzlement. The items: 127. Most 128. 2nd ____ a) extroverted ____ c) introverted b) reserved d) outgoing Select how a close friend is likely to describe you. 149. Most ____a) talkative b) silent c) in between 150. Most ____a) enthusiastic b) sober c) in between When I am at work, I: 1.Most ______ 2.2nd ______ a) Read an interesting article b) Meet and talk with my friends. c) Work by myself on interesting things d) Talk to people in the breakroom. I am more interested in: a) Being a salesperson b) Working on technical things c) Talking about my favorite subject 392 | P a g e 393 Prepublication Copy Example: cognitive items: An array of cognitive items is used on the seven different measuring instruments. Below are just a few. A. Numerical analogies Choose the correct analogy: 48:4 179. ______ a) 1:12 b) 12:1 c) 12:4 d) 4:48 B. Verbal analogies Choose the best response to the analogy. Happy is to "sad" as tired is to: 180. ______ a) sad b) successful c) happy d) energetic C. Spatial block counting What is the total number of seen and unseen blocks? D. Spatial manipulation 393 | P a g e 394 Prepublication Copy Example: perceptual speed items Answer the addition and subtraction items: Time limit 2 minutes 394 | P a g e 395 Prepublication Copy 395 | P a g e 396 Prepublication Copy Example: career and Interest Items Please respond with “yes” or “No” to indicate your preferences for the following vocational items. 010 Being a technician 018 Being less structured in solving problems 019 Changing an approach to a problem situation that does not work 026 Creating models for leisure 051 Knowing special subjects 053 Having a technical problem-solving style 054 Having the freedom to solve problems in any manner 056 Having specialized knowledge to solve problems 064 Liking many possible solutions to daily problems 067 Liking the technical part of computers 078 Not being bound by the constraints of a problem 079 Noticing differences in architectural designs 104 Reading technical journals for information 106 Reading to solve a problem 109 Seeking knowledge to solve problems 110 Showing others how to solve problems 116 Solving problems in nutrition 119 Taking toys or objects apart to understand 123 Thinking about many different problem situations 124 Thinking about how to solve technical problems 126 Trial and error problem solving with technical equipment 127 Understanding the complexity of computers 396 | P a g e 397 Prepublication Copy 138 Using tools to solve problems 161 Working on many different possible solutions to problems 192 Liking calculus problems Problem-solving categories defined by measurement For the instruments used in the elementary grades and with managers, the score on the differential problem-solving subscale is an extended scale; all the rest of the scales such as conceptual are basic scales. The differential problem-solving subscales is a calculated score based on the inverse of the general problem-solving scale. Therefore, it is not recommended for use in research when the Ps30 or Psa scale is used. In essence, rather than using the Ps30 scale as a bipolar scale with low representing the differential problem solvers, a separate scale is created making it easier for people to interpret. A secondary reason is that for younger children the Psa scale is a composite of non-cognitive variables such as learning perception, self-concept, achievement, and independence. As children become more socially perceptive in the selection of item responses, the non-cognitive items tend to move toward the middle of the distribution and do not differentiate and therefore are not used for high school children and above. For high school age and older, the problem-solving categories are based on a combination of characteristics that involve interests, cognition and personal problems solving style, and perceptual speed. We described some of the following: personal characteristics (motor, conceptual, extraversion, flex, and control), cognitive (analytic and spatial), perceptual (Perceptual Flexibility Tests, letter identification), memory (memory tests), and vocational interests (mechanical, technical, social, etc.). Our work of forty years has amassed a tremendous amount of data which suggests that statistically significant differences do not exist between many groups of people with different problem-solving categories since there is less group variation in young people and much older people. The statistically significant differences between groups of people who exhibit similar problem-solving characteristics are small--the more dis-similar the group, the greater the likelihood of statistically significant difference, depending on where each group is on the continuum. To understand the concept, suppose one had a jar of chocolate chip cookies made from the same batch with the same ingredients. There would be no statistical difference between the cookies since there exists no variation. Now add a ginger snap cookie to the group. The jar still holds cookies, but one is different. How different? Not vastly different since ginger snap cookies are made out of flour like chocolate chip. The more distinct kinds of cookies that are added, the more variegated the population of cookies. When our batch has 200 cookies, some 397 | P a g e 398 Prepublication Copy chocolate chips, some ginger snaps, some Oreo as well as many other kinds, then the variation is greater and soon it is possible to distinguish a group of chocolate chips from a group of ginger snaps. The composition of cookies is all interrelated but chemical analysis allows us to get finer discrimination between groups---that is, the greater the variability in cookies, the better our discrimination. That is precisely the case with our groups of problem solvers. The greater the variability in the combination of characteristics the more likely we are to detect differences where they exist. In fact, on a logical continuum, the statistical differences are evident depending on which elements and/or which taxonomic classification system (cognitive, semi-cognitive, personal characteristics, or vocational interest) is used. Even if a difference is not found, this should not deter us from using the information since it is extremely valuable in understanding individual differences. Most of the early biological classification systems were descriptive; soon the descriptive information leads to better understanding. The individual differences, involving the extremes of any distribution of people are significantly different. Using subgroups allows finer discrimination when comparing a single profile to its nearest neighbor. The IPS model attempts to fill in the gaps not identified by statistics by using subgroups or ideal composites. Before exploring the different taxonomy of problem solvers, several points need to be emphasized. First, taxonomies or categorizations are only a guide or a way of helping us understand behavior. Behaviour is so complex that it is difficult to understand actions fully without asking numerous questions. Even after asking questions, one cannot be certain about the meaning of the responses without trying out different problem-solving strategies with the adult or child. Realistically, problem-solving behaviors exist at all different levels of the subconscious with many thoughts vying simultaneously for admission to consciousness. When an outcome is assigned to taxonomy, it certainly does not exclude others but indicates that one which may be dominant or overriding in a specific problem-solving situation. The term intra-individual and inter-individual is used throughout. Our experience in measuring categories or subgroups of people is that the closest the subjects are matched on gender, educational background, age, socioeconomic status, and within family subgroups, the better the prediction. We determine the scores of a single individual (intra-individual) and then compare them to subgroups of people with similar characteristics (interindividual) or their subgroup. When making a comparison, the larger and more diverse the subgroup, the greater the error of prediction. 398 | P a g e 399 Prepublication Copy Measurement issues using rank scoring Two basic issues occur when using the current scoring method. The first issue results from the method of scoring, the selection of item responses, and the people’s preference patterns. In essence, when items from two opposing subscales that are conceptually related are ranked by the respondent, the total subscale score correlation may be inversely related to each of the constructs. For example, on the control and flex subscales, a person’s relative rank may be high, middle, or low. If enough people have a high relative rank on control and low relative rank on flex, there can be a strong inverse relationship, perhaps .65. Of course, this is sample related. Even with a large sample of 500, a strong relationship might exist. The high correlation is slightly inflated due to the juxtapositioning of comparative items from related constructs and allowing the person to rank the items. This same measurement inflation provides the separation necessary to achieve accurate classification. For us, classification accuracy is more important as verified by independent observers as well as the participants. The second measurement issue comes from treating the outcomes of rank scores as interval data. Remember from the examples above the sums of 6, 4, 2, 0 are reduced to 3, 2, 1, 0. Numbers are then treated as interval data. For the purist, rank data should be analyzed by rank methods. In our long journey, many different methods of scoring and their validity for our purpose of classification have been tested. The method provides the greatest validity and the most accurate and reliable classification. In this next section, there is a theoretical overview of the ten problem-solving categories or behaviors and some obvious examples of items that are used as a basis of measurement. The items differ according to a) the development and grade level and b) the measuring instrument. There is a great deal of difference between management tests and tests for 3 rd graders. The items on the following subscales are similar to those found on other measurement instruments for personality, interests, and cognition. What makes our model more precise is the algorithms used for the integration of the cognitive scales with the vocational and personality characteristics around the model representations of brain functions. Some people argue that it is easier to administer a battery of instruments and interpret the information. Our response to that suggestion is that it depends on one’s objective. A category system can be more precise as long as demographic information is utilized within the system. Chapter Summary This chapter provides examples of items used on various kinds of instruments to identify subscales related to solving problems. Some of the items are cognitive, some are non- 399 | P a g e 400 Prepublication Copy cognitive, and some are semi-cognitive. Issues of scoring and measurement are addressed and explained. Chapter references Lamiell, J. T. (1998). Nomothetic and Idiographic: Contrasting Windelband's understanding with contemporary usage." Theory and Psychology, 8, 6-22 400 | P a g e 401 Prepublication Copy Chapter 21 General Measurement Concerns Introduction The information in Chapter 21 is rather unique as it provides the philosophical measurement basis of classifying objects using techniques of data mining and statistics. Data mining, for some, is a new science that attempts to use large datasets for prediction and trends. Data mining can incorporate both statistical and non-statistical techniques. One major difference between the use of data mining vs. statistical techniques is that data mining does not try to infer or predict. Data mining presents outcomes based on present trends. For example, machine learning seems to be more of a data mining technique than a technique based on statistical inference. Theory as known Information in class predictions Events in life could be random or “chaotic” but our experience suggests that having reliable and valid prior information changes events from being random to being more biased or sometimes more predictable. The degree to which the prior information is less valid, and less reliable suggests more chaos or randomness and vice versa. Theory or that which has been previously validated as ‘known information’ can help in prediction and classification. Theory, for us, is a compilation of known facts that include supposition. Suppositions are based on the assumption of the principles inherent in the facts. Facts are known information that has been verified continuously over time but even facts are subject to error when random affect them. So, we suppose that even known facts have an error. In IPS theory, the degree to which known information or theory can reduce error and increase prediction is proportionate to the degree to which “known information” can reduce the error in the classification equation, similar to using Bayesian statistics. Classification is defined as the accurate assignment of an object to a group or class. When the classification is accurate, the class is a superordinate construct encompassing the subordinate constructs of attributes defining the class. In the language of classification, subordinate constructs are defined as features that include members and subgroups. In 401 | P a g e 402 Prepublication Copy our theory, additional or known information provided by demographic factors of gender, socioeconomic status, ethnicity, and problem-solving attributes helps to define subgroups and features. If a class becomes a superordinate concept, then a subclass is a subordinate construct of the class, and the member is the smallest individual point, variable, number, or object containing the features of the class. In the psychological or academic measurement, a profile set containing all the profiles may represent a class, a set of profiles representing a subgroup can represent a subclass, and a person’s profile is a member. This is important as a set of similar profiles constitutes the subgroup in IPS theory. If attributes (traits, cognition, interests) are variables or objects which define a subclass, the attributes are likely to be correlated in some ways and uncorrelated in other ways. For example, two attributes of a bird (the size of the bird’s wings and the color of the bird) might be used to assign a bird (class) to a subclass called redbirds (small wingspan and red color or large wingspan and red color). On the surface, the color of the wings (phenotype) might be independent of the size of the bird’s wings (genotype). However, when the attributes of the feature occur in a single known biological entity at the member level, a correlation or relationship between the two attributes might occur since the body systems (integumentary, muscular, and skeletal) are interrelated. Thus, attributes that might appear independent at a subclass level (redbirds with small wingspan and red color) could be correlated at the member level (biological). The designation of the subclass as a construct for prediction is artificially constructed and the analysis of the class can be statistically independent as one refers to a random selection of members of the class or subclass (Zena and Duncan, 2015). How is this information applied to our model? If our interest in prediction and classification is at the level of the population (all people who solve problems) and the variables in the population are independent, then there is less error. Moving from the measurement of the population and applying the same logic to our subgroups (groups of the subclass defined by motor, conceptual, or problem-solving model, etc.), as long as the subclass is independent, there is less prediction error. However, our subclasses are not independent as some of the variables which make up the subclass are correlated with each other. If our interest is really at the level of predicting a single member (a particular person) of the class, the classification error is going to increase as the correlation of the features at the member and subclass level increases. Correlated subgroups pose a true measurement problem in the classification of problem solvers. 402 | P a g e 403 Prepublication Copy True and false positives Two concepts that are useful in determining the amount of error in classification and prediction are true and false positives. If one is interested in predicting people who do well at problem-solving, then a true positive is the degree of probability that the prediction is true. If one predicts that a group of people is good at solving problems and all the members of that group do well at solving problems, then that is defined as true positive and there is no misclassification. When the prediction of the class is accurate then the probability is 100 percent. The probability of misclassification increases as errors based on attributes (subscales on problem-solving) increase. In any group of people, one can predict that 70 percent of the group solves problems well and 30 percent do not. If the group is tested and 60 percent of the group solves problems well and 40 percent did not, then individuals are misclassified as 10 percent of the total group. Thus, sometimes a prediction is made in error and the original misclassification is a false positive or false negative. Statistically, the error rate of false positives is (1-p) where p is the probability of true positives or correct classification. Principles garnered at the group population or subgroup level may break down when applied at the member level. Factors of misclassification There are many factors in both theory and analysis which lead to true and false positives at the class level, subclass level, and member level. Statisticians usually analyze data at the class or subclass level whereas a doctor, clinician, or teacher usually analyzes patients or students at the member level. Theory or known information can lead to many true positives if the facts of the theory are valid, reliable, testable, and repeatable (with less error). For example, if a doctor is educated by the theory of the conditions which lead to type I and type II diabetes, then when encountering those conditions in practice, the opportunity for a diagnosis leading to accurate diagnosis is increased. Therefore, if a doctor is presented with a set of profiles including technical information about blood glucose levels as well as descriptive information about clinical symptoms, “known information” can lead to better diagnosis, treatment, and prognosis. For a statistician who ascribes to Bayesian Theory, ‘known information’ can lead to better diagnosis or increase the number of true positives. Known information under controlled conditions (experiments) can lead to tentative outcomes. However, even in controlled experiments, statisticians often encounter problems related to correlated features. At the class and subclass level, the error in misclassification (false positives) could be due to 403 | P a g e 404 Prepublication Copy many things including the co-linearity of features (correlation between). Thus, prediction (from a statistical point of view) is usually best when features are uncorrelated as one can then determine the contribution from individual features which lead to the prediction. One of the reasons that a theory is tenable is because the variables that represent the facts are interrelated predictably. The task of research is the extraction of sets of independent variables which provide a prediction for the theory. In other words, when scientists test theories, they try to extract the features of the independent variables so they can describe the contributions of the parts to the whole. This leads to an accompanying problem of colinearity, that is, the correlated variables (known information) may be useful in the diagnosis and prediction but are dropped out of the analysis. This is often true in the use of regression-like statistics. The crux of our current problem addressed in this chapter is how to extract the known information existing in a correlated matrix at the different levels and use it for diagnosis and classification at the subclass and member levels? A second purpose is to understand the construction of written profiles and their contribution to solving different kinds of problems. Again, let us explain the nomenclature used in the discussion of profiles as an example. When administering a test to a person, the scores on the test represent one profile or one member. To give meaning to that profile, the scores in the profile are compared to the nearest profile group (subclass) which has been defined by a set from all similar profiles in that subgroup. This is a form of discrepancy analysis. All profile scores are defined either by their correlation matrix and represent the class or by the averages of the profile members and represent the subclass. But first before going further in our illustration let us digress to examine the role of feature extraction in providing help for our problem. Feature extraction Feature extraction is a general term that assumes that the elements making up the model occur in many different random combinations and that different models and different methods can accurately predict the outcome but not with the same degree of accuracy. Feature extraction is a simple concept suggesting that a simpler and less complex model can explain the dimensions of a complex entity. Suppose one sees and captures the structure of an object on a computer screen? By its shape and position, the object appears to be a bird. Using a model of morphological features such as color, wingspan, bones in the body, and measurements of a bird’s dimensions (4 outcomes), the task is to predict if it is a bird. The following task is to identify the kind of bird (bald eagle). 404 | P a g e 405 Prepublication Copy Of the four outcomes, wing span and color are the best in predicting whether an object is a bird. Feature extraction decreases the model from 4 features to 2 morphological features which predict that the object was a bird. However, feature extraction did not necessarily predict the kind of bird (Bald eagle). The outcomes of feature extraction are improved with training defined by many random capturing of images on the computer screen which is then used to define different models. Our purpose is to use the mathematical elements of feature extraction and apply them to profile analysis and classification in the areas of human endeavor specifically personality, interests, and cognition. Feature extraction allows us to define subgroups of personality, ability, and interest profiles in people which represent the structure of the whole in the same manner as the morphological features of the bird are used to define the image on the computer screen. Of course, the assumption is that if it behaves like a bird, is shaped like a bird, and looks like a bird then it is a bird. Which, of course, could be wrong, but is less likely! Feature extraction and dimension reduction There are many unusual types of mathematical models and methods for classification and prediction. Many methods utilize techniques first leading to dimension reduction then prediction and classification. The methods most commonly used for dimension reduction include Factor Analysis, Principal component analysis (PCA), Kernel PCA, and Multilinear PCA. A dimension reduction technique is a methodology that reduces an original group of X variables representing X dimensions to a smaller subset of variables representing one or fewer dimensions. Reducing a set of explanatory variables from 3 to 2 allows a smaller model to represent a larger model. A special case of PCA utilizing kernels is particularly appropriate as the function computes the coordinates of the data in space by using inner products between all pairs of data. In pattern analysis, the task is for the algorithm to find clusters, pairs, correlations, or relationships and thus reduce the larger model. The data mining techniques map the data in a high-dimensional feature space where the data can be transformed into a set of points in Euclidean space. This procedure gives rise to a host of ways of identifying methods (such as the nearest neighbor) of determining the algorithms model of denoting a cluster. Likewise, the algorithms operating with kernels are useful in classification and prediction (linear discriminant analysis, and support vector machine). Throughout this book metric and non-metric, correspondence analysis, detrended correspondence analysis, and principal components analysis are used in Pictures (1-8). 405 | P a g e 406 Prepublication Copy Classification is based on many interrelated factors, especially if one is using algorithms. The use of algorithms in classification has problems also. For example, an algorithm may produce an outcome that is skewed at the expense of other factors being measured. Algorithms are interpolations designed to calculate missing information based on averages. Thus, improvement in accuracy in one area by its very nature causes errors in others. Regression methods have increased since the early 1960s when the predominant methodology was linear regression, multiple regression, and non-linear regression. Now the most useful techniques for prediction are machine learning kernels that build classification trees through recursive partitioning based on categorical, ordinal, interval, or ratio data. Some of the most current methods are log-linear logistic regression with a ridge (Hastie et al., 2007), Lasso penalty (Tibshirani, 1996), and random forest (Breiman, 2001). Current problems with almost all classification methodologies include correlated groups, overfitting, ill-conditioning of the matrix, and high dimensionality associated with having too small a sample and too many variables for predictions. Other models that directly impact prediction, classification, and control are in the form of fuzzy models. Fuzzy models (fuzzy rule-based systems) were first developed by Zadeh (1965) of the University of California at Berkeley. He reasons that one can use a fuzzy set with linguistic insertion instead of just discrete logic of ones and zeros. A linguistic insertion utilized the knowledge and experience of an expert in the form of an if-then statement. As an example, if a score on “math achievement” is greater than “80 percent” and the person has a “graduate education” then the “reading score” of that person is likely to be above “65 percent.” System dynamics theory (Forreste, 1961) originally developed to determine the success or failure of a corporation can be equally applied to issues involving human dynamics. The concept of system dynamics is used as a guiding methodology. Mathematical modeling techniques help in understanding complex issues of predicting a class, subclass, and member in the areas of personality, cognition, and interests. The mathematical system underlying the profile analysis and classification of human dynamics is both deterministic and stochastic. The system is deterministic when the problem-solving goal is clear, defined, and achievable. The system is stochastic when the goal is unclear, ill-defined, and achieve by trial and error. Earlier, the analogy of bird wingspan and color was used to represent issues of prediction and classification. However, any model involving human actions is so complicated that any representation cannot be accurate and concrete. The areas of human thinking and emotions are very abstract so our model must be equally complex and can use feature 406 | P a g e 407 Prepublication Copy extraction as a methodology for understanding, framing, and elucidating complex issues of human interaction. As a guiding methodology, another complex abstraction called dimensionality is used in the measurement. Dimensionality represents variables in diverse kinds of space and allows us to use space-time relationships to define profile analysis and classification. Space-time relationships are a method of explaining how certain variables of personality, interest, and cognition may interact at a certain time and location. At the basic level, correlation and random matrices are building blocks of system analysis. Representation in space Representation can occur in many diverse kinds of space. The simplest kind of space is represented by a point while multiple kinds of space are represented by linear and nonlinear dimensions. Linear space can be predicted by simple models while non-linear space must use many different kinds of feature extraction to provide the best classification and prediction. Non-linear space may include objects such as spheres where spheres may be the best model for representing complex interactions. A sphere such as the surface of the ball can be represented as a two-dimensional manifold or a collection of twodimensional maps. In areas, such as differential geometry and topology, a manifold is a topological space that when reduced in size resembles Euclidean space or a dimension of a manifold. A manifold is defined such that for a topological space X, every point in X has a neighborhood homeomorphic to the Euclidean Space E. D. B. Gauld. (1974). "Topological Properties of Manifolds” explains the basic concepts of manifolds. In the language of mathematics, there are certain properties that allow us to distinguish the manifolds of different objects. For example, although the manifold represents Euclidean space locally, there can be a difference globally. Any circular area around a two-dimensional point on a sphere can be flattened so that it becomes a circular region of the plane as found in a geographical map. If the resulting structure of the sphere is not homeomorphic to the plane, then that allows the structure of the manifold to be described by a series of mappings or charts rather than a single map. Homeomorphisms preserve the topological properties of the space such that a continuous function has a continuous inverse function. Each chart (profile) could then become a compendium for defining differences in the same manner that our morphological features define the image of our bird and allow us to classify the object. Objects do not have to be spheres. Objects can be of any morphological shape! 407 | P a g e 408 Prepublication Copy As above, the differences found in local Euclidean space which represent the points in profile allow us to define a chart that characterizes each profile and to define “images” of our subgroups. The use of manifolds to define our images allows more complex structures (non-linear and p-dimensional) to be understood in terms of more simple structures and to differentiate these angles and distances mathematically through the use of Riemannian metrics. Since a profile is represented by a chart, this “image” can be used in artificial intelligence. Images in neural networks can be used to train. After training, the chart or image can be selected by a computer. A complex entity such as a description of a profile group can be reduced to a single number such as Profile 19 or Profile 1. At different levels of measurement (ratio data vs. categorical data), the interaction of personality variables with cognitive variables and interests are not simple linear relationships. For example, two personality concept’s “structure” and “organization” which show a linear relationship with cognition are well documented. However, many non-linear and multivariate relationships also exist between the concepts. The measurement process as found in the monogram entitled, “Measurement of DeNovellis 36 Problem Solving Group” begins with the simplest (linear correlations) technique and moves to the more complex (non-linear) as a methodology of explicating relationships using techniques of dimension reduction, prediction, and classification. Correlated subgroups and distance profiles According to Cronbach and Gleser (1953), trait profiles can vary in three key ways: elevation (the average level of scores), scatter (the variability of scores), and shape (the pattern of scores). One can determine the differences between profiles by measuring distance. An individual’s score and that of the subgroup is similar if both sets of scores are exactly the same, i.e. there is zero difference. This does not occur very often. Instead, profiles are usually the same on elevation; that is, both sets of scores are high on a similar set of scales. However, scores that have the same elevation can differ in that the scores of both vary widely, the score is scattered and differ with respect to variability. Both sets of scores would be similar in shape if each set agreed with respect to the rank ordering on each variable. Cronbach and Gleser developed three different measures to account for the source of profile elevation, scatter, and shape—D2, D02, and D002. The most common is D2, the sum of the squared Euclidian distance between the two sets of scores. D02, a set measure, is calculated by summing the squared distances between the first profile and the second profile after centering each profile around its mean. This measure is sensitive to differences in scatter and shape. Finally, D002, the sum of squared distances between the 408 | P a g e 409 Prepublication Copy two sets of scores after each profile has been standardized. D002 is sensitive to differences in shape. The distance measures of D2, D02, and D002 are typically correlated but each provides information about the differences in a set of scores. What is a correlated profile? In the simple “member” case, a person’s self-report on a group of continuous variables can be exactly the same as another person’s self-report on the same variables. Their standardized profiles would not differ. If one response is different than their profiles are similar but differ by a single variable. The measurement of two person’s profiles are highly correlated (.99). As an example, see Table 83 below: Table 83 V1 V2 V3 V4 V5 Subgroup 1 .8 1 .4 .6 -.3 Person 1 .8 1 .5 .6 -.3 Two Similar Profiles with 5 variables The prediction and classification of two profiles using correlation as (dis) similarity index are relatively straightforward). However, as shown in Table 84, the differences increase due to a large number of people who respond to an instrument, the measurement problem becomes more complex. Table 84 409 | P a g e 410 Prepublication Copy V1 V2 V3 V4 V5 P1 4.2 6.2 .1 .7 -2.1 P2 .3 -.1 4 -.6 -.3 Two Disparate Profiles with 5 variables In general, vectors represent the scores on j variables by person I, so that xij corresponds to the jth variable score made by the ith person. x1 = [ 4.2 6.2 .1 .7 -2.1] x2 = [.3 -.1 4 -.6 -.3] Two Similar Shaped Profiles 1.2 1 Z-Score 0.8 0.6 0.5 0.4 0.3 0.2 0 -0.1 -0.2 -0.3 -0.4 V1 V2 profilePersTraits 1 V3 V4 V5 profile 2 410 | P a g e 411 Prepublication Copy From the image of the two profiles, the shapes (rankings on the variable) are similar. The average on the scores of the vector (level) is similar however profile 2 is slightly higher than profile 1 (elevation). The standard deviation of each variable is not shown but represents scatter around the variable. In the picture shown, the correlation is a good measure of similarity (rank) however if the level and scatter differ considerably then the correlation can be misleading or biased. For a single variable, when shape and scatter are low and the level is close, then a prediction can be good as is evident in a single regression that produces a least square line and almost all points fall on or near the line with relatively little error. Minimizing bias Our data matrices for taxonomies and classification contains a large number of correlated profiles. Our task is to reduce the bias created by the correlated profiles and to use that information to find a subgroup and a member. Bias is a fact of mathematics and impossible to eliminate. By its very nature, bias is the result of a single or cumulative mathematical determination. To structure a formula as a series of variables means that the bias inherent in each of the variables is compounded in any classification. Our task is to minimize and clarify the nature of bias by using large samples, normally distributed variables, and true variance estimators where possible. For example, a small sample of numbers give bias estimators and expected values. Increasing the sample of numbers allows the expected values such as the mean to represent a larger population. Error decreases with large samplings and hopefully, so does bias. Descriptive outcomes Using a theory known the information is going to produce a descriptive outcome rather than a predictive outcome. A descriptive outcome might not be reproduced or replicated precisely. To create a correlation matrix of all variables in the profiles, a large sample is required. The task is to reduce the correlation matrix to a group of variables that have the best predictive value through measures of feature extraction and the theory of known information. A bias correlation matrix can be composed of an almost infinite number of combinations and permutations of individual sets of scores. However, theory (based on demographic factors, experience, and literature reviews) can reduce the number of combinations from infinity to a reasonable guess. 411 | P a g e 412 Prepublication Copy Our theory on how to find subgroups Using a reasonable guess, how does one find a subgroup or a member profile? Suppose one collects data on 2 known variables of math and reading achievement. Math achievement is defined as a high score on math standardized tests and reading achievement is defined as a high score on reading standardized tests. Assuming a reliable and valid measuring instrument of both variables, 3500 student scores are collected on math and reading achievement and the data indicate that the correlation between reading and math achievement over repeated sampling is between .79 and .92. Regardless of the number of samplings, the correlation is in the same range with an average of .85 and standard error around the mean of .06. A large number of sampling and the stability of the correlation leads us to believe that there is a high correlation between math achievement and reading achievement. This becomes “known information” which can be replicated by anyone else since the sample size is large and there is less error. Next, the process is to use other known information and reduce the subgroups by demographic variables of age, ethnicity, educational level, and gender. The groups are no longer random as the demographic variables combined with our theory of math achievement have limited the universe of possible scores and resulted in a generalization that math achievement and reading achievement for a particular age group, educational level, gender, and ethnicity can reasonably be determined. Thus, by using known information to decrease the error, there is an increase in our statistic of prediction. Our correlation matrix of math and reading achievement which has an average correlation of .85 can be deconstructed and then reconstructed. Deconstructing and reconstructing our correlation matrix Our correlation matrix had only two variables which consist of only two sets of scores, one score for the math and one score for reading. Before we correlated the scores, we could have changed the scores to categorical data representing 3 groups of low, medium, and high. How is this accomplished? In practice, having multiple large samples of real standardized data that have been used to derive the correlation between math and reading achievement allows us to inspect the scores, establish a cut point in the distribution for high, middle and low. As an example, if the standard scores are in a range of 1 to 99th percentile, we use the 33rd percentile as low, and above the 66th percentile as high. We then analyze the number of patterns that make up the distribution. We find one student who scores high in reading, and high in math. Another score low in math and low 412 | P a g e 413 Prepublication Copy in reading. Likewise, the patterns show all different combinations such as high reading, low math, or average reading, low math. Our task is to find a finite number of profile groups that represent the data. Collecting all the similar patterns into subgroups, we define 9 profiles as representing a similar group who score in a similar pattern. We assigned each of the 3500 members to one of the nine profile groups. We then re-correlate the profiles of the subgroups and find that the subgroups indeed show comparable correlations to the original large matrix. In the deconstructed matrix (Table 85) math and reading are profiled from low to high using Math as the base. Table 85 Math Reading Profile1 low low Profile 2 low average Profile 3 low high Profile 4 average low Profile 5 average average Profile 6 average high Profile 7 High low Profile 8 High average Profile 9 High high Possible profiles subgroups using standardized math and reading scores The 9 profiles/subgroups represent a fuzzy set and are nominal data that allow the use of correspondence analysis, principle components analysis, redundancy analysis, and distance measures. Correspondence Analysis (CCA) and multiple correspondence analyses are used with contingency tables or nominal data. Now from a theoretical point, the important attribute is that characteristics of the fuzzy set and nominal data capture all the conditions of the total set. In other words, even though all characteristics (low, medium, high) may not seem to equal importance, a score 413 | P a g e 414 Prepublication Copy found in the total set is equally important in the reduced set. In essence, the reduced set must capture a portion of the total set. We are suggesting that each subgroup is manifested as part of the total group. Think of it akin to staking out the territory of a portion of land that is found in the larger area of land. Why is this important? The attributes of personality, interests, and cognition must represent a portion of the reality of the whole. The original large correlation matrix was mapped into a fuzzy set using the same methodology as one might use for a steam controller (Zadeh, 1965). That is, the correlation matrix which represents a whole was deconstructed into a set of profiles. The deconstructed set can be classified or predicted via rules, fuzzy logic or fuzzy sets and the probability can be assessed based on the frequency of the number of people fitting that profile group. The variables in the deconstructed correlation matrix can be re-correlated to determine if the new value falls within the sampling range and standard error. This is a practical example of the information in Table 85 where profile one is low on math and low on reading. From the 3500 profiles, perhaps 1300 people have a score which is less than the 33rd percentile for math and reading. The group of 1300 is subdivided by gender, ethnicity, educational level, and age through feature extraction. We can then use 1) our known information on demographic factors, 2) our fuzzy sets and 3) our theory to choose a method of feature extraction. For example, one method of feature extraction is the use of machine learning with recursive sets to build a classification tree. We have probability data from the demographics of the group. Using the rules of fuzzy logic (if/then statements), one can suggest that there is a greater probability that a person with various problem-solving characteristics who is solving a number and word problem (math and reading) is more likely to fall into a certain profile. Most people with a measurement background will complain that using this type of methodology requires a large sample size. That is, as the number of variables in the profile increase so does the complexity of the analysis and sample size necessary to complete the task. We agree. For one purely mathematical approach, please read the article: B Class: A Bayesian Approach Based on Mixture Models for Clustering and Classification of Heterogeneous Biological Data by Julio Collado-vides, J. Andres Christen, and Arturo Medrano-Soto (2004) published in the Journal of Statistical Software. They use mixture models and Bayesian methods to calculate and model continuous/categorical data of heterogeneous sets. By calculating posterior probabilities, the heterogeneous set is transformed into a set of homogeneous characteristics for entry into the classification. They use standard Metropolis-Hastings and Gibbs sampling algorithms to construct a sampler to approximate posterior moments and grouping probabilities. In essence, by using a known database, they can approximate a classification system consistent with current knowledge. 414 | P a g e 415 Prepublication Copy Our experience suggests that purely mathematical models do not result in the proper classification of human subgroups. Only a combined approach using theory, logic, and mathematical models can achieve a proper classification. In the IPS model, empirical data and its resulting theory represent known information; logic represents fuzzy logic; and mathematical models are the process of finding the best set of variables that can identify the closest relationship to the nearest neighbor or profile subgroup. For people who prefer only mathematical models- “Each to their own” as they say. The 36 subgroups The example above describes the basic process which was used to deconstruct a correlation matrix but the question for many is what matrix was deconstructed for the 36 subgroups and why? First, many correlation matrices can be deconstructed as the correlations vary first and foremost with samples as well as demographic factors. The random sample has to be large and based on at least 2 of the most important demographics, gender, and age. Certainly, a male who is seven years old is going to score differently than a female of 14 or a male of 25. When dealing with managers, the matrix of correlations was based more on older males. This generic matrix (see Table 86 below) was deconstructed into standard score forms to obtain 36 subgroups and 10 variables. As expected, the accuracy of fit and prediction increased when standard scores were separated into two tables, one for males and one for females. There are many subgroups within the 36 subgroups. For example, the first 9 profiles of the 18 profiles are extroverts and the second nine of the 18 profiles are introverts. The 18 remaining profiles are ambiverts. The profiles for introversion and extraversion show a lot of ` ` variation, as reflected by eigenvalues, means, and standard deviations the best generic correlation matrix which is used for deconstructing the personality problem-solving variables is shown below: Table 86 PSLAP PSSP PER CN MT AN SO CT PSLAP 1.00 PSSP 0.52 1.00 PER 0.24 0.02 1.00 CN 0.34 0.27 -0.09 1.00 MT -0.22 -0.23 -0.02 -0.53 1.00 AN 0.38 0.28 0.44 -0.04 -0.10 1.00 SC -0.38 -0.23 -0.47 0.23 0.06 -0.52 1.00 CT 0.22 -0.14 0.53 -0.14 0.02 0.14 -0.24 1.00 FX -0.32 -0.09 -0.35 0.41 -0.23 -0.14 0.39 -0.54 FX EI 1.00 415 | P a g e 416 Prepublication Copy EI -0.17 0.16 -0.05 0.16 0.08 -0.09 0.37 -0.07 0.34 1.00 Correlation matrix of the 36 subgroups Notice that in our ideal matrix, extraversion (EI) and social (SC) are positively correlated .37 while motor (MT) and conceptual (CN) are negatively related (-.53). Analysis (AN) and social (SC) are inversely correlated (-.47) as are control and flex. As expected, there is a strong positive relationship (.52) between (PSLAP) and spatial (PSSP). Perception, a focus variable, is correlated (.44 and .53) with (AN) and (CT) respectively. Surprisingly, for some but not us, conceptual is positively correlated with flex (.41). One can compute the discrepancy score between the ideal matrix and any randomly collected data set of the same variables. The amount of information found in the discrepancy scores is useful for profiling and designing new outcomes for any new sample of scores. For example, in one company we collected data from their group of employees and computed discrepancy scores so we could develop design protocols for use of their information processing system. In another company, the discrepancy score helped us locate security measures that were appropriate for their company. There is a separate matrix for career and interest variables (see Chapter 17) as well as the speed of processing variables. The differences (not discrepancy scores) as a result of deconstruction are visible in each of the pictures (see Table of Contents for the Location in Pictures 1 through Picture 10) in the different chapters. The Pictures show the separation by the distance of the 4 groups (speed of processing, personality, career, and cognition) as well as their distribution around the 36 subgroups. Writing the descriptions of subgroups: Appendix A contains a description of the parameters used for defining 36 subgroups. Thirty-six profiles might seem like a lot but Cattell, using the 16 PF, characterized 81 different profiles for clinical and normal populations. If a person wants to better understand their management, learning, or descriptive profile, then we must accurately define their subgroup and indicate how their scores differ from the subgroup. Our fuzzy logic programs define their level of subgroup classification first by level of cognition, next by perceptual speed, finally by personality, and last by interest. The order can be changed depending upon several other demographics, gender, ethnicity, and socioeconomic and educational status. 416 | P a g e 417 Prepublication Copy The 5 levels of perceptual speed categories (indicated in the chart per profile) assist in determining their facility with letters, numbers, and spatial. This orientation is further clarified by determining which of the 5th level of scores on cognition best fits their problem-solving orientation. Next, after noting whether they are a General or Deferential problem solver, we classified the person according to his or her personality and interest scores. The written descriptive profile defines the subgroup while the person’s scores define how he or she is different. The written profile can be illustrated by the following process using the information above. Expand each profile group by adding demographic variables and set up more tables for gender, (male and female), cultural background, educational level, occupation, and personality. That is, analyzing the subgroups by demographic variables, we might suggest that a subgroup of older students, more educated, (college education), and of a particular cultural background (Asian) are more likely to fall into profile 9 with a high score on reading and a high score on math. In other words, we can use a combination of our theory (known information), and the trees found in random forests (or discriminant function) combined with the rules of fuzzy logic to predict and classify. Based on demographic variables for personality, cognition, and interest, we define a person as more likely to fall into a particular subgroup. Our description of a particular subgroup is based on actual data points that have been compared to known profiles. The results are interpreted much like a clinician interprets a clinical pathology report. Using feature extraction, we suggest that an Asian male who is 28 years old with a graduate background and an interest in engineering is more likely to fall into profile Y or subgroup X. Profile Y is defined by the scores on all areas of personality, interest, and cognition. Therefore, we can also suggest that by the person’s combination of scores he or she is more likely to be cognitively flexible, have a preference for using logical thinking, or be more structured in approach to problem-solving. Is there an error? Of course, each prognostication has some errors in the same manner as diagnosing a person with a disease has some errors. The estimate is probability based. Weather people are wrong; doctors are wrong, and of course, we could be wrong. Which leads to the following principle? At this point in time, the current statistical method of analysis (multivariate, multidimensional, etc.) cannot accurately predict the classifications of people. Only theory combined with algorithms that are used with statistical analysis based on feedback from real people in real situations can decrease errors to acceptable levels in profile analysis. 417 | P a g e 418 Prepublication Copy Analysis of subgroups Each of the created subgroups is correlated in a direction that mirrors actual population variation. Therefore, when the subgroups are analyzed, one can understand how a person in a particular subgroup differs from other people in the subgroup. To clarify, on an elementary level, no two people are exactly alike. Likewise, no two types of subgroups called trees are identical, but knowing that the objects are similar to trees helps to classify. Similarly knowing that two people have similar profiles on one variable helps us to understand them better and perhaps to better understand preferences. If one wants to design a workstation that is better suited to a person’s job and preferences, then knowing their classification is useful. The workstation for a person is suitable as long as the people in the subgroup mirror the behavior of the best performance. Likewise, if one wants to improve the education of certain groups of people in education, then educational materials can be designed for the subgroup. Subgroups can be divided hierarchically. Extraversion, a broad construct is divided into very extroverted, mild extraversion, and less extraversion and when combined with other cognitive constructs, then the combinations are extroverted and field independent or introverted, global, and field dependent. Determining the frequencies of people who respond to various preferences helps to explicate the relationships and produce better predictions. Predicting a part of the whole is better than trying to predict the whole. Predicting smaller subgroups provides more information than predicting a large group that encompasses the subgroup. In ecology, for example, it is easier to describe how a species of plants in an identified riverbed in Colorado behaves than trying to describe the same species behaves in the whole Western part of the US. Likewise understanding the relationship between the subgroups provides basic information about the interaction of cognition, personality, and interests. Let's examine a factor analysis of the 36-subgroup cognitive matrix. There are three kinds of variables in the matrix. The first group of reading and math follows Raymond Cattell’s classification of crystallized intelligence. This group represents actual academic achievement. The fluid categories of analogies, sequences, blocks, and drawings represent the ability to achieve. The third groups of four elementary cognitive tests represent accuracy and speed. One expects a factor analysis with Varimax rotation to sort the groups into three separate groups. A typical matrix of factor loading (N= 106) is provided below in Table 87 as small samples do not separate data well in factor analysis. 418 | P a g e 419 Prepublication Copy Table 87 Achievement Potential Speed Cogflex 0.54 Letid 0.3 Parts 0.5 EmD 0.49 Blocks 0.41 Spatial 0.98 Lap 0.31 Reading 0.65 Math 0.95 SS loadings 1.47 1.23 1.08 0.16 0.14 0.12 0.16 0.3 0.42 Proportion Variation Cumulative Variation of Factor Analysis of Achievement and Aptitude variables (N=106) Similarly, a more diverse group (n=166) ages 12-30 whose average ability is higher has more definitive factor loadings. See Table 88 419 | P a g e 420 Prepublication Copy Table 88 Variables Achievement Potential Speed Cogflex 0.35 Letid 0.912 EmD 0.158 Arith 0.287 Sp 0.652 Lap 0.92 Math 0.867 Reading 0.818 0.398 Factor1 Factor2 Factor3 SS loadings 1.643 1.411 1.18 Proportion Var 0.205 0.176 0.147 Cumulative Var 0.205 0.382 0.529 Factor Analysis of Achievement and Aptitude variables (N=166) The measurement of these problem-solving categories has been identified by variables on different kinds of instruments, particularly the Problem-solving Technical and Personalstyle Indicator (PTPI) and the Learning Problem Style Indicator. The following is a synopsis of the major variables and their identification by a group of equations called specification equations. Rate of misclassification What is the expected rate of misclassification? The answer depends on so many different things; it is difficult to give a single answer. Let us revisit some basic concepts of reliability, validity, measurement issues, surface characteristics, layers, demographic factors, and intended use. 420 | P a g e 421 Prepublication Copy The ability to quantify a subgroup using numbers revolves around reliability, validity, and measurement techniques. We have chosen distance measurements, fuzzy models, and applied statistical methods as a method of quantification and noted that classification (ability to assign a person to a subgroup) is a difficult process that only has validity based on theory, a prior and posterior probabilities, as well as item and subscale response patterns. In our model, all people are different from our subgroup (individual differences). Why? The subgroup is an “ideal composite” established on a theoretical and empirical basis. The assumption is that having characteristics in common with an identified subgroup provides information to and about the individual. Likewise, knowing how one is different from the subgroup as identified by distance measures gives information about the error, misclassification, and individual characteristics. Are there acceptable levels of error in classification for being nearest to a subgroup.? All measurement theory is based on error. For some researchers, the measurement error is too great, for others not so much. Intended use is another important variable in determining the error. In general, we have found that if there is any personal threat associated with the assessment situation, the error rate in misclassification is increased substantially. Why? Individuals are afraid that the information will be used negatively, and their response patterns reflect less variability (become more conservative), and they choose more socially desired responses. There are ways to compensate for the variation in averages due to the assessment situations, but the best solution is not to use the instruments for classification in any situation where a personal threat exists. Age and demographic factors are also important. The ideal situation is for average scores of comparisons to be adjusted via differences in demographic factors (age, ethnicity, education, etc.). In the late seventies, a user complained that a group of fellow professors at his college thought their scores were in error. The computer program that was being used was set to measure a group of 18-19-year entry-level college students based on our normative data. Normative profile scores change substantially for a group of highly educated 45-70-year-old professors. Enough said. Surface characteristics are especially important when trying to classify individuals or their behaviors. Surface characteristics are likely to represent true feelings, behaviors, and thoughts when layers are thin and pliable. As the depth of the layer increases, surface characteristics are false representations of thoughts and ideas which cause misclassification, and misrepresentation. That is, thick layers or complex and multiple neurological pathways filtered through unusual parts of an emotionally charged brain may produce responses that are not representative of the individual’s true feelings, ideas, or thoughts. Because surface characteristics vary substantially from one person to another, one cannot classify an individual into a subgroup in two very distinct situations. 1. A person does not want to be classified into a subgroup so purposely falsifies responses on questionnaires. 2. An individual has multiple layers that interfere with surface 421 | P a g e 422 Prepublication Copy characteristics and therefore the person is unaware of their true response pattern. In either case, since the subscales are in error, the person responds vociferously that there is not a match between them and their profile classification. Guess what? True enough! Extended scales Can one combine diverse scales to increase measurement classification? The essence of this is found in one of the accompanying papers on measurement and classification. Conceptually Dominant Problem-Solving Category (C) Many different elements make up this problem-solving category, but the dominant ones are Ideation (c), Achievement, (ps), Literary (c), Artistic (c), and Creativity (c) Definitions of each of these are provided in the Appendix. Analytic Problem-Solving Category (A) Logical Analysis Preference (ps), Independence (ps), Investigative (c), Computational (c), Technical (c) Social Problem-Solving Category (S) Social Concern (ps), Social Orientation (c) Motor Problem Solving Category(M) Practicality (ps), Mechanical (c), Outdoor (c), Realistic (c) Perceptual Problem-Solving Category (P) Cognitive Flexibility, Letter Identification (pc), Business (c), Clerical (c), Conventional (c) Differential/General Problem Solver (L) Analytic, Spatial (c), Speed of processing on Embedded Designs and Arithmetic Distraction (pc) Control (C)/structure Structure, Preceptive, Detail Flex Adaptability, Achievement 422 | P a g e 423 Prepublication Copy Measuring instruments (reliability and validity) Two primary questions regarding a measuring instrument are "How reliable are the instruments?” and” Is the instrument valid?” Said another way will a person score the same on each item, each subscale, and each scale every time the instrument is administered, and does the instrument measure what it purports to measure (validity). The author taught research graduate courses as well as Tests and Measurement from 1984 to 2008. Many teachers in my class tested the children whom they taught as part of their class assignments about reliability and validity. The questions about reliability relate to the stability of the items over time. The items on a measuring instrument must be easily interpreted, not subject to distortion, and allow the responder to answer the same way each time. The questions of validity are even more definitive since it is important to know whether the instrument is intact (factorial validity), measures the same as other instruments (concurrent validity), or can predict the future (predictive validity). Our studies (95 different samples) have taken place over 40 years. During this period, each kind of validity (factorial, concurrent, and predictive) has been examined repeatedly. Likewise, questions of internal and external reliability have been answered as separate groups of items have been inserted with specific groups or populations. The long journey has allowed us to follow groups of individuals and perform repeated testing over time. In many cases, the situations in which the data was gathered were unintentional. Individuals have voluntarily requested testing or have been tested by their company or trainers. The data were collected by happenstance or as data of opportunity. In other instances, the studies were conducted by the author as an area of interest or study, by graduate students as part of graduate research projects, or by graduate students as part of their studies in graduate school. These last studies were systematic, testing specific kinds of hypotheses. Reliabilities, when measured by test/retest over short intervals, range from .66 to .94 depending on the age of students, the instrument involved, and the subscale and items measured. Internal consistency (Spearman-Brown and Cronbach Alpha) were lower and ranged from .60 to .91, depending on sample size, study, and age of students. Our measures of managers on the management tests provided the most stable results (testretest reliabilities on most subscales of .85-.93. One of the significant issues in the use of the instruments is the use of Cronbach Alpha vs test-retest reliability. In various places throughout this book, we have argued that the use of Cronbach Alpha is more important to define a narrow concept while test-retest can be 423 | P a g e 424 Prepublication Copy used to define broader concepts. Classification requires broad concepts to encompass the extremes of the groups. Items for classification have less internal validity (do not hold together well) .60-.70 instead of .85-.95. If we use a lot of different items to predict then Cronbach Alpha is lower than if we use a few comparable items, then Cronbach Alpha is higher. The extensive length of time that we have studied the issues has allowed us to examine the questions of reliability and validity many times with many different instruments written for specific samples or in some cases whole populations. As an example, we might take the general test and modify it for specific populations--managers, teachers, elementary students, secondary students, and the general adult population. Each of these modifications was designed to garner a better match between the group being tested and the individual. The personal characteristics section of the instrument was designed originally to measure personality while the cognitive components of the instruments were designed to measure spatial and thinking processes. Each study conducted gave a unique contribution to the understanding of individual differences but not necessarily an accurate classification of people. As time evolved, the instruments were gradually changed to assess the relationship between personality, cognition, and interests and the solving of many different kinds of problems. In essence, we have created several separate instruments and integrated them into one large instrument. Or then again, in many instances, we used only parts of some instrument. The reliability and validity of each of the components have been examined in detail many times. For example, the components of the tests which are associated with career and interests, cognition, and personal style have established separate reliability and validity for that section. The use of multi-method profiles increases the stability, therefore the reliability, over time. Our re-analysis of many previous studies has provided us with correlations between a host of different kinds of existing standardized tests including intelligence, aptitude, achievement, interests, and personality. This has also provided us with an extensive database that provides the foundation for many assertions in this book. Chapter references: Breiman, L. (2001). Random forest. Machine Learning 45, 5–32 Collado-vides, J, Christen, J. A, & Medrano-Soto, A. (2004). BClass: A Bayesian Approach Based on Mixture Models for Clustering and Classification of Heterogeneous Biological Data. Journal of Statistical Software. Vol. 13, Issue 2. 424 | P a g e 425 Prepublication Copy Cronbach, L. J., & Gleser, G. C. (1953). Assessing similarity between profiles. Psychological Bulletin, 50(6), 456-473. http://dx.doi.org/10.1037/h0057173 ... Gauld, D. B. (1974). Topological properties of manifolds". The American Mathematical Monthly, 81(6),633-636 Forrester, Jay W., 1961. Industrial Dynamics, Portland, Oregon: Productivity Press. Hastie, T., Taylor, J., Tibshirani, R., and Walther, G. (2007). Forward stage wise regression and the monotone lasso. Electron. Journal of Statistics, 11–29. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B Zadeh, L. A. (1965) Fuzzy sets, Information and Control, 8, 3, 338-353. Zena, H. M. &Duncan, F. G. (2015). Advances in Bioinformatics (Ed). Zena M. A Review of Feature Selection and Feature Extraction Methods Applied on Microarray Data Volume 2015, Article ID 198363, 13 pages http://dx.doi.org/10.1155/2015/198363 425 | P a g e 426 Prepublication Copy Chapter 22 Problem Solving Subgroups and Machine Learning Introduction In earlier chapters of this book, the focus was on the process of solving various kinds of numerical, spatial, and verbal problems, the characteristics of the problem and problemsolver, and the respective subgroup to which individuals belong. However, a detailed method of mathematically classifying individuals into subgroups was not explored. The purpose of this chapter is to explain a computer-based machine learning methodology for classification, using the 20 different variables of the IPS system. Some of the theoretical constructs related to machine learning were discussed in the previous chapter as “General Measurement Concerns.” The objective here is not to give an exhaustive examination of machine learning, but to concentrate on the aspects of the field most closely related to the mathematical procedures used in classifying individuals into one of the 36 subgroups. In this chapter, actual mathematical and non-mathematical examples are given. The first part of the chapter provides a brief history of machine learning and its terminology, while the latter part shows various practical methods of finding and classifying individuals into one of the IPS 36 subgroups. A brief history of machine learning Machine learning, a term generally credited to Arthur Samuel (McCarthy, J.&; Feigenbaum, E., 1990) while working at IBM in 1959, was applied to artificial intelligence (AI) problems which prophesized that computers, as machines, could learn without being programmed (IBM, 1959). That is, according to a paraphrase by Samuels, a machine could be programmed to display, at some future moment, a move, action, or insight does not present in the original computer code. On TV, on February 24, 1956, Arthur Samuel demonstrated this potential capability using a self-learning checker program (IBM, 2011). This computer learning capability, which was in its infancy in the 1960s, eventually resulted in the development of a number of remarkable AI feats. For example, in 1997, Deep Blue, a computer program actually beat Garry Kasparov, the world chess champion (IBM, 2011). Later, in March 2011, Watson, a computer program developed by IBM, beat former Jeopardy Winners Brad Rutter and Ken Jennings and won a one-million-dollar first-place prize (IBM, 2011). Similarly, in March 2016, Google’s DeepMind AlphaGo AI program defeated the Go world champion Lee Sedol four games to one. The match, which 426 | P a g e 427 Prepublication Copy was watched by about 60 million people, amazed viewers with the uniqueness of positions not programmed into the computer. This capacity to play “Go” was learned by the computer as it played multiple games against itself over months before the contest (Jaderberg, 2017). Since the 1960s, machine learning techniques have developed roots in many different academic fields and disciplines, as well as many non-academic software industries. Today, these roots include diverse areas such as computer science, pattern recognition, data mining techniques, computational statistics, optical character recognition, and neural networks—to name a few. Some authors (Marr, 2016 & Colner, 2016) trace the beginning of machine learning to earlier centuries by focusing on the underlying mathematical techniques used in computing programs. Bayes theorem, least squares, and Markov chains are the three most often used mathematical procedures in machine learning. These techniques which were discovered by Thomas Bayes (1763); Adrien-Marie Legendre (1805), and Andrey Markov (1913) respectively are now used extensively in computing solutions to machine learning algorithms (Hayes, 2013). Other authors (Ganguly, 2016 & Gonzales, 2017) use events in the last few decades as a basis for establishing historical precedent about machine learning. Particularly important is the early work of Alan Turing’s learning machine (1950); Frank Rosenblatt’s (Rosenblatt, 1958) invention of the perceptron as well as Marvin Minsky ‘s and Seymour Papert’s (1969) publication of their book called Perceptron. In 1967, one of the fundamental techniques used in machine learning- the “nearest neighbor algorithm” was written to detect basic patterns. The 1990s through 2017 produced many machine learning software programs for a myriad of different purposes. These programs, with increased microcomputer chip speed, allowed the computer to “see, hear, mimic, and follow” human reactions at a fantastic rate. As a result, many new facial and pattern recognition programs came to fruition. These programs obtained instant use at airports, large department stores, and security areas. Particularly important in the history of machine learning is the change in the way academic information was disseminated. In the early years, students in schools and universities did not have access to sophisticated computer algorithms being developed with proprietary computer software. Now, with many open-source publications, latest information and research are more quickly available. Likewise, the appearance of Journals, such as the Journal of Statistical Software, and Machine Learning Research, provided access to information about statistical theory, computer programs as well as algorithms written in programming languages and analyzed via R and math lab platforms. These developments, which promoted a free flow of information via the Internet, augmented 427 | P a g e 428 Prepublication Copy the development of many new computer programs and algorithms. The almost instant use of non-proprietary computer programs and packages contributed to the non-linear growth and popularity of machine learning programs. Machine learning computer programs Over the past 30 years, a host of computer programs, packages, and algorithms have been developed, especially those provided by the R software environment for statistical computing and graphics (R Core Team 2017). The programs and packages related to classification are known by names such as the nearest neighbor, decision trees, rule learners, neural networks, naïve Bayes, and support vector machines. Major milestones in the history of machine learning algorithms and techniques included Classification and Regression Trees (CART). This was introduced by Leo Breiman et al. (1984). Quinlan (1979, 1986) provided induction rules via the early developed algorithm known as Iterative Dichotomiser 3 (ID3). The successors of ID3 were named C4.5 and C5.0. Other algorithms included CH-squared Automatic Interaction Detector (CHAiD), a program used to perform multilevel splits in the process of classification, and MARS, a program that facilitates the number crunching in decision trees. In Table 89 below, the computing tasks of each of the machine learning supervised algorithms were summarized by Lantz (2013). Three of the classifiers (model trees, decision trees, and support vector machines) play a prominent role in classifying individuals into the 36 subgroups in this book. The theory of machine learning suggests some data collected by experimenters can be separated either linearly or non-linearly. This separation allows subsets of data points to either be in one group or another. As noted in the following table, many different kinds of supervised classification algorithms can perform the separation into subgroups. 428 | P a g e 429 Prepublication Copy Table 89 Supervised Learning Algorithms Task Nearest Neighbor Classification naive Bayes Classification Decision Trees Classification Rule Learners Classification Linear Regression Numeric predictions Model trees Neural Networks Numeric predictions Classification /Numeric predictions Classification Support Vector Machines /Numeric predictions Lance (2013) Different Kinds of Machine Learning Classifiers and their Functions Support vector machines (SVM) If the theory of SVM, Model trees, and Decision Trees is to separate groups of data into subsets, how is this accomplished? In reality, not all data is separable. Separation depends on the spatial or numerical arrangement of data on a measured platform (grid, number line, etc.). The example given here is an oversimplification of a complex mathematical process but is illustrative. Suppose there are 10 pieces of data (1,2,3,4,5,6,7,8,9,10) which, for this example, have been divided into 2 number classes of a and b. The classes are noted as training and can be identified by a simple vector containing the a’s and b’s in a linear sequence (a, a, a, a, a, b, b, b, b). By simple inspection, the division point which separates the two classes is at positions 5-6. Therefore, these data are linearly separable. Using mathematical set theory, the numbers closest to the division point are known as support vectors. The support vectors in the SVM process identify where the division into classes occurs. For instance, in the example above the 4 support vector points used to separate the two classes are denoted as 4,5,6,7. That is, the division between the two classes at positions 5-6 can use the points (4-5) and (6-7) as being able to identify the separation area. Two of the support vector points are on one side (4-5) and two of the other support vector points are on the other side of the division point. (6-7). Therefore, the first class (a) is divided into the class at the position of (1-5) while the second class (b) is at the position of (6-10). 429 | P a g e 430 Prepublication Copy Can you identify the support vectors for the following classes? Sequence is 1,2,3,4,5,6,7,8,9,10 while classes are a, a, a, b, b,b,b,a,a,a,a). Correct! Support vectors points are (1,2), (5,6,7), and (9,10). Notice the number close to the first division (3) is missing as well as the number close to the second division (8) is missing. Therefore, there may be some errors in the prediction of the actual division into classes. A slightly more complicated example attempts to find support vectors in hyperspace by using hyperplanes. Suppose the data are separated in space in such a manner as to have a margin and a division line between two groups. The margin is the shaded area, and the two groups are colored red and turquoise. The division line runs in the center of the margin. In Figure 3 below, there are two support vector points colored red and turquoise on the edge of each margin. SVM margin Figure 3 To find the best separation between the groups, an additional parameter C is added. This allows one to establish the cost of a tradeoff between having a wide or smaller margin and less error in correctly classifying the data (accuracy). The C parameter may be set to different dimensions (.10, 1, 10). The width of the margin decreases as parameter C increases. Increasing or decreasing the margin may lead to more or less accuracy in classification. Another method of increasing the accuracy of data that are not as linearly separable is to adjust the kernel of the classifier. The kernel is a mathematical formula that extends our two-dimensional non-separable data into 3-dimensional space so that the data can be better separated by hyperplanes. There are many different kinds of kernels used to project the data; three of the following are the most popular: Radial Base Function (RBF), Linear, and Polynomial. Adjusting the kernel is a way of converting 2-dimensional space into 3dimensional space and thus increasing the chance of finding a new space that is linearly 430 | P a g e 431 Prepublication Copy separable. In Figure 4, the original space is called the “input space” while new space is called “feature space.” Figure 4 SVM 2D to SVM 3D The shape of the separating boundary in the original space depends on the projection into the new space. In the projected space, this is always the “best” hyperplane that separates the data and solves a linear programming optimization problem. The kernel computes what mathematical values would be if you had projected the data and helps determine the best hyperplane which separates the groups for classification. Decision tree types Our focus is on the algorithms of decision trees and support vector machines which are two major kinds of supervised learning algorithms used to separate the 36 subgroups. Now that the concept of support vectors is relatively clear, let us examine the decision trees. Everyone is familiar with a tree and its branch-like structure. The tree has large strong branches which give rise to smaller and smaller branches. The decision tree type requires a decision at each branch with the assumption of a hierarchical structure. As an analogy, the structure of a “tree” is used by many programmers to represent binary changes, that is, decisions leading to one set of conditions vs decisions leading to the second set of conditions. In fact, Arthur Samuel's algorithm in his checker program used a binary tree-like structure to “look ahead” to potential future moves by the opponent. Originally, programmers presented tree-like structures with branches and symbols to trace the code in a computer program. With each branch came a decision to go in one direction or another. This tree structure was represented by the branches which showed how each binary decision point resulted in an endpoint—a target represented by leaves. 431 | P a g e 432 Prepublication Copy Two major types of model decision trees have been developed. The first type has the target variables represented by a discrete set of values in the form of categories. In decision trees representing categories, the tree structures represent class labels and branches represent the features of the class labels. This end result of the classification is an outcome or prediction about the class to which the data belong. In decision trees of the second type (continuous variables), regression programs are used for prediction. The common methodology used in machine learning classification Many of the terms and philosophies used in the theory of machine learning are presented in Chapter 21. Concepts of misclassification, true and false positives, feature selection, dimension reduction, and known information are commonly used concepts in describing machine learning theory. Here, the discussion is on the recent practical terminology involving computer programs and the methodology used in the area of classification. One common term used in machine learning is predictive. In the predictive machine learning model, the first outcome is derived with explicit instructions of what to learn (training) and a second outcome to determine the degree of accuracy (testing). In other words, the attributes of a partially collected dataset through an algorithm are refined by mathematical methods into a model and result in a prediction. Often a model is derived from one-half of the data collected. In such cases, the terminology which describes the process of defining the model suggests that it is trained (supervised). The model is then tested to determine the accuracy in the classification of the outcome variable on the remainder of the collected dataset. In other words, is the model actually useful for predicting an outcome? As a practical example, one could collect data on all the wins of NFL football teams through November. Then using part of the data, come up with a model that predicts which football team will win the Super Bowl in January. The outcome of the model may or may not be a true prediction. It could represent a probability (95 percent chance of winning the Super Bowl) or cataloging of attributes (number of points scored against opponents, number of yards gain versus opponents, etc.) which gives a rank (1st, 2nd, or 3rd for winning. The final type of machine learning model is descriptive or unsupervised. In an unsupervised model, the data are summarized within the model for a particular purpose such as making a market basket analysis or determining a particular pattern that is evident during a data mining exercise. 432 | P a g e 433 Prepublication Copy Using a machine learning methodology The use of machine learning methodology is quite straightforward. There is an assumption that data has been collected and that a model describing that data is to be developed using the process of machine learning. The 5 steps are: collect the data, prepare the data for analysis, use theory, propose a model and then begin the process of training using samples from the data collection process, and evaluate the model either using random cross-validation, in-sample, or out-of-sample testing. Finally, after looking at the results, see if the model can be improved. Improvement is usually determined by model characteristics and type of methodology. Before we show an actual example, let us briefly review important ideas found in previous chapters as those concepts are integrated into the data analysis which is to be analyzed via machine learning. In this book, there are 20 variables that determine how problems are solved by people in 36 ideal subgroups. Each of the 20 variables comes from one of the 3 major categories: personality, cognition, or careers. Cognition is subdivided into analogy (C1/Pslap) and spatial (C2/Pssp) problems. Another subdivision of cognition is dubbed semi-cognition and is a series of 4 perceptual/achievement speed tests called cognitive flexibility (S1/CF), letter identification(S1/LD), embedded designs(S3/EB), and arithmetic distraction(S4/AD). The personality variables are fairly standard and found are many other personality preference instruments. They are perceptual (P1/Per). conceptual (P2/Cn), motor (P3/Mt), analytic(P4/An), social(P5/Soc), control (P6/Ct), flex (Pt/Fx), and extraversion/introversion (P8/EI). The career variables, for this book and research purposes, are similar to Holland’s categories of realistic (CR1/R), investigative (CR2/I), artistic (CR3/A), social l(CR4/S), conventional (CR5/C), and enterprising (CR6/E) along with 5 other subscales. We contend that these 20 variables represent real-life attributes that work in an integrated manner when problems are being solved. Throughout life, some attributes become more dominant, others become secondary. The dominant attributes are useful in the classification of people into subgroups. Knowing information about the individual and the ideal subgroups can help in differentiating individual attributes as well as how each person solves problems. Using the known information (correlation matrices of personality, career, and cognition as well as a theory about the interrelationships of the variables), 36 profiles were developed. The 36 profiles came from a series of deconstructed correlation matrices found in the research literature in each of the areas of personality, cognition, and career assessment. An example given in the previous chapters suggests a profile standard score can be obtained by deconstructing the correlation between any two variables. For example, if a group of 20 people has an average correlation of .89 on a math test and 433 | P a g e 434 Prepublication Copy reading test, there exist multiple sets of standard scores that divided the people into various groups of high, middle, and low or just high and low (See Chapter 21). Using data from existing correlation matrices in the areas of personality, cognition, and career, the following table of standard scores was constructed. Across the top are 20 variables scores and along the side of the last column are the designated subgroups. Table 90 represents the standard scores of the Differential Problem solvers on the 20 variables. There are other deconstructed tables for the General Problem Solve (not shown) but can identify them since the standard scores average about 90 while the standard scores in the following matrix are about 52. Likewise, for the differential problem solver with standard scores in the 30 or below, a third matrix must be used and constructed. Table 90 Standardized Tests Scores for the 36 Profile Groups of the Differential Problem Solver Use machine learning to classify the subgroups As noted earlier in the chapter, there are many machine learning algorithms and programs that can be used from the Comprehensive R Archive Network (CRAN). For ease of use, the package called E1071 is selected as there are many vignettes, tutorials, and examples 434 | P a g e 435 Prepublication Copy available on the Internet. The package, of this time, was updated as of February 2017. The procedure is quite straightforward and is found in the documentation of the pdf accompanying E1071. There are 4 steps: 1. Download the E1071 program from CRAN. The library is called E1071 2. Copy the matrices found in the Tables below. 3. Use either the continuous scores or the last binary matrix as the classification matrix. 4. Execute the E1071 program to determine the accuracy of the prediction Table 91 is the rotated matrix. The 36 profile groups are now along the top (columns) and 20 variables are rows. Using this matrix, continuous scores can be analyzed in the present form or converted to a binary form. Table 91 Rotated Differential Problem Solver Matrix Assume that we decide to convert the matrix into a binary classification with a predetermined point of linear separation. For example, the above matrix which represents the Differential problem solver can be converted into a binary matrix with separation at a standard score of 52. This matrix is shown below in Table 92. 435 | P a g e 436 Prepublication Copy Table 92 Binary Matrix of Standardized Scores Most machine learning programs have the data in the first columns (1-36) and the classification category at the end of the data matrix (column 37). After any person finishes taking the instruments, their scores can be converted to binary (1=high/correct/0=middle/incorrect) and added at the end of the matrix above. In Table 93 below, a hypothetical set of scores from an individual are labeled as class 19. This binary set of scores is identical to subgroup 19. A machine learning program selects subgroup 19 with 100 percent accuracy in every run as long as the binary scores match a subgroup. If the set of scores from the individual is not identical to one of the subgroups, then the nearest subgroup representing the individual’s pattern of scores is selected. Accuracy deteriorates based on the degree of differences from an identical match. That is, in the situation that a person did not have a high score on any subscale, the classification accuracy would be zero for this classification matrix. Another matrix encompassing the average standard scores of the differential problem solvers must be used-- 4 matrices usually suffice. Table 93 Binary Matrix of Continuous Score with Class Designation 436 | P a g e 437 Prepublication Copy Decision trees There are many ways to display the relationships of how cognition, personality, speed/achievement, and career variables each relate to subgroups in the IPS. For ease in understanding a complex system as well as following the theory generated by various research studies, a hierarchical system is displayed first. According to various research studies, cognition is the overall major contributor to solving problems. Under the umbrella of cognition comes various levels related to perceptual speed followed by personality that is immersed and interspersed around cognitive attributes. Each subgroup from one through 36 displays this hierarchy. Within a subgroup, each member based on age, experience, and maturity displays strengths in career preferences. The hierarchical system which results in a classification of subgroups is best shown using a tree structure. The entire tree structure is found in Appendix E. An abbreviated example of the hierarchical tree structure is shown in Figure 5. There are two levels of problem solvers under the IPS banner (General, Differential). Only a partial list for the general problem solver is illustrated below. Appendix E contains the full tree. The decision tree below shows 4 levels for the general problem solvers who have high arithmetic scores, high scores on analogies and spatial (g), high scores on speed, and high scores on flex, conceptual, and analytical. This pattern results in the classification of a person into subgroups 7 and 25. People who score high on Flex and conceptual as well as analytical and social are classified in subgroups 13 and 31. The decision tree allows for a person to be classified into a subgroup regardless of if they are a general problem solver or a Differential Problem solver. Although not shown here, the same decision tree is displayed for the Differential problem solver. Thus, based on the matrix used, either differential or general problem solver, every person is classified into one of the 36 subgroups. Figure 5 1 IPS 2 ¦--General Problem Solver 3 ¦ ¦--high arithmetic 4 ¦ ¦ °--high g 5 ¦ ¦ 6 ¦ ¦ ¦--Flex 7 ¦ ¦ ¦ ¦--conceptual °--high speed 437 | P a g e 438 Prepublication Copy 8 ¦ ¦ ¦ ¦ ¦--Analytical 9 ¦ ¦ ¦ ¦ ¦ ¦--7 10 ¦ ¦ ¦ ¦ ¦ °--25 11 ¦ ¦ ¦ ¦ ¦--analytical 12 ¦ ¦ ¦ ¦ ¦ °--social 13 ¦ ¦ ¦ ¦ ¦ ¦--13 14 ¦ ¦ ¦ ¦ ¦ °--31 15 ¦ ¦ ¦ ¦ °--Social 16 ¦ ¦ ¦ ¦ ¦--1 17 ¦ ¦ ¦ ¦ °--19 18 ¦ ¦ ¦ °--motor Partial Listing of a Hierarchical Tree Chapter summary This brief chapter on machine learning and the implementation of its algorithms provides insight as to how the 20 variables used throughout this book can be connected to the 36 individual subgroups. Each of these ideal subgroups solves problems in diverse ways depending on how the dominant strengths are exhibited throughout a lifetime. More importantly, the information in this chapter provides a way to link the scores of a person to a particular subgroup. This permits one to examine the differences between the actual person’s scores and the subgroup's scores to which he or she belongs. Chapter references Breiman, L.; Friedman, J. H.; Olshen, R. A.; Stone, C. J. (1984). Classification and regression trees. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software. ISBN 978-0-412-04841-8. Colner, R (2016). A brief history of machine learning. SlideShare. Retrieved November 20, 2017, from https://www.slideshare.net/bobcolner/a-brief-history-of-machine-learning 438 | P a g e 439 Prepublication Copy Ganguly, R (2016). A Brief History of Machine Learning. Retrieved November 20, 2017, from https://www.linkedin.com/pulse/brief-history-machine-learning-dr-jaideepganguly Gonzalez, V. (n.d) A Brief History of Machine Learning. Retrieved November 20, 2017, from http://www.synergicpartners.com/en/espanol-una-breve-historia-del-machinelearning Hayes, B. (2013). First Links in the Markov Chain. American Scientist. Sigma Xi, The Scientific Research Society. 100, 2, 92. doi:10.1511/2013.101.1. Retrieved November 20, 2017, from https://www.americanscientist.org/article/first-links-in-the-markov-chain IBM’s 100 Icons of Progress (2011) A computer called Watson. Retrieved on November 20, 2017, from http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/watson/ IBM’s 100 Icons of Progress (2011) The IBM 700 Series: Computing Comes to Business. Retrieved on November 20, 2017, from http://www03.ibm.com/ibm/history/ibm100/us/en/icons/ IBM’s 100 Icons of Progress (2011) Deep Blue Retrieved on November 20, 2017, from http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/. Jaderberg, M. (2017) Google DeepMind. Google Inc. on Retrieved on November 20, 2017, from https://deepmind.com/research/alphago/ Lantz, B. (2013). Machine Learning with R. Packt Publishing Ltd. Birmingham B3 2PB, UK. ISBN 978-1-78216-214-8 Legendre, A. (1805). Nouvelles méthodes pour la détermination des orbites des comètes (in French). Paris: Firmin Didot. p. viii. Retrieved on November 20, 2017, from https: // archive.org/ details/ nouvellesmthodegoog/ Markoff, J., (2011). Computer wins on 'Jeopardy!': trivial, it's not. New York Times. p. A1. Retrieved on November 20, 2017, from http://www.nytimes.com/2011/02/17/science/17jeopardy-watson.html Marr, B. (2016) A short history of machine learning - every manager should read. Forbes. Retrieved on November 20, 2017, from https://www.forbes.com/sites/bernardmarr/2016/02/19/ McCarthy, J. &; Feigenbaum, E. (1990) Arthur Samuel: Pioneer in Machine Learning. AI Magazine (3). Retrieved on November 20, 2017, from https://www.aaai.org/ojs/index.php/aimagazine/article/view/840/758 439 | P a g e 440 Prepublication Copy Quinlan, J. R. (1979). Discovering rules by induction from large collections of examples, In D. Michie (ed.), Expert Systems in the Micro Electronic Age, Edinburgh University Press, pp.168–201. Quinlan, J. R. (1986). Induction of decision trees, Machine Learning1(1):81–106. R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/. Rosenblatt, F. (1958). The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review. 65 (6): 386–408. doi:10.1037/h0042519. Samuel, Arthur (1959). Some studies in machine learning using the game of checkers. IBM Journal of Research and Development. 3 (3). doi:10.1147/rd.33.0210. Turing, A. (1950). Computing machinery and intelligence. Mind. 59 (236): 433–460. doi:10.1093/mind/LIX.236.433. Retrieved on November 20, 2017, from http://www.loebner.net/ Prizef/TuringArticle.html. Further Reading: Wahba, G. (1998). Support vector machines, reproducing kernel hilbert spaces and the randomized gacv. In Advances in Kernel Methods - Support Vector Learning, Bernhard Scholkopf, Christopher J.C. Burges and Alexander J. Smola (eds.), MIT Press, Cambridge, MA, Vapnik, V. (1979) Estimation of Dependences Based on Empirical Data [in Russian]. Nauka, Moscow (English translation: Springer Verlag, New York, 1982). Vapnik, V. (1995). The Nature of Statistical Learning Theory. Springer-Verlag, New York. Vapnik, V., Golowich, S. and Smola, A. (1996) Support vector method for function approximation, regression estimation, and signal processing. Advances in Neural Information Processing Systems, 9:281–287. Weston, J., Gammerman, A., Stitson, M. O., Vapnik, V., Vovk, V., and Watkins, C. Density estimation using support vector machines. Technical report, Royal Holloway College, Report number CSD-TR-97-23. 440 | P a g e 441 Prepublication Copy Chapter 23 A Different Perspective on Problem Solving Introduction The next five chapters (23-27) are reference chapters for those who lack a background in biology, physics, and psychological theory. Chapters 23 and 24 explain the psychological, biological, and chemical basis of solving problems. The reference chapters expand on the theory. Are there processes at work in the human body that cannot be seen at an observable level of everyday interaction? Are there chemical and physical actions occurring at the cellular and organ level which work following scientific principles? The answer to both questions is obviously “yes.” Since that is true, perhaps, there are yet-to-be-explained phenomena that have an effect on the solving of complex and compound problems. If so, their discovery could contribute to another perspective on problem-solving. This chapter explores the question: Are the process that is known as reasoning (analytical thought) and memory just an unbounded energy process, with energy existing in a form of energy packets and waves which are evolutionary remnants of either gravitational waves or another energy form of light energy known as quarks. Higher dimensions The IPS model attempts to explain individual differences from a different perspective. Our approach explicates the process of learning and solving problems as an analytic process occurring in higher dimensions. Many readers and colleagues instantly will stop reading at this point as the question arises--are there higher dimensions and if so, what is meant by the statement? To understand this point of view, consider the revolution taking place in physics where scientists are willing to consider that “We” may have shortchanged our thinking by conceiving problems too narrowly, only in the three dimensions. Many physicists are willing to consider that many problems that exist today may be better understood by considering at least 10 dimensions!! (See String Theory later in the chapter) 441 | P a g e 442 Prepublication Copy To understand this phenomenon from an intuitive sense, consider how the war and the battlefields today differ from that of World War I or World War II, or even the Middle Ages. The recent war in Kuwait (1990) was fought with the aid of satellite technology which gave generals pinpoint information about troop movements, strategic targets, and battlefield engagements. Today’s battlefields are scanned by drones and satellites. Contrast this new technological perspective with previous wars where commanders only knew their immediate areas and not the picture of the overall war or battlefield. Remember how commanders in the Middle Ages and earlier moved to the high ground on a hill overlooking the battlefield to get an overall view and a new perspective. From a two-dimensional point of view on the battlefield, the battle might seem to depend only on winning at an individual location but from a vantage point higher up, the war might be won more strategically by placing troops at a variety of locations to counter the opponent's overall troop strength. Losing a battle in one location might not be as bad as losing the war. In other words, by adding another dimension, specifically a higher dimension, perspectives changed. Mathematical techniques, using higher and different dimensions, actually help solve problems that cannot be solved in lower dimensions. Again, using a limited example as an illustration (See picture A). Assume one is trying to separate different kinds of people who solve problems. Let each person and their subgroup be represented as a point in a single one-dimensional plane. The task is difficult as one cannot find a dividing line to separate the people. By changing from a single dimension to a higher dimension, the separation process is easier from a mathematical point of view. This is a concept used in support vector machines (SVM) which is used for feature extraction, a methodology for extracting pertinent features in complex equations. 442 | P a g e 443 Prepublication Copy Picture A The revolution in mathematics and physics has a lot to do with the manner and way that this book is written. With the aid of computer databases and information, knowledge in one area is transferred rapidly to problems being explored in other areas. The problems of physics and biology are the problems of psychology, business, and education, and vice versa. Physics, since the 1960s, has been seeking a unified theory that helps to explain disparate actions in nature. Psychologists, as well as educators, have long sought after such a theory, one which has explanatory power as well as the power to predict individual differences. Law of parsimony Science has always considered the laws of parsimony as a way of developing formulas to explain the natural phenomena of the world. Think about Einstein's simple formula that energy equals mass divided by the speed of light. Did not this simple formula lead to many different revolutionary developments in physics--one being the atomic bomb? One of the major tenets of IPS theory is that such simple formulas can apply to biology and psychology, not just physics. To develop ideas about energy, concepts from a number of areas such as genetics, biology, physics, child and adolescent development, and educational psychology are needed. The journey into those areas may become a bit tedious and technical for some, especially practitioners who may choose just to go to 443 | P a g e 444 Prepublication Copy specific chapters that relate to their area of interest. Let’s begin the long and winding sojourn into energy, quantum theory, higher dimensions, and superstring theory. Energy Chapter Twenty-Two begins with a review that indicated the importance of energy in our lives. Is it possible to live without energy? What would happen if the sun, one of our most important sources of energy were to disappear tomorrow? Could life as it is known today still survive? Without a doubt, energy is the basis of life as it is known today. Consider the behavioral difference between a child who goes to school with a hearty breakfast and one who has not eaten for three days, or the difference between a rock lying stationary on the ground and rock flying through the air and hitting your front window. Consider a light bulb without an electrical current as opposed to one with electricity flowing through it. Energy is present everywhere but in different forms. The difference in forms makes the concept of energy elusive but necessary. Was the energy present in our universe during its original expansion? If so, how did energy create the big bang as well as the laws which govern our universe? That was the question that Einstein considered for most of his life as he searched for the single equation which would explain everything. Consider the meaning of Einstein's equation E=mc 2. Energy is equal to mass when taking into account the velocity of light. To understand the simple concept, think about the sun. It is probably not a surprise that our sun is a yellow star composed of the elemental particles of hydrogen which are continually forming helium. Since the protons in hydrogen weigh more than the protons in helium, the excess mass is converted to energy via Einstein's equation and radiant energy from the sun warms our planet, provides oxygen to our atmosphere through photosynthesis, and is the basis of our life today. Based on Einstein's general theory of relativity as well as the big bang theory, the universe should be filled with a uniform sea of low-temperature electromagnetic radiation. This prediction received credence in 1965 when radio astronomers Arno A. Penzias and Robert W. Wilson of the US discovered a cosmic radiation background that seemed to bombard the earth equally from all directions. Later in 1992, an orbital satellite called the Cosmic Background Explorer detected temperature differences coming from microwave radiation in the form of clouds of gas. These clouds of gas were surrounded by slightly less dense bands of matter arrange with a sort of rippling effect--a ripple effect consistent with the theory of the Big Bang. Predictions based on simple theory have utility! (Kaku, 1999) 444 | P a g e 445 Prepublication Copy Einstein's theories along with the Big Bang suggest that our universe is constantly expanding and contracting. This fact was announced in 1929 by Edwin Hubbell. According to Hubbell's Law, the farther that a star or galaxy is away from us, the faster that it is receding in the universe. Our sun, a star, is composed of hydrogen and helium and like other stars in our universe is receding from us at a great velocity. Other stars in our universe, as measured by the Doppler Effect in many experiments over the last fifty years, have been receding to distant parts of our galaxy. In other words, the theory of the Big Bang has resulted in a number of predictions about the universe which have been verified by science. Could energy be important in the development of life and contribute to every day solving problems? Without a doubt. But to understand how, another detour into the world of physics is necessary. While Einstein was developing his theory of relativity, many other physicists were concerned with finding the energy forces that govern the world of the atom—the world of quantum physics and distinct kinds of forces. Different kinds of forces The four natural forces in the universe are described as electromagnetic force, strong nuclear force, weak nuclear force and gravitational force. Electromagnetic force has many different forms, including magnetism, electricity, and even light itself. The power of these forces is unmistakable in everyday life—quantum mechanics is prevalent in computers, lasers are used in surgery, electricity provides power for our cities, and microwaves are for heating our food. Strong nuclear force is the energy found in atoms. Gravity is the binding force that keeps the earth and planets in orbit; while weak nuclear force is, the force governing distinct kinds of radioactive decay. Weak nuclear force can be destructive as it the case of Three Mile Island, Hiroshima, and Nagasaki where radioactive by-products cause massive destruction. One of the major tasks of the physicist is to determine how these forces affect our daily lives and the universe as a whole. Forces in higher dimensions Our lives are not confined to what can be seen and touch. There are many phenomena occurring on a daily level in which our experience is limited but let us resort to explanations that have intuitive appeal. Many people before us have considered that 445 | P a g e 446 Prepublication Copy other dimensions exist. For instance, in 1884, a clergyman named Edwin Abbot wrote a novel called Flatland: A Romance of Many Dimensions by a Square. He used literary license, a method of social satire and criticism, to castigate those who would not believe in the possibilities of other dimensions or worlds. With his two characters, Lord Sphere and Mr. Square, Abbot challenged others to think about the unseen world of a third dimension. Mr. Square (two dimensions), who represented the establishment of that time, is visited by Lord Sphere who patiently tries to explain that he comes from a world where everything is three dimensional. To a two-dimensional thinker like Mr. Square, three dimensions are impossible. When Mr. Square is hurled into Spaceland, the world of threedimensional objects, his life is changed. The experience of visiting Spaceland causes him to challenge existing authority and the sacred belief that only two dimensions exist. Our senses tell us that a third dimension exists, but what about a fourth dimension or even a fifth or six. Individuals have come to understand three dimensions because of simple Euclidean Geometry, an invention of Euclid in the 300 BC. This system of Euclidean assumptions helped us measure planes, and solid figures, especially those concerned with dimensionally. Non-Euclidean Geometry (developed by Fracas Bolyai and Ni Lobachevsky in the early 19th century) was an advancement which helped scientist conceive of new applications. These mathematical principles were later applied to Einstein's Theory of Relativity. If life, as it known today, were to exist in more than four dimensions, as visualized through Euclidean Geometry, perhaps the rules of logic and common sense would no longer apply. We could see this by studying the life of a mathematician named Charles Hinton who was intrigued by trying to visualize a four-dimensional object. Hinton realized that he could not see a four-dimensional object in its entirety but reasoned that he could see it in a cross-section. To bolster his arguments, he developed a set of cubes that others used to visualize hypercubes or cubes in four dimensions. To understand his thinking, let us first try to conceive how a person who sees only in two dimensions (call him a flatlander) can understand three dimensions. If a three-dimensional cube is unravelled, it forms a cross. When the three-dimensional cube is reassembled, a person in two dimensions sees only the square in the two dimensions. All of the squares in three dimensions disappear. Being a flatlander, he can only see things that are flat. We are similar to the flatlander since we can only see things in three dimensions not four or more. What happens to our three-dimensional senses if the fourth dimension disappears? If we unravel a four-dimensional cube, it is the form of a tesseract (See diagram 7). If the cube is reassembled in the fourth dimension, all the sides are lost to our experience, except for what we could visualize in cross-sections. That is difficult to visualize; however, by analogy think back to the two-dimensional person who tries to see a sphere in three dimensions by cross sections. First, he sees a small circle; next, he sees the parts of the circle which appear to get larger and later reach the maximum 446 | P a g e 447 Prepublication Copy circumference of the circle. The final circles start to contract or get smaller and then disappear (diagram 8.) To understand the concept of four or more dimensions, simply look out the window of your home. As I look outside my window, I see many different things, my backyard fence, some flowers, trees, green grass, the house next door and many other things. This observation suggests to me is that each of these objects has more dimensions than length, width, and depth? No doubt to measure each object, we could impose a system which defines each object mathematically within the framework of Euclidean Geometry. However, what happens if we did not impose a pre-existing set of assumptions about the area of view? Would not the mathematical assumptions which govern the understanding the objects come from each object itself--- including those aspects of the object which are not immediately in our sphere of consciousness? Abstract, not spatial What if higher dimensions can be represented as abstract dimensions (mathematically, but not necessarily spatially)? Our brains prefer spatial representations because of our ability to visualize. Our brain, however, can understand phenomena which are not spatial or visual. Sight and touch are part of our senses and are important in manifesting experiences as real or visual. An abstract representation of the unknown, such as mathematical formula, might be just as important as a visual or spatial representation. If one could only represent higher dimensions in the form of formulas, mathematical representations, or even a set of numbers then visual representation might follow. That is what is currently taking place in physics. Higher dimensions are being explored in terms of a system of numbers. The representations are not visual or spatial and therefore cause many to doubt their authenticity; however, the reality of higher dimensions is now being assessed. Does the exploration of the system of higher dimensions have any impact on people solving problems? The answer is certainly not straightforward but has to be inferred from other things happening simultaneously in the world of science-the explorations of the quantum theory. Quantum theory Early in 1925, a new theory of physics burst into the limelight. The theory, called quantum mechanics, attempted to explain the secrets of the subatomic world. Atoms, as defined in quantum theory, are made up of many small particles, with names like mesons, leptrinos, and neutrinos. Ever since Newton, scientists have considered a force to be the interaction between two bodies that have mass, regardless of distance in the universe. Quantum 447 | P a g e 448 Prepublication Copy theory attempted to account for interactions within the subatomic world as a method of understanding the basic elements of matter. What kinds of subatomic particles determine the composition of gases, metals, and stars? By 1925 and 1926, Erwin Schrodinger and Werner Heisenberg had developed a complete mathematical description of hydrogen and were predicting that the chemical properties of the universe would soon be derived mathematically. Quantum theorists such as Paul M. Dirac were beginning to herald the beginning of the new era where the universe is understood in its microcosm. The identification of hundreds of subatomic particles would lead to success in the understanding of how three of the different four forces of nature (weak, nuclear, and strong) operated (not gravity). What did the quantum theorist mean? (Kaku, 2000) In the microcosm of quantum theory, light is divided into different packets called photons. Forces are created from the exchange of discrete packets of energy called quanta. Thus, electrons bump into each other, repel each other, and exchange a packet of energy, the photon. Electrons, in quantum theory, act like particles and waves, depending on the situation. Recent studies have found many substances when photographed at the subatomic level, act according to quantum rules. That is, as aluminium electrons smash again a solid surface act, the electrons act as a wave with a circular pattern called trains. The trains or pathways of electron continues to follow a similar path over and over again, showing properties of a memory! Yes, memory! Electrons follow a similar path over and over, showing properties of memory. Electrons, in quantum theory, have the capability to tunnel or make a "quantum leap" through an almost impenetrable barrier. Electrons are point-like particles that cause waves when striking each other. These waves can be calculated by Schrodinger wave equations. These waves are important to our theoretical basis and thus will be discussed later in relation to memory and thinking as the question is posed--Is the process known as thinking and memory really just an energy process, with energy existing in a form of energy packets and waves which are evolutionary remnants of either gravitational waves or another energy form known as quarks? Gravitational waves were predicted by Einstein as part of his theory of relativity. His basic prediction was that gravitational waves exist as a result of the collision of black holes in space. The announcement of the discovery of gravitational waves was made on February 11th, 2016, at a news conference. Gravitational waves, which come from the collision of two black holes with a gigantic mass many times greater than that of the sun, can tunnel through matter and are invisible. 448 | P a g e 449 Prepublication Copy This research was organized under an NSF grant involving thousands of scientists, using the Laser Interferometer of Gravitational-Waves Observatory (Ligo). The Ligo was discovered by three men, Rainer Weiss of the Massachusetts Institute of Technology, Kip Thorne, and Ronald Drever of the California Institute of Technology. (Calla, 2016) Quarks Gravitation waves are one form of energy; quarks are another. One of the reasons that heavy particles of the atom, such as electrons, neutrons, and protons, are not fundamental is because of the tiny particles of which they consist of are called quarks. According to quantum theory, different forces are caused by the exchange of different quantum. Thus, weak forces come from the exchange of different types of quantum called the W (weak) particle while the strong forces holding protons and neutron together are caused by the exchange of subatomic particles called tau mesons. Quarks are held together by small particles of energy called gluons and have a tendency to maintain symmetry. For example, in the diagram at the right, the proton can be compared to three steel balls held together by a y shape string (gluons). The same is true for the tau meson which is held by a single string. The strings undergo vibrations that help identify it as a different subatomic particle. Each of the various kinds of particles seems to maintain symmetry, another important point for our discussion as we digress slightly. What is symmetry? Symmetry is defined as the exact correspondence of form on opposite sides of a dividing line or plane or about a center or an axis. Symmetries occur often in the physical and biological world. A starfish looks the same even if it is rotated by 60 degrees. Think of the symmetry of snowflakes, flowers and other physical and biological entities. Symmetries become important in the process of solving problems because they are important in our natural environment. We see symmetries; therefore, logically, we try to recreate symmetries as abstractions when problems are solved. Now back to the story. In one theory, quarks are various kinds of strings that undergo vibrations. These vibrations are important in the identification of subatomic particles. The vibrations are also the basis of string theory. 449 | P a g e 450 Prepublication Copy Superstrings String theory was developed and evolved over time by many contributing physicists, with credit being given to many who expanded the theory. Depending on the source that is read a few of the earliest and influential people were Werner Heisenberg, Pierre Ramond, Andre Neveu, Michael Green, John Schwarz, Ed Whitten, and Joel Scherk. Superstring theory was developed as a method of uniting quantum theory with Einstein's theory of gravity. Remember that quantum theory help provides explanations of three of the different forces of nature but failed to include the theory of gravity. In Whitten's String theory, particles are strings that move in space. The strings can break, collide with other strings, or form longer strings. According to Whitten, each of these actions are measurable and finite. The actions are not considered random but must obey a set of conditions or restrictions called self-consistency conditions. (Briane Greene, 1998). The self-consistency conditions are very tough and may not be accomplished in our current concept of four dimensions, i.e., three dimensions plus time as a fourth dimension. The self-consistency conditions require that rotations or spins occur only in the 10th or perhaps 26th dimensions. It is the restrictions or the conditions of vibrations that identify the type of subatomic particle. Likewise, according to many physicists (but not yet accepted by any reputable journal) if strings make certain turns or resonance vibrations, then it is also possible to derive Einstein's equations relative to space and time. In other words, the movement of particles at the quantum levels satisfies not only the conditions of space and time but also matter and energy. At the time of this writing, a scientist at Cern, Geneva, Switzerland, have discovered 12 different kinds of particles (quarks) and have predicted a 13 th. These particles called quarks make up all living and non-living matter. Based on assumptions and inference from above, the superstring theory has implications for solving problems as energy in the forms of strings probably make up the purine and pyrimidine bases (adenine, guanine, cytosine, and thiamine) chemical structure of a substance known as Deoxyribose Nucleic Acid (DNA), an important biological substance whose story is examined in the next chapter. Two of our basic building blocks of biology (RNA and DNA) may be composed of superstrings that vibrate at the subatomic level and satisfy the conditions of space, time, matter and energy. Our body utilizes charged particles which are part of the energy system related to electromagnetism and the photon. We know that the photon (light) is important in the development of the food chain. The energy of the photon is incorporated into plants, animals, and almost all living things. In the body, there are many chemical reactions taking place. ATP is converted to ADP and vice versa. Enzymes are a catalyst for energy reactions. In every chemical reaction, there 450 | P a g e 451 Prepublication Copy is an exchange of electrons; some electrons are bounded (combined with another chemical while others are unbounded, released in the form of energy. Unbounded energy exists everywhere that electrons travel in myelin sheaths. In IPS theory, the energy which is not bounded (in chemical compounds) is called unbounded energy. Unbounded energy is the energy in the brain which becomes available and is used in the energy process of reasoning. Reasoning is the basic thought process that solves problems in everyday life!! If the assumption is true, then where and how becomes the question? Quantum theory was developed to explain how subatomic particles interact in the microscopic world. How can actions related to light as defined by superstring theory relate to biological cellular actions? The only way is for the characteristics of electrons in neuron transmission to act similar to characteristics of light in photon transmission. This, of course, can only occur if there is an evolutionary remnant passed genetically from generation to generation. That is, the particles, strings, and wave-like functions (which causes resonance vibrations, and self-consistency found in light) must be similar and result in energy transformations in a biological organism. This same logic applies to the characteristics of electrons found in the basic building blocks of DNA. Evolutionary remnants If the assumption of unbounded energy has validity, then where are the evolutionary remnants. Certainly, unbounded energy must be available in various kinds of singlecelled organisms in the evolutionary tree. What is the evolutionary relationship between cellular functions and DNA? In the evolutionary tree, there are the single-celled prototypes called prokaryotes and Eukaryotes. Single cells such as prokaryotes have DNA but not a membrane. Eukaryotes (our human species) have DNA and a cellular membrane. Energy fuels single-celled viruses and/or bacteria both of which contain basic DNA. From where did the energy forces which fuel the single-cell prototypes come? Originally was it the sun’s rays and light which provided the energy in the form of quarks? Our concept of neuphons packets resulting in twists and turns relative to the process of analytic thought is based on tenets of the superstring and evolutionary theory. Our statements about energy and its form of transmission in the brain is an evolutionary remnant from the earliest building blocks of physical and non-physical entities. The transformation from non-physical (rocks) to physical forms (life) required energy. To understand “how” read the next chapter. 451 | P a g e 452 Prepublication Copy Chapter reference: Abott, E. A. (1884). Flatland. A Romance of Many Dimensions. London: Seely and Co. Calla, C. (2016), Historic first, Einstein's gravitational waves detected directly. Space.com. Greene, B. (1998). A universe of at least 10 dimensions: String theory finally reconciles theories of relativity and gravity. Columbia University Record, 23, 18. Kaku, M., 1999: Introduction to Superstrings and M-Theory, 2nd Ed., New York, Springer Kaku, M., 2000: Strings, Conformal Fields, and M-Theory, New York, Springer 452 | P a g e 453 Prepublication Copy Chapter 24 Review: Biological Foundations Introduction This chapter is a compendium of information about the brain, evolutionary history, genetics, energy transformation and problem-solving. It is a reference chapter as not everyone is familiar with the basics of biology. Intuitively, the process of solving problems seems simple enough; however, as one examines all the different functional biological levels, the complexity is almost overwhelming. Alas. So is beauty! What is the price of understanding the “why” and “how” of beauty? Genetics We pick up the physical story of energy, strings, higher dimensions, and problem-solving by examining some basic fundamentals from biology and recent studies using the latest technology of electroencephalography (EEG), magnetic resonance imagining (MRI), functional magnetic resonance imagining (fMRI), and positive emission tomography scans (PET). In this chapter, we explore the issues of energy and development. How does a newborn baby develop from a one-celled fertilized ovum during a nine-month period? What part does energy play in this process? Does biological development influence the solving of problems? How does energy contribute to the equation P (p, c, I) ->verbal, numerical, and spatial problem solving? We can first examine the characteristics of newborn babies. Physical features or phenotypes are different but the general external and internal manifestations of humans are remarkably similar. Many relatives of the newborn excitedly note the physical similarities to one or the other of the parents. How can the differences be explained? Are the differences really related to the mixtures of genes that came from either parent? Genetic principles underline the transmission of some individual differences; others come environmental interactions after birth. To understand the process let’s review some basic facts related to genetic transmission. Genes are responsible for the initial passing of traits from generation to generation. The early study of genetics began with Gregory Mendel. Through the process of observation, he noticed that when crossed, white and pink flowers had offspring that were white and pink. Without really knowing why Mendel thought that there might be some underlying controlling mechanism which gave rise to these 453 | P a g e 454 Prepublication Copy similarities and differences. His further study of peas confirms some basic genetic principles which formed the basis of the science of heredity known as genetics. Basic codes in genetics Let’s start with the basic question in genetic—What is a genome? Researchers and scientists banter the word “genome “about all the time. Basically, the genome refers to all the genetic material found in the nucleus and cytoplasm of the cell, i.e., the complete set of chromosomes. Chromosomes come in pairs of two with each strand being composed of a double-stranded chemical substance known as deoxyribonucleic acid or DNA. DNA has a cousin which is very similar and is known as ribonucleic acid or RNA. The only difference between the two sugars is an oxygen molecule. DNA, the double helix structure discovered by Watson and Crick in 1953, consists of many different pairs of bases known as purines and pyrimidines. Each of these bases is paired in a double helix structure, resembling a twisted ladder. The purine base contains adenine and guanine which is always pair with a specific pyrimidine known receptively as thymine and cytosine. The purine is linked to the sugar called ribose. Nucleotides are nucleosides (A, T, G, C) with 3 phosphate groups that make up structural units of DNA. A specific portion of the chromosome, based on the order and sequence of nucleotides, is called a gene. A gene is a linear sequence of base pairs (adenine, thymine, guanine, and cytosine) that carry instructions that determine some of our individual characteristics (eye colour, hair colour, etc.). Each group of nucleotides found on the gene code for specific kinds of proteins and amino acids using messenger RNA and various methods of transcriptions thereby providing instructions for building the basic units of life. DNA and RNA are basic building blocks that allow an organism to undergo self-duplication, maintain self-consistency, and preserve a memory! Yes, the attributes that are part of the subatomic particles (waves?). Remember the quanta in Chapter 22. A living organism can start with a single cell coded with DNA and becomes trillions of cells that result in organs and body systems that carry out functions such as eating, drinking, and running. How can this happen! The overall answer is that development is not programmed in a single DNA cell but comes from the interaction of many intracellular and extracellular energy components that contribute to individual differences as cells divide and become organs. A single cell contains 46 chromosomes that contain many genes (somewhere between 18000-23000). 454 | P a g e 455 Prepublication Copy All matter, including humans, is composed of atoms. In turn, all atoms are composed of subatomic particles such as quarks. Atoms and subatomic particles in base pairs tend to maintain self- consistency as electrons tend to replicate movements which may form the basis of memory making up the nuclear and brain pathways. In other words, the environment (extracellular, organismic, and physical) is a key interactional component in biological development and contributes energy to the embryological development of the cell. Mitosis The body has a wonderful mechanism called mitosis which allows a single fertilized cell to develop into a multi-complex organismic being. Mitosis is a cellular process that allows for the identical formation of a new cell. During this transformation event, the DNA strand in each chromosome of the old cell forms an identical strand of DNA. This process occurs as the purine and pyrimidine bases of the DNA are paired and split. In other words, the pairing of adenine with thymine and guanine with cytosine results in the formation of an identical component of DNA. This occurs during a mitotic division when the helix splits into two pieces with each purine or pyrimidine bases picking up its compliment from the cytoplasm of the cell. Meiosis The fertilized egg is created from a union of the sperm, from the father and ovum or egg from the mother. The sperm and ovum, called gametes, have 23 chromosomes, one half the number found in the regular cells. The development of gametes occurs through the process of meiosis. Meiosis is important since genetic material is transferred from one chromosome to another by a crossing over between the innermost pair of homologous chromosomes after initial replication. Since the genetic material of DNA occurs in random order along the sides of the helix, only chance and random mutations determine which chromosome from a homologous pair will end up in the same gamete. Meiosis occurs in the male resulting in sperm cells; in the female, it is called an ovum or unfertilized egg. Sperm cells, carrying half the number of chromosomes, only have nucleus mitochondrial cells to power their journey to the egg. The ovum, on the other hand, has mitochondrial DNA in its cytoplasm. The mitochondria in the egg are important as the energy process for further cell differentiation into organs comes from these organelles. The union of the sperm and egg is called a zygote or fertilized egg which forms the basis of embryological development. Before going further, let’s examine the cell in more detail. 455 | P a g e 456 Prepublication Copy The Cell The cell is the single living component. Many living things exist as a single cell where the cell can be as small as a single virus, bacteria, or as large as the yolk of an egg. For us, it is the focal point since the fertilized cell is what duplicates and forms the basis of a new individual. Individual differences are, in part, born in the union of the zygote. Going back to the theme of the IPS, earlier the question was posed “How important is energy in the physical universe? A more important question is “How important is energy in the biological process?” Assume that superstrings are the basis of atomic particles (a big assumption I admit but if not superstrings then what energy particles??). Atomic particles of carbon, hydrogen, and oxygen make up the vast majority of living elements in the cell. Nucleotides are made of purines and pyrimidine bases which consist of various forms of molecules and atoms. Remember that atoms are made of quarks which probably maintain self-consistency by rotations in different dimensions. Is it not too farfetched to assume that the self-consistency which is inherent in quarks that make up atoms in the nucleotides are inherent in the strings of DNA and other chemical elements that are present in the initial zygote? Would this not provide us with at least a plausible explanation of how the single cell under the impetus of some form of energy multiplies to two cells, four cells, eight cells, blastula, gastrula, and the beginning of life as we know it? The energy process is responsible for fueling the changes that occur during each mitotic division. Interruptions of energy flow are disastrous for the cell. Development is impeded. Where does energy come from during development? It is both intracellular and extracellular with its engine being the chemical structures of Adenosine diphosphate (ADP) and Adenosine Triphosphate (ATP). From an intracellular standpoint, the cell is composed of many different components, not the least important is the mitochondria, nucleus, and ribosomes. The mitochondria are the energy production unit. Most of the energy needed by the cell occurs by a chemical process called oxidation and reduction. Food components (environmental or extracellular) enter the cell through a semi-permeable cellular membrane and chemically are changed to release energy. The nucleus contains all of the genetic material, chromosomes and DNA, and the capacity to divide through mitosis. The ribosomes produce a protein synthesizing mechanism including a chemical call RNA, the cousin of DNA. RNA is Ribonucleic Acid, a substance which differs from DNA by a single oxygen. Hence the name de-oxy ribonucleic acid for DNA. 456 | P a g e 457 Prepublication Copy The point emphasized here is that the living cell receives energy the very nanosecond that the zygote is formed. Energy from the mother's body is transferred to the developing zygote in molecular form through mitochondrial cells present in the ovum but not in the sperm cell. The template for cell differentiation into organs (brain, liver, etc.) is found in the mitochondrial DNA and the chromosomal DNA. If energy from the mother was not present, the cell would die. If energy is not present, none of the cognitive processes and structures would adequately develop and there would be a lack of problem-solving. Adenosine triphosphate Evolutionary Remnants! The cell needs energy in a form that it can use, and Adenosine Triphosphate (ATP) and Adenosine Diphosphate (ADP) are nature's way of responding to the need. The fact that ATP is made of adenine (the amino acid found in DNA and RNA) and ribose, a sugar related to RNA, is probably not an accident. Remember that DNA and its cousin messenger RNA are the primary building blocks of nature as mRNA codes for proteins that form the basis of other cellular components. When adenine and ribose combine with a high energy bonded phosphate, a tremendous amount of energy is needed. Likewise, when those bonds are broken, energy is released. This constant process of developing bonds and breaking the bonds is an efficient energy transaction. Chemical energy from the breakdown of foods (organic energy from the sun’s energy photons) goes into the mitochondria, the cell's energy-producing unit. In the mitochondria, the energy is converted into the electro-mechanic-chemical energy of ATP. This differs from plants that utilize the sun's radiant energy directly to convert chlorophyll to ATP. In other words, both plants and animals use the sun's physical radiant energy in different forms to fuel the living cells and organisms. Again, the mitochondria are also the site of mitochondrial DNA which is passed from generation to generation from the mother. The DNA in the nucleus comes from the father and the mother while the DNA in mitochondria comes only from the mother. The energy which forms the basis of symbolization, the precursor to language, is mitochondrial DNA. How important is this? The basis of almost all cognitive processing comes from language and its inherent manipulation of symbols (symbolization) in the form of written and oral expression. 457 | P a g e 458 Prepublication Copy Enzymatic activity Most of the cell's energy which is released occurs through enzymatic activities. An enzyme is a chemical that either increases or slows down other chemical reactions. During the increase reactions, energy is released to form ATP. The body has thousands of small reactions that must occur at very low temperatures but could not occur without the aid of enzymes. Without enzymes, most of the chemical reactions would be too slow. The body's metabolic activity is dependent on energy reactions occurring in the mitochondria. One energy activity is called Krebs’s Citric acid cycle. Krebs’s citric acid cycle is an efficient energy production system involving the shifting of 8 hydrogen electrons through a series of chemical compounds. This process produces energy every time the hydrogen atom makes its shift through the cycle. The Krebs production system produces energy which helps in the process of developing ATP. ATP is a primary energy unit for the body--being involved in such diverse actions at muscle contraction, and ion exchange. Muscle contraction and its importance in learning and education will be discussed later. Ion exchange is extremely important in cognitive thought processes. To understand the effect of energy on other parts of development, let's examine how the brain follows a sequential pattern of growth from birth. Neurotransmitters There are many different types of neurotransmitters in the brain that produce either excitatory or inhibitory actions. Five neurotransmitters are acetylcholine, glutamate, catecholamines, serotonin, and histamine. Two transmitters (serotonin and dopamine) are important in both cognition and personality. The brain has many neurons that increase and decrease electrical currents. Between each neuron is a small gap called a synapse. The neurotransmitters dopamine and serotonin are secreted in the synapse and facilitate the transmission of the electrical current. The transmitter floats across a synapse and binds to the receiving neuron. This causes a fluctuation in the electrical activity. Serotonin and dopamine are released in many different parts of the brain and the effect depends upon where, when, and how the transmitter is released. Most often dopamine is associated as a reward chemical as it is released in the reward pathway. In contrast, serotonin is involved with mood and feelings. Serotonin is more likely to depress and inhibit positive feelings. Both dopamine and serotonin attach to various neurons and contribute to the functions of the neurons in that particular part of the brain. What produces a consistent functioning of the pathway in the brain? 458 | P a g e 459 Prepublication Copy According to Wilson and Cowan (1972) neurons, the single unit of brain functioning, interacts with other neurons in electrochemical energy units. Key elements of the neuronto-neuron function involve both excitatory and inhibitory interactions resulting in energy transmission. Chemical secretions of neurotransmitters such as glutamate assist in the binding of protein transmembrane receptor triggering depolarization that facilitates neural electron activity along nerve fibers. When groups of neurons are involved, the nerve action causes highly localized redundancy in nerve groups allowing specialized consistent response patterns. If these large distributed neural networks represent competing responses from different neural networks in different parts of the brain, cognitive dissonance is produced Cognitive dissonance requires a decision. The decision (discrimination between alternatives) can be based on emotions, values, or logical thought. Lack of a decision results in anxiety and more emotional stimuli. Dopamine is secreted at the synapse in instances where chemical release occurs in the reward pathway. When encountering an object, action, or occurrence value is assigned based on the amount of serotonin or dopamine. If dopamine is increased, then local redundancy acts to increase its positive value. When dopamine is decreased, or serotonin is increased value goes down. Addictions are the result of too much value. Overall, constant use of repeated pathways and concomitant decisions over long periods of time result in characteristic patterns often denoted as a cognitive style but what we call” habitual and consistent use of the same neural pathways.” 459 | P a g e 460 Prepublication Copy Picture: The “tree of life” Illustration (c) Smithsonian Institution The tree of evolutionary life from the Smithsonian Institute in Natural Museum of Natural History in Washington, D.C. (pictured above) is simplistic as it is impossible to display complex changes in life over millenniums. However, one concept in the evolutionary tree is evident. Vertebrates (a genre of birds, reptiles, fish, amphibians, and humans) developed after invertebrates such as Protostomes. Likewise, mammals (where humans are located) and primates are on a different branch than birds, reptiles, and amphibians. The tree is useful for showing the similarities and differences in various species. Evidence from various fossils over 500 million years ago suggests how neural development occurs in different species of vertebrates. From the notochord of the earliest ancestors to the fully developed brain and vertebral column, vertebrates have come to dominate the sea, land, and air. Almost all species of the early common ancestry of mammals have brains divided into the forebrain, midbrain, and hindbrain. Our early ancestors of genus Homo habilus had small brains and were small of statue (3-4 feet tall). The famous “Lucy” (Australopithecus afarensis), a hominid that lived roughly 3 460 | P a g e 461 Prepublication Copy million years ago, was bipedal and had a cranial capacity of 300 ccs. Although intelligence cannot be synonymous with brain size, brain size increased with the development of the forebrain (used in problem-solving). One of the forerunners of Homo sapiens was Homo habilis, a species man who had an increased cranial capacity of about 450 cm3. Homo sapiens have a cranial capacity of about 900 cm3. Over a period of almost one half million years, cranial capacity double for Homo habilus to Homo erectus to Homo heidelbergensis with the latter being similar to the range found of cranial capacity in the modern genus. Why is this important? One hypothesis is that the development of brain size was directly related to the climatic conditions of the environment. To survive, early ancestors had to find methods to adapt to an environment that was constantly changing (monsoons, shifting food base due to climate, earthquakes, ice age, volcanoes, and draught). Homo sapiens, the only species not extinct in the genus Homo, survived with the development of tools and problem-solving. The energy requirement of Homo neanderthalensis, the species most related to Homo sapiens was about 5280 calories a day. Being hunters who survived in the ice age, the caloric intake was highly dependent upon meat which required being close to their prey. How much (energy) running is required to be close to a large prey which is a source of food? The average life span of H. neanderthalensis was 30 years. This life span was directly related to the energy needed to hunt its food source without getting killed. The brain size of the Home neanderthalensis was also similar to Homo sapiens. The brain The brain is an energy factory (20 per cent of energy is consumed by the brain) and is one of the important evolutionary developments of Homo sapiens. From an evolutionary perspective, energy compounds were outside of the cellular environment and over millions of years as DNA and RNA were passed from generation to generation. According to theory, the mitochondria or energy compounds outside of the cell gradually were engulfed. The brain develops many different kinds of specialized cells (pyramidal). Composed of billions of brain cells or neurons, the brain has a basic structure and organization which is similar in many different kinds of animals, including humans. Brain regions The brain can be divided into four main parts: the first of those parts is called the diencephalon which contains two important structures, the thalamus, and the 461 | P a g e 462 Prepublication Copy hypothalamus. The thalamus is like a switchboard while the hypothalamus controls hormones. The cerebellum contains a motor system responsible for movements. The cerebrum is responsible for sensory, motor, and other cognitive functions. The cerebrum contains a thick sheet of neuron cell bodies, often referred to as the cerebral court. The subcortex contains white matter, which is neural fiber tracts. Another structure in this cortex is the basal ganglia. The basal ganglia are important in motor and non-motor functions. The regions of the brain are varied with the area in the front denoted as frontal lobes. From an evolutionary perspective, the frontal lobes developed last and are thought to be the centers of higher-level processes such as discrimination and concept processing. The region in the back of the brain is the occipital lobes, involved in visual processing. The sides are temporal and parietal. As noted in diagram 9, the temporal lobes are just below the cortex area and are associated with memory storage and processing. MAJOR FUNCTIONS OF THE LOBES Frontal lobe: a) Planning, decision making, b) Discriminating between alternatives, b) Guiding and coordinating movements, d) Sequencing, e) Holding memories about emotions, and f) Storing short-term recognition memory, speech, and language. Parietal lobe: a) Identifying the spatial location of objects b) Performing computation Occipital lobe: 462 | P a g e 463 Prepublication Copy a) Visual processing of environmental objects including the relative position of shapes, and objects, b) Interacting with the temporal and parietal lobes Temporal lobe: a) Receiving information from the occipital lobes b) Storing the information into long-term memory, c) Processing language and stimuli heard in the environment, and d) Classifying stimuli. Brain layers The human brain is a structural phenomenon, with layers built on layers, built on layers. Some suggest that development over thousands of years has contributed to each new layer being built. The early layers were the cortex, and the new layer is the neocortex. Structurally, the neocortex which composes 6 layers of the cerebral cortex contains perhaps more than 10 billion neurons. Within the layers of the cerebral cortex are fiber tracts and connections to other parts of the brain. The neocortex overlays the limbic system which contains a host of structures involved in long-term memory, basic emotions, fiber relay stations, and hormone regulation. The limbic system regulates autonomic and endocrine functions, particularly in response to emotional stimuli. Some scientist suggests that the limbic system is the source of species preservation because of its involvement in sexual arousal, the olfactory system as well as motivation and reinforcing behaviors. Additionally, many of the structures are critical to particular types of memory. Structurally, the limbic system contains the hypothalamus, amygdala, hippocampus, cingulate gyrus, and limbic cortex. Frontal lobes The development of the frontal lobes is important in our discussion of problem-solving since Luria's (1959) work on the brain and its functions provides a foundation for many of our assertions earlier. From early work on lesions of the brain and the associated dysfunction, many clinicians understand the functions of different parts of the brain, particularly the frontal lobes. Functional lobes control and regulate the conscious activity of the individual. Injury to this area disturbs impulse control, perceptual processes, and the regulation of voluntary action. Also, a person who has lesions in this area has problems with different kinds of spatial activity. 463 | P a g e 464 Prepublication Copy According to Perecman (1987) and Fuster (2001), the prefrontal cortex is the specific region of the brain which performs the superordinate functions of organizing cognitive and motor activities. This includes allowing novel and complex behavior as well as structuring goal-directed activity. Brain pathways Anytime we talk about the functional organization of cortical systems, it is necessary to indicate how closely aligned structure and function are. Functions are things like controlling respiration, perceiving objects, moving, talking, and other similar activities. When we speak of structure, we are referring to anatomical structures and their relationship to the underlying physiology. Therefore, we talk about pathways we are referring both to the anatomical structure as well as the functional structure. It is similar to a home with people living in it. The house is a structure while the people are the functions. By analogy, if we change the structure too much, then the people cannot live in the house. Recent research has revealed that the pathways in the anatomical brain are logically constructed in an east-west fiber pathway with a vertical pathway perpendicular to it. One might conceive of the east-west pathway being two-dimensional while the vertical pathway provides the third dimension. During the embryological state, the pathways are interwoven much like one would weave a blanket. As the embryo develops, the nerve fibers in the pathways tend to curl up. Researchers used to think of nerve pathways as being similar to a bowl of spaghetti. Today researchers are aware that the pathways conform to curved dimensions of the skull as development occurs thereby appearing to be curved and tangled. Through research over the last few decades, we know that the mammalian cortex is not organized as separate functional units. Instead, systems that support a particular function are organized as distributed networks with many communications to sub-regions. Each of these separate regions supports a multidirectional flow of information and interacts with other sub-regions. For example, when we see something (visual), we must also interact with where the visual images are stored in memory. These broad superhighways share information between the left and the right cerebral hemispheres. The left hemisphere may process the details while the right hemisphere may process a broader picture. 464 | P a g e 465 Prepublication Copy Sensory perceptions What gives us common or shared experiences? Our senses (perception) are the first source of experience from the outside world. Our perception starts with what is called "topdown perception." Top-down is the conveying of information from its multi-dimensional experience to a two-dimensional picture. From the time of birth, our senses feed us information about the common-sense part of life ---a dog has legs, a tree has branches, a car has wheels, a house is different from a person, etc. Visualization, such as conceiving a rock, utilize many different biological pathways. One can feel a rock, see a rock, smell a rock, and thus comprehend a rock. According to Paivio (1971), concrete objects are more real to most people since multiple pathways exist for understanding their inherent pathways. In our model, sensory-motor, at its simplest level, represents a simple reflex. One sees something and then reacts through motor responses. Memory Memory is the temporary or long-term storing of information in the brain. Memory may be immediate, held long enough to finish an immediate single task by manipulating the information (working memory), short-term-held (STM) long enough to accomplish a task over a short period (20 seconds), or long-term (LTM), held for a period of a lifetime or a few days. Memory is dependent upon the cerebral hemispheres, particularly the brain's trillion neurons as well as other brain structures. When a person learns new information, a memory image or new pathway is formed in the brain, or the memory image is linked with an existing pathway. This memory image can be revived or revisited once it has been formed. The trace or pathway is formed since a single neuron may be linked by dendrites to as many other neurons. Because the brain has so many neurons, thousands of memory traces can be formed over a lifetime. Think of a memory trace as similar to a road traveled over the countryside. One has difficulty traveling the countryside unless a roadway is present. The forebrain is often considered first since the cortex; the higher cerebral brain centers are located there. In terms of structural development, the cerebral cortex of humans is 465 | P a g e 466 Prepublication Copy more complex than any other species. In the evolutionary chain, most animals have fairly simple cerebral hemispheres, while Homo sapiens have cerebral hemispheres which have grown over the brain stem, forming two halves much like a walnut. These thought centers are responsible for many of the advanced decisions that people can make. The midbrain houses the brain stem which has the visual and auditory centers as well as the relay centers for information passing from one side of the brain to the other. The hindbrain is important for balance and motor coordination. Embryological development The first step of conception is primary as one cell will develop into two. At about two months, the fetus has almost all primary organs developed. Between one minute and two months, some of the most miraculous events occur. At five days, primary genes begin to turn on and turn off various primordial functions. Hundreds of identical cells begin to specialize into 350 different cell types. At one week, cells with cilia begin to sweep in a clockwise manner which activates genes that are going to be organs. There is not a blueprint as some chemical variations give rise to mutations which are the basis of ectoderm, endoderm, and mesoderm. A layer of flat cells folds to form a tube-like structure. A thin line of cells forms the CNS along the crease of the fold. When the brain first develops in the embryo at about 3 to 5 weeks, a mass of primordial cells forms through the process of mitosis in the neural tube. These cells eventually migrate (energy impetus) to a position in the forebrain, midbrain, or hindbrain. Later the midbrain and hindbrain develop. The first cells to undergo development are called primordial, meaning that they are undifferentiated. Undifferentiated means the cells contain all the energy stores needed for development but as yet have not developed to the point that they can carry out a specialized function. After migration, these primordial cells become differentiated into neurons, which consist of a cell body with a number of fibers. The longest-extending fiber is called an axon. The axon conducts messages from the cell while the other branch-like fibers called dendrites carry messages toward the cell body. Each cell has a small space between it and the next cell. Impulses are carried electrically along the axon to the synapse where a neuro-chemical transmitter called acetylcholine facilitates the transfer of messages between cells. Again, the basic transfer is energy, one in the form of electrical impulses and the other in the form of chemicals. 466 | P a g e 467 Prepublication Copy Glia Cells The brain is composed of another kind of cell other than a neuron. These glial cells do not send or transmit any kind of message to other cells but have an important function--the development of a myelin sheath which is a form of insulation for the axon as it promotes the efficient conduction of nerve impulses. Glia cells continue to develop throughout the lifetime of the individual whereas the neurons are active during a short time of brain development in the early embryo. By 6 months, most of the neurons have completed their migration to the cortical area. The location and direction of the neuron are probably under genetic control. When the undifferentiated cells have arrived at their location and have a specific direction, they begin to differentiate into neurons. Each neuron with its axon and dendrites continues to proliferate, forming proximity with other neurons through synapses. A synapse is a gap or junction between the axon and dendrite over which electrochemical impulses travel. Neuronal degeneration Theoretically, the formation of specific synapses is not under genetic control but is based on experiences (energy-driven activities in the environment). Research by Spreen (1984) has suggested that the differences in the combination of neurons are so great as to be beyond the potential combinations to be carried by the original chromosomes. Thus, the synaptic contacts made by different neurons appear more random. The survival of a particular neuron depends on many miscellaneous factors, particularly stimulation (energy-driven activities coming from outside of the newborn). If the neuron is continually stimulated, then it flourishes by forming new dendrites and connections with other neurons. Likewise, a lack of stimulation results in neuronal degeneration that results in a lack of function. Cognitive Theory Early development of the brain Because the brain is such a complicated structure, we need to address its development over the life span of the individual. Development can be roughly divided into age groups with birth to 2 years of age as the most important. Changes occur in the brain up to approximately 22 years of age. Even before birth, the brain receives stimulation and stored experiences. After birth, concept development occurs at different levels and at different 467 | P a g e 468 Prepublication Copy rates in different children. At each of these different times in development, stored memories and emotions lead to different levels of concept development. At each early stage of life, brain processing is the primary sensory motor. Sensory refers to seeing and hearing, touching and perceiving. Proprioceptive motor refers to actions such as the movement of legs and other parts of the body. There is an observing then executing relationship. Children see; children do. Imitation is one of the earliest forms of learning. In the early years of life (birth to 5), the infant builds vast quantities of semantic representations which are the result of experiences. Experiences are the daily encounters of talking, moving, and interacting with our environment. Jeffrey Binder (1997) and his team of researchers note that brain activation patterns show that “during rest” the network of neurons is quite active. In other words, the resting brain is active. We often think of this process as ‘mind wandering.’ That is if we are bored, and nothing is occurring in the external environment the active brain is still processing information or thinking. Likewise, if we are sleeping or resting, the brain is active. Energy is constantly being processed chemically in the neural system and the resting brain may be solving a problem, reliving past events, or getting ready for a future event. The best studies suggest the sensory-motor areas of the brain receive information from hearing, seeing, tasting, feeling, and perceiving, i.e., encounters in the environment. The recording of this information in the neurons of the brain is constant and ongoing. There is a stream of consciousness in different parts of the brain (cortex, temporal lobes, etc.). Observing and executing Oftentimes, brain energy is measured while an activity is in progress. For example, a simple brain experiment may involve seeing a banana and picking it up and measuring the difference in brain activity between the time of observing and the time of executing. Or the brain activity is measured against a baseline which in many cases is simply “resting activity.” The individual or animal is doing nothing or is in a state of mind wandering. In most cases, the observation of ‘grasping something’ results in brain activity related to the superior temporal lobe in a portion of Boca’s area in the left hemisphere. We have already indicated that brain imaging is a methodology for capturing brain energy. Brain energy is represented by wavy lines on the screen. Increased activation is represented by larger wavy lines or motor evoked potentials -- MEP. Decreased activation is a small wavy line. Often individuals wear skulk caps that pick up electromagnetic activity, or electrodes are implanted in particular neurons of animals so that when the neuron fires or energy is activated the electrode picks up the information and sends it to 468 | P a g e 469 Prepublication Copy the screen. Therefore, we can see the association between observing and executing. Another method of recording brain activity rather than making static images of the brain is called positive emission tomography or PET. Another cousin is called functional MRI or magnetic resonance investigation. When brain activation occurs, there is also an increase in glucose oxygen, and other metabolic chemicals in the area. Learning Learning involves a change in behavior from a previous state. Learning is crucial to problem-solving as concept formation is incomplete and constantly changing. Learning is the result of energy transformations as a change in concept formation occurs as the depth of processing increases. Depth of processing is a function of time spent, rehearsal, repetition, and practice. That is, depth of processing, the ability to give meaning to an abstract concept, occurs only from spending time processing the concept in the brain. Learning is Cattell’s crystallized intelligence. Learning is not independent of fluid intelligence as both fluid intelligence and learning are energy dependent. Learning involving energy transformation of words, numbers, and spatial activities is highly dependent upon stores of neural transmissions requiring memory. When we speak of the plasticity of the brain, the reference is the brain’s capacity to generate new neurons in much the same way as one stokes a fire to increase heat and light. A stimulus is an energy agent which initiates an activity, either internally or externally. A stimulus can be as inane as talking, eating, seeing, feeling, or touching. From the moment of conception, stimulation of the cell occurs. Stimulation is a basic energy process. Stimulation involves energy transfer or energy initiation (self-consistency?). For the newborn, there can be many different kinds of stimuli. In our thesis, the activation of those stimuli is energy in different forms. Whether the stimulus is physical (touch), representing excitement or invigoration, or verbal, representing sound, the result is an increase in brain activity. In other words, energy, in some form, is responsible for increased brain activity. Does an increase in brain activity necessarily result in learning, where learning is conceived as a change from previous experience, or perhaps acquiring a new experience, ability, or skill in a particular area? No! Any increase in brain activity (stimulation) creates a memory trace that may or may not be very long or results only in immediate recall, affecting short-term memory if very short or long-term memory if repeated and persistent. When an activity is associated with episodic memory, not isolated, but associated with personal experience, the memory trace can be either long or short-term. When the 469 | P a g e 470 Prepublication Copy stimulation is semantic, used over and over in different kinds of contexts from reading or personal activity, the memory trace can be either long or short-term. Either long or shortterm memory can be reactivated when stimulated; however, working memory (temporary storage) is less likely to become reactivated since it has not become permanent (information has been rewritten) in either long or short-term memory. In the IPS model, stimulation comes from the environmental press (light, heat, objects,) or press from the individual (approval, disapproval, love, spanking, etc.). Hierarchical organization In our model of concept formation, the ability to conceptualize abstractly increases as the number of environmental experiences increases. The type or kind of experience is as important as the number of experiences. Concrete experiences are those which involved real objects in the environment. Concrete experiences may be as simple as using the hand to perform simple actions in the environment (hammering, sweeping, cleaning, hunting). Concrete experiences increase the knowledge represented in sensory-motor with lowlevel conceptualization. Representations (the match between what is seen, felt, or heard in the environment and the memory formation and association in the brain) increase based on the varied number of encounters with concrete objects. Showing a child an apple and uttering the word “apple” is a method of building a representation. Letting the child feel, smell, and eat the apple builds concept formation. Storing the representation is memory and processing through sensory-motor pathways (hearing, seeing, touching) forms low-level conceptualization. Spending time processing the representation through pathways interconnected with the temporal lobes and forebrain builds depth of processing. Thus, increased time, as well as the depth of processing, use the hierarchical organization of top-down and bottom-up processing. Processing of information which is based more on memory and daily experience is one level while depth processing (time spent) leading to abstract conceptualization is a second level. The two levels interact but exist as a hierarchy with depth processing being processed more dorsally than ventrally. Brain processing So how does the brain process low-level and high-level concepts? The answer is simple – all different ways. Motor pathways are more ventral. Conceptual processes are more dorsal. Sensory-motor is ventral moving through reflex actions of spinal columns. The IPS model is recursive with differences becoming evident at different periods of development (child, adult, senior). All lobes of the brain interact as energy is constantly moving from neuron to neuron, cell to cell, organ to organ, and system to system. But as 470 | P a g e 471 Prepublication Copy we age and are successful, the method of processing becomes more consistent, so patterns are evident. The recursive model becomes more stylized as success occurs in solving problems. And the great part is that through the process of learning and aging, we can change patterns to be more balanced. Origins of different types of problem-solving Our basis for the selection of the different subgroups of people comes from the modus operandi of the brain as well as information and sensory-motor processing. For example, the concept of children dominant in motor activities comes from the predominant use of motor pathways while the concept of children dominant in conceptual processing is based on interaction from dorsal processes of brain functioning interacting with the ventral process of brain functioning. Of course, people use both dorsal and ventral processing, but dominance occurs through use, especially over a lifetime. That is the basis of style and mode. The social components of our theory arise from emotional images stored in memory that interact with the cognitive functioning of the individual. A person sees an event, analyzes the components of the event, and combines this information with previously stored memory images that also have evoked emotional components. This gives rise to the social nature of thinking. In our theory, a person can perceive an event, completely bypass any analysis, either logical or otherwise, and react socially and emotionally. The concept of energy flow either inward or outward during social interaction give rise to introversion and extraversion while the energy flow to the body provides the impetus for perceptual activities. All of the coordinated mental and physical actions give rise to problem-solving behavior which has their culmination in goal-oriented or outcome measures. Chapter References: Binder, J. 1,2, Frost, J.1, Hammeke, T. A1, Cox, R.W., & M. Rao S. M. (1997) Human Brain Language Areas Identified by Functional Magnetic Imaging. The Journal of Neuroscience, 17(1), 353–362 Fuster, J. M. (2001) The prefrontal cortex--an update: Time is of the essence Neuron, 30, 319–333, doi=10.1.1.211.7359. 471 | P a g e 472 Prepublication Copy Kilpatrick, Z. P. (2013) Wilson-Cowan Model Encyclopedia of Computational Neuroscience. Springer Science+Business Media New York. doi.10.1007/978-1-4614-73206_80-1. Luria, A. R. (1959). The directive function of speech in development and dissolution. Word,341–452. Paivio, A. (1971). Imagery and Verbal Processes. New York: Holt, Rinehart, and Winston. Perecman, E., & Institute for Research in Behavioral Neuroscience (U.S.). (1987). The Frontal lobes revisited. New York, NY: IRBN Press. Spreen, O., Tupper, D., Risser, A., Tuokko, H., & Edgell, D. (1984). Human developmental neuropsychology. New York: Oxford University Press, Watson, J.D. & Crick, F. H. C. (1953) Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid. Nature 171, 737 - 738 (25 April 1953); doi:10.1038/171737a0 Wilson, H.R., Cowan J.D. (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Journal of Biophysics, 12(1),1–24. 472 | P a g e 473 Prepublication Copy Chapter 25 Review: Energy and Cognition Introduction The literature review in this chapter and the next Chapter (26) represents the foundation for two major themes in this book: a) personality, cognition, and interest come from energy packets in the brain that are intertwined, interwoven, and integrated and have different kinds of contributions to problems involving words, numbers, and spatial activities and b) measurement and subgroup categorization models can help explain the process of problem-solving. Any attempt to draw a single unifying theme from the vast array of diverse research literature would be incomplete. So, we focus on a brief history of the elements in our theory, selected those theorists whose tenets fit our IPS model, and streamlined our approach to deriving a measurement and categorization model. To emphasize again, the 10 major problems solving measurement constructs of Conceptual, Analytic, Motor, Perceptual, Social, Extraversion/Introversion, Control, Flex, General, and Differential Problem Solver are primarily derived from regular personality, interest, and cognitive primary subscales. Extraversion, Introversion, Preceptivity, Receptivity, and Achievement Motivation are auxiliary subscales used in classification. There are 36 personality subgroups, 6 interest groups, and many cognitive factors that give credence to the importance of these 10 supra-ordinate concepts. The literature review for all 10 constructs is found in these two chapters (25 and 26). This chapter focuses on the first five constructs: energy, speed of processing, perception, analysis, and conception. Chapter 25 addresses four more constructs as well as interests. For each construct, we provide a statement of IPS theory and a historical review. Let's begin with a historical review of energy which is crucial to all processes within the human body. Historical view Energy is crucial to the basis of our theory; so, let us start this review of the literature at the origin of the universe and trace energy from its inception. The first question is how, where, and why did energy evolve? There are many theories about how our universe and energy evolved 13.8 billion years ago. Most theories suggest a “big bang” occurred at the 473 | P a g e 474 Prepublication Copy beginning. According to those theories, years ago, dust and gas, compressed by starlight and aided by gravitation force formed “protoplanets” (Urey, 1952). Later, the accumulation of matter, “planetesimals” amassed at very high temperatures. The high temperatures were similar to the temperature of molten lava in our present-day volcanoes. The cooling temperatures resulted in black earth with crystal-like rocks found in meteorites that come from outer space. Gaseous clouds in space contain similar elements to our current atmosphere. Our atmosphere is a mixture of different gases comprised of carbon, oxygen, hydrogen, nitrogen, and phosphorous. According to Poole (1951), the atmospheric mixture may have come from the gaseous release of hydrogen in methane (CH4) and ammonia (NH3). The ubiquitous nature of hydrogen and oxygen in the atmosphere with the help of energy from the sun could have easily formed water needed for forms of life. The more recent technical explanation for energy release in our universe suggests that before the big bang, two of the fundamental forces (electromagnetism and a weak force resulting from the radioactive decay of atomic nuclei) were a single unified force. A millionth of a second after the big bang, as the earth cooled, these two forces separated, and a transition phase occurred. Then, according to the electroweak theory (generated by a young postdoctoral physicist named Alan Guth), these forces underwent a transition changing the nature of space to a background field known as the Higgs field. The Higgs field is quite well known today as scientists have been studying different particles and their effect on gravitation. Recently, in 2012, there was a discovery of a new particle predicted by Higgs. This particle called the Higgs boson sheds new light on how the weak force and electromagnetic force interact differently in the Higgs field. In Einstein’s Theory of Relativity, gravity is a weak force compared to other energy forces. Gravitation waves can only be measured indirectly. If scientists are correct, when the universe was very young (i.e., smaller than an atom) quantum field theory suggests matter was wildly fluctuating and the amount of energy packed into a tiny space was tremendous. This caused a process known as inflation. Inflation (contributing to the big bang) during a phase transition released enormous amounts of energy which aided the formation of the planets, stars, and sun in our universe (Guth, 1997). Some argue that this theory is incorrect. These authors suggest that inflation did not contribute to the big bag because the process of inflation would still be occurring. Other authors such as Andrei Linde, a physicist at Stanford, suggest our universe completed its phase transition while the rest of the space was continuing with small seeds in different locations (Linde, 1990). 474 | P a g e 475 Prepublication Copy According to Alex A. Starobinsky (1982), inflation should produce gravitational waves. In March 2014, a team of scientists at the South Pole, using a microwave telescope, claimed to have seen the original gravitational waves emanating from the big bang. Those waves would have traveled millions of miles, perhaps billions, to enter our solar system. The detection of gravitation waves has been recently announced by a team of scientists in February of 2016 (Connaughton et al, 2015). The energy at the origin of life The IPS theory posits that energy in its many evolutionary forms is responsible for cognition and the thinking process. The forms that energy can manifest are many, including but not limited to radiant, electrical, chemical, electrochemical, strong forces, weak forces, gravitational, and waves. Only a few (electrochemical, waves) are manifest in the cognition of Homo sapiens, but a long and tempestuous evolutionary past has provided the foundation for many other manifest forms. The sun, a star which is the source of our energy, is at the center of our universe and to the best of our knowledge, resulted from a supernova. Supernovae are extremely rare; the last one noted in 1604 by astronomer Johanne Kepler who described the supernovae “as outshining everything in the night sky but Venus.” All supernovae recorded in more recent times took place in other galaxies that are millions, if not billions, of light-years away (Westman,2001). Of course, no one really knows how and when the earth was formed or how life actually began. There is a lot of speculations with some actual evidence. What we do know from geologic, fossils, and radiologic evidence is that the earth is approximately 4.5-5 billion years old, and that life of some sort has been on earth 3.5 -4.3 billion years. Fossils of stromatolites are dated at 3.5 billion years. Fossils of Homo sapiens, the roots of our genera, Homo neanderthalensis or hominids were present some 100,000-200,000 years ago. Billions of years of immense physical pressures from environmental forces resulted in a distinct earth formation. During the same period differentiation, mutation, and combinatory chemical activities contributed to different forms of life on the earth---forms of life which existed prior to our species. The accepted theories suggest the vast majority of living species cannot exist without the energy of the sun. The sun’s energy is involved in photosynthesis, the process by which plants convert C02 and water into food and oxygen. The oxygen in the atmosphere contributed to life in general. With the help of energy, the original chemicals (Hydrogen, Carbon, Oxygen, Phosphorous, and Nitrogen) in the atmosphere and on earth have developed into the building blocks of life, i.e., amino acids, RNA, and DNA. 475 | P a g e 476 Prepublication Copy Amino acids could have developed in many ways. For example, based on a 1977 discovery, some scientists suggest that the energy from deep-sea hydrothermal vents, which exist at a temperature of 600 degrees Fahrenheit, resulted in forms of amino acids with life-like properties. Currently, living organisms, such as worms, ghostly fish and shrimp with eyes on the back of their head live on energy, not from photosynthesis, but from the hydrothermal vents. The energy for chemosynthesis originates from molten lava spewing from the ocean floor. In 1952, Stanley Miller and Harold Urey of the University of Chicago suggested the possibility that some basic building blocks of life such as amino acids, could have formed spontaneously given the right conditions. Based on the Urey/Miller experiments, other scientists advised that with the aid of energy some rudimentary self-replicating molecules could have evolved through natural selection (Castelvecchi, 2012). Recent experiments propose that it would have been possible for genetic molecules similar to DNA or to its close relative RNA to form spontaneously. These molecules can curl up in different shapes and act as rudimentary catalysts. As such, they are able to copy themselves--to reproduce--without the need for proteins. The earliest forms of life could have been simple membranes made of fatty acids--structures known to form spontaneously These chemical forms would then envelop water and become selfreplicating genetic molecules, like RNA and DNA. The resulting genetic material would then encode the traits that each generation handed down to the next, just as DNA does in all things that are alive today (Hazen, 2001). Fortuitous mutations, appearing at random in the copying process, would have then propelled evolution, enabling these early cells to adapt to their environment, compete with one another, and eventually turn into the life forms of today. What is the evidence for energy relationships in neurological activity and cognition? Electrical-chemical energy is pervasive in neurological activities. Studies of animals suggest there is a direct relationship between activity in the environment and neurological activity in the brain. In 1989, Georgopoulos and his colleagues examine the electrical activity in the brain of a rhesus monkey when engaged in a mental rotation task. Using computer graphics, the team illustrated that individual neurons in the motor cortex show a spike in electrical voltage based on the direction of the mental rotation. The neuronal cells which fired most frequently occurred during a counterclockwise movement (Georgopoulos et al, 1989). The firing from neuronal cells is what is known as “cognition” today. 476 | P a g e 477 Prepublication Copy Cognition To fully understand the concept of problem-solving and the integrated IPS model, a historical overview provides the manner in which early researchers addressed the process of cognition. The concept of solving problems is broad and inclusive, rather than narrow and targeted. The history associated with solving problems began with philosophers, scientists, and armchair theorists. Each group collected information about and speculated on the forms of energy and cognition. IPS theory-cognition Cognition in our view is a form of electrochemical energy generated by the neurotransmission of electrons in the brain and therefore is an evolutionary remnant. Energy, in the individual, manifests itself in different forms of attention directing, emotion, thinking, logic, and perceiving. Without energy, problems are not solved. Many research studies in the seventeenth and eighteenth centuries addressed cognitive processes as related to energy transformations. Historical view According to Fancher (1979), most of the early research on cognition in psychology has its roots in the philosophical works of authors like Rene Descartes, David Hume, and Immanuel Kant who read the great works of Plato, Aristotle, and Socrates. Each of these men offered a different view of the nature of man, knowledge, and thinking as their assumptions about life were different. Descartes was a rationalist, Hume an empiricist, and Kant a combination of both. For the philosophers, cognition involved the mind and thinking. Descartes (1596-1650) lived during the Renaissance and with a background in physics, geometry, physiology, and language suggested that “Man” gained more insight from the mind then the senses. He introduced the concept of mental objects or structures-what is now called mental representations. David Hume (1714-1776) was much more empirical than Descartes. Being interested in the source of ideas and the relationship among them, he postulated that reasoning was an operation that combined simple ideas into complex ideas or relations. Hume introduced the notion that operations of the mind included comparisons and associations. Immanuel Kant (1724-1809) distinguished between mental structures such 477 | P a g e 478 Prepublication Copy as dimensions, categories, and schemas. His idea of dimensions suggested that objects are extended in space and time. His 12 categories of reasoning defined the manner in which the human mind creates an experience and included quality, quantity, and causality. According to Kant, schemas were rules used to describe a concept in a general way. That is, the concept of “animal” is a schema which brings to mind a class of objects based on images with similar characteristics (mouth, legs, teeth, and body). The works of philosophers provided a theory for the experimentalist of the late 1800s and the early 1900s (Fancher, 1979). How was cognition studied in the early periods of experimental psychology? Cognition was studied as an energy transformation in physiological processes, i.e., reflex arcs, and memory. A few researchers studied cognition in a perceptual manner involving embedded figures, camouflaged targets and reaction time. The age of experimental psychology brought in new ideas from men who received their training in the scientific areas of physiology and physics: William James, Wilhelm Wundt, Johannes Mueller, Herman Van Helmholtz, and Gustav Fechner. The work of Wundt heralded the age of intra-individual measurement (Popple and Levi, 2000). These scientists applied a cognitive model build on measuring intra-individual attributes which were extended to broader domains of study. For example, Wundt studied the qualitative nature of consciousness, applying these concepts of experience to sensations, images, and simple feelings. By using models applied within the individual, the differences between individuals were lost. Wundt (1832-1920) was famous as he founded the first psychological laboratory. Another of his colleges, William James became interested in the scientific study of consciousness and his work extended to the study of everyday problems. This period of structuralism and association introduced the work of Herman Ebbinghaus (1850-1909) on the study of memory and the building blocks of memory (associations). Ebbinghaus also introduced the paired associate’s method, a method of studying nonsense syllables and memory. Early scientists were interested in the physiology and speed of human decision making. Descartes introduced the concept of the reflex arc and Helmholtz used the reflex to determine the speed of neurotransmission along motor pathways. The mental chronometry studies emphasized reaction time (RT) and latency involved in neural transmission. Donders, a Dutch physiologist, used the information to measure the duration of mental operations. Using a key to be pressed and a light, Donders determined the time it took for decisions to be made when the subject was faced with alternatives. Merkel (1885) determined that reaction time (for a rat) increases proportionately as the number of alternatives increase. 478 | P a g e 479 Prepublication Copy The Behaviorist period began in the late 1800 and early 1900s with cognitive experiments in animal psychology. Edward Lee Thorndike’s studied puzzle boxes and cats in 1898. The scientist named Small observed rats that navigated mazes; while John Watson's (18781959) dissertation on the relationship of rat’s learning and neurological development contributed to the view of behaviourist psychology as purely objective and science of the mind (Gardener, 1985). In 1909, Yerkes & Morgulis describe Ivan Pavlov’s studies of conditioning in dogs. Pavlov’s background was medicine, specifically physiology and the digestive systems. He noticed quite by accident that dogs began to salivate as they were led from their cages to the laboratory where they were to be fed. Using a tuning fork and meat as a stimulus, Pavlov noticed that the meat caused the dog to salivate (unconditioned stimulus). Later the meat was paired with the tuning fork and finally, the tuning fork by itself caused the dog to salivate (conditioned stimulus). Pavlov was one of the first to study conditional learning (Pavlov, 1927). Quantitative period In the IPS theory, cognition incorporates more than the traditional areas of IQ theory and human intelligence. This is concurrent with the general definition of cognition in the research literature. Today, cognition subsumes the areas of emotional intelligence, cognitive processes, and ability testing. This was not true with many studies in the early 1900s. In the early 1900s, the study of cognition was equated with the assessment of human intelligence. This was a time of studying individual differences by comparison of interindividual attributes. As such, very early scholarly articles and books addressed the process of cognition as related to intelligence testing. A collection of 66 articles from many early scholars (1869-1959) was found in the book of individual differences by Jenkin and Patterson (1961). For instance, Peterson’s book (1925) on “Early conceptions and tests of intelligence” summarizes the work of psychologists such as J. M. Cattell (1890), Galton (1883/1928) and Binet and Simon (1905/1908). The approach of Binet and Simon was to use measurements that tested memory, attention and cognitive functions in children. Galton, on the other hand, was more involved in large scale testing of adults. He focused, not on intelligence, but on the lower-level cognitive processes such as hearing and sensitivity. J. McKeen Cattell followed Galton’s work by testing college students (J. McKeen. Cattell and Farrand, L, 1896). 479 | P a g e 480 Prepublication Copy Intelligence as an ability In the IPS theory, problem-solving is a broad construct that subsumes social and emotional as well as a cognitive activity. The solution of the problem is not based solely on ability but is derived by constant experience and exposure to existing and new problems in a domain of interest. Ability has genetic roots that are expressed through concepts related to fluid intelligence. There is not a doubt that solving academic discipline-based problems requires some ability. The problems in an academic discipline such as math, science or history require prerequisite knowledge which must be spatially and rationally transformed and manipulated. Similarly, problem-solving in the nonacademic and subsidiary areas uses specialized experience and abilities gained over time. Ability is this view can be considered more of talent and talents are usually learned over time. Again, that is not the dominant view of many authors in the field. There is a general consensus among researchers in the field about how cognitive abilities are related to each other and as a measure of intelligence. The most prolific theorists are Carroll (1993), Horn (1966), Vernon (1950), and Cattel (1971/1987). From a measurement standpoint, most of the early theorists have modelled general intelligence (g) as a major factor followed by broad groups of second and third level factors. Carroll's factor structures have wide acceptance. His structured model of intelligence uses two concepts originally coined by Raymond Cattell called fluid intelligence and crystalline intelligence. Fluid intelligence relates to sequential and inductive reasoning while crystalline intelligence includes verbal and reading comprehension. Another factor of Carroll's is knowledge and achievement which incorporates general school achievement as well as verbal information and knowledge. Perceptual speed memory and mental reasoning are also separate factors. Closely related vectors include visual perception and closure. The issue for many theorists is how to measure fluid intelligence. If fluid intelligence is a measure of sequential and inductive thinking, what types of items provide the best measurement? Are analogies a good measure of fluid intelligence and if so, what is their relationship to spatial processing? What type of items best measure the spatial qualities of fluid intelligence? Recent theory and empirical studies by Johnson et al. (2005) suggest that fluid and crystalline intelligence could be replaced by another model denoted as Verbal, Perceptual, and Image Rotation (VPR). The hierarchical “g” factor (general factor) of Thurstone (1938) consists of 3 broad highly correlated factors identified as verbal, perceptual and image rotation. In the model of Johnson et al., the three factors are then subdivided into 8 specialized factors. Verbal consists of verbal (6 tests), scholastic (11 tests), and fluency (8 480 | P a g e 481 Prepublication Copy tests); perceptual becomes number (10 tests), memory (4 tests), spatial (10 tests), and perceptual (14). Imagine rotation is defined by 4 separate tests. Speed of processing In IPS theory, the speed of processing is not paramount in the solving of problems, except in threat or controlled time testing situations. Problem-solving that is related to interest and work patterns are often solved by extending the amount of time devoted to the solution of the problem. That is the reason that differential problem solvers contribute so much to society. The differential problem solver, a group that makes up a large part of society, often gain expertise in areas of interest or work. Since time is not a pertinent or contributing factor, many hours of deep processing occur based on an individual’s resources and motivation. That is, the differential problems solver can use hours and moments of time outside of the normal expected working parameters. The research literature usually focuses on general problem solvers, people who solve academic problems (verbal, numerical, and spatial) quickly and efficiently. These general problem solvers receive reward and recognition for domain-specific problems in highly specialized fields as noted next in the studies of current literature. The current research literature on the speed of processing Energy, in the form of electrochemical activity, uses neural pathways as the basis of the mental speed, i.e., time parameters that measure the beginning and end of cognitive tasks. These chronometric cognitive tasks are often measured by two research paradigms called inspection time (it) and reaction times (rt). In general, the literature is replete with studies that suggest that mental speed, i.e., faster processing of information, is strongly related to a narrow construct of either “g” or fluid intelligence (Gf). In 1995, Eysenck in an article in Intelligence cited a host of research studies about cognitive speed which encompassed diverse racial and ethnic groups (Jensen, , & Whang, 1993; Lynn, Chan & Eysenck, 1991; Saccuzzo, Johnson & Guertin, 1994; socio-economic groups (Jensen, 1987); clinical status (Gold, et al., 1995; Kirby & Thomas, 1989; Wade, Newell & Wallace, 1978; Zahn, Kruesi, Leonard & Rapoport, 1994) and a variety of age groups (Anderson, 1988; Cerella, 1985; Jenkinson, 1983; Myerson, Wagstaff & Hale, 1994; Nettelbeck & Rabbitt, 1992; Salthouse, 1994; Smith, Poon, Hale & Myerson, 1988; Smith & Stanley, 1983; Tomer & Cunningham, 1993). 481 | P a g e 482 Prepublication Copy A review of 172 studies by Sheppard and Vernon (2008) reported an average correlation of -.24 between intelligence and speed of processing measures. Using Hunt’s (1980) threshold of .30 as a boundary for correlations, that average correlations account for 5 per cent of the variance. According to Schubert et al. (2015), this suggests that “more intelligent individuals have a higher speed of information processing;” the dominant view in the research literature today. Historical view Since the classical Greeks or British philosophers had little to say about reaction time or speed in processing, Myer et al. (1988) trace the history of mental speed back to the early works of Muller (1838). Muller conjectured that the rate of neural conductivity was similar to the magnitude of the speed of light (translation cited in Boring, 1950, p. 41). Myer et al. developed a family tree to show pertinent research studies over time. In their family tree of events leading up to today’s studies of reaction time, the diagram of elementary cognitive tasks (etc.), and inspection time included two main branches which began with Helmholtz (1850). Each branch was a major contributing author and the method of measuring reaction time. For example, there were: Donders (1868): subtraction method; Wundt (1880): analysis of processing stages, Neisser (1967): serial vs. parallel distinction, and McClelland (1979): cascade model. The other branch which traced reaction time followed Hick, 1952: the rate of transmission, and Wicklegren (1977): a critique of reaction time models. Their tree did not mention the early contribution of Galton (1890) who used reaction time to explain individual differences. Using a selection of over ten thousand men women and children Galton suggested that differences in intelligence were a reflection of variations in response patterns to sensory stimuli. Research in studies of mental speed today uses tests such as those devised by W. F. Hicks (1952) and Saul Sternberg (1966). Hicks nine tests have equal possible choices. By measuring reaction time during a trial, the experimenter determines the relationship between a number of choices and the time required to make a decision. According to Hick’s law, the individual’s reaction time increases as a function of the number of choices (complexity of the problem). Sternberg’s short-term memory test measure’s reaction time relative to the number of recalled digits. The subject must do a serial search of working memory to determine if a probe contained a previous set of digits. As the number of digits increases, the subject’s reaction time also increases. Both of these tests are crucial in measuring the increase and decrease in the individual thinking process. 482 | P a g e 483 Prepublication Copy Studies in the last 15 years have used a combination of cognitive tests, along with neurological testing. Extensive studies of the last decade use a plethora of intelligence measures. Regardless of the methodology, (e.g., protocols, scanners, and/or human samples), there is a consensus that IQ and cortical volume are robustly and positively correlated (Deary & Caryl, 1997; Wickett, Vernon, & Lee, 2000). For example, Wickett et al. (2000) found a significant relationship between cortical volume, fluid, intelligence, and memory but did not measure the speed of processing. Typically, correlations in these studies are about .40. The relationship has been hypothesized to be of genetic origin (Posthuma et al., 2002). Walhovda (2015) extended the study of cortical volume to include the speed of processing. Cortical volume was calculated as the size of the cortex, not the skull size, while intelligence was measured by the abbreviated form of the Wechsler Adult Intelligence test. Speed of processing was measured in their study using electrophysiological potential (ERPs). This methodology allows calculations in milliseconds, however, there are differences in opinion about what ERPs actually represent. In this case, electrophysiological potential represented speed. The researcher’s results suggested that cortical volume and speed of processing both are complementary in predicting performance intelligence (multiple R2 =.51). Categories of Perception, Conception, and Analysis Introduction Three of our measurement constructs have a cognitive bias as determined by neuroanatomy and neuronal processing. Perception is often associated with perceiving, attention direction, and visual search processes in the environment. Conception, with its adjective form of conceptual, has as its root meaning in “concepts” and is often associated with the generation of ideas, sometimes new, sometimes not. We often refer to the process as ideation as it is involved with idea generation. The third measurement construct is analysis –breaking a whole unit into smaller components parts. The three categories, in our opinion, are more closely associated with brain functions and cognition than with personality, although science has been very slow to provide separate explanations of how and why. 483 | P a g e 484 Prepublication Copy IPS theory- perception In the IPS system, we have preference tests to measure the selection of items that suggest greater use of perceptual actions. Likewise, we have cognitive tests that provide scores on the speed of processing, visual search, dis-embedding designs, spatial rotation, and arithmetic operations. The preference test items give information on preferences about attention direction and perception, while the cognitive tests provide an actual measure of cognitive speed and performance. Our cognitive tests involve visual search, mental image processing, and image rotation. The word “perceptual” is the adjective form of the noun termed perception. Perception refers to the detection of environmental stimuli. Physical energy is transformed into neural energy as we read a book, listen to a concert, smell cologne, or taste caviar. Often the process begins with an image developed from the external stimuli, but perception can begin with a simultaneous internal representation. Perception relates to concepts of attention in the research literature as attention is a broader construct that includes detection, filtering, and search. Detection is the presence or absence of a stimulus, filtering is the selection of one or more attributes, and search is the identification of a target amongst a large group of distractors. Our theoretical concept of perception begins with an individual’s choice of items that affect learning and understanding. That is, the person selects items related to visual, aural, and tactile stimuli that bring about learning or change. Our performance tests measure detection, filtering, and search. How does this approach relate to the historical studies of perception? Historical view The earliest questions about the concept of perception probably go back to the Greek philosophers, but we start with seventeenth-century philosophers. Descartes, in the seventeenth century, worked on the eye of an ox. His work revealed the basic properties of vision. Others, the British empiricists-- John Locke, George Berkeley, David Hume, and David Hartley, conceived of mental imaging as basic elements of thought. In the assessment of qualitative period, Galton (1880/1883/1907) used questionnaires to study images. From the questionnaires, he developed instruments to measure individual differences. Stimulated by Galton’s work, Itchier (1909) and Betts (1909) had subjects rate their ability to visualize objects such as 1) apples, 2) sun sinking below the horizon, and 3) the contours of the face. Visualization and perceiving objects were intertwined with mental imaging. During the period of the Behaviorist, studies on mental imaging waned 484 | P a g e 485 Prepublication Copy (Watson, 1913), but were revived mainly in the 1960s and 1970s as Sheehan (1967); Bugles (1970); and Pavia (1969) provided a substantive theory of how images and words are stored and represented. Neurocognitive scientist, Farah (1988); and Pinker (1985) provided additional theoretical considerations on the relationships of imagery and perception. Particularly important was the work of Shepard and Metzger (1971) on spatial rotation and reaction times. One of the major findings to come from the studies in the 1970s and 80s was that there are large individual differences in imagery ability. There are semantic differences in the cognitive activity of spatial relations, spatial manipulation, and visual search. Spatial relations are the ability to mentally rotate an object about its center (Shepard and Cooper, 1982). Rotations of the object occur around one or more axes (Shepard and Metzler, 1971). There are a variety of different objects from blocks to spatial representations. Spatial manipulation (termed spatial orientation by Ekstrom et al., 1976) is the ability to mentally manipulate an image into another arrangement. Visualspatial activities occur at different cognitive levels of abstraction and affect different parts of the brain depending on task goals. Visual search is putting a line through a letter in a crowded field of letters. Simple visual search (people, houses, letters, faces) activate the visual cortex while visual rotation activates the prefrontal cortex. Selective attention and memory are both actively involved. The fundamental problem for visual search is to determine precise target locations, without any advanced information. Eimer (1996/2008)) has divided the visual search process into 4 stages (preparation, guidance, selection, and identification) with neural feedback occurring in each phase. Visual search is a product of spatial global working memory. According to him, representations exist in the visual cortex. The issue is whether pathways associated with visual activity (such as goal selection) are position invariant. Or based on a shift in attention, and goal selection in the prefrontal cortex, does the pathway change? According to some authors, the activated patterns which are sensitive to current task goals may be part of top-down processing. As thinking proceeds, the prefrontal cortex controls target selection which is buffered by attention preparation and attention shifting. Similar to other researchers, Koffka 1935, Duncker (1945), and Wertheimer (1945) studied the cognitive operations of perception and thinking. They wanted to study the perceptions related to the stimulus configuration as a whole (Gestalt). Since they relied on an experience-based approach where subjects described their experience, their approach was named “phenomenological” from which they developed Gestalt principles. One of their major contributions involved changing one’s cognitive set. That is, according to the Gestalt psychologists, changing the way that a person thinks about a problem can led to better solutions and insight. 485 | P a g e 486 Prepublication Copy Gottschaldt (1926) was one of the first to examine the cognitive process of finding a camouflaged target. The target was a geometrical form, embedded in a larger more complex pattern. The problem of finding the target involved speed and thus was a measure of reaction time (RT). By manipulating a figure, that is, turning the targets, it was possible to measure different reaction times. The question was: “If presented with a target, how much time does the subject need to circle the embedded target?” Studies involving embedded figures often examined the effects of practice (Gottschaldt, 1926; Hanawalt, 1943). Practice or learning involved a different strategy of moving from the whole to looking for a specific target (Hanawalt, 1942). Research on this cognitive process was done by Thurstone (1938) using a factor analytic approach. Thurstone decided that the factor, defined by these types of perceptual tests, illustrated “Freedom from Gestalt Bindung” or a type of cognitive flexibility. Later authors called the process by different names such as Guilford’s (1967), “convergent production of figural transformation”, “closure flexibility” (Ekstrom, French, Harmon, and Derman, 1976), or Carroll’s (1993) perceptual speed. One kind of visual-spatial processing is called dis-embedding. Dis-embedding comes from the early of Gottschaldt’s (1926) camouflaged targets. In visual environments where multiple objects compete for attention, the challenge is to find relevant information and to ignore objects and events that are unrelated to current task goals. This is particularly true of part-whole relationships that involve a completely different part of the brain and encompass different kinds of cognitive processes than spatial rotation. This type of visualspatial processing is a left-brain activity and processed separately and simultaneously in the center for words and numbers. Often the terms field independence and field dependence are applied to this activity. People who are field independent tend to be highly analytic in their perceptions and parse information into organized units thus reducing size and complexity. Whereas people who are field dependent tend to process ﬁgural information spatially in its original (whole) form, making it more difﬁcult to disembody its component parts (Witkin, H. A., et al., 1977). Interesting enough, studies examining the cognitive concept of embedded designs suggest that the underlying process of perceiving, remembering and processing was a regularity develop around personality traits (Witkin and Goodenough, 1981). Witkin, who worked with both Koehler and Wertheimer, was struck by the consistencies of results involving the Gestalt-like tasks using the Rod and Frame Test (RFT) as well as the Body and Adjustment Test (BAT). The Rod and Frame Tests had a subject in a darkened room to view a luminous rod surround by a tilted frame that was set to true vertical while the BAT required a subject to sit vertically in a tilted room. Subjects who were highly dependent upon visual cues (field dependent) scored lower than subjects who were less 486 | P a g e 487 Prepublication Copy reliant on visual cues and more reliant on vestibular and gravitational cues (fieldindependent). Analysis Some people suggest “analysis” is of Greek origin; literally meaning up-release or separation. In Greek philosophy, the term meant the dissolving of a problem and was used by Aristotle and Socrates. (Byrne, 1997). In medieval times, Thomas Aquinas may have used a Latin derivative of the term to suggest a decomposing, an action prior to the concept in problem-solving known as synthesis (Sweeney, 1994). These interpretations contrast with the ideas of Sigmund Freud whose psychological therapy (i.e., psychoanalysis) consisted of free association, dream interpretation, and the exploration of repressed and unconscious impulses. How does this process work? When the memory store is in the form of an image, it is recalled as a mental representation. This image can be static, that is, appearing exactly as it is recalled. In such cases, the image is like a picture from a camera but exists only in a mind’s eye. The image can also be mentally rotated with energy. Try it. In your mind, think of the picture of your mother. Now rotate the image of your mother sideways. Can you, do it? This analytic energy process is called mental imaging. For example, sound out the word "mother" to yourself (aural form). Now--form an image of your mother. Visualized the spelling of the word "mother." All of those actions occurred in your mind, but for you, each process is individual. The actions involved more than memory since the forms differ as sound or image. At one level, the process of visualization requires the representation of mental images. At the molecular level, the biochemical process is indeed an energy transformation in the brain. This transformational process involves electron transfer from chemical units. Before we look at the complicated mechanisms which are involved at the cellular level. Let’s just do some visualizing. If you spent a lot of time thinking, were you tired? Do you remember studying in school, sitting for a period of time working on a school lesson? If you had to work for an exceptionally long period of time, were you not tired, perhaps exhausted. To say that thinking involves energy utilization is a reality, not an imposed supposition. Analysis is a transformation of energy generated during a particular form of thinking. In an analysis, a person is trying to find out how parts are linked so that the whole can be decomposed or broken down. For a simple problem, minute amounts of energy are used. For a complex problem, tremendous amounts of energy are used over an extensive amount of time. Certainly, thinking about routine things (figuring out what time you are going to work, or picking up the kids) does not involve as much energy as spending hours 487 | P a g e 488 Prepublication Copy writing a paper or solving a complex mathematical equation. The writing of the paper and the solving of complex mathematical equations require more time and thus more total cumulative energy. Time, the condition of observance, and energy are related to Einstein’s theory. Now to the cellular level for the mechanism of how it works. Remember earlier we suggested that E=Mc2 (energy equal to mass times the speed of light squared) may have an application to biological not just a physical phenomenon of the universe. What did we mean—a literal application? No! Simply, the characteristics and functions of energy transformations at the subatomic level, as held in the quantum theory, are similar to those at the subatomic level in biological processes. Since electron transmission occurs in both, the characteristics of electron transmission are similar (again, see the reference Chapters 23 and 24). What are some of the similarities? First, Einstein’s equation refers to light or photons. In the equation, light is constant (186,000 miles per hour) and time is the differential. In Einstein's theory of special relativity, time is different relative to positional variants. With the constant of light, it is time that differs. For example, assume one is inside a fast-moving space capsule and wishes to measure the movement of sand in an hourglass, using a light clock that is one meter long. The metric for time is 1 sec per movement of 1 meter. The spaceship is travelling at a very high rate of speed. When an hourglass is turned over, the sand travels to the other end in 5 seconds. Since we defined the metric for a time as 1 sec per 1 meter, the spaceship should travel 5 meters in 5 seconds. However, when viewed from outside, light travels in waves (not at a different speed) but at a time which is different from that which has been calculated inside. Instead of moving 5 meters based on the time that the water travelled inside the spaceship, the fast-moving spaceship travels 7 meters. In other words, the time has expanded; the amount of time is 7 seconds when calculated from the outside versus the time differential of 5 seconds calculated inside. For the sake of clarity, let’s use the same analogy but apply the phenomena to biological function. Rather than referring to photons, let us refer to our concept of “neuphons”. For neuphons (see Chapter 23) we change the formula slightly to Energy=mass multiplied by the (velocity) of the energy emitted by a moving particle during chemical reactions. We are suggesting that time differentials including time expansion, occur at the level of the neuphons. In essence time at the quantum level has passed differently for the particles (neuphons). This difference leads to differences in perceptual and neuron transmission or speed of processing. In other words, energy transformations at the quantum level occur differently for individual people. This leads to differences in analytic thought. We addressed the issues of biological energy in Chapters 23 and 24 including the action of the Krebs cycle, enzymatic activity, and formation of ATP and ADP. Most of the actions of energy in the biological system involve chemical reactions with different masses 488 | P a g e 489 Prepublication Copy (organs, organelles, chemical elements, and chemical compounds). Remember the energy released by hydrogen in the Krebs cycle (velocity of energy from moving particles) moving between different chemical compounds (mass), and the low-temperature enzymatic reactions (energy from the velocity of moving particles) which increase or decrease the energy reactions (mass associated with chemical compounds). Perhaps a better formula for biological functioning becomes E=M (mass) x (speed of the energy (electron orbital shift) or E=Ms2 in chemical reactions. Ion exchange, a constant process involved in the neurological transmission, involves mass (ion, an electrically charged particle) and the velocity of the moving particle (exchange of ions between compounds). If the formula E=mass multiplied by the (velocity) of energy from a moving particle) has a basis, why have we not been able to measure it successfully? For the answer, read superstring theory in Chapter 23 and think about the fact that gravitational waves have only recently been discovered. Chapter 24 explains how vibrations (energy waves) maintain self-consistency, and how the rotations of quarks (the smallest known particles of atoms) may be conceived in terms of superstrings. If the superstring theory has any validity, then the energy reactions of the biological systems may take place, not in our conventional one two or three dimensions but mathematically, like those in superstring theory, in 10 dimensions. The IPS theory posits that the release of energy in mathematically higher dimensions, the 10th dimension, constitutes a form of thinking known as analysis. In other words, in the previous examples related to our cognitive tests, the operation in the brain which results in the symbolic rotation of the mental figures in the brain is an energy process that we define as thinking. When Einstein was trying to resolve his equations about a form of energy called light, current theory in physics suggested two different approaches. The first theory was that light travelled at variable speed while the second theory suggested that light travel at a fixed speed. To resolve these inconsistencies, Einstein focused on time and the meaning of the term “simultaneous.” Time, according to Einstein, was simply a variable that was measured according to a derived standard. In his analysis, he suggested time was a variable that was measured differently according to whether an observer was moving or standing still. That is, when measuring 2 bolts of lightning, the meaning of ‘simultaneous’ is relative to the condition of observance. As an example, consider the same event from two different perspectives. First, imagine a man standing on a train platform who observes 2 bolts of lightning striking an equal distance from him. Second, think of a woman who observes the same 2 bolts of the lightning strike; however, she is travelling on a train passing the platform on which the man stands. Again, for the man the observation occurs while he is standing still. For the woman, the observation occurs travelling close to the speed of light. Both people observer 489 | P a g e 490 Prepublication Copy the same 2 events. For the woman, she sees the first bolt of lightning strikes the platform at one time and the second bolt of lightning strikes at a different time. The man sees two bolts of lightning striking at the same time or simultaneously. Thus, the meaning of simultaneous is relative to conditions of observance. This observation that time and space were relatives was central to Einstein’s theory of special relativity. Now let’s take another example but at the level of quantum mechanics. But first let us review some basic properties, according to quantum mechanics, wave-like subatomic particles may be here or there or here and there. These entities may also exhibit properties of entanglements, self-consistency, memory, and maintenance. Assume that one is trying to observe these subatomic particles—mesons, positrons, etc. The debate in quantum mechanics is similar if one argues Neil Bohr’s (Bohr, 1963) position. Subatomic particles seem to follow the laws of randomness. That is a wave-like particle may be here or there but impossible to predict. One cannot indicate with certainty that a subatomic particle is going to be a certain place, but one can say that at the time of measurement (observance), that there is a greater probability that one might find more subatomic particles where their wave-like occurrences indicate. That is, the meaning of the measurement of the subatomic particle is relative to the conditions of observance similar to Einstein's special theory of relativity. Analysis as logical thought We just examined the process analysis as simple discrimination and the breaking down into components or parts. Now we examine the process of analysis as reasoning or logical thought. Is analysis the same as reasoning or logical thought? Not as it is used in our theory. Reasoning uses a form of rules and relationships where the outcome can be verified by others. Analysis is simply dissecting or taking things apart. One can analyze a situation by breaking it into smaller segments or scenes, none of which require that the outcome is logical or verified by others. On the other hand, one can attempt to make an analysis logical. If others can verify the outcome, deductions, and inferences, and how the individual pieces fit together, the analysis is logical and follows the rules of reasoning. In the IPS theory, analogies and sequential thinking represent the individual’s performance on logical thought processes. Our performance construct of logical thought is based on understanding the relationship between verbal constructs as well as being able to infer sequences. We have tested children and adults at all different ages (6-82) with analogies and sequence problems. The analogies are based on the construct of fluid intelligence. Data suggest that fluid intelligence is very important at a very young age but less importance outside of discipline-based, structured knowledge or as the complexity of the problem increases. In complex problem solving, divergent thinking and evaluation are as important as convergent thinking involving logical thought. 490 | P a g e 491 Prepublication Copy As is shown in later chapters, there is a cascading development effect on the scores of analogies and sequence items from the very young to older adults. That is, young children have low scores on analogies and sequence items while older children and adults have much higher scores. there is a large variation in scores on these items for different age, ethnic, educational, and gender groups. Theoretically, there should be a difference in those who select preference items indicating “a person likes to take things apart” and a performance score on problems requiring analysis of smaller units. However, in reality, the correlation coefficient of groups of people who respond to both preference and performance items in our data, taking into an account sample size, is significant. Studies in the area of neurocognition (Gazzaniga & Sperry, 1967; Corballis, 1989; and Milner, 1968) and clinical observation by Luria (1976/1979) and Farah (1988/1995), address the functions of lesions in the brain and impairments. The finding from these studies supports the theory that in the logical thought process, there is a different method of coding and at least two methods of storing information. One system is for coding or processing of visual information: another for the coding or processing of verbal information. Thus, different pathways exist in the brain for processing verbal (words) and visual (spatial) information. How did early theorists conceive of these processes? Historical view The study of cognition as logical thought combines ideas found in both the syllogistic and informational processing of analogies. In one sense, the analogy is propositional. Following the form of A: B: C: D, or (9:36:1:4), individual processing requires memory, discrimination, and isolation of distinct patterns. Finding an answer to an analogy requires an understanding of concepts in language and the ability to infer relationships. This entails picking out patterns, identifying a recurrent theme, and manipulating symbolic abstractions. The historical records of many cultures emphasize the unique place of analogies in religion, literature, and philosophy (see Holyoake and Taggard, 1995). Early Greek and Roman Civilizations used analogies as tools for advancing science, especially in the building of aqueducts and structures to bring water from distant sources. One of the earliest recorded uses was in a scientific theory about how sound is propagated. Many philosophers, theologians, and psychologists have studied the area of cognition as logical thought. One of the earliest to deal with the concept of logical thought was the student of Plato known as Aristotle. Being an astute observer, intensely concrete, and practical, Aristotle relied on his sensory observations to develop a coherent system of philosophical thought. To know or understand, one used the instrument of logic (“organ 491 | P a g e 492 Prepublication Copy on”) or the formal rules for correct reasoning. Aristotle’s basic principles of categorical thought were accepted by western philosophers until the nineteenth century. Of recent note is the work of Jean Piaget (1954). Piaget’s theory of logical thought was embedded in his developmental theory about children’s thinking. According to his theory, children develop mental structures and accommodation by reacting to external stimuli. Early information is sensory motor. Through the process of assimilation and accommodation, schemas are developed. The process continues throughout adolescence when formal logic develops. In the final stage of formal reasoning, children can construct a combination of elements, isolate and manipulate concepts, and form mental representations of abstract ideas and events (Favell, 1963) Johnson-Laird and Wason (1972) suggested that one line of research on cognition as logical thought could be traced to the Wurzburg school and Gestalt psychology while a second line was related to the behaviorist school. Current researchers who study logic are divided into three camps a) those following Piaget b) those who used a psycho-linguistic approach (propositional and syllogistic) and c) those who follow informational processing theory. Most current researchers have concluded that working memory (memory activated to accomplish an immediate task) is of paramount importance in the development of logical thought. Other factors related to logical thought include the ability to inhibit irrelevant stimuli or incorrect alternatives, the increase in domain-specific knowledge, and the ability to integrate various abstract representations with existing memory. Conception IPS theory-conceptual As noted earlier, the root meaning of conception comes from the word “concept”, a term that signifies the unique ability of individuals to derive a common set of ideas about a class of objects. The adjective form is conceptual. Cognitively, conception is measured as ideational content, word, and/or verbal fluency. Having conceptual ability allows individuals to categorize and sort by common characteristics and to put objects and things that are similar in a common group. It also allows for common associations of classes. With this unique capability, individuals can quickly relate to and associate common ideas which increases communication. A friend of mine is a classic conceptualizer. In almost every discussion, he plays words against words as a form of humor. Another friend constantly finds unique associations with sports concepts. Reading the classic quotes and quips of Mark Twain (My complaint 492 | P a g e 493 Prepublication Copy simply concerns the decay of the art of lying---Twain, 1880) and Will Rogers (I never met a man that I didn’t like- Smallwood & Gragert, 2010) helps one idealizes the meaning of conceptual. In IPS theory, ideas are one of the basic units of our base scale known as Conceptual. Most people are familiar with the concept of an idea. An idea is a mental formation, often in graphical form, which comes from generated concepts. Ideas come from real-life experiences, past or present, and represent knowledge, thoughts, opinions, convictions, or just abstractions. To some people, an idea is conceived as a funny graphical image of a light bulb emanating from a head, signifying the generation of new or novel solutions or ideas. For us, ideation is the process of generating and implementing ideas, either at the applied level or at a level of abstraction which may or may not have immediate application. In the latter case, the abstraction may be new, novel, different, or divergent processes which are defined as creative ideation. In contrast, according to IPS theory, people who apply ideas to everyday phenomena, objects, or common-sense situations are defined as applied or practical ideation. To summarize, ideas are just thoughts and concepts applied in different ways to different things. The majority of people apply ideas to different situations every day. One usually responds, “Great idea” when these ideas are suggested as a solution to the problem. They are useful ideas, very practical, and applied immediately to the situation at hand. Creative ideation may be less useful but more novel, different, or abstract and not easily applied. In some cases, the value of an idea may not be evident until years later. In our model, each person has the same cognitive structures with which to produce ideas. Individual variation is the result of long-term memory, existing knowledge, exposure, and various personality traits such as persistence. Individuals use the same cognitive structure to either refine existing knowledge or transform existing knowledge into a new form of original knowledge. Historical view Historically, most researchers are interested either in creative people as a group or the personality characteristics which characterize the creative person. Thus, the body of research on ideation and conceptual thinking is found in the literature about creativity. The review generally comes from 3 different viewpoints: a) animal research b) evolutionary development of humans and c) studies that characterize the creative persons. 493 | P a g e 494 Prepublication Copy Animal research Generating and exploring the implication of an idea is the essence of creativity. Animal studies in comparative psychology suggest that animals use creative ideas in the form of “insight” learning. In “insight” studies, animals are given problems which involve their ability to go beyond the existing fact present in real life situation. For example, for a rat in a maze to retrieve food, the animal must learn new routes or use unfamiliar tools for retrieval. This exploratory behavior may require rehearsal, elaboration, and evaluation before choices are made. Generally, the tasks involve the prefrontal cortex as well as controlled working memory. Taylor et al. (2010) noted a case of insight learning involving the Caledonian Crow. After observing an experimental situation for over a minute, the crow was able to retrieve food from within a cage on the first trial. Other studies involving monkeys and rats have suggested a similar problem-solving solution. Simonton (2003) suggests that conditioned animals deviate from a suggested pathway to exhibit psychological creative behavior. Of course, there is only inferred evidence of how “insight behavior” occurs in animal research studies. Evolutionary development Ideation is common to creativity when viewed in an evolutionary context. Across the ages, people have developed new ideas and ways to adapt to the environment. The majority of evidence about creativity comes from the collection of ancient artifacts discovered in major digging sites. According to many evolutionary historians, early hominins were skilled in making stone tools. The making of stone tools requires the shaping of objects by cutting and striking. Although the reconstruction of the shaping technique is inferred, trial and error techniques were probably part of the technique. Early men had to plan to sequence the proper strikes on stones (Schlanger, 1999). Again, the making of tools may not exhibit creativity or novel ideas until new and different shapes and figures were made. The earliest known artifacts come from the era of Homo heidelbergensis (Coolidge and Wynn, 2009). Some authors argue that for ideation or conceptual behavior to develop, there must be a cultural framework that rewards it. Creative products in societies (art, jewelry, painting) began about 50,000 years ago while Homo sapiens emerge over 100,000 years ago (McBreaty and Brooks 2000; Henrich, 2004). The creation of new and different ideas is displayed in 494 | P a g e 495 Prepublication Copy many different forms such as poetry, dance, music, body art, and written narratives and myths (Pinker 2003). What evolutionary changes led to people who could generate new and different ideas? According to some authors, the differences in cerebral cortex size are implicated. Coolidge and Wynn argue that the distinctive enlargement in the posterior parietal cortex is the culprit. This region is implicated in human working memory (Bruner 2008/, 2010). According to some researchers (Jonides et. al., 2008), the difference in cerebral cortex size led to creative differences in the two species of early man (Homo sapiens and Homo neanderthalensis). Philosophical period There is authoritative disagreement as to whether early philosophers--Plato, Aristotle, and Socrates mentioned the creation of new ideas or creativity in their writing. Most early authors tend to discuss creativity from the standpoint of cultural history. Thus, the creation of new ideas is interpreted in terms of language development, painting, arts, sculpture, and the production of great works. In this context, creative works have existed since the earliest civilization when writing on walls in Egyptian societies was a way of telling stories or recording historic events. In the early days, stories and ideas were passed orally--generation by generation. As such, many types of myths were part of the cultural heritage. This is illustrated by divine being or gods having superlative creative power. Many doctrines of the Muses were creative and recorded heroic and epic situations. Muses presided over many of the arts such as heroic and epic poetry, tragedy, comedy, music, and dance. Many authors chronicle the research on new and applied ideas within the context of the famous schools of psychology--Gestalt, Behaviorism, and Psychoanalytic. The Gestalt school, particularly studies conducted by Wolfgang Köhler (1925), was the source of insight studies cited earlier. In the problem-solving exercises of the Gestalt school, creative outcomes involved the restructuring of the problem, so the problem was perceived in a new light. Skinner, the name most associated with the Behavioristic movement, only wrote tangentially about generating new or applied ideas. He was more interested in the arts in general. The psychoanalytic tradition emphasized creativity as part of psychopathology as well as normal functioning in humans. Freud related the creation of new and applied ideas to daydreaming. This line of thought was not unusual in those days as other authors conceived of creativity and idea generation as being related to the mad genius phenomena. 495 | P a g e 496 Prepublication Copy Quantitative period The assessment period began with Galton who examined individual differences in human abilities. Galton, a mathematician, was exposed to Darwin’s Origin of the Species which led him to investigate the degree to which human beings were subject to natural selection through biological inheritance. His monograph of 1869 “Heredity Genius: An Inquiry into Laws and Consequences” addressed issues relative to creativity. Galton’s monograph provides a basis for other researchers such as Terman (1916) to give a range of scores on an IQ test that defines ‘genius.” Later researchers examined the notion of whether a person defined as a genius (a high IQ) could be defined as creative. (Gardner, 1983; Simonton, 1999; Sternberg & Lubart, 1995). Psychometric studies IQ tests measure abilities, including an IQ of over 130 as a genius, but does it also measure ideation? Most researchers developed separate instruments to measure ideation or creativity, depending on how it is defined. Is ideation or the conceptual ability the capacity to generate remote associations or to give a large number of associations to various stimuli? Is the creative person more likely to generate different, original, and unique categorical responses to a stimulus? That was the question for Mednick (1962) and Guilford (1967) as their studies on divergent thinking and convergent thinking heralded a new era in the research of creativity. Other researchers decided to cast the questions in a different light by asking- What are the personality characteristics of a creative person? Perhaps for many researchers, the assessment instrument defined the answer to the question. Some authors used the Minnesota Multiphasic Personality Inventory (MMPI); or Eysenck’s Personality questionnaire (e.g., Eysench et al., 1992; Barron, 1969; Cattell & Butcher, 1968; Francis et al. ) while others used Gough (1970) the Creative Personality Scale constructed from the Adjective Checklist. Torrance (1962, 1974), building on the work of Guilford, continues the study of divergent thinking and added scales to measure the resistance to flexibility closure. Are the mental processes that define a creative person different from those defined as less creative? According to Ward (1999), mental processes are the same but are used differently by different people. One person may draw on existing knowledge to create a different outcome from another person. According to Simon (1995), providing background knowledge to problem situations changes the formulation of the problem and the outcome of the solution which may be defined as creative. For example, Weisberg (1999) argued that sudden insight (creative thought) is the result of a series of small incremental steps. In other words, creative insights occur over time, rather than a brilliant 496 | P a g e 497 Prepublication Copy flash of insight. The new idea may be an old idea or existing knowledge modified and elaborated. Brain Studies Several studies of the brain have alluded to or studied creativity about differences in males and females as well as differences related to creativity in general. One study addressed differences in males and females concerning 4 divergent thinking tasks. There were no overall differences in a creativity index derived by the researchers but when specific tasks were analyzed then male and female differences appeared. In females, specific areas of the brain were identified (modularity) with less connectivity, suggesting that females’ creativity was related more to the task involved (painting, music, sculpture). In contrast, in highly creative men, the areas of the brain that were identified were closer in location and there was greater connectivity to different parts of the brain. Chapter summary IPS theory has 10 basic constructs with 3 of those driven by energy relationships, i.e., perception, conception, and analysis. These three constructs along with energy are traced through various historical periods and IPS theory. Neuronal energy, as the engine of cognition, is important as it undergoes various transformations to produce ideas, concepts, and a means of perceiving. The transformations of energy include its chemical components as well as its electron movements along the nerve fibers. Sensory input via the senses of feeling, hearing, and seeing represent occurrences in the environment. The order of the relationship is first to perception, second to conception, and third to analysis. Philosophers and armchair theorists have speculated on the meaning of these integrative actions of perceiving, conceiving, and analyzing for years. During these periods, many people suggested that the trio manifests actions in neural pathways which result in characteristics of ability. Other people have separated the actions into qualitative and quantitative outcomes related to creativity and intellectual capacity (ability). A final group of researchers suggests that each outcome is a separate function understood by its actions on objects in the environment. Chapter references Barron, F. (1969). Creative person and creative process. New York: Holt, Rinehart, and Winston. 497 | P a g e 498 Prepublication Copy Bohr, N. (1963/1987), Essays 1958–1962 on Atomic Physics and Human Knowledge, reprinted as The Philosophical Writings of Niels Bohr, Vol. III, Woodbridge: Ox Bow Press. Bruner, E. 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(1981). Cognitive styles: Essence and origins: Field dependence and ﬁeld independence. New York: International Universities Press. Witkin, H. A., Moore, C. A., Goodenough, D. R., & Cox, P. W. (1977). Field dependent and ﬁeld independent cognitive styles and their educational implications. Review of Educational Research, 47(1),1–64. Further Reading. Bohr, N. (1914). The spectra of helium and hydrogen. Nature. 92 (2295): 231–232. Kohler, W. (1947). Gestalt Psychology: An Introduction to New Concepts in Modern Psychology. Rev. ed. New York: Liveright. Milner, B., & Petrides, M. (1984). Behavioural eﬀects of frontal-lobe lesions in man. Trends in Neuroscience, 403–407. 502 | P a g e 503 Prepublication Copy Schlanger, N. (1999) Early Hominid Stone Tool Production and Technical Skill 2.34 Myr Ago in West Turkana, Kenya.” Nature. 399. Sweeney, Eileen C., 1994, Three Notions of Resolution and the Structure of Reasoning in Aquinas, The Thomist, 58, 197-243 Cattell, J. M. (1890). "Mental tests and measurements." Mind, 15, 373-380. In Cattell, R. B. (Ed.) (1950). Personality: A systematic and factual study. New York: McGraw-Hill. Torrance, E. P. (1988). The nature of creativity as manifest in its testing. In R. 503 | P a g e 504 Prepublication Copy Chapter 26 Review: Personality Introduction In the IPS theory, personality is the energy associated with emotion and affect which is manifested by different forms of self-regulation, i.e., control and/or less control. Traits and states are short and long-term reflections of energy directed toward objects and people. Emotional energy directed at people is social while emotional energy directed at objects is less social. The concepts of social and less social, control and less control, reflect substantive differences that directly affect the types of problems that one chooses to solve. How do these personality traits influence the problem-solving process? If traits are influential, which trait is the most dominant in simple and complex problem-solving? Which personality trait is most likely to influence the solving of words, numbers, or spatial problems? We provide a foundation for answering these difficult questions by examining the history and origin of various personality traits. Extraversion/Introversion, Conceptual, Motor, Social, Control, Flex, and Achievement Motivation- and applying this information to the problem-solving processes in the early chapters of this book. Historical view There is not a single definition of personality, although most personality theorists would agree that personality represents how the behaviors, emotions, thinking, feelings, and actions of the individual influence the environment (APA, 2000). Others, such as Jung (1953), perceived personality as a persona or mask, surface characteristics, generally more social, but hiding the true nature of the self. A review of the literature confirms that there are hundreds of theories on personality as well as many isolated measurements of personality that are not based on any theory. These range from humanist, trait theories, type theories, and psychoanalytic theories to more behavioristic and bio-psychological theories. A few theories contribute substantially to the IPS framework as IPS constitutes both a temperament and trait approach. Many psychologists argue that personality consists of a broad range of individual traits that emerge later in life while temperament encompasses more narrowly defined consistencies appearing earlier in life. Since ours is a developmental model of both 504 | P a g e 505 Prepublication Copy children and adults, we use both temperaments and traits in our review. See other authors who address the same issue (Caspi & Shiner, 2006, Clark & Watson, 2008, McCrae et al., 1994, and Zentner, & Bates, 2008). The concept of temperament has a long history, beginning with the ancient Greek idea that a person's typical mood and behavior result from the balance of four humors in the body: blood, black bile, yellow bile, and phlegm. In this perspective, temperament emanated from biological and emotional processes, a view consistent with the current conceptualizations of temperament (Clark & Watson, 2008; Bolger & Zuckerman, 1995). In more recent times, the empirical study of temperament in childhood stems from the work of Alexander Thomas and Stella Chess, who started a longitudinal study of children’s early-emerging behavioral styles in 1956 (Thomas, et al, 1963). To those authors, the child’s socialization experience was the primary source of one’s personality. The research of Thomas and Chess also emphasized biological differences that are important in a child’s total development. Rothbart and colleagues argue that temperament was more inclusive. For them, temperament includes individual differences in affect, activity, attention, and self-regulation (Rothbart & Bates, 2006). In contrast to temperament, there are many traits theories and general theorists. The American Psychiatric Association (2000) suggests that personality traits are “enduring patterns of perceiving, relating to, and thinking about the environment and oneself that are exhibited in a wide range of social and personal contexts.” Certainly, the early works of C.G. Jung (1916), Raymond Cattell (1963), Gordon Allport (1921), H. J. Eysench (1947), and Lewis Goldberg (1992) were influential in establishing a basis for trait theories. Later authors, Costa, McCrae, R., and Tellegen (1992) provided support for a more succinct group of measurement factors (Big Five) related to traits. Personality Trait-Extraversion/Introversion IPS theory-extraversion/introversion Extraversion and introversion have been studied for many years by many different researchers. Introversion, extraversion, and ambiversion are measures of energy flow, either inward or outward or both. We summarize our thoughts about the constructs and then give the historical view. From our theoretical perspective, the extrovert manifests his or her “energy” in finding others to engage, converse with, and interact with. The extrovert is more likely to talk 505 | P a g e 506 Prepublication Copy and seek out others. Talking and conversing is a mechanism for expressing inner thoughts about daily experiences and feelings--- becoming energized. Likewise, the extrovert prefers to be engaged, and involved in social activities where emotions, feelings, and spirit can be exhibited. Ambiverts, the group between the extrovert and introvert, is just as important in IPS as either extraversion or introversion. In our view, the ambiverts are a real identifiable group. This assumption holds true for others who score as the in-between groups on our measurement subscales. Ambiverts exhibit patterns of both introversion and extraversion. The traits which are exhibited depend on situation and circumstance. The preferences of ambiverts are just less defined in either direction. Introversion is a preference, not a condition. An introvert can be warm, affable and have concern for others. In contrast to stereotypes, introverts are not necessarily shy. Introverts are often problem-oriented as the problem is a matter of puzzlement. Enjoyment, for the introvert, is interacting with thoughts, ideas, and things. The introvert, in contrast to the extrovert, may or may not want to talk about feelings. Instead, the introvert may prefer to engage others in discussions about an object in question, be it a book, a concept, or perhaps an art piece. The study of the object of interest requires interaction with the object, just as reading a book about art provides the information to be discussed. An object in the environment is the source of interest. This often results in the introvert spending an inordinate amount of time with things. The type of work chosen for a lifetime often contributes to patterns of introversion as well as extraversion. Historical view Allport In 1936 using 18000 terms in Webster’s International Dictionary, Allport and Odbert published “Trait-Names: A Psycho-Lexical Study”, a paper designed to uncover the “underlying structural units of personality” (Allport & Odbert, 1936, p. 353). One of the most dominant traits addressed by Allport was the concept of introversion and extraversion. For Allport, introversion and extraversion were adjustments to environmental stimuli and situations, traits that can be independent statistical variables. Many studies in the research literature indicate the tri or bipolar nature of the concept called extraversion. 506 | P a g e 507 Prepublication Copy Early theorists To many, extraversion/introversion is a bipolar construct (example: hot water-cold water) with extreme attributes more readily studied and classified. In contrast, the middle layer of scores (for example -warm water) may or may not have different characteristics than the extremes. The tendency is to assume that the middle distribution of introversion and extraversion is really a combination of the traits denoted by the extremes (Cohen and Schmidt, 1979). However, the middle may either represent a different and unique group or perhaps a tendency to mark a scaled from 1-5 items in the mid-range of 3. Conklin (1923) introduced the term “ambiversion” to describe this middle group. In his analysis, ambiverts were people who consciously fluctuated from introversion to extraversion or vice versa. Guilford and Braley (1931) noted that introversion and extraversion are states of mind which as “can be turned on and off at will.” Thus, the introvert can be an extrovert; just as the extrovert can be an introvert. The extremes of the continuum can be more easily identified; but those in the middle, the ambiverts are not as easily categorized or identified. The early work of Jung (1925) focused on the psychodynamics of the construct while the latter work of Eysenck (1947) addressed the behavioral aspects. Jung (1920) identified the energy of the mind as libido and characterized extraversion as the flow of “libido.” For the introvert, the flow of the libido is from the object to the individual. Jung’s theory assumes that one is characterizing a person whose behaviour is modified by the situation and has other characteristics that intertwine and mingle with the major tendency of extraversion. The general descriptions provided by Jung are often so broad that they can encompass so many different types of people. They represent tendencies or implied patterns. As Jung indicated these patterns represent mental mechanisms that can change at will with situations. Thus, the introverts “extroverts” or vice versa when put in a position required by work (giving a presentation), acting as a host of a gathering of friends, or required by a general activity to show some inner part of their personality. McDougal and Kempf McDougal (1926) suggested that on the basis of his data that introversion and extraversion are indeed opposite tendencies of temperament. Kempf (1921) noted that these different tendencies result from a general property of the autonomic and central nervous systems. The chemical nature of these systems is such that energy can be shifted, either by increasing or decreasing resistance through the neurons and at the synapses. The basis of McDougal’s theory was witnessing of the marked effect of drugs with various individuals. If introversion and extraversion are measured on a single scale with a central point, maximum and minimum, then the individual’s response on the scale is shifted toward 507 | P a g e 508 Prepublication Copy one end or the other by various drugs. For example, one may become more extroverted with alcohol, chloroform. or either; while others may become more introverted by alkaloids, strychnine, or morphine. McDougal further suggests that cyclomanics and hysterics (extreme extroverts) can be shifted through hypnosis. In other words, temperament (introversion and extraversion) can be affected either by outside influence or internal neurotransmission which may, in fact, be genetically determined and environmentally influenced. Other theorists Most theorists and researchers assume that extraversion is a higher order construct that subsumes lower order dimensions. H.J. Eysenck’s (1947) theory had two factors Extraversion and Neuroticism and a later factor of Psychoticism (1963) while Raymond Cattell’s found a higher order factor called “Extrivia” which is a combination of lower order traits on the 16 PF. Cattel’s Scale B (intelligence) was a simple ability scale of 10 analogies that was integrated into his instrument but did not show a relationship to Extrivia, the extraversion -like scale. Two reviews (Digman, 1990 and Goldberg, 1992) suggested that personality can be explained by 5 broad factors. The five-factor model, also known as the big five, is widely researched. Costa and McCrae (1992) conceptualized the five factors which are called extraversion, agreeableness, conscientiousness, emotional stability, and openness to experience. These five factors of Costa and McCrea can easily be interpreted by using marker adjectives developed by Marco Perugini et al. (1996). In developing the adjective list, Perugini and co-authors used different approaches. The first was the 100 adjectives list from Goldberg (1992). The second used the big five intrapersonal adjectives by Trapnell and Wiggins (1990) and was based on pyscholexical tradition adapted from Hendricks, Hoftee, and De Raad (1999). The adjectives are illustrative and are listed in the Appendix. Overall, they provide definitive insight into the meaning of Costa and McCrae’s five factors. Personality Trait: Sensory Motor In the IPS theory, we use the general classification of the motor as an abbreviated form of the well-known term--sensory-motor or kinesthetic. The category which represents a group of people as Motor represents a broad construct and originates from those who in the early years of life relies heavily on the sensory-motor and bottom-up processing. Their 508 | P a g e 509 Prepublication Copy life is dominated by physical activities, concrete objects, and practical solutions as they mature. The skill in finding, naming and manipulating concrete objects suggests the ubiquitous nature of this kind of people in many vocational areas. A large proportion of the population falls in this category as it includes people with fine and gross motor skills as well as those people to whom physical activity skills are a part of vocational life. For example, a bodybuilder, mountain climber, and an athlete are included at one end of the vocational spectrum. A seamstress, a sculpturer, an engineer, and a person in a shipping department might be on the other end. In the early years of research on motor development, the constant question was: “What or who is in control. Is control related to the brain, central nervous system, or local muscle mass? According to Schmidt & Lee (2011), the obvious choice is the brain, but in an integrated system, all parts of muscle masses function together simultaneously to bring about coordinated action. From conception, according to embryological development, there is gradual unfolding as cells interact with their environment. After birth, continuous development of all organs, bones, and muscles brings about integrated functioning. Some muscles, bones, and organs do not reach maturity until years after birth. During infancy and childhood, muscles receive additional training by those athletes who rely heavily on sensorimotor systems. Those same people continue to train or use their bodies in primary activities for years to come. The dominant strength of this group come from bottom-up or sensory-motor processing. Bottom-up processing suggests that reflex arcs and motor neurons are processed quickly which could result in a speed of processing as well as intellectual functioning. Many academic journals such as Perceptual Motor Skills are devoted to the myriad of topics concerning motor skills. Distinctions of motor skills range from observable behaviours such as the change in joints position or movement of the body or both. Related topics include motor learning, motor control and cognitive strategies used for coordination of muscle groups. Because mental and physical health issues impede motor activity, many writers make comparisons between unimpaired individuals and recovery in impaired individuals. Interactions of bodily-kinesthetic activities with cognitive strategies for reaching goal attainments cue sharp categorical distinction about objects and people in the environment. As such, people in this category develop very concrete ways of handling existing problems. Adjectives that characterized motor children and adults and their orientation in the IPS system include practical, efficient, and realistic as well as body driven, competitive, and athletic. 509 | P a g e 510 Prepublication Copy Historical view: Most of the early theorists and researchers of motor development had deep roots in biology and wrote about brain and motor development as unfolding. That is, there were critical periods in which morphological changes occurred leading to body and organ maturation at different ages. Biological processes shape human development. Perhaps Darwin (1877), who studied his own children, was one of the first to informally write about motor development. Certainly, the contribution of Arnold Gesell 1933) and Nancy Bayley (1936) was important for normative comparisons of infants and adults. Both Mary McGraw (1945) and Mary Shirley (1931) contributed to their studies of infants. The early emphasis in these research studies was on observable changes in motor development and descriptive change. Interest waned in studies of motor development in the period from 1946 through the early 60s. Those years are often called ‘the dormant period.’ The work of Berstein (1967) emphasized body development in the context of environmental constraints as well as environment pressure. Today’s researchers have more of a developmental systems approach to motor develop (E. J. Gibson & Pick, 2000) with an emphasis on perceiving and then acting (Gibson, 1969). Work by Bril and Sabatier, 1986 suggests that motor skills in Eastern cultures are highly influenced by childcare practices and belief (Mali) and differ substantially from skill development in Western Cultures. Campos et al (2000) investigated cultural differences in crawling and its effect on spatial cognition. Those who rely on their primary sense of what can be seen and interpreted in their environment were categorized as sensorimotor by Piaget (1954). Piaget was one of the first to characterize the early stages of cognitive development as sensorimotor. He noted how infants with acute perceptual systems and rapid reflex arcs gained rapid knowledge of the world by relying on their senses. The infant moves through this early stage of cognition very rapidly. Concept and symbolic development occur early. For some children, the satisfaction and enjoyment of developing physical skills accentuate neural pathways as a primary mode of gaining information through adulthood. People who have excellent sensory motor skills are resourceful in cognitive processing. They excel at location processing, finding, naming, and manipulating objects; thus one finds a pilot, a military career officer, or as a fireman as representative of those with this trait. Rita and Kenneth Dunn (1978), after an extensive review of the literature, observed children in the classroom whose primary method of learning appears to motor driven or hands-on. They described these children as being kinesthetic. They observed that these children were delayed in developing audio and visual skills but relied heavily on motor skills early in life. 510 | P a g e 511 Prepublication Copy Personality Trait: Social Social concern (Social) is a product of emotions and feelings which result from memory, perceptions, and attention directed toward real objects in the environment. Social concern assumes that the intended object (person, etc.) is valued, loved, or has societal importance. Social concern, similar to most concepts in IPS theory, is independent but intertwined with cognition as cognition gives meaning to the intended object. The interdependence of social concern is directly related to stored emotions and feelings that are part of memory. Socialness is an outcome. Social(ness) is neurologically related to chemical concentrations of neurotransmitters. Emotions and feelings are elevated or depressed by energy transformation according to environmental situations. Cognition is a way of channelling and controlling emotional energy and/or social concern. The cognitive system and affective system are separate, interactive systems operating with the checks and balances of environmental stimuli. However, at any moment, one or the other may be more dominant. Thus, feelings of emotions can be held in check or temporarily suppressed by logical thought (a cognitive energy process which attempts to give meaning and understanding to events around us). Or then again, the strength of emotion and feeling may be so powerful as to cancel out and override the effect of the cognitive system. Social concern or gradations of less social concern may be expressed as a result of the energy manifest in any given situation. In IPS theory, social concern is a form of conscious and unconscious emotional energy which emanates from feelings derived by the sensory signals in the environment or from memories manifest from creative and practical ideation. Social concern is generally altruistic in nature but may become self-destructive when unconscious emotions result in a concern for oneself only or when feelings erupt into a rage, anger, or self-despair. Emotions are often described as anger, love, despair, hope, embarrassment, and anxiety. Again, social concern while dependent upon the energy of emotions and feelings are not antithetical to any other biological or cognitive functions. For example, when the emotional energy from an event in the environment occurs, the cognitive functions are intact and operating to identify possible threats or comforts. 511 | P a g e 512 Prepublication Copy Historical view According to Homiak (2015), the topic of social concern was addressed during the philosophical and experimental phases of psychology. From early times, the concept of “socialness “was defined as a struggle between reason and emotions-- thinking and feeling. The early philosopher Plato in the Republic idealized the mind as 3 compartments of reasoning, emoting, and desiring. For Aristotle, the social concern of people was characterized by wrapping emotions in the complex of morality, thus incorporating reason in control of feelings by making the right choices in moral situations. David Hume wrote that reason was a slave of passion and feelings while Spinoza wrote about emotions as “affections of the soul.” American psychologists William James and Carl Lange were influential theorists in the 1800s. Each developed a theory that eventually became known as the James-Lange. James conceived of social emanations as related to the biological sensations of the autonomic and motor systems. For Lange, emotions and socialness were responses to experience but also rooted in biological systems. Both Lange and James wrote that emotions are physiological responses, contributing to reflex actions of the autonomic system such as dryness in the mouth and a rise in the heart rate. In the 1900s, the most influential theorists were Magda Arnold, Richard Lazarus, and Herman Simon. Arnold was known for the appraisal theory, Lazarus for emotions and stress, and Simon for the influences of cognitive systems such as decision making and artificial intelligence theory (Francher, 1979). In the late and middle 1900s, sociologist Emilé Durkheim wrote about the customs and practices in the Australian aborigines. Totemic rituals often whipped the individuals into a frenzy. Durkheim characterized this as a “heighten state of emotional energy.” This emotional peak came from worshipping sacred objects. Emotional energy in this context is a feeling of confidence, boldness, and the power to overcome. These feelings intensified as people gather together and interfaced. Sociologists study the socialness associated with cultural norms and rules. The late 1900s and early 2000s have seen a plethora of authors and researchers who study socialness from the perspective of neuroscience and cognitive theory. Again, major issues revolve around how cognitive systems interact or fail to interact with affective systems. The cognitive systems are often characterized using terms such as judgment, evaluation, reason, and logical thinking. The affective systems are the social interactions from emotions, feelings and the objects of intentions. Socialness, feelings, and emotions are evaluated, judged, or understood in relation to particular cognitive thought. 512 | P a g e 513 Prepublication Copy The most frequent social situations according to current psychological theorists is a conscious process with understanding related to the object of intention. One connotes socialness through emotions and feelings such as happiness by helping others. The term “helping” suggests that meaning is given to the object of the intention. The person he or she loves (through actions, pathways, and ontological developments) is explicated so each may see how the actions occur. In contrast, an unconscious process (anger) may never be evaluated or judged in relation to the object of the intention (person, abstraction, etc.). The reason, of course, is that there is not a cognitive association; therefore, there is no evaluation or judgment. A psychologist, Klaus Scherer at the Swiss Center for Affective Sciences in Geneva, is representative of cognitive theorists. His appraisal theory is multidimensional, describing emotions, feelings, and socialness around specific situations that allow for positive and negative emotional valence. He sanctions the idea that emotions can be divided into 5 different components: 1. Cognitive appraisal or evaluation 2. Physiology 3. Motor expression 4. Motivational (behavioral intention or behavioral readiness) and 5. A subjective feeling state. Accordingly, in his theory, there is an average (modal) state which accounts for frequently occurring patterns of emotions and feelings. There are different stimulus evaluation checks on the central nervous system which predict the interrelated component processing and allow for the prediction of response patterns (Scherer, 2000) According to a neuroscientist, there are different structures in the brain that are more likely to be involved in emotions such as socialness and fear. Emotions are triggered by sensory input which is processed in the amygdala. The functions of the amygdala and hippocampus include the processing of memory as well as emotional information. The juxtaposition of the hypothalamus to the amygdala is not accidental as the hypothalamus sends signals to the Autonomic Nervous System. (ANS). The ANS regulates the involuntary responses such as breathing and heart rate. Therefore, an emotion such as fear is interpreted based on the need to survive with an increase in adrenaline and blood flow stimulating a flight or fight syndrome. An emotion such as fear is processed quickly with stimuli moving in concert to other brain structures. The left prefrontal cortex along with limbic and non-limbic structures are often cited. Recently, Lövheim (2011) posited that different chemicals such as dopamine, adrenaline, and serotonin are related to eight basic human emotions. In his model, each of these chemicals interacts in a coordinate system with basic emotions. Silvan Tompkins (1991) suggested emotion is related to different types of specific chemical concentrations. As an example, anger might produce a low amount of serotonin. 513 | P a g e 514 Prepublication Copy Personality Trait: Control Control is a cognitive and feeling manifestation in behaviour relating to the need for structure and order in one’s life so that decisions regarding life events can be made more efficiently and easily. We often used control and structure interchangeably as controlling an external situation is an attempt to bring structure and order through planning or forethought. Structure and order literally address the arrangement and relationships between the elements of a complex entity. Elements are positioned in a particular sequence or pattern relative to each other. Structure and order, in personality theory, suggests that a person views objects, things, and people in the environment and cognitively and emotionally imposes structure and order where there may be some, little or none. The manner in which a person imposes control may be by planning, verbal or non-verbal direction, or general behaviour. Control is a learned behaviour but probably has genetic roots. There are different kinds of cognitive control; those which are internally based and those which are externally based. Each shows a different manifestation of behaviour. A person who has a ‘need for structure’ controls situations and plans often to relieve the stress of not meeting one’s goals. The need for structure is often related to emotional feelings such as anxiety, fear of failure, or a desire to understand a non-structured situation. A person who is structured follows the rules, obeys others, and is selfdisciplined. They imbibe social, cultural, and parental rules and strive for goal attainment. In The Ego and the Id, (1923), Freud defines the concept of superego or conscience. According to Freud, a person with a strong superego is responsible and controlled. Structure is based on the active behaviour of self-control such as planning, organizing, and carrying out tasks to completion. People who are high on the structure are goal-oriented, punctilious, and determined to achieve. People with less need for structure are more relaxed in pursuing their goals. Perhaps, at times, they are less punctual, and occasionally less reliable (Jastrow, 1932). Some environments have less exposure to variability. Other environments are continually changing. Environments that change continually require more flexibility and adaptability to solve problems that are fluid and changing. Neuroplasticity of the brain literally increases with increased environmental change, i.e., there are a constant ebb and flow of neuro-transformations and changing of neuropathways. Control and Flex are two constructs that are influenced by the variability in the environment. Our concept of structure and order has many facets. Correlations in the literature empirically suggest a relationship with another well-known concept called conscientiousness. Costa and McCrae (1995) defined conscientiousness with the adjectives 514 | P a g e 515 Prepublication Copy of dutiful, self-discipline, and competence. Are structure and order and conscientiousness related? The correlation between the variables is usually high and significant. Our measurement instruments have subscales related to control and structure. The items which are listed next come from our control subscale. A person who is structured –1. makes lists to control, 2. plans ahead 3. is conscientious and follows the rules, 4. organizes (to control their environment) and 5. tries to order their activities in a meticulous and methodical way. IPS internal and external control There are two types of control, internal structuring of one’s behaviors and external structuring of other behaviors. External structuring is the most obvious as the child directs others to solve a problem by way of verbal commands such as ‘do this or ‘do that.’ Usually, the behaviors related to the neural pathway are internalized by the child from parental instructions but occasionally the neural pathway is learned through discovery. Internal structuring of one’s behavior more likely reflects the behavioral control learned from parents, church, teachers, and other significant figures. How are these control systems displayed as the child ages? Usually, they are just extensions of behaviours and ideas learned earlier. When they are not, the new control systems are extensions of independent thinking designed to obtain immediate goals. The control systems are learned through repetition in regularized and controlled environments. That is, the children do almost the same thing and have the same routine day after day. The reward of internal and external control comes from the solving of academic problems, or the satisfaction gained from learning to solve problems in the “real world.” Both mental operations result in an internal locus of control. Our research suggests that an internal locus of control is related to higher academic standardized test scores and favourable treatment from others. Many children do not show the extremes of identifiable attributes but instead display behaviours which are characterized as the normal process of maturing. That is, children sometimes make mistakes but try hard to overcome any adverse conditions related to them. When the control systems are not internalized or operational, then children’s behaviours are well documented. A statement characterizing such behaviours is stated as “out of control.” Occasionally self- or other-directed destructive behaviours occur. How important is it for the child to learn how to control emotions and thinking?? This construct is usually highly related to learning and scores on achievement tests. Those who 515 | P a g e 516 Prepublication Copy choose ideas related to internal control also score quite well on independent academic performance tests. Preceptivity and receptivity Because of its importance, we expanded the definitions of control for older children and adults by developing another subscale which measured the constructs of receptivity and preceptivity. Even in late adolescence, the process of specialization, such as choosing a profession (medicine, law, or engineering), can lead to different internal structuring of information. By internal structure, we mean neurons and pathways that are built, dissolved, and rebuilt through constant reading and experience. By constant rebuilding, the memory pathways are multilayered with many different sources to draw upon. It is the everyday encounters involving social situation which makes a person rely more on two ancillary methods of responding to problems ---preceptivity or receptivity. Receptivity and preceptivity contribute to internal boundaries. Receptivity and preceptivity are a method of orientation and response. They are ways of controlling the flow of information and emotions. Receptivity is a process used often by counsellors. With clients, a counsellor must find out information about the person and their situation. This can only occur by asking questions. They ask questions as a method of combining information with information already catalogued in their minds. Counsellors, who follow Carl Rogers are generally receptive! Preceptivity is responding to the generic structure of the problem or statement to propose a solution or to give an explanation from memory or thought. In other words, people have preconceived ideas of what is the outcome is based on their previous encounters and problem-solving. Internal structure results from rigorous practice habits such as continually studying a particular area. Any time a person spends long hours engage in repetitious study or obsessed thought, the result is mental layers used to think about solutions to problems. These mental layers result in more rigid boundaries. Thus, the reference is internally structured. One can hear how concepts are mentally structured in the conversation of the person as they discuss issues. I recently watched the 2016 presidential debate on television. Some candidates had spent considerable time thinking and studying issues of foreign policy. Their responses to questions indicated the internal structuring of the knowledge they had gained with practice, mental rehearsal, and thoughtful hours of preparation. Therefore, they responded to simple questions with very well thought out knowledgeable preconceived answers. They would have scored high on preceptivity or having a defined knowledge base with a developed internal structure. Other candidates had either not 516 | P a g e 517 Prepublication Copy studied foreign policy as well or tried to gain further knowledge by listening to the responses of others than repeating their thoughts. They would score high on receptivity. In reality, everyone uses both receptivity and preceptivity, however, there is a propensity to use one thinking process more than the other. Here are two more examples to clarify the meaning of receptivity and preceptivity. Suppose the teacher says to two math students in the class that "some numbers are neither rational nor irrational." To understand that statement, one has to understand the mathematical definitions of rational and irrational. There are only two classifications. Irrational is any real number that cannot be expressed as an integer or as a ratio between two integers. Rational is any number capable of being expressed as an integer or a quotient of integers, excluding zero as a denominator. A student high on receptivity might ask for further clarification or want more information. The student might ask for more examples, definitions or even want to know why the person made the statement. Being internally structure, the student would know by definition what was being said but want to explore further information which would augment his existing information. In contrast, the preceptive person might dismiss the statement as being illogical, since there exist only two classifications. Numbers must fit into one of the two classifications. Ergo, the statement must be false, to begin with. Likewise, the preceptive student might just argue the point based on the definitions of the words. In other words, for the latter student, the statement, as given, did not fit into their preconceived pattern or thought. The two patterns of receptivity and preceptivity have an immense impact on how people solve problems. Since a person uses both processes, let's examine each procedure. When just memorizing and retrieving information, a person is likely to be preceptive in response. When memorizing a single fact, the information is memorized as individual units and retrieve as a unit, thus it sounds memorized and rehearsed. What is the capital of California? Sacramento. When information is stored in an organized form for solving different kinds of problems, retrieved in relation to an environmental stimulus and the form is different from a unit retrieval, it is still preceptive. Question: What is the capital of California? Response: A place where the governor’s house resides--Sacramento. Receptivity can also take different forms. If the units in the memory are modified or changed on the basis of incoming information or questions, the information retrieval is considered as receptive. For example, let us say that the memory unit stored was a concept of the animal with the subset concept of dog. The subset concept of dog might be a memory further modified through experience to include the concept of St. Bernard. In other words, modification of the original concept 'animal' resulted in a memory store of a 517 | P a g e 518 Prepublication Copy specific kind of dog--St. Bernard. The modification of the original information is still considered as part of receptivity. Historical view The early philosophers (Plato, Aristotle, and Socrates) did not speak directly to the concept of structure and order in people but address the issue in terms of ethics. Those people who plan, organize and try to control their behaviour are usually ethical. The term of control was not popular in schools of Experimentalism, Behaviorism, or Gestalt. However, each of these psychological approaches studied the concept but under different names or from different theoretical perspectives. Behaviorist, for example, we're interested in reward and reinforcement for goal-oriented behavior. They suggested that a person planned or behaviorally changed to obtain a goal and was rewarded. Many studies have indicated that conscientiousness or structure is associated with a vast array of concepts, and this contributes to the ability to use it as a predictor. Two areas receiving a lot of attention are academic and career success (Judge, Higgins, Thoresen, & Barrick, 1999; Lounsbury, Sundstrom, Loveland, & Gibson, 2003; Noftle & Robins, 2007; Ozer& Benet-Martinez, 2006; Preckel, Holling, & Vock, 2006). Because personality encompasses so many emotions and enduring traits, a simple trait such as control may correlate with a wide spectrum of variables. According to Costa and McCrea (1992), based on how the original variable is defined, it may measure different slices of reality. For example, Lee and Ashton (2004) found that conscientiousness has different facet structures depending on whether it is correlated with a narrow or broad spectrum. A variable narrowly defined and operationalized may correlate more highly than a variable more broadly defined. A recent meta-analysis suggests that being structure, dutiful, and organized correlates from .24 to .27 with college grades, and .21 with academic achievement at high school, with these relationships holding after accounting for cognitive ability (Noftle & Robbins, 2007; O’Connor & Paunonen, 2007; Trapmann, Hell, Hirn, & Schuler, 2007). Thompson et al. developed a 12-item scale which was called Personal Need for Structure. Individuals who score high on their subscale are more likely to display black-and-white thinking, shunning information that is ambiguous or a threat to their existing belief system. Their cognitive systems are less likely to be integrated, complex, or multidimensional. 518 | P a g e 519 Prepublication Copy Personality Trait: Flex In IPS, the neuroplasticity of the brain contributes to Flex. Our measurement is based on the interaction of three scales, flex, conceptualization, and control. Most of the literature focuses on the concept of control/flexibility and interprets the extremes as rigidity and cognitive flexibility. Other articles in the literature focus on flex as related to creativity, artistic temperament, and originality. Some measurement theorists suggest that flex is relatively congruent with the self-report measures of Goff and Ackerman’s (1992) concept of Typical Intellectual Engagement (TIE) and Costa and McCrea’s (1992) Openness subscale. For us, flex along with the ability to conceptualize underlie both areas of research. The so-called “kicker” is that Flex is mediated almost simultaneously with control and structure as its origin may be in emotional impulse regulation. The impulse to act follows from feelings generated by associations with memory representations. We interpret the scales in the cognitive sense of representing energy actions in cognitive brain processing. Flex, when regulated based on previous experience, is the ability to break from a conscious mental set when solving problems. A set is defined as a method or way of viewing the problem. People developed mental sets by seeing the same situation day after day and attempting to solve the problems the same way each time the problem presents itself. Flex in daily life is analyzing the problem situation, then being open to various solutions based on the information presented. Flex in the extreme is using the impulsive urge for a trial-and-error approach for every problem, even if the same problem is presented multiple times. Cognitive flexibility is based on having a goal such as solving a specific kind of problem then expending cognitive energy to think of numerous alternatives to solve the problem. Each person has the same brain power to solve the problem, but some people are more willing to think of different alternatives. Thus, flex is learned through exposure to many different kinds of problems (energy utilization) from childhood to adulthood. People who score high on flex seem to be looking for an easier way to solve a problem even if it takes longer to do it. The enjoyment of exploration seems to outweigh the amount of time needed to solve the problems. The ability to solve problems is a function of many different attributes, but the flexibility/control dimension is extremely important. Directly affecting the flexibility/structure dimension are the concepts of conceptual and practical ideation, 519 | P a g e 520 Prepublication Copy cognitive independence /dependence, and receptivity /preceptivity. In our research, we start with concepts of cognitive flexibility and rigidity and then apply this research to our subgroups. Historical view Is flex the opposite of Gestalt’s functional fixedness and the same as Guilford’s divergent thinking? Does flex (cognitive flexibility) incorporate the definition of innovative or novel thinking? Is cognitive flexibility the same or does it result in behavioral adaptability? Operational definitions are ways of defining very broad constructs so each can be measured. But, then again, there are so many different operational definitions. The inability to arrive at common definitions has created controversy in the study of behavioral and cognitive flexibility. Areas of agreement by researchers suggest that cognitive flexibility is a fundamental process in human cognition and often results in intelligent decision-making (Boroditsky, Neville, Karns, Markman, & Spivey, 2010; Deak, 2003; Jordan & Morton, 2008; Karmiloff-Smith, 1992). Areas of disagreement come from the fact that many human actions and concepts which inter-correlated cause multiple kinds of operational definitions. For example, some suggest that cognitive flexibility or flex is the shifting back and forth between multiple tasks (Huizinga, Dolan, & van der Molen, 2006; p. 2019) while others use a definition associated more with creativity. The latter definition indicates that one is either a flexible problem solver (i.e., “one who knows multiple solution procedures or one who can invent or innovate to create new procedures” (Star & Seifert, 2006, p. 282). Are flexibility and rigidity a unidimensional continuum? Early 1900 theorists and experimentalists had a difficult time deciding exactly how to interpret and define the dimensionality of flexibility/rigidity. A unidimensional definition suggests one end was cognitive flexibility while the other end was a kind of rigidity. Spearman (1927) defined rigidity as “mental inertia”; Werner (1946) suggested that rigidity was just a lack of variability; and finally, Rokeach (1950) indicated that it was the inability to change the set when necessity requires it. Lately, most authors are content to use “mental set” in their definitions. The cognitive approach is for a person to have expectations about events or problems and to continue to hold on to the attitude or belief even if the set is not effective, or efficient in finding a solution to the current situation. Historically, the usual research procedure was to define a single continuum with flexibility on one end and rigidity on the other. By studying either cognitive flexibility or rigidity, the meaning of both becomes clear. This was especially true in Gestalt school. 520 | P a g e 521 Prepublication Copy Kounin (1948) and Werner (1946) explained the concept of cognitive rigidity as either structural or functional. In the structural interpretation, there are mental regions. When these mental regions are well defined and distinct, the regions are more independent, and a person is more likely to be rigid. Individuals who need structure to order their environment perform established patterns that may become ritualistic. Thus, a person is more likely to do things the same way and have a routine. According to their theory, repetitive experiences establish distinct boundaries in mental structure. In the functional interpretation, rigidity is the tendency to preserve or hold on to a previous or establish experiential set. Functional interpretation is often associated with the solving of problems. A person learns to solve a problem using an established method or a developed set of steps. Preservation tendency is defined as holding on to the established method, set, or procedure to not fail in solving the problem. Personality Trait: Achievement Motivation Motivation is a drive, a force emanating from biological functions in the form of emotional, social, and cognitive energy as well as goal attainment. Motivation comes from sensory stimuli in the environment as well as internal energy in the body. When the energy is directed toward a goal of needing to improve and perform well according to a standard of excellence, then it is called achievement motivation. This type of motivation is an indicator of competition, accomplishments, and commitment to achieve. Historical view Historically the concept of motivation has been studied in relation to learning, evolutionary behaviour, psychoanalytic theory, and physiological behaviour. In classic cases of behaviour (McClelland, 1985; McClelland, 1985b), motivation comes from arousal or drive and is characterized as guided, directed and goal-oriented. This is contrasted with the psychoanalytic theory of Freud and McDougall which found motivation was instinctual and satisfied basic needs (hunger, thirst). Murray (1938) and Maslow (1954) suggested a hierarchy of needs. Lower needs at the bottom of the hierarchy were more basic and instinctual while higher needs to achieve growth potential and excel (achievement motivation) were at the top, Kurt Lewin (1943) addressed the problem of motivation in terms of field theory. Field theory came originally from physics where it was a conceptualization of electromagnetic 521 | P a g e 522 Prepublication Copy phenomena in terms of fields of electromagnetic forces. The psychological perspective was to analyze causal relationships through positive and negative valences. Atkinson and McClelland McClelland, & Atkinson, (1948) studied the concept of achievement motivation as fantasy or imaginative behavior. Using content analysis, they studied imagery as a fantasy that takes the form of thoughts about performing a task well. When blocking imagination, a subject exhibits various levels of achievement while experiencing joy or sadness. More recent studies about individual differences have emphasized goal orientation rather than needs and drives. The personal striving of the individual (Emmons, 1996) is characterized in terms of a) obtaining goals b) expectancies, and avoidance of failure. Ultimately, personal striving is related to measures of psychological well-being, emotional satisfaction, and physical happiness. The outcome of personal striving or achievement motivation is goal attainment and goal implementation. The self-perceptions related to personal striving indicate that strong ideal integration is important in setting realistic goals. A weak perception of self leads to negative outcomes (Higgins, 2007). Interests IPS theory suggests that people use their energy in various activities in the environment and this process helps establish interest patterns. Interests as an environmental activity represent social and non-social goal activity. The research on interests is diverse. Silva (2006) in a review of the literature describes that diversity by noting many contributions come from personality, organization behavior, meta-cognition, and vocational psychology. Although interest definitions are just as diverse; two definitions are more prominent: a) interest as a personality trait (Holland, 1997) and b) interest as a transient state related to one goal. When goals are a primary endpoint, they are usually related to achievement motivation or other affective states either separate or integrated with cognition (Mary Ainley, 2006, Bryan J. Dik and Jo-Ida C. Hansen, 2011). Historical view Vocational guidance and career counseling played an important part in the emphasis on careers and interests. According to J. M. Brewer in his 1942 article on “History of 522 | P a g e 523 Prepublication Copy Vocational Guidance,” the emphasis was due to societal upheaval, transition, and change. The latter part of the nineteenth century brought industrialization and migration of people to major urban cities. There was a need for direction in how to employ people and these stimulated tools helped counselors. According to Brewer, in 1914, Jesse Davis published the Student Vocational Self Analysis and in 1917, a psychologist, James Miner developed an interest questionnaire. In 1920, a standardized interest inventory was published by the Carnegie Institute of Technology Bureau of Personnel Research. In 1927, E. K. Strong develop two inventories published by Stanford University Press. Strong has previously worked at the Carnegie Institute of Technology. The Strong Vocational Interest Blank (SVIB) and The Vocational Interest Blank for Women relied heavily on empirical justification with items from school subjects, hobbies, amusements as well as forced choice preferences for occupations and activities. In 1947, another empirically based interest instrument was developed by L.L. Thurstone at the Psychometric Laboratory at the University of Chicago. (Wightwick, 1945) Most of the early interest inventories were empirically developed and did not have a coherent theory. Only lately have theorists attempted to develop an integrated framework for interests. The Vocational Preference Inventory developed by John L. Holland was to assess personality. Holland (1965) in his first work described six personality types and environments. He used the terms Realistic (R), Investigative (I), Artistic (A), Social (S), Enterprising (E), and Conventional (C) as referents. Accordingly, there is a link between the personality of the individual and the activities of the work environment. People are more likely to thrive and work productively when there is a match between the two. The RIASEC model is hexagonal with Realistic (R) and Investigative (I) on the north end and Enterprising (E) and Social (S) on the south end. Conventional (C) is located on the west side while Artistic (A) is located on the east end. The RIASEC types of personality have a “preference for” or an “aversions against” activities and demands in the work environment. Holland (1965) in his original work, as well as his other papers (1997, 1998), popularized the notion that interests were expressions of personality. Waller, Lykken, and Tellegen (1995), and, Hansen (1984) have expressed doubts about the linkage as the correlations between the two are quite low. Many have tried to link the two areas using instruments such as NEO Personality Inventory-Revised (NEO-PI-R) Costa & McCrae, 1992) or Tellegen’s (1982) Multidimensional Personality Questionnaire (MPQ). Roe’s (1956) circular model was developed independently and concurrently with Holland’s (1985) original work. Her circular mode has eight categories (Science, Outdoor, Technology, Arts and Entertainments, Service, General Culture, Organization, and Business). Roe’s fields have a continuum based on responsibility, capacity, and skill. The categories show a continuum: Professional and managerial 2; Semiprofessional and small business; 3. Skilled; 4. Semiskilled and finally 5. Unskilled The continuum ranges from more responsibility to less responsibility. 523 | P a g e 524 Prepublication Copy In 1979, Gati proposed a hierarchical model with two major grouping—soft sciences and hard sciences. The major demarcation followed Roe’s “toward others” and “not toward others.” The classification was based on a several steps algorithms with specialization of occupations occurring with finer discrimination similar to hierarchical clustering. In 1994, the Strong developed personal interest scales which were described as the broadest level of interest description (Donnay & Borgen, 1996). These interest-based descriptions were similar to personality factors (Harmon, Hansen, Borgen, & Hammer, 1994). Lindley and Borgen (2000) suggested that the four personal styles are related to the big five factors. Studies by Holland, Johnston, & Asama, 1994; Tokar & Swanson, 1995; Tokar et. al., 1995 noted the relationships between the two interest themes (social and enterprising) and the personality variable of extraversion. Other authors have tried to relate two of the three areas: 1) interest and abilities (Mary Ainley, 2006), or 2) interests and personality (Lori D. Lindley and Fred H. Borgen, 2000). The closeness in assumptions of person and environment interactions allowed Holland’s work to be tested via social cognitive theory. Recently, Hung-Bin Sheu et al. (2010) used meta-cognitive path analysis to show a definitive relationship between social cognitive career theory and Holland’s broad occupational themes (RIASEC). They used a 6-variable version of interest/choice with the categories of Realistic, Investigative, and Enterprising and a 4-variable version in the model with Artistic, Social, and Conventional. The best and strongest model suggested that choice/goals were mediated by self-efficacy and outcome expectations. As early as 2000, Lubinski proposed integrating individual differences around the areas of personality, abilities, and interests. As mentioned earlier, Ackerman et al. (1994) developed a model for integrating personality, interests, and abilities. Armstong et. al. (2008) formed an integrative model using personality, traits, and interests. Chapter Summary This chapter helps to define 6 of the 10 personality traits which are part of the IPS model. In contrast, how the terms are used in IPS theory with the general historical research view, the use of each term is clarified. The 6 terms are common in the psychological literature, but each has been defined and redefined over many studies. 524 | P a g e 525 Prepublication Copy The first term, sensory-motor, is a variant of kinesthetic relating to the motor skills of the individual. Individuals focus on physical activities, concrete objects, and practical solutions in everyday life. The second personality trait is social which is a product, an outcome of the individual’s feelings and emotions toward an intended person or object, usually with the assumption that the intended person is loved, valued, or of societal importance. The third trait is more cognitive as control is the need to impose structure through general behavior, planning, and verbal or non-verbal directions. Control imposes structure while the fourth personality trait of flex attempts to find release from control and mental sets so that flexible alternatives to problem solutions can be examined. How this occurs is highly dependent upon the flow of mental energy in the person. When the energy is directed inward, the concept is introversion, outward, the concept is extraversion, and both ways, the concept is ambiversion. The quantitative flow of energy is usually defined in terms of a drive or motivation. If that motivation is based on achieving the goal at a high standard, then it is achievement motivation. The last part of the chapter defined interests as measurement variables associated with various instruments. Hollands, Strong, Roe, Gati, and others have consistently tried to associate interests with personality. The associations and broad interrelationships have resulted in some integration into a unified framework. 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Lounsbury, J. W. Sundstrom, E., Loveland, J. M, Gibson, L. W. (2003). Intelligence, ‘‘Big Five’’ personality traits, and work drive as predictors of course grade. Personality and Individual Differences, 35,1231–1239 Lubinski, D. (2000). Scientific and social significance of assessing individual differences: Sinking shafts at a few critical points. Annual Review of Psychology, 51,405–444 Maslow, A. H. (1954). Motivation and personality. New York: Harper. Chicago 529 | P a g e 530 Prepublication Copy McClelland, D. C. (1985a). How motives, skills, and values determine what people do. American Psychologist, 41, 812 – 825. McClelland, D. C. (1985b). Human motivation. Glenview, IL: Scott, Foresman. McClelland, D. C., & Atkinson, J. W. (1948). The projective expression of needs: Part I. The effect of different intensities of the hunger drive on perception. Journal of Psychology: Interdisciplinary and Applied, 25, 205 – 222. McCrae, R.R. (1994). 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Perugini M, Leone L (1996). Construction and validation of a Short Adjectives Checklist to measure Big Five (SACBIF) European Journal of Psychological Assessment.; 12,33–42. Piaget, J. (1954). The construction of reality in the child. New York: Ballantine. Preckel, F., Holling, H., & Vock, M. (2006). Academic underachievement: Relationship with cognitive motivation, achievement motivation, and conscientiousness. Psychology in the Schools, 43,401–411. Roe, A. (1956). The psychology of occupations. New York, NY: Wiley. Rokeach, M. (1950) The effect of perception time upon rigidity and concreteness of thinking. Journal of Experimental Psychology, 40(2),206-216. Rothbart, M. K., & Bates, J. E. (2006). Temperament. In W. Damon, Lerner, & N. Eisenberg (Eds.), Handbook of child psychology: Vol.3. Social, emotional, and personality development (6th ed., pp. 99–166). New York: Wiley 530 | P a g e 531 Prepublication Copy Scherer, K. R. (2000). Emotions as episodes of subsystem synchronization driven by nonlinear appraisal processes. In M. D. Lewis & I. Granic (Eds.) Emotion, development, and self-organization: Dynamic systems approaches to emotional development (pp. 70– 99). New York/Cambridge: Cambridge University Press. Schmidt, R. A., & Lee, T. D. (2011). Motor control and learning: A behavioral emphasis (5 ed.). Champaign, IL: Human Kinetics. Hung-Bin Sheu et al. (2010 Shirley, M.M. (1931). The first two years, a study of twenty-five babies: I. Postural and locomotor development. Minneapolis, MN: University of Minnesota Press. Silva (2006 Spearman, C., Abilities of Man (1927). New York: Macmillan Star, J. R., & Seifert, C. (2006). The development of ﬂexibility in equation solving. Contemporary Educational Psychology, 31, 280–300. Strong, E. K., & Campbell, D. P. (1966). Strong Vocational Interest Blanks manual. Stanford, CA: Stanford University Press. Tellegen, A. (1982). Brief manual for the Multidimensional Personality Questionnaire. Unpublished manuscript. Thomas, A., Chess, S., Birch, H. G., Hertzig, M. E., Korn, S. (1963). A Temperament Questionnaire for Early Adult Life New York: Psychological Corporation, 1963-196 Tomkins, Silvan S. (1991), Affect Imagery Consciousness Volume III. The Negative Affects: Anger and Fear New York: Springer. Thompson, M. M., Naccarato, M. E., Parker, K. C. H., & Moskowitz, G. (2001). The Personal Need for Structure (PNS) and Personal Fear of Invalidity (PFI) scales Historical perspectives, present applications, and future directions. In G. Moskowitz (Ed.), Cognitive social psychology: The Princeton symposium on the legacy and future of social cognition (pp. 19-39). Mahwah, NJ: Erlbaum. Trapmann, S. Hell, B., Oliver, J.; & Schuler, H. (2007). Meta-Analysis of the Relationship Between the Big Five and Academic Success at University. Tokar, D. M., & Swanson, J. L. (1995). Evaluation of the correspondence between Holland’s vocational personality typology and the ﬁve-factor model of personality. Journal of Vocational Behavior, 46, 89–108. Tokar, D. M., Vaux, A., & Swanson, J. L. (1995). Dimensions relating Holland’s vocational personality typology and the ﬁve-factor model. Journal of Career Assessment, 3, 57–74. 531 | P a g e 532 Prepublication Copy Trapnell, P. D., &, Wiggins, J. S. (1990). Extension of the Interpersonal Adjective Scales to include the Big Five dimensions of personality. Journal of Personality and Social Psychology, 59, 781–790. Waller, N. G., Lykken, D. T., & Tellegen, A. (1995). Occupational interests, leisure time interests, and personality. In D. Lubinski & R. V. Dawis (Eds.), Assessing individual differences in human behavior: New concepts, methods, and ﬁndings (pp. 233–259). Palo Alto, CA: Davies–Black. Werner, H. (1946). The concept of rigidity: a critical evaluation. Psychological Review 53: 43–52. Wightwick, M. Irene. (1945). Vocational interest patterns: A developmental study of a group of college women., (pp. 69-82). New York, NY, US: Teachers College Bureau of Publications, vi, 231 pp. Zentner, M., & Bates, J. E. (2008). Child temperament: An integrative review of concepts, research programs, and measures. European Journal of Developmental Science,2, 7–37. Further Reading De Raad. B., Barelds, D. P. H., Levert, E. &Katigbak, M.S. (2010). Only Three Factors of Personality Description Are Fully Replicable Across Languages: A Comparison of 14 Trait Taxonomies. Journal of Personality and Social Psychology 98(1):160-73 Gudykunst, W. B., & Ting-Toomey, S. (1988). Evidence for universality and cultural variation of differential emotion in K. R. Scherer (Ed.), Facets of emotion: Recent research (pp)Hillsdale, NJ: Erlbaum. Lubinski, D. (2000). Scientific and social significance of assessing individual differences: Sinking shafts at a few critical points. Annual Review of Psychology, 51,405–444 Lubinski, D., & Benbow, C. P. (1994). The study of mathematically precocious youth. In R. F. Subotnik & K. D. Arnold (Eds.), Beyond Terman (pp. 255–281). Norwood, NJ: Ablex. Lubinski, D., & Benbow, C. P. (2000). States of excellence. American Psychologist, 55,137– 150 Lubinski, D., Benbow, C. P., & Morelock, M. J. (2000). Gender differences in engineering and the physical sciences among the gifted: An inorganic Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent identification and development. Personality and Individual Differences, 49, 344–351. 532 | P a g e 533 Prepublication Copy 533 534 Prepublication Copy Chapter 27 Review: Identification of Subgroups Introduction This chapter addresses some of the issues involving the identification of subgroups of people. As noted in Chapter 3, when daily experiences and individual personality, cognitive thinking patterns, and interests influence problem-solving behavior in such a manner that groups of people utilize the same mental and behavioral pathways to solve a problem, then a potentially identifiable subgroup develops. A subgroup, as the name implies, is a category subsumed by a larger group. Any group can be subdivided into smaller groups by a defining characteristic such as gender, i.e. male and female. Therefore, a subgroup can be almost infinitely divided within any group. The assumption is that the subgroups contain some common characteristics of the major group but also differ in some ways. In our case, many different attributes are identified as a basis for grouping and defining subgroups. Some of those attributes are defined as general and differential problem solvers, introversion/extraversion, and the demographic factors of ethnicity and culture. One of the easiest ways to understand subgroups is to examine various known research models that exist in the literature. These models are identified as unipolar, bipolar, and multipolar. Most of these models are well-researched and have a plethora of studies that illustrate correlations and associations with academic problem-solving. We briefly introduce each model and then discuss models more thoroughly in the next section. Overview of subgroup models A single scale that has one end of its continuum defined as better, right, or having more worth is defined as unipolar and defines a single subgroup. The unipolar end of a continuum characterizes either ability or preference and assumes a preferred end. This includes, for example, a high score on the Scholastic Aptitude Test (SAT) as a reflection of ability or Kagan’s reflective vs. impulsive (1966) as a reflection of preference. Kagan’s subscale has two ends- reflective and impulsive. Reflective is assumed to be a preferred attribute and arguably the scale is assumed to be unipolar, 534 535 Prepublication Copy A continuum that has both ends defined by worth, value, or correctness is defined as bipolar. One well-known bi-polar model is by Witkin et al. (1977) and is called field independence and field dependence. Many people consider both ends of the continuum valuable. The last kind of model is labeled as multigroup. The work of Gregorc (1979) has 4 subgroups.; other authors use many more subgroups. For example, the research model of Sternberg (1997) has 13 subgroups. The Myers-Briggs (1988) has 16 subgroups while Raymond Cattell’s 16 Personality Factors (1981) has 81 different potential patterns. Unipolar or one-group model Certainly, from a historical viewpoint, the unipolar or ability model has the greatest number of research studies. Many researchers in different camps consider the ability model to be an “intelligence” model. A unipolar model has a positive end and in the case of intelligence, those who score the highest are considered the brightest or gifted. Using criterion 130 or greater as a cut point on an IQ test, there is no doubt that there is a single group characterized as “genius.” Members of that subgroup solve certain types of problems well. Under timed conditions, power tests are used to select those who solve problems well in the areas of numbers, words, and spatial activity. Generally, in the unipolar model, as task difficulty and complexity increase, accuracy and speed of processing decrease. The assumption is that as the memory load and efficiency requirements are taxed, there is an accompanying decrease in neural activity in the prefrontal cortex even for those who have previous experience with the problem. The subgroup that spends more time processing problems has greater neural activity based on fMRI studies as they activate multiple areas of the brain. However, oddly enough, the select group of the brightest and fastest problem solvers may not be the best general problem solvers, especially when the problems exist outside of their immediate area of expertise and experience. In World War II, the best code breakers were not the brightest (general problem solvers) but, instead were the best pattern problem solvers (differential problem solvers). Another unipolar model that does not incorporate abilities can be seen in the work of Kagan (1966). Early research by Kagan and Kagan (1970) contrasted the continuum of reflective vs. impulsive where reflection implied the examination of alternative solutions in problem solving and impulsive was a bee-line for a single convergent response. Empirical data collected on the two constructs suggested positive significant relationships for reflective thinking in the areas of mathematics, reading, statistics, and visual perceptive tasks. The single group or subgroup was a good predictor of ability. 535 536 Prepublication Copy Bipolar or two-group models Research by Witkin and Goodenough (1981) reflected a bipolar construct termed field independence and field dependence. Earlier work by Witkin et al. suggested that field independent people who were suspended in space had the ability to maintain their directionality in space independent of body position. Field dependent people were more inclined to judge spatial relationships via their body position. In later studies, Witkin’s theorized that the ends of a continuum suggested that people designated as field independent were able to better extract visual figures from a background pattern. An alternate test called the Embedded Figures Tests (EFT) was developed to identify two groups of people called field independent and field dependent. The EFT is timed; requires spatial rotation, and uses the process of dis-embedding, an analytic technique to separate figure from ground. The fact that field independent people process information faster than field dependent people is well-known as a measurement speed factor has been found many times. Many research studies in the literature do not factor out the speed factor and sometimes reach erroneous conclusions. A number of studies suggest that field independence is associated with higher academic achievement as well as domain-specific scores in areas such as mathematics and engineering. In general, according to literature studies, field dependent people are more likely to favour social relationships. When considering the bipolar continuum, both ends are supposedly valued; however, field independence is given more weight in academic performance since a higher score signifies faster processing, better perceptual analytic ability, and the ability to dis-embed. For our research, we adopted a variant of the EFT which was more age appropriate and useful across all age groups from age 5 through 77. Our assessment instrument is called the Embedded Designs test and was originally adapted from one of Witkin’s colleagues (‘Kit of Selected Distractions’ by S. A. Karp, 1962). Our embedded designs test requires dis-embedding but does not have the difficulty level of spatial rotation and dis-embedding required by the EFT. The results from these instruments were published in the American Educational Research Association conference proceeding of 2002 (DeNovellis and Dehler). Multiple group models Gregorc’s model Multiple group models as the name implies are designed to identify more than 2 subgroups of people. An example of the multi-subgroup model was developed by the research of Gregorc (1979). Using time and space, Gregorc defined 4 cognitive style subgroups that he called abstract random, concrete sequential, abstract sequential, and concrete random. How these terms are defined varies; however, for Gregorc, the term ‘abstract’ connotes those who do not need to 536 537 Prepublication Copy experience the information but can find common elements by decoding written, verbal, and imagery content. Concrete refers to those children who learn through hands-on experience. A trial-and-error approach to problem-solving is denoted as random while approaching a problem by having a goal in mind is called sequential. If these subgroups have any validity, then there should be some relationship with academic achievement. With younger age children, O’Brien (1991), using Gregor’s terminology, found a greater association between higher grade point averages and those who process information in a concrete sequential manner. As a generalization, younger children with concrete sequential orientation had better overall academic achievement, regardless of the type of problem or environment. Of the 4 subgroups identified, concrete sequential performed better in academic situations at the high and middle school level (a place where the problems presented by teachers often require answers which are analyzed in a concrete and sequential manner----our assumption). In another study at the college level, abstract students performed better in academics (O’Brien, 1994). Contrasting abstract random with abstract sequential, abstract sequential had better overall performance (Ross and Shultz, 1999). These results were contested in other studies. Miller (2005) suggested that concrete random students did better than concrete sequential although the type of problem was not given. In IPS theory, both concrete and abstract sequential students can be either general or differential problem solvers. The speed of processing on timed tests is a major contributor to both groups. Gregorc’s model is a good example of using somewhat independent subgroups. When subgroups are independent, there is a greater research tendency to link a specified group with the academic assessment. Many researchers attempt to establish the “independence” of subgroups to compare attributes and use statistical analysis. The statistical independence model is appropriate for both short-term and long-term research of independent groups. When randomness is introduced, the error is equally distributed. In contrast to the independent method of subgroup research, there are just as many research models for working with non-random, integrative, and interdependent subgroups as our 36 subgroups. Profile analysis of interdependent subgroups is appropriate for classification models where the independence of subgroups has not been established. Profile analysis uses descriptive distance methods to separate interdependent groups, a methodology similar to the biological classification of chromosomes, DNA, and other blood-related analyses. Results that come from assessing different levels of education (high school, middle school, and college) and which have different kinds of problems are likely to produce mixed results. True differences, along with sampling error, which exist at different developmental levels, are likely to extract individual differences that represent different modes of information processing for different types of problems. 537 538 Prepublication Copy Sternberg’s Model In Robert Sternberg’s research, there are 13 different subgroups, many of which are interdependent. The first five subgroups representing Type I are labelled as legislative, judicial, global, liberal, and hierarchical; the next 4 representing Type II are conservative, monarchic, local, and executive; and the last 4 subgroups representing Type III are different combinations of Type I and Type II These four subgroups are labelled as internal, external, anarchic and oligarchic. According to Zhang (2008), Robert Sternberg’s Model has constantly evolved since he developed his Triarchic Theory in the 1980s. As the number of subgroups increases, there is usually more interdependence which causes other researchers to regroup and re-classify the subgroups so each can be researched as independent groups. In Fang’s regrouping, the 13 subgroups emphasize two themes (structure and cognitive complexity) which are dominant attributes found in the research literature. Structure, according to Fang, is a primary variable that has shown a positive relationship to academic achievement, particularly in traditional environments. Type I manifest characteristics of lower structure and lower cognitive complexity while Type II displays high structure and cognitive simplicity. The characteristics of Type III will vary depending on problem characteristics. Cognitive complexity increases as individuals expand their knowledge base related to career and daily decisions. Sternberg’s models which originally designated as thinking or intellectual styles have also the capacity to incorporate emotions. Myers Briggs Type Indicator The Myers Briggs Type Indicator (MBTI) has 16 subgroups. Using a combination of four bi-polar continuums (thinking feeling; introversion, extraversion, sensing, intuition; and judging and perception), the instrument is used to assign people to subgroups based on the strengths of multiple responses on contrasting subscales. The extremes (7.5 per cent in each tail of the normal distribution) of each bipolar scale are more likely to represent an independent subgroup. Based on the scoring method of the MBTI, a person who scores higher on (Extraversion, Sensing Feeling and Judging) is assigned to be assigned to the subgroup of ESFJ. The attributes of the subgroup are established from the attributes of each of subscales (E, I, S, N, T, F, J, P) used to assign a person to that group. Based on Jung’s theory of psychological type as interpreted by Isabell Briggs-Myers, the instrument has a long and varied history as seen from the numerous research articles published. The research of the instruments has established its value and contributions to the literature. One of the most notable early articles castigated the construction of the instrument (reliability, validity), as well as its basic premises (Pittenger, 1993). According to Pittenger, despite having 538 539 Prepublication Copy face validity, the MBTI was originally dropped by a number of prestigious groups including the US Army and Educational testing service. However, as of this time, the tremendous amount of research reported on the instrument has given it widespread and momentous use. Sixteen Personality Factor Questionnaire (16 PF) The Sixteen Personality Factor Questionnaire (Cattel et al., 1970), which was developed over several decades, is a self-report instrument that measures 16 primary traits. This group of primary factors originally came from the factor analysis of multiple clusters of traits underlying normal personality. Currently, the 16 primary traits are organized into 3 secondary global traits which are identified by individual factors. The secondary groups are identified on a bipolar continuum: Extraversion vs. Introversion, Receptivity vs Tough-Mindedness, and Self-controlled vs. Unrestrained. The primary factors which make up the global factors are E/I (warmth, Liveliness, Social Boldness, Forthrightness, and Affiliation); Receptivity vs. Tough-Mindedness (Abstractness, Openness, Sensitivity, and Warmth) and Self-Control (Seriousness, Groundedness, Perfectionism, and Rule Conscientiousness. The 16 PF Questionnaire has 81 different profile patterns as interpreted by Samuel Krug (1981) of the Institute of Personality and Ability Testing. Each profile pattern, in IPS theory, represents a subgroup. Because the 16PF was developed over a long period of time by a distinguished group of researchers and used by a group of select professionals, the number of subgroups identified by profile analysis was not questioned. Each of the profiles identified by Krug is accompanied by a short and concise descriptive related to profile interpretation. Issues related to the measurement of subgroups First, let us answer a very difficult question. Are there really measurable subgroups of people who solve problems in different ways? That depends upon what assumptions are used to answer the question and how one attempts to objectify the answer. For the greatest sceptics, the answer is No! Such persons could argue (ad nauseum) tenets underlying differences in cut points on a single continuum -extraversion, ambiversion, and introversion and then use the perennial arguments that measurement subgroups could only be identified by modes within a universal distribution (Boltz, 1972). At the very beginning of this book, our thesis indicated that the identification of subgroups is based on a descriptive system which includes numbers, theory, and fuzzy logic as a method of quantification. Also, as noted in Chapter Two, because surface characteristics vary substantially from one person to another, one cannot classify an individual into a subgroup in two very distinct situations. 1. A person does not want to be classified into a subgroup so purposely falsifies responses on questionnaires. 2. An individual s has multiple 539 540 Prepublication Copy layers which interfere with surface characteristics and that person is unaware of their own true response pattern. The ability to quantify a subgroup using numbers revolves around reliability, validity, and measurement techniques. We have chosen distance measurements, fuzzy models, and applied statistical methods as a method of quantification and noted that classification (ability to assign a person to a subgroup) is a very difficult process that only has validity based on theory, a prior and posterior probabilities, as well as item and subscale response patterns. In our model, all people are different from our subgroup (individual differences). Why? The subgroup is an “ideal composite” established on a theoretical and empirical basis. The assumption is that having characteristics in common with an identified subgroup provides information to and about the individual. Likewise, knowing how one is different from the subgroup as identified by distance measures gives information about the error, misclassification, and individual characteristics. Are there acceptable levels of error in classification for being nearest to a subgroup.? All measurement theory is based on error. For some researchers, the measurement error is too great, for others not so much. Since one of our principle tenets is built around speed of processing, the issues related to timed and untimed situations are paramount in classification. In IPS theory, time tests and threat situations, regardless of content separate people into groups. In other words, there exists a general measurement speed factor that is found in every timed situation involving a cross-section of society. General problem solvers who have exceptional memories and who are quicker processors of familiar information should score higher on timed tests. Differential or general problem solvers who tend to process many different alternatives and those who are slower in reaching a convergent solution often score lower on timed tests unless they have learned how to compensate by strategies, practice, and time on task. In many research models, time is a significant factor in activities involving academic achievement, especially when standardized achievement tests are used. Many studies use subgroups and academic achievement scores as a standard of comparison or correlations from those groups in determining value or worth. Our 36 subgroups The IPS system of measurement has 36 subgroups. The separation between each of the subgroups is pictured by a non-metric system in Picture 8 below. Since the number of groups may seem overwhelming, a taxonomic conceptual framework was provided in Chapter 3. The Category Framework provides an overview and a methodology for organizing the process. The Category Framework is built on the assumption that all of us have strengths in multiple areas of problemsolving. At different periods of our life, the combination of strengths helps in solving problems 540 541 Prepublication Copy in one area as opposed to another. Likewise, these problem-solving strengths lead to a career choice and life's work in certain vocations. In the figure below labelled as Picture 5, there are 36 subgroups. Notice how certain subgroups are closely related to dominant characteristics of individual variables within the 4 processing groups (speed, career; etc.). Some subgroups appear to be separated by a greater distance. Picture 5: 36 Subgroups Overlay of cognition (C1-C2), speed of process (S1-S4), personality (P1-P6), and interests (CR1-C16), and the 36 subgroups Subgroups within subgroups Using the statistical methodology of canonical correspondence analysis, the next picture shows how, in our model, subgroups exist within subgroups. In our integrative system, pairs of subscales and model characteristics work in opposition and conjunction with one another (extraversion, introversion, perceptual accuracy and global processing, conceptual and motor, 541 542 Prepublication Copy analysis and social, flex and control). The scores for the picture come from the standard scores derived from the Table of 36 subgroups. The Table contains columns across the top such as Extraversion, Conceptual, Motor, Analytic and Social. Each column is converted to a word designation where a high standard score on analysis is termed Analytic, a low score is termed Social and an intermediate standard score (48-54) is designated as Analytic Social. These measurement profile subgroups are displayed on a two-dimensional graph as A; S; or AS. In Picture 6, those higher in analysis (A) are in upper left quadrant, those dominant in social (S) are in the upper right and those sharing in the lower left quadrant (AS). In essence, the table represents three distinct measurement subgroups. The subgroup of people who have a dominant characteristic of Analysis when solving problems is different and separate from the subgroup of people who approach the solving of problems in a social manner. Likewise, there is even a third subgroup of people who are mixtures of both approaches. If neurological pathways of the brain work both in opposition and similarity due to differences in stored memory, then these competitive differences should be evident in dominant approaches to solving a problem. Picture 6: Analytic (A), Social (S), and Analytic Social (AS) In Picture 7 below, those higher on the conceptual subscale (Cn or Con) are in lower left quadrant; those dominant in motor skills (Mt or Mot) are in the lower right; and those sharing the same orientation of are straddling the upper quadrant (CM). \ 542 543 Prepublication Copy Picture 7: Motor (Mot); Conceptual (Con); and CM Picture 8: Centroid for Motor; Conceptual; CM 543 544 Prepublication Copy Picture 8 plots each profile and shows the location of the centroid for each of the three groups conceptual Con, motor-Mot, an average score on both conceptual and motor (CM). There are outliers; individual points on the extremes of the centroid. Chapter summary The information in this chapter provides a basis to conceptualize issues associated with the classification of subgroups. The 36 problem-solving subgroups developed and identified in this book are interdependent by definition. However, a classification system by distance methods is possible, when prior information, statistical analysis, and theory are available. The descriptive profiles represent ideal composites, not real people. The subgroup composites are similar in many ways to those identified by the 16PF, and other similar profile mapping methods. Chapter references: Boltz, C. (1972). Personality Types (Chapter 5). In Multivariate personality research: contributions to the understanding of personality in honor of Raymond B. Cattell. Ralph Mason Dreger. (Ed.) Baton Rouge, LA: Claitor's Publication. Division, 161. Cattell, R. B., Eber, H. W., & Tatsuoka, M. M. (1970). 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Effects of model persistence and statements of confidence on children's self-efficacy and problem solving. Journal of Educational Psychology, 73, 485-493. 581 582 Prepublication Copy Appendix B Descriptions of 36 Cognitive, Interest, and Personality Subgroups Subgroup descriptions represent groups of people and do not describe any single individual! In research, these subgroups are often called reference groups as each is compiled from data and contains reference vectors as a means of locating the centroid of the multivariate distribution. Reference groups are “ideal composites,” a taxonomic classification based on the Category Framework for describing subgroups of people. An “Ideal composite” is a classification system used in a manner similar to other classification systems developed by biologists. That is, an “ideal composite” should be conceived as a class objects such as trees. There are many different types of trees- oak trees, maple trees, redwood trees, etc. The general concept of a tree is neither unique nor specific. Only by adding a label, the general category becomes more specific. The category of oak trees is more specific than a tree. For example, an oak tree in your yard has even greater specificity as you can go out and touch it. Ideal composites have greater specificity then comparisons to amorphous groups but less specificity than an actual description of a real entity. The information about the concepts contained in each subgroup can be found in the book entitled “Problem Solving: The Integration of Personality, Cognition and Interests Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning.” One should read either this book or the synopsis of the book so as to understand the research implications of the 36 subgroups. The descriptions are written specifically for Integrative Problem-Solving System (IPS). The first 18 subgroups emphasized extroversion, and the next 18 subgroups emphasize introversion. In the research book, there are explanations of how different groups of people with different patterns of personality, interest and spatial scores solve everyday problems. The two major patterns represent the General Problem Solver and the Differential Problem Solver. Both groups of problem solvers contribute greatly to society by solving similar and different kinds of problems. There are no restrictions on problem-solving as people’s motivation, skill, and experience can change over a lifetime. By definition, a General Problem Solver can become a Differential Problem Solver and a Differential Problem Solver can become a General Problem Solver. Both groups solve numeric, verbal, and spatial problems at home, school, and work. The terms are just used as a placeholder to help in the classification process. Both groups of problem solvers, General and Differential, have many things in common and many differences. Often times for both groups, the greatest difference between the problemsolving approach to numeric, spatial, and verbal problems is found in the educational background of the first five years of life. After five years of age, experience, exposure, interest, and many different social factors often contribute to a separation between subgroups. For us, the commonalities and differences are understood in terms of speed of processing, cognitive 582 583 Prepublication Copy characteristics, interests, as well eight different subscales of measurements labelled as extraversion/introversion, conception, sensory-motor, social, analytical, cognitive flex, and control. The many different kinds of tables that precede each subgroup labelled from 1 to 36 are computerbased categories that help differentiate the complexities involved in categorization. The tables represent interests, personality, cognition, perceptual speed, as well as the ten concepts used to describe the subgroup. The tables found before each subgroup description are patterns that are analyzed to correctly classify an individual to an appropriate subgroup. The major tenet that guides the construction of a subgroup is that the variation with an area such cognition, perceptual speed, personality or interests is so great, that categorization is dependent upon a designated level and pattern. As a simple example, consider there are various ways that a single person might score on a test of cognition about verbal, numerical, and spatial problems. Let a plus denote better than average, an N or A designate average, and a minus be “less than average.” A person who scores greater than average (a single standard deviation above the mean) on all three types of problems has different experiences in school than a person who scores less than average (a single standard deviation below the mean). Each of these differences is denoted by levels (A-G). Therefore, a person’s taxonomic classification in an appropriate subgroup (1 through 36) is influenced by the pattern of interests, personality (our category of 10 concepts, and perceptual speed (A-G). One important assumption is that every person is different from the nearest subgroup in meaningful ways. Reference subgroups (1-36) are used mainly for research purposes. The validity of reference subgroups can be ascertained by taking the scores of all people who are categorized as belonging to a subgroup and then determining the commonality which exists within that group. Because of large sampling variations, the differences within a group could be greater than the differences between a group; thereby causing consternation about the validity of the subgroup. In such cases, the researcher must be careful to follow the criteria used to set the parameters of classifying members of the subgroup. Further subdivisions occur via demographic characteristics such as age, etc. The set of scores from a single individual can be compared to scores from many different subgroups using machine learning. The differences are interpreted by a researcher, counselor, vocationally trained person, or psychologist. What becomes important is not the subgroup reference description but how any individual scores differently than the reference subgroup. Providing an individual with information from his or her subgroup involves several assumptions. The first assumption which may or may not hold true is that scoring in a similar pattern to an ideal composite provides information about both individual and the ideal 583 584 Prepublication Copy composite. The second is that differences in scores reflect reliable and valid differences in individual responses. Both assumptions must be continually tested. 584 585 Prepublication Copy 585 General Problem Solver-1 trial and error approach. After becoming familiar with a problem, they either fit the problem into their previous experience (59) or try to invent a new way of doing things. This pattern (Level A) is for individuals with a higher general problem-solving score and more positive scores on verbal, number, and spatial problems. These scores are bolstered by a high score on the conception and cognitive flexibility. Making up about five percent of the general population, these individuals can be called "the motivator In problem-solving situations, these individual works in bursts of speed powered by enthusiasm, especially in an area of interest. They may spend an inordinate amount of time on problems that they like. When interacting with others in a problem-solving situation, they often jump to conclusions or even make errors of fact because they do not like to take time for too much precision. Others in a group may follow their intuitive notions initially but later as the problem becomes more focused, others follow a more methodical approach Identifiers How are people in this subgroup characterized? Generally, they are considered responsive, affectionate, and sentimental. They emphasize social interests in the home, with the family, and at work (88). Their friends regard them as generally friendly, outgoing, adventurous, and occasionally intrusive." Individuals in this group enjoy learning a new skill, solving a new problem, and using it. Often, one finds this individual doing new things well. This group of people likes to meet and talk with their friends (88). They are very social being, outgoing, and easy to get to know (95). Career The career scores paint a picture of one who is less interested in mechanical and realistic occupations. These individuals have a good chance of ending up in applied vocations like teaching, scientific research, management, medical areas, or basic administration. Other areas of occupational interest might include judicial service and legal work, behavioral science, life science, mining and petroleum engineering, health care services, and building services These individuals are generally visuallyoriented. They have good powers of observation and watch others closely. For example, these folks are good at remembering names and faces. They are also sensitive to verbal and non-verbal cues from other people. They are quick to notice a change in facial expression or a change in the pitch of the voice. Quite often they gather too much information about people and have some difficulty determining what is important. In terms of a vocation, this person find his forte in guidance, counseling, nursing, advertising and marketing, speech therapy, psychology, clinical psychology, medical doctors, social workers, graduate school teachers, school principals, high school teachers, education, college professors, judges, playground directors, public health officers, rehabilitation workers, director of welfare agencies, foreign missionaries, world peace organizers, human resource managers, writers, insurance sales, personnel managers, and ministers. Problem Solving How does a person in this subgroup solve everyday problems which are verbal, numerical, or spatial? When approaching a problem, they use an intuitive, random approach (65). Sometimes this approach Is combined with a Note: Numbers in parentheses show the percentage of people in this group who agree with the statement. Interpret your scores relative to the pattern of the subgroup. Usually, these individuals get other people interested in their current activities. They try to 586 may score in the average range or lower for spatial acumen. The greater emphasis on verbal or words may be applied in many different areas including sales, group endeavors, and jingoism. During the younger years, the search or application of primary skills can be quite confusing as a career field is not always evident. In group problem solving, this individual is process-oriented, focusing on how others in the group solve problems. There is evidence of a tendency to dominate verbally especially when ideas, values, and interests are close to one’s heart understand both the world in which they live and the people in it. This understanding allows them to win support for the kind of projects in which they are engaged. This pattern is more prevalent in women although quite a few men show their strengths in literary and musical endeavors. The contact personality in older adults is less likely to show areas of compensation suggesting more positive experiences through childhood and early adulthood. Perception is average and the tendency to spend time analyzing is average. Differential Problem Solver Differential problem solvers (Levels F, G) with very difficult early life experiences might show all kinds of acting-out behaviors that pose problems for parents and those in authority. When there is not a match between environmental pressures from home, family, church, or sibling, confusion and a lack of goal orientation results. In such cases, there is a tendency to meet adversity with solemnness and passivity. Stress and environmental pressures can lead to all different kinds of compensation including the use of skillful ways of circumventing conventional rules and traditions. For the differential problem solver (Level C), the pattern of problem-solving scores is in the average range. The differential problem solver is motivated by interest patterns which are quite varied. His or her life is dominated by the desire to help others. Achieving personal goals is a means to an end; the end is to apply social and interpersonal skills in social situations. At times, the tendency to be impulsive dominates. Emotions and feelings may be quite evident. Hence the phrase, he or she wears their emotions on a sleeve. The need for order and organization is achieved later in life as goal orientations are more associated with making a living. Potential Obstacles to Solving Problems Obstacles to solving problems for these folks come in many different forms. For these individuals, the fit between work and preferences is of paramount importance. Many problems result if these people are placed in a job that is too restrictive. The tendency to leave tasks unfinished is much more evident in the differential problem solver. Their feelings and impulsivity often overwhelm them. Often they are more likely to react to their feelings which causes them to move to another task leaving the present task undone Being socially concerned, individuals in this subgroup are eager to engage in problems that assist other people. However, value issues can be a gigantic obstacle to the solution of everyday problems. The career theme is strong for the differential problem solver. He or she is less likely to be a truck driver, operate machinery, or applied one talent to plumbing. Instead, creating literary works, writing music, or helping others is the key to success. These individuals have to be especially cautious to not undertake more responsibilities than they can handle. Often, their "eyes may be bigger than their stomach," especially where projects are Differential Problem Solvers with less computational interests and greater verbal skills 587 concerned. If they are not attentive, active inspiration and initiative will deteriorate in a lot of half-done jobs. Thus, in such cases, they may appear unstable, undependable, and even fickle. Management Identity is low except when an entrepreneur or executive of the individual business. Greater numbers are middle or first-level managers. One of the greatest problems for these individuals comes from conflicts resulting from controlling people. These folks are Inclined to resist direct authority and control and the people who use it. They react better to requests for help and assistance. As a youngster, these folks became angry and showed their anger in several volatile ways. As they matured in a professional capacity, they became slower to take offense or anger. In their older years, temper is held in check but results in passive resistance. One of the major problems for this subgroup is the need to achieve. They have the potential for leadership. It is achieving that potential which causes problems. Sometimes a lack of selfconfidence makes them an underachiever. They may not undertake some problem which is encountered. Some view this subgroup as lacking the desire or being too lackadaisical, while others note their lack of initiative. This is especially true when they have underachieved. Usually, these people are very aggressive and dominant in leadership qualities. They decide on their true identity. A subgroup of this general typology tends to mobilize individuals for less than humanitarian reasons. They tend to use their unique ability to analyze situations for more personal ends. Such a person is very successful in many activities that need management ability with less than noble ends. These individuals are competitive, and this competitiveness shows itself in several different ways, especially in the manipulation of other people for the sake of winning. 1. 2. Task Orientation Versus People Orientation: Greater numbers in management activities involve people or people-related activities. Can manage where expertise is involved. 3. Leadership: Shows greater management leadership for diverse and diffuse situations. Better leadership where creativity is involved. Task leadership is good where expertise is involved. 4. Problem-Solving Orientation: Trends for these managers show adaptability, less structure, and more receptivity. 5. Independence in Decision-Making: Varies with the individual but with experience will consult others. Can be stubborn about value issues. 6. Efficiency Index: Scores higher on people relative to tasks. 7. Assessment of Social, Practical, and Complex Situations: Better with social, complex, and creative. 8. Information Processing: Logical, Analytical scores generally average 5.5 with spatial higher for mechanically oriented people. 9. Sales Management: Usually is less direct and more indirect. Pattern 1: General Parameters Parameters: Pattern 1 Managers 1. Age: 26-49. Management Identity: Trends show that Non-Management and Entrepreneurial identity is average or high. Senior 2. General Preferences: Prefers management in educational, social, 588 health-related, therapeutic, or religious vocations. 3. 4. 5. 6. 7. Preferred Roles or Activities: Prefers management activities involving social, aesthetic, and religious expressions including individual or group projects related to individual interests. Usually performs in a service role for an organization or group. Avoids: Avoids routine or humdrum activities; avoids work involving carpentry or building unless it is creative; avoids manual labor if possible. Achievement-Creativity: Creative and imaginative. Strives to achieve. Self-Perceptions: Independent, creative, original, self-accepting, impulsive, moody, cheerful, sociable, helpful, concerned, self-interested, democratic, spontaneous, and emotional. Other's Perceptions: Impractical, sentimental, unruly, versatile, intriguing, and adaptable. 8. Perceptions: 68% are Field Dependent. 9. Aptitude: Special abilities and intelligence. Scores higher on verbal, clerical, and form perceptions; latent mathematical aptitude. IQ range is 90130. 10. Preferred Style of Learning: Learns by doing and discussing, social discourse, group interaction, oral communication, and modeling. 589 11. Personality: Reduces stress by increasing social relationships and conforming. Defends self by "open rebuttal", self-analysis, and submissive behavior; avoids confrontation. Can be influenced by higher-level managers. 12. Motivating Factors: Recognition, social affiliation, approval, and being socially motivated. 13. Conceptual Versus Perceptual Motor Dominance: Conceptual. 14. Sensory Modality Preference: Auditory, and visual. 15. Automatization: Strong. 16. Constricted Versus Flexible Control: Flexible control. 17. Risk-Taking Versus Cautious: Risktaking. 18. Reflective Versus Impulsive: Prone to act impulsively. 19. Leveling Versus Sharpening: Leveling. 20. Cognitive Complexity versus Simplicity: Cognitive complex I ty. 21. Compartmentalizing: Open system. 22. The breadth of Categorization: Broadly categorizes. 23. Ego-Orientation: Other-oriented, then individualistic. 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 not like to spend long amounts of time working individually on a single task. This may pose a problem for them, especially if that attribute is needed in work or a project. These individual likes to stick to the known facts when solving problems (62). They approach a problem by relating most things to their past perceptions and experiences. They prefer to use their previous experience as a springboard for their current decisions. General Problem Solver-9 This pattern represents a subgroup of individuals with a higher general problem-solving score and more positive scores on verbal, number, and spatial problems. These scores are bolstered by a high score on cognitive flexibility. All scores in this subgroup suggest an applied person who is more extroverted, and very reliant on motor skills and goal orientation. These folks approach problems from a task perspective. They enjoy everyday problems, finding quick solutions, and then moving on to a new problem. Since they get bored easily, a new and different task is always welcomed. Identifiers People in this subgroup are resourceful, energetic, businesslike, and analytical. With a sincere desire to make the impossible possible, they try to succeed where others have failed. Found in about seven percent of the population, these individuals can handle difficult assignments and people of all kinds. In a group problem-solving situation, they focus more on the problem and how to get it solved. They can be resistant to solving some problems, particularly if they do not agree with the solution. One obvious attribute of these individuals is their combination of preferences. In their public life, they are conservative yet spontaneous, preferring to plan only important things. However, contrary to this pattern, he or she wants everything in their job to be well thought out. They want to spend time directing their energies appropriately for the fulfillment of their life. They do not want people to think that they are not competent. So, they want to appear methodical in the way each approaches work. However, they are not methodical in their approach to problems. Instead, they are more likely to be unorthodox, examining many different kinds of alternatives and missing details. Career The career scores paint a picture of one who is more interested in mechanical and realistic occupations. There is a preference for analyzing process mechanisms related to goal orientation and success. Their fortune is found in many different areas, especially in business, education, administration, banking, real estate, and entrepreneurial enterprises This person places more emphasis on letting events be as they may be. They may be an artesian as he or she strives to make an object in the environment a perfection of reality. Perception is strong as is the appreciation of things in the environment. There is less emphasis on control. Problem Solving Being extroverted (78), they work on a variety of tasks, spending a lot of time moving from one task to another. However, they do Often, these people like the outdoors. They might or might not like sports; however, they probably tried some athletic endeavors in their early years. __________________________________________ Note: Numbers in parentheses show the percentage of people in this group who agree with the statement. Interpret your scores relative to the pattern of the subgroup. A young person often likes crafts and other kinds of work that need hands-on experience. As this person matures, he or she does well in real estate, personnel work, and jobs requiring social skills. Other areas of possible occupational interest 605 Differential problem solvers with very difficult early life experiences might show all kinds of different behaviors which pose problems for parents and those in authority. When there is not a match between environmental pressures from home, family, church, or sibling, confusion and a lack of goal orientation results. In such cases, there is a tendency to meet adversity with solemnness, isolation, and passivity. Stress and environmental pressures can lead to all different kinds of compensation including the use of skillful ways of circumventing conventional rules and traditions. include bookkeeping, pharmacist, mathematical analysis, production record work, automobile service work, farming, navigation, mechanics, cosmetology, purchasing, traffic management, police work, business executive, mid-level administration, and retail store management. Differential Problem Solving For the differential problem solver, the pattern of problem-solving scores is in the average range. The differential problem solver is motivated more by interest patterns which are quite diverse. His or her life is dominated by the desire to achieve specific goals related to current interests. Achieving personal goals is a means to an end; the end is to dominate and conquer whatever. At times, the tendency to be impulsive is pervasive. Emotions and feelings are hidden under the veneer of stability Potential Obstacles to Problem Solving One characteristic of these individuals is their slightly domineering manner. They may, on occasion, dominate other individuals, particularly those who are less socially inclined. Often, they have great faith in their ability to effect a solution in the real world. So, they feel at ease in structuring situations for other persons. The career theme is strong for the differential problem solver. He or she can be in diverse areas of construction, the food industry, or small entrepreneurial businesses. This person may be a truck driver, operate machinery, or apply one talent to plumbing. However, if any one of those careers becomes the current obsession, the desire to achieve is overwhelming. Problems arise when they view other individuals as less capable than themselves. In those instances, they are too harsh with those who look at the world with more sympathy and understanding. This, coupled with their occasional explosive temper, may cause them some unnecessary problems. These people need a partner who is very sensitive to the individual needs of other people to give them insight into situations where they may be trampling on personal feelings. Differential Problem Solvers with more computational interests and greater verbal skills may score in the average range or high for spatial acumen. This person is more of a risk-taker. The greater emphasis on verbal or words may be applied in many different areas including sales, group endeavors, and advertising. While a greater interest in computation can lead to a career in computers or software design. During the younger years, the search or application of primary skills can be quite confusing as a career field is not always evident. In group problem solving, this individual is process-oriented, focusing on how others in the group solve problems. There is evidence of a tendency to dominate verbally especially when ideas, values, and interests are close to one’s heart Parameters: Management Pattern 9 606 1. Management Identity: Trends show that Non-Management, Entrepreneurial, or Middle Management Identity Is average or high. Senior Management Identity Is low except when the head of his own business is an Entrepreneur. Greater numbers are middle or first-level managers. 2. Task Orientation Versus People Orientation: Greater numbers in Some evidence suggests a preference for subordinate-supervisor roles. Prefers independent situations which are not social so he or she can work. management activities Involving tasks. Can manage where the motor or mechanical expertise is involved. 3. Leadership: Shows greater management leadership for tasks, and occasional creativity. Task leadership is good where expertise is involved. 4. Problem-Solving Orientation: Trends for these managers show adaptability, less structure, and more receptivity. 5. Independence in Decision-Making: Varies with the individual but will consult others with experience. Can be stubborn as a middle manager when direct experience or expertise is involved. 6. Efficiency Index: Scores higher on tasks. 7. Assessment of Social, Practical, and Complex Situations: Better with practical and areas of complexity if direct experience is involved. 8. 9. Information Processing: Logical, Analytical scores generally average 7.5 with spatial scores higher for mechanically inclined. 4. Avoids Social situations requiring independent expression such as personalized and artistic roles. Avoids confining situations and problems. Also avoids intellectualism, artistic social sensitivity, and skill. 5. Achievement-Creativity: Achieves primarily in technical and administrative areas; identifies with material possessions. Can apply ideas better than create them. 6. Self-Perceptions: Masculine, dominant, under-achieving (academically), conservative, stable, and self-accepting. Perceives self as practical-minded, cheerful, and making a good impression. 7. Other's Perceptions: Rate him or her as unsure, cheerful, independent, and preferring simple to complex outlook. 8. Perceptions: Is more of a divergent thinker. Sees the world from an Individual standpoint and is inflexible in readjusting adaptive level (stereotypical and unoriginal); subject to position-influence (constricted). Unable to reorganize well. 9. Aptitude: Special abilities and intelligence. Higher scores on clerical and form perceptions; latent mathematical aptitude. IQ range is 90130. 10. Preferred Style of learning: Learns by doing and discussion, prefers a lecture, and assignments with the open-ended learning approach. Sales Management: Usually is more direct. Pattern 9: General Parameters: 1. Age: 26-49. 2. General Preferences: Prefers management in economic and conventional values. Less preference for aesthetic and religious but can do clerical and computational tasks. 3. Preferred Roles or Activities Prefers activities involving administration, business, and conventional trades. 607 11. 12. 13. 14. 15. 16. Constricted Versus Flexible Control: Constricted. 17. Risk-Taking Versus Cautious: Cautious Risk-taking. 18. Reflective Versus Impulsive: Prone to act impulsively at times. 19. Leveling Versus Sharpening: Sharpening. 20. Cognitive Complexity versus Simplicity: Cognitively direct. 21. Conceptual Versus Perceptual Motor Dominance: Conceptual. Compartmentalizing: Some compartmentalizing. 22. Sensory Modality Preference: Auditory, and visual. The breadth of Categorization: Narrowly categorizes. 23. Ego-Orientation: Individualistic, some group. Personality: Reduces stress by limiting social relationships, and defends self by "open rebuttal" or reason. Maintains self-control by being understanding and self-accepting. Dislikes are put in a situation where the contingencies involved cannot be involved. Expresses life succinctly, is not rule-oriented, and lacks conformity to cultural norms and values. Motivating Factors: Management recognition for special abilities, approval, and special identity. Automatization: Intermediate. 608 609 610 611 612 613 614 615 616 617 618 619 620 621 624 625 626 627 Individuals in this group can be an enigma at times. Their world is a very personal one filled with meaning as they have encoded it. Thus, they encounter others in their environment in a very personal way. General Problem Solver-19 This pattern represents a subgroup of individuals with a higher general problem-solving score and more positive scores on verbal, number, and spatial problems. These scores are bolstered by a high score on conception and cognitive flexibility. All scores suggest a quiet, creative person who is more introverted, quiet, and affiliative. Individuals in this subgroup often use their academic ability to analyze issues. This information is shared with other persons within their group. With free time, they are more likely to read a book and work on things that interest them (70). Identifiers The basic adjectives describing these folks are selective, aloof, personable, intimate, and sometimes very unadaptable. Found in about five percent of the population, they find their forte in endeavors needing individual effort and knowledge. Problem Solving Problem-solving behaviors help this person rely on process mechanisms for obtaining goals. Process mechanisms are ways of dividing complex tasks into simple ones or recognizing the many steps involved in solving complex problems. The combination of traits that pervade their personality is introversion, imagination, and feeling. These three preferences interact to produce uniqueness in the individual which is often difficult to describe. The approach to problems is usually intuitive, random, and based on thoughtful trial and error (80). Individuals like to solve problems by noting relationships and then dealing with known facts (82). The mind jumps from one part of the problem to the other (60). People in this subgroup are better at problems that have fewer constraints (60). This person interacts very carefully with people and objects. They are an observer, constantly receiving immense amounts of information on the actions, behaviors, and attitudes of people around them. In their daily world, they watch and listen constantly. Why? Most of the time, it is because of their sincere interest in the actions, thoughts, and ideas of others. Being unique in perspective, there is a tendency to operate independently of others, sometimes in a world of one’s own. However, being socially aware, creative impulses are usually channeled into socially acceptable alternatives. The individual's attributes of introversion and feeling make them the serious and quiet person who works in his or her manner. They do not prefer large groups of people. Instead, they like to discuss significant topics of interest with people who understand them. Being excellent observers of people, they choose others who can share their insights and complex innuendos. This pattern of problem-solving is more prevalent in women although quite a few men show their strengths in literary and musical endeavors. The contact personality in older adults may show areas of compensation suggesting both positive and negative experiences through childhood and early adulthood. Perception is average and the tendency to analyze is often covered by social etiquette and social sensitivity. Note: Numbers in parentheses show the percentage of people in this group who agree with the statement. Interpret your scores relative to the pattern of the subgroup. 628 truck driver, operate machinery, or applied one talent to plumbing. Instead, creating literary Career works, writing music, or helping others is the key to success. Having better than average verbal, computational, and spatial skills, there is often confusion about how to apply these diverse sets of skills to the world in general. The future holds many different possible career patterns depending on how emotions and creative impulses are handled when encountering problems. The career profile paints a picture of one who is less interested in mechanical and realistic occupations. Instead, there is a preference for social value-oriented activities that present a nurturing and altruistic theme. There is less emphasis on control and more emphasis on letting events be as they may. Differential Problem Solvers with less computational interests and greater verbal skills may score in the average range or lower for spatial acumen. The greater emphasis on verbal or words may be applied in many different areas including sales, group endeavors, and advertising. During younger years, the search or application of primary skills can be quite confusing as a career field is not always evident. Potential Obstacles to Problem Solving In group problem solving, these individuals are process-oriented, focusing on how others in the group solve problems. There is evidence of a tendency to dominate verbally especially when ideas, values, and interests are close to one’s heart Differential Problem Solver (C) The basic adjectives describing the subgroup of differential problem solvers are selective, aloof, personable, intimate, and sometimes very unadaptable. Found in about five percent of the population, each finds his or her forte in endeavors needing individual effort and knowledge. This person scores higher than other persons on temperament tests measuring nuclear traits, such as gratefulness, kindness, idealism, friendliness, softheartedness, generousness, and introspectiveness. These traits are related to their perception of themselves and others. Tasks or jobs which allow one to see value beyond the routine of the job are motivating. For the differential problem solver, the pattern of problem-solving scores is in the average range or level C. The differential problem solver is motivated by interest patterns which are quite varied. His or her life is dominated by the desire to implement individual interests and find socially acceptable channels for emotions. Achieving personal goals is a means to an end; the end is to apply social and interpersonal skills in social situations. At times, the tendency to be impulsive dominates. Emotions and feelings are lurking near the surface, awaiting an entrance. The need for order and organization is achieved later in life as goal orientations are more associated with making a living. Differential problem solvers with very difficult early life experiences might show all kinds of acting out behaviors that posed problems for parents and those in authority. When there is not a match between environmental pressures from home, family, church, or sibling, confusion and a lack of goal orientation results. In such cases, there is a tendency to meet adversity with solemnness and passivity. Stress and environmental pressures can lead to all different kinds of compensation including the use of skillful ways of circumventing conventional rules and traditions. If he or she is too sheltered or fails to interact with enough people, each becomes The career theme is strong for the differential problem solver. He or she is less likely to be a 629 selfish and relies too much on one’s feelings. When compensating or relying on feelings, behavior is emotional and somewhat unpredictable. If one puts them in charge of a task or job they like, they do more than an adequate job. They do not do as well in jobs that do not match their ideals or strength. Parameters: Management Pattern 19 1. Management Identity: Trends show that Non-Management and Entrepreneurial Identity is average or high. Senior Management Identity is low except when the head of his or her own business, is like an Entrepreneur. Greater numbers are middle or upper managers in specialized businesses such as publishing, literary or creative professions. 2. Task Orientation Versus People Orientation: Greater numbers in management activities involve people. Can manage where motor or mechanical expertise is involved but does not prefer It. 3. Leadership: Shows greater management leadership for diverse and diffuse situations, especially creative situations. Task leadership is good only when expertise is involved. 4. 5. 6. 7. Assessment of Social, Practical, and Complex Situations: Better with social and practical situations. 8. Information Processing: Logical, Analytical scores generally average 7.5 with spatial higher for mechanically inclined. 9. Sales Management: Usually is less direct, more selling. PATTERN 19: General Parameters: Problem-Solving Orientation: Trends for these managers show adaptability, less structure, and more receptivity. Independence in Decision-Making: Varies with the individual but with experience will consult others. Can be stubborn when value Issues are involved. Efficiency Index: Scores higher on tasks related to people. 630 1. Age: 26-49. 2. General Preferences: Prefers aesthetic, literary, artistic, and social values; committed idealist. Lower preference for computational and clerical tasks, except to accomplish current interests. 3. Preferred Roles or Activities: Prefers management activities involving the giving of expertise and advice. Likes indirect roles where they are not in the spotlight. Prefers roles such as supervisor-subordinate, doctor-patient, and teacher-pupl1. 4. Avoids: Situations involving too much structure and control. Usually avoids conflict, numerous direct relationships, conventional values, and the use of tools or machines. 5. Achievement-Creativity: Achieves primarily in artistic, intellectual, and social areas. Achievement is underestimated. Achievement depends on the alignment of values and interests. 6. Self-Perceptions: Nurturing, achieving, impulsive, imaginative, self-accepting, tolerant, and dependent. 7. Other's Perceptions: Original, quiet, and sees the world from an individual standpoint. 12. Motivating Factors: Social welfare; creating a medium for approval (art, knowledge, etc.); social motives. 8. Perceptions: More field dependent than Field Independent. 13. Conceptual Versus Perceptual Motor Dominance: Conceptual. 9. Aptitude: Special abilities and Intelligence. Scores higher on verbal and form perceptions; latent mathematical aptitude. IQ range is 90130. Can possess special abilities in art, music, and architecture. 14. Sensory Modality Preference: Auditory, and visual. 15. Automatization: Moderate. 16. Constricted Versus Flexible Control: Flexible control. Preferred Style of Learning: Learns by reading and discussing; prefers Individual assignments, and open-ended responses. Learns best with an empathetic and caring teacher. 17. Risk-Taking taking. 18. Reflective Versus Impulsive: Prone to act impulsively but changes with maturity. 19. Cognitive Complexity Versus Simplicity: Cognitively complex. 20. Leveling Versus Sharpening: Leveling. 21. Compartmentalizing: Open system. 22. Breadth of categorizes. 23. Ego-Orientation: more other-oriented. 10. 11. Personality: Reduces stress by limiting social relationships. Asserts and enhances himself by helping dependent persons (gains love, recognition, and status); needs for admiration, power, and prestige are unconscious. Diminishes stress and anxiety by avoidance and denial where social roles are welldefined; can be passive-aggressive. Can be hostile and very resentful, if emotionally upset. 631 Versus Cautious: Categorization: Risk- Broadly 632 633 634 635 636 637 638 9. 639 640 641 642 643 644 645 646 . 647 648 649 650 651 652 General Problem Solver-30 with the statement. Interpret your individual scores relative to the pattern of the subgroup This pattern represents a subgroup of individuals with a higher general problem-solving score and more positive scores on verbal, number, and spatial problems. These scores are bolstered by a high score on control and structuring. All scores suggest a practical person who is less talkative, more, organized, very reliant on motor skills, and goal-oriented. experience and solve the problem by association or by focusing on detail (57). They learn best by doing and by reading (92). In a group problem-solving situation, they are confident about what works and does not work in solving any kind of problem with which they have previous experience. Oddly enough, although less talkative, they are quick to give their "two cents" about what works. Identifiers In a problem-solving situation, individuals in this subgroup go directly for the solution, not process. The quickest way to a solution is in a straight line. They are action-oriented and quick to determine what has worked in the past and applied it to the future. Find a way to calculate a solution or use standard practice as a methodology for the current problems. These folks are easy to identify. They are downto-earth and practical. Others characterized them as serious, quiet, usually hurried, and logical. The single adjective which characterizes this subgroup is "solid." They use ideas, but mainly those which have practical significance. They prefer to be conservative, thorough, and painstakingly accurate. With experience, standard practice is a measure of almost all problems to be solved. Tradition is to be upheld. These individual does not prefer large crowds. Instead, they prefer to work either alone on things which interest them, read a good book, or be with a small group of people (82). They are unlikely to engage in idle chit-chat but prefers to talk with close friends (67). They like to talk about important things. "Important things" are usually ideas that interest him at a point in time. Career The career scores paint a picture of a one who is interested in many different kinds of occupations such as accounting, math, and computer science or conventional occupations such as planner, architect, and professional. There is a preference for keeping things in order and getting things accomplished. This leads to goal orientation and success. In many cases, the person has what is known as tough poise, i.e., the ability to make difficult decisions, not getting too close to the interpersonal parts of the problem. This person follows protocol. That is there are rules and regulations which must be followed. Perception is strong as is an appreciation of objects, and structures in the environment. These people work for long periods of time on tasks that must be finished (63). Their hardworking, industrious nature makes them particularly difficult to stop once they have started a project. Problem Solving They are more likely to score in the middle or high ranges on preceptivity (77). They prefer to plan and think things out. When approaching a new problem-solving situation, if the problem is a familiar area, they use them Areas of occupational interest for this individual include accounting, middle-level administration, army officer, banking, high school teacher, Note: Numbers in parenthesis show the percentage of people in this group who agree 653 same way. The greater emphasis on verbal or words may be applied in many different areas including editorial, printing, or literary fields. While a greater interest in computation can lead to a career in accounting, computers, or software design. During the younger years, the search or application of primary skills can be quite confusing as a career field is not always evident. In group problem solving, this individual is less process oriented, focusing less on how others in the group solve problems. There is evidence of a tendency to dominate verbally especially when ideas, values, and interests are close to one’s heart service station manager, experimental psychologist, technical writing, computing, production record work, health care physician, public service, clerical work, mechanical engineering, and technical photography. This pattern is equally prevalent in men and women. The creative impulse finds its strength in replicating and extending patterns found in the environment. The contact personality in older adults is less likely to show areas of compensation suggesting more positive experiences though the child and early adulthood. There is some evidence that the constant analytic orientation is related to the early detection of threats as a means of survival in childhood. Perception is above average as is the need to constantly analyze everything. Differential problem solvers with very difficult early life experiences might show all kinds of different behaviours which pose problems for parents and those in authority. When there is not a match between environmental pressures from home, family, church, or sibling, confusion and a lack of goal orientation results. In such cases, there is a tendency to meet adversity with defiance and retaliation. Stress and environmental pressures can lead to all different kinds of compensations including the use of skillful ways of circumventing conventional rules and traditions. Differential Problem Solve For the differential problem solver, problemsolving scores are in the average range. The differential problem solver is motivated more by interest patterns which can be quite diverse. His or her life is dominated by the desire to achieve specific goals related to current interests. Achieving personal goals is a means to an end; the end is to dominate and conquer whatever. At times, the tendency to organize is pervasive. This can lead to a compulsive need for structuring things in the environment. Potential Obstacles to Problem Solving The greatest problems for this person arise from too much ambiguity from others in stating what they want. This individual thrives on the clarity of expression and explicitness. They do not prefer too much complexity. Complexity interferes with getting closure. They resist talking for great lengths of time because it interferes with his own productivity. They have many things they can be doing and just talking about them is not sufficient or nearly as efficient as doing them. Because they work with much care and patience, they often receive rewards and recognition for a job well done. They are proud of his accomplishments. Many people would not spend an equal amount of time to do the same task. The career theme is strong for the differential problem solver. They are found in construction, the food industry, or small entrepreneurial businesses. This person could be a truck driver, operate machinery, or apply one talent to construction. However, if any one of those careers becomes the current obsession, the desire to achieve is overwhelming. Differential Problem Solvers with more computational interests and greater verbal skills may score in the average range or high for spatial acumen. This person is less of a risk taker, and more cautious in orientation; that is, never get burned twice in the 654 6. 7. Because these individuals immerse themselves in a particular job or task that they enjoy, they may have difficulty understanding the needs of others. Primarily, this is because they feel that everyone should do a job as well as they do. Therefore, they have difficulty understanding why others do not finish tasks to their level of specificity. These individuals have a bent for completing a task with perseverance and industriousness. This makes them feel quite secure. They gain confidence from being able to do daily tasks. This is a suitable reinforcement for them. In instances where they are not allowed to complete a task to their level of specification, it becomes upsetting and distracting. 8. 9. Efficiency Index: Scores higher on tasks. Assessment of Social, Practical and Complex Situations: Better with practical situations and sometimes, complex situations, if technical. Information Processing: Logical, Analytical scores generally average 5.5 with spatial higher for mechanically inclined. Sales Management: Usually is direct, more likely to sell. PATTERN 30 General Parameters 1. Age: 26-49. 2. General Preferences: Prefers management in economic, and conventional areas. Less preference for aesthetic and religious. Can manage clerical and computational tasks. 3. Preferred Roles or Activities: Prefers management activities involving technically skilled trade, and engineering vocations. Likes athletics, mechanical drawing, marksmanship, racing, gardening, and surgery. 4. Avoids Social situations requiring independent expression such as personalized and artistic roles. Avoids ambiguous situations and problems. Also avoids intellectualism, artistic expression, social sensitivity, and skill. 5. Achievement-Creativity: Achieves primarily in technical and athletic areas. Identifies with material possessions. 6. Self-Perceptions: Persistent, mature, practical, organized, conservative, stable, and conventional. 7. Other's Perceptions: Convergent thinker, sees the world from an individual standpoint. 8. Perceptions: Field independence scores range from 41 high, 20 middle and to 39 low. This person has problems with unpleasantness in groups or situations where his or her skills are not appreciated. Parameters: Management Pattern 30 1. Management Identity: Trends show Middle Management and First Level is average or high. Senior Management Identity is low except when in a technical area or head of business as an Entrepreneur. Greater numbers are middle or first and middle-level managers. 2. Task Orientation Versus People Orientation: Greater numbers in management activities Involved with tasks. Can manage where a motor or mechanical expertise is involved. 3. Leadership: Shows greater management leadership for tasks. Task leadership is good where expertise is involved. 4. Problem-Solving Orientation: Trends for these managers show adaptability, more structure, and more preceptivity. 5. Independence in Decision-Making: Varies with the individual but with management experience, learns to consult. Can be stubborn. 655 9. 10. 11. 12. 13. Aptitude: Special abilities, and intelligence. Higher on clerical, and form perceptions with good mathematical aptitude. IQ range is 90-130. Preferred Style of Learning: Learns by doing and discussing. Prefers lecture, and assignments with right and wrong responses rather than open-ended. Learns best with a systematic, sequential and organized approach. Personality: Reduces stress by limiting social relationships. Defends self by "open rebuttal" passive-aggressive, or hostility. Maintains self-control by being organized and knowing what to expect. Dislikes being put in a situation where they or she cannot control the contingencies involved. Expresses life succinctly. Rule-oriented and conforming to cultural norms and values. Conceptual Versus Perceptual Motor Dominance: Conceptual. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 656 Motivating Factors: Rationalism, independence, and the common good. Sensory Modality Preference: Auditory, and visual. Automization: Moderate. Constricted Versus Flexible Control: Constricted control. Risk-Taking Versus Cautious: Cautious. Reflective Versus Impulsive: Prone to act and reflect. Leveling Versus Sharpening: Sharpening. Cognitive Complexity Versus Simplicity: Cognitively complex. Compartmentalization: Moderate system. Breadth of Categorizing: Broadly categorizes. Ego-Orientation: Self, individual, common good, and other-oriented. 657 . 658 659 660 661 662 663 664 665 666 667 668 Appendix C Analytic Items Version 2.0 Raw Score/Means, S.D. By Age and Education Age Male S.D. Female S. D. Range ED N Sp.E. S. D N. 09 2.34 2.90 1.85 2.90 0 4 4 143 .96 .36 45 10 3.61 2.11 3.51 2.03 0 5 5 156 1.07 .76 35 11 4.63 2.63 4.22 2.08 0 6 6 178 1.43 .98 59 12 5.12 2.42 4.42 2.32. 0 6 7 195 2.32 1.43 41 13 6.48 2.53 5.92 2.35 1 9 8 221 2.45 1.11 34 14 7.21 1.93 6.34 2.02 1 10 9 264 2.85 1.07 32 15 7.34 1.83 7.11 1.95 3 12 10 283 2.92 1.10 23 16 7.7 1.89 7.21 1.86 4 12 11 292 2.75 1.43 25 17 8.0. 1.64 7.34 1.93 4 12 12 234 18 8.7 1.54 8.3 1.75 4 12 13 211 19-20 8.6 1.93 8.4 1.76 4 12 14 345 21-22 9.4 1.53 9.2 1.84 4 12 15 167 23-2 49.7 1.2 9,3 1.43 5 12 16 194 25-26 10 1.1 9.7 1.54 5 12 17 175 27-28 10.2 1.1 9.8 1.76 6 12 18 187 Low Group 11-12 5.83 1.96 4.3 1.96 0 9 6 60 Michael (7th Grade) 14-17 5.85 1.76 6.54 2.09 1 12 10 91 Woolley (Alternative School) 14-17 6.10 1.92 6.24 1.92 0 10 10 172 Bernal-incarcerated delinquents Average Group 14-15 7.75 2.66 8.54 1.94 2 12 12 53 Goldstein 16-17 8.48 1.72 8.15 1.68 2 12 11 150 Jour 669 15-16 8.82 1.93 8.36 2.31 3 12 10 45 Miko 1.25 5 12 10 40 Cote-Private School 12 12 30 High School (High Group-Gifted) 16-17 9.5 1.34 9.5 16-17 10.2 1.23 9.6 2.3 21-24 8.81 3.02 8.5 2.82 2 11 13 165 Buck 19-21 9.83 1.83 8.0 2.83 2 11 13 12 Continuation Group 5 Spats-Gifted HS College Graduate School 26-28 8.22 1.13 8.76 1.45 5 12 17 29 Public (Education) 34-35 9.66 1.83 9.00 1.38 6 12 17 14 Public (Education) 27-34 10.55 1.83 9.92 1.55 5 12 17 56 Public (Agri) 28-39 10.6 1.84 8.76 1.48 4 12 17 38 Public (Education) 24-28 10.92 1.50 10.5 1.70 8 12 17 38 Private (Elite) 2 12 12 57 TRW m 57 2 12 14 220 Industry, Government, Military 24-42 8.28 1.56 24-42 8.40 3.29 29-36 8.80 1.32 2 12 12 36 TRW M 36 24-42 8.91 2.02 2 12 12 12 TRW 7/90 29-36 9.29 2.04 9.43 2.56 2 12 12 50 TRW-50-590 24-42 9.62 1.39 8.70 1.82 2 12 14 39 TRW sodata 24-39 10.2 2.04 8.68 1.85 Catalog 3 m&f Spatial items version 2.0: Age and Education Age 09 Male S.D. Female S. D. Range ED N Sp.E. S. D N. 6.68 4.90 6.85 4.95 0 4 143 2.0 .36 45 8 670 10 6.97 4.11 6.51 4.03 0 8 5 156 4.07 .76 35 11 7.54 4.63 6.22 4.08 0 10 6 178 4.43 .98 59 12 8.75 4.42 7.42 4.32. 0 10 7 195 6.32 1.43 41 13 9.26 4.53 8.92 4.35 1 12 8 221 7.45 1.11 34 14 12.45 4.93 9.34 4.02 1 14 9 264 8.85 1.07 32 15 13.21 4.83 11.11 4.95 3 18 10 283 8.92 1.10 23 16 14.50 4.89 12.21 4.86 4 20 11 292 9.75 1.43 25 17 14.85 4.64 12.34 4.93 4 22 12 234 18 14.10 4.54 13.3 4.75 4 24 13 211 19-20 14.50 4.93 13.4 4.76 4 24 14 345 21-22 15.12 4.53 14.2 4.84 4 24 15 167 23-24 15.60 4.2 14,3 4.43 5 24 194 25-26 15.80 4.1 14.7 4.54 5 24 17 175 27-28 16.10 4.1 14.8 4.76 6 24 18 187 Low Group 11-12 10.22 4.40 8.8 4.97 2 22 6 60 Michael-7th Grade) 14-17 10.98 5.26 11.7 5.46 2 22 10 91 Woolley-Alternative School) 14-17 10.75 5.92 2 22 10 172 4.94 2 24 12 63 Bernal-incarcerated delinquents Average Group 14-15 12.87 5.45 8.54 15-16 14.98 4.75 11.9 4.63 3 24 10 150 16-17 15.09 3.47 13.8 4.95 2 24 11 45 Goldstein Hunt DeNovellis High School (High Group-Gifted) 16-17 16.92 4.42 13.85 4.13 3 24 10 40 Cote-Private School 16-17 16.57 3.97 14.7 3.69 3 24 12 30 Spats-Gifted HS 14.45 3.02 14.10 2.82 2 24 13 165 College 21-24 671 Buck 19-21 16.00 5.32 14.33 3.01 2 8.76 1.48 4 24 13 12 Continuation Group 12 17 38 Public (Education) Graduate School 28-39 10.67 .74 26-28 15.90 4.02 13.9 4.42 5 12 17 294 03 87 (Education) 34-35 15.67 3.26 12.95 6.98 6 12 17 14 544 (Education) 24-28 16.83 3,86 14.33 3.93 8 12 17 38 Private (Elite) 27-34 17.89 4.08 17.24 4.14 5 12 17 56 Public (Agri) Industry, Government, Military 24-42 13.00 5.04 1.96 2 24 12 14 TRW 7/90 24-42 14.36 4.31 1.96 2 24 12 57 TRW m 57 29-36 14.11 4.23 2 24 12 36 TRW M 36 29-36 16.61 2.04 16.68 2.56 2 24 12 50 TRW-50-590 24-39 16.30 3.08 14.61 4.33 2 24 12 40 TRW sodata 40 672 Cog flex Cog Flex 5 Age Male S.D. Female SD. Range 05 2.8 1.2 2.5 1.2 0 5 16 0.00 0.0 00 06 3.5 1.6 3.5 2.30 0 9 66 2.36 1.8 22 07 4.2 2.3 4.6 2.24 0 11 185 3.40 1.4 42 08 5.5 2.3 6.0 2.54 0 12 324 4.65 1.36 15 09 5.6 2.8 6.1 2.60 0 12 135 5.33 2.0 47 10 5.7 2.7 6.6 2.78 0 13 142 5.6 2.3 41 11 7.1 3.0 6.7 3.31 0 13 188 6.15 2.5 25 12 7.5 3.2 8.5 3.25 1 13 94 6.6 2.4 92 13 8.3 3.1 9.3 5.3 0 13 125 7.0 2.56 32 14 9.9 3.1 8.2 6.6 0 13 63 6.8 2.5 32 17 7.5 2.8 8.7 3.0 5 13 79 18 8.5 2.8 8.5 3.3 5 13 89 19 8.4 2.6 8.3 3.4 5 13 97 20 7.5 3.8 8.0 3.5 6 13 89 21 8.3 4.4 8.1 3.5 8 13 77 22 7.7 3.6 7.9 3.2 6 13 74 23-24 6.8 3.0 7.5 3.4 7 13 74 25-26 6.8 4.2 7.4 3.6 6 13 75 27-28 7.0 2.8 7.4 3.6 6 13 72 29-30 8.0 2.0 8.5 3.4 6 13 70 31-32 9.5 3.5 8.4 3.0 6 13 67 33-34 9.0 3.1 9.2 2.9 6 13 67 35-36 8.0 3.5 9.3 2.8 6 13 58 37-38 7.5 3.0 8.3 3.2 6 13 58 39-40 7.3 1.7 8.3 3.1 6 13 61 673 N. Sp. Ed Std. D N 41-42 8.7 2.6 8.2 3.2 6 13 66 43-44 7.5 1.8 7.7 3.4 6 13 48 45-46 7.5 2.2 7.6 3.5 6 13 52 47-48 6.8 3.0 7.5 3.6 6 13 58 49-50 5.3 2.7 7.3 3.2 6 13 53 51-52 7.2 2.8 7.7 3.5 6 13 58 53-54 6.2 2.6 7.6 3.2 6 13 59 55-64 7.2 2.6 7.5 3.6 6 13 59 674 Letter identification Age M. Mean S.D. F Mean SD Range 05 7.8 4.9 6.1 3.4 0 29 06 10.06 6.0 11.6 4.6 9 07 13.9 6.5 14.2 5.7 08 18.1 6.6 20.4 09 21.01 10.5 10 23.2 11 Sp Ed M. S.D. 16 6.08 3.2 25 28 44 9.54 5.1 22 9 30 131 10.92 5.5 42 8.4 0 39 277 13.59 6.5 32 22.7 9.2 0 47 111 16.51 8.3 45 8.2 23.7 8.7 0 49 142 18.62 7.2 35 25.8 8.6 27.3 8.3 0 49 188 20.05 7.7 19 12 27.4 8.1 29.4 8.7 5 48 94 23.92 6.9 41 13 30.6 8.1 34.3 8.0 2 48 125 25.5 7.5 34 14 35.31 9.3 37.7 8.2 26 44 54 24.81 8.2 32 15 34.8 6.3 36.8 8.3 22 47 44 30.17 8.2 23 16 35.4 7.8 36.9 8.6 22 48 67 33.6 6.3 15 17 37.6 6.8 39.6 8.5 23 49 30 18 36.6 8.1 38.9 8.2 21 49 27 19 37.1 6.2 39.2 9.1 21 49 77 20 37.7 7.2 38.6 9.1 20 48 79 21 37.5 6.2 38.5 9.0 21 48 79 22 34.3 5.9 37.5 9.6 21 48 89 23-24 37.3 4.3 37.6 9.6 22 48 74 25-26 38.0 7.4 38.5 9.5 22 48 76 27-28 32.5. 6.8 39.6 9.3 22 49 72 29-30 37.5 7.7 38.5 9.5 22 49 70 31-32 38.8 4.5 39.6 9.4 22 49 67 33-34 32.5 9.2 38.6 9.3 22 49 67 35-36 35.4 8.2 37.6 9.2 22 49 67 675 N. N. 37-38 32.2 8.2 35.2 9.1 22 43 58 39-40 32.8 7.2 38.9 8.7 22 43 61 41-42 35.0 7.3 38.5 8.8 22 42 66 43-44 31.7 6.4 38.4 8.4 22 44 48 45-46 29.5 6.4 34.6 8.3 22 43 42 47-48 25.5 8.4 35.6 8.7 22 42 48 49-50 26.4 8.5 33.7 8.6 22 41 58 51-52 23.8 4.9 35.6 8.5 22 40 58 53-54 26.4 5.9 36.3 8.3 19 35 59 55-64 29.5 6.02 38.2 8.8 15 41 59 676 Embedded designs Age M. Mean S.D. F. Mean S.D. Range N Sp Ed S.D. N 05 1.5 4.2 2.8 1.9 0 5 16 0.00 0.0 00 06 7.8 5.6 6.2 3.9 1 21 44 2.37 4.8 22 07 7.94 6.0 6.8 5.9 3 11 131 5.26 4.9 42 08 9.0 6.0 11.5 8.7 0 28 277 9.03 6.4 32 09 13.7 9.4 12.1 8.6 0 32 111 13.84 9.5 45 10 16.4 7.8 14.5 8.3 1 32 142 12.88 7.1 35 11 14.3 7.5 14.2 8.2 1 32 188 14.00 7.5 19 12 15.8 8.2 17.1 8.3 6 24 93 15.00 7.9 40 13 17.6 8.9 18,4 8.1 0 32 125 16.14 8.1 34 14 19.3 8.1 21.5 7.9 0 32 66 15.65 7.1 32 15 22.5 5.8 23.9 7.9 10 32 54 25.30 8.3 23 16 23.7 7.0 25.5 7.3 7 32 66 25.2 7.2 15 17 23.8 7.4 25.5 7.3 8 29 67 18 17.1 10.5 26.7 7.6 9 30 48 19-20 15.2 13.6 27.7 7.5 7 30 45 21-22 15.0 10.7 26.5 7.5 8 30 66 23-24 16.0 10.5 25.4 7.4 7 30 60 25-26 21.7 7.4 26.4 7.2 8 30 75 27-28 17.6 8.6 25.4 7.6 9 31 62 29-30 28.6 11.4 26.4 7.1 8 29 60 31-32 27.5 5.8 27.6 7.9 18 30 77 33-34 19.6 6.3 26.1 6.7 19 31 67 35-36 26.5 5.0 25.4 6.9 18 31 70 37-38 21.6 7.2 24.3 7.2 17 31 68 39-40 23.3 8.0 24.1 8.1 16 31 61 41-42 21.7 6.9 23.5 6.9 17 31 60 43-44 22.6 7.0 22.6 7.3 18 31 58 677 45-46 21.4 5.9 22.7 7.5 19 31 42 47-48 20.0 7.8 21.8 7.2 18 31 48 49-50 14.9 6.1 20.8 7.3 19 31 53 51-52 20.7 8.4 20.7 6.8 15 31 58 53-54 20.3 5.6 21.6 6.9 16 31 59 55-64 18.2 6.4 20.4 6.9 15 31 59 Arithmetic Distraction Memory Total Memory-right Age Mean S.D. Range N. 5 0.00 0.0 0 00 00 0.00 0.0 0-00 00 6 00.00 0.00 0 00 00 2.79 1.93 0-05 14 7 06.23 3.92 0 14 24 03.64 3.00 0-10 14 8 07.68 3.48 0 16 47 04.64 4.94 0-14 14 9 08.39 5.08 0 16 60 04.20 3.66 0-12 15 10 09.65 5.09 0 23 54 05.27 3.73 0-12 15 11 10.60 5.23 0 26 187 08.13 6.46 0-22 22 12 00.00 0.00 0 00 00 05.48 4.86 0-17 33 13 00.00 0.00 0 00 00 07.21 5.02 0-22 23 14 10.60 4.50 4 18 10 06.38 4.78 2-15 13 15 10.90 4.58 1 16 10 16 10.16 2.74 6 14 06 678 Sp. E Wrong 5.12 Sp Ed M. S.D. Age N. Appendix D Sample Sizes, Means, and Standard deviations from selected studies 1977 to 2002. Frequent Question: Total does not add up to 5000. Why? The list does not include many small samples that are non-public as they represent proprietary data from Fortune 500 companies. Gender 3 is composite male and female. Gender 1 is male, Gender 2 is female. Original means and standard deviation have since been revised based on re-scoring or psychometric item analysis. ID 21 22 23 24 25 26 27 28 29 30 Catalog LSI Rating LSI Rating LSI (0a) LSI (0a) LSI (1) LSI (1) LSI (2) LSI (2) LSI (3) LSI (3) Date 8801 8801 8801 8801 8901 8901 9201 9201 9201 9201 Age 5&6 5&6 8&9 8&9 8&9 8&9 9&10 9&10 9&10 9&10 Education Level 1 1 3 3 3 3 4 4 4 4 Version no. 2 2 2 2 2 2 2 2 2 2 Test 3 3 3 3 3 3 3 3 3 3 Criterion 1st grade 1st grade 3rd grade 3rd grade 3rd grade 3rd grade 4th grade 4th grade 4th grade 4th grade Gender 2 1 1 2 2 1 1 2 1 2 Sample size 71 48 15 13 28 41 41 28 22 24 Ps30 (Psa) 12.37 14.01 13.29 13.27 Perceptual 29.54 33.72 27.72 30.14 22.84 28.18 29.07 26.86 27.26 26 Conceptual 31.18 34.5 35.2 35.06 32.7 29.88 28.68 32.71 27.44 28.66 Motor 33.06 35.9 18.66 22.46 23.42 29.56 29.56 23.43 30.72 28.16 Analytical 30.52 33.96 29.86 30.76 38.7 45.36 45.37 38.71 47.44 40.38 Social 33.86 36.3 44.52 43.38 47.84 38.72 38.73 47.86 30.9 37 Control/Str. 33.62 36.34 48.8 47.68 45.84 38.52 38.54 45.86 31.08 36.6 Flex 67.57 59.1 83.34 82 84.65 84.1 66.29 65.57 85.64 87.66 Exint 15.15 17.37 16.8 17.23 17.64 16.82 16.83 17.64 16.55 17.25 ID 109 110 89 90 31 32 33 34 35 36 Pslap Pssp Dif 679 Catalog name LSI (4) Err LSI (4) Err LSI J LSIJCx LSI (4) Lau LSI (4) Lau LSI (5) An LSI (5) (An LSI (5a) (B.h.) LSI (5a) Bth Date 9901 9901 9506 9506 9001 9001 8901 8901 9201 9201 Age 10&11 10&11 10&11 10&11 12 12 13 13 14 14 Education Level 5 5 6 6 7 7 8 8 9 9 Version no. 2 2 3 3 2 3 2 2 2 2 Test 3 3 3 3 3 3 3 3 3 3 Criterion 5t h grade 5th grade 6th grade 6th grade 7th grade 7th grade 8th grade 8th grade 9th grade 9th grade Gender 1 2 1 2 1 2 1 2 1 2 Sample size 60 54 91 83 38 44 33 49 25 32 10.76 11.05 11.88 11.9 10.29 10.73 10.77 11.05 13.87 12.4 8.78 9.43 11.88 12.32 12.58 13.35 11.94 12.5 13.68 13.32 11.78 12.13 14.64 14.04 Ps30 (Psa) Pslap 12.25 12.36 Pssp Dif 12.75 12.68 Perceptual 39 39.93 31.28 29.78 36.42 38.28 36.54 30.28 35.68 36.24 Conceptual 41.53 46.44 35.76 38 35.3 37.9 33.94 36.52 31.6 31.5 Motor 36.93 33.48 32.3 29.1 34.52 32.76 34.18 34.5 37.76 39.92 Analytical 47.07 45.48 32.7 28.66 38.14 32.18 40.68 31.22 37.68 28.12 Social 44.63 49.52 41.02 45 42.58 59.94 28.78 38.2 42 48.74 Control/Str. 48.4 58.37 57.84 61.14 64 61.04 39.74 51.26 59.36 51.74 Flex 54.6 46.89 80.29 80.51 74.14 75.22 78.55 82.86 74.56 75.69 Exint 23.03 22.52 17.41 17.03 15.42 21.81 15.08 19.96 15.04 16.81 ID 38 41 42 43 44 94 95 2 3 4 Catalog name LSI (6) LSI (7)W LSI (8) LSI (9)Nny LSI Nny Linny (LSI)Nny cat 401-700 cat 7011000-f cat 10001491 Age 14-17 14-18 14-18 14-18 14-18 14-17 14-17 17+ 17+ 17+ Date 8701 8801 8801 8801 8801 8801 8801 8601 9101 8901 Education Level 10 11 11 9 & 12 9 & 12 11 11 13 13 13 Version no. 1 2 2 1.5 1.5 1.5 1.5 1 2 2 Test 3 3 3 1 1 1 1 1 1 1 Criterion tenth thru senior eleventh grade eleventh grade ninth thru twelfth ninth thru twelfth Juv. Delinq Juv. Delinq Students Work Work Gender 2 1 2 1 1 2 2 1 1 1 680 Sample size 31 42 49 161 172 149 50 94 56 96 Ps30 (Psa) 11.62 10.64 11.08 10.67 11.13 11.64 1.09 11.3 12.63 13.23 Pslap 13.04 10.07 11.04 10.44 10.3 11.27 1.44 11.86 13.54 15.34 Pssp 12.48 11.99 12.39 11.88 12.86 12.42 0.46 12.42 14.23 14.55 Dif 12.24 13.97 13.29 13.84 13.42 13.17 0.83 12.86 11.12 10.06 Perceptual 36.9 34.76 38.66 34.84 26.68 32.33 4.76 40.08 40.5 40.36 Conceptual 34.18 32.16 34.38 34.12 38.1 34.09 4.21 33.32 34.92 33.92 Motor 32.24 33.96 34.42 35.26 31.18 31.68 5.09 34.9 31.82 35.7 Analytical 34.32 34.28 28.38 33.3 32.9 36.24 6.08 35.42 38.88 43.08 Social 42.16 33.1 40.76 35.78 35.44 40.81 6.81 34 31.96 35.24 Control/Str. 36.24 34.6 35.32 44.38 46.66 45.8 9.89 43.28 44.92 61.36 Flex 77.81 76.37 75.38 86.18 79.14 75.54 10.1 39.94 46.74 44.56 Exint 25.41 13.71 18.72 17.36 13.83 16.96 13.87 12.96 ID 5 6 7 8 9 10 11 12 13 14 Catalog name cat 1 14912000-f cat 114912000 cat 3 m cat 4 m cat4f ca5m ca1 1-400 cat 401-700 cat 7011000-f cat 10001491-f Age 17+ 17+ 17+ 17+ 17+ 17+ 17+ 17+ 17+ 17+ Date 8801 8401 8801 8801 9001 8901 8401 8601 9101 8901 Education Level 13 13 15 13 13 15 14 13 13 14 Version no. 2 1 2 2 3 2 1 1 2 2 Test 1 1 1 2 2 1 1 1 1 1 Criterion Work Work Work Work Work Work freshman -seniors freshman/so phomores Work Work Gender 1 1 1 1 1 1 2 2 2 2 Sample size 140 416 464 427 195 80 148 57 39 119 Ps30 (Psa) 13.79 12.71 13.25 13.06 12.4 12.08 12.84 12.6 Pslap 15.99 13.78 14.2 13.4 12.92 12.66 13.93 14.23 Pssp 15.34 14.27 15.15 15.18 14.09 13.57 14.46 13.83 Dif 9.34 10.98 10.33 10.71 11.5 11.89 10.81 10.97 Perceptual 42.5 34.32 41.38 40.4 38.7 39.64 38.56 41.76 Conceptual 34.04 32.32 33.72 29 32.98 29.36 30.8 33.04 41.42 31.02 Motor 36.28 29.94 35.48 40 35.66 38.64 35.64 33.46 26.1 37.4 Analytical 39.66 39.22 40.18 46.76 44.62 36.88 29.52 27.88 33.88 35.14 Social 39.76 34.26 39.18 42.6 47.84 39.18 39.8 38.28 34.34 43.38 681 Control/Str. 67.2 43.74 57.2 58.4 60.94 65.14 45.72 46.94 46.46 59.54 Flex 50.48 40.9 50.52 53.22 54 47.46 42 43.48 52.4 45.4 Exint 11.6 14.48 13.49 14.17 14.38 12.42 19.11 19.44 17.85 14.84 ID 15 16 17 18 19 20 39 40 47 48 Catalog name cat 1 1 cat 2 f cat 3 f cat 4 f cat 4 f cat 5 f Gifted Gifted Miko Miko's Date 9001 8401 8801 8801 9001 8901 9001 9001 8501 8501 Age 17+ 17+ 17+ 17+ 17+ 17+ 14-18 14-18 17+ 17+ Education Level 14 14 14 14 14 15 9 9 11 11 Version no. 3 1 2 2 3 2 3 3 1 1 Test 1 1 1 2 2 1 3 3 1 1 Criterion Work Work Work Work Work Work ninth thru twelth ninth thru twelth elevent h/tweth eleventh grade Gender 2 2 2 2 2 2 1 2 1 2 Sample size 250 291 530 152 71 140 50 49 60 31 Ps30 (Psa) 13.26 12.42 12.91 13.32 11.87 11.7 11.86 11.58 Pslap 15.54 13.47 13.72 14.6 11.96 11.95 13.02 12.86 Pssp 14.5 13.86 14.72 15.09 13.5 13.18 12.95 12.48 Dif 9.98 11.34 10.78 10.16 12.27 12.44 12.02 12.33 Perceptual 45.5 33.72 42.06 41.7 0 0 32.12 33.5 Conceptual 30.36 32.84 32.74 28.6 33.08 32.62 37.64 38.12 30.6 28.78 Motor 40.72 29.54 36.7 40.6 35.68 36.2 31.88 32.6 31.12 34.68 Analytical 35.1 33.02 34.44 39.64 39.8 31.96 38.12 32.6 42.72 33.7 Social 44.92 38.18 45.78 48.6 51.82 45.94 33.16 39.9 36.32 42.46 Control/Str. 77.92 41.48 57.14 51.76 57.8 67.5 46.72 51.1 38.52 38.06 Flex 49.88 36.94 49.92 48.76 54.92 50.18 0 0 31.6 32 Exint 12.98 17 17.27 16.38 15.96 16 13.12 21.38 17.83 20 ID 49 50 51 52 53 54 55 56 57 58 Catalog name Cote's Study-m Cote's Study-f Spats -m Spats -f 544 544 jour-45 m jour-45 f Cont-m Cont Date 9201 9201 9001 9001 8901 8901 8701 8701 9001 9001 Age 16-17 16-17 14-17 14-17 22+ 22+ 16-17 16-17 19-14 19-14 Education Level 11 11 11 11 11 11 11 11 14 13 682 Version no. 3 3 3 3 2 2 1 1 3 3 Test 1 1 1 1 1 1 1 1 1 1 Criterion eleventh/ twelvth eleventh grade eleventh grade eleventh grade eleventh grade eleventh/t welth grade Journalis m eleventh journalism eleventh grade freshma n/soph omores freshman/ sophomor es Gender 1 2 1 2 1 2 1 2 Sample size 26 14 19 11 108 42 11 34 6 6 Ps30 (Psa) 14.11 13.34 14.2 13.59 11.03 11.36 12.57 12 13.96 13.08 Pslap 16 16 16.71 16.13 10.88 11.93 12.68 12.65 16.33 14.5 Pssp 15.96 14.43 15.79 14.86 12.37 12.5 14.55 13.43 15.5 14.67 Dif 9.02 9.79 8.75 9.51 13.38 12.79 11.39 11.96 9.09 10.42 Perceptual 42 45.14 39.78 41.8 40 35.34 39.62 41.54 38.66 43.34 Conceptual 29.22 28.42 38.52 35.08 33.34 26.58 37.62 39.1 30.66 35 Motor 42.06 42 32.2 36.36 34.82 35.92 31.08 32.16 40.66 35.66 Analytical 40.14 35.14 46.32 39.62 35.34 24.5 39.8 29.22 32 30 Social 40.3 46 33.36 38.18 34.32 37.28 30.54 39.4 48.32 51.34 Control/Str. 63.84 79.7 45.68 50.54 42.46 38.06 44 44.7 34.66 68.66 Flex 49.22 54.84 48.84 53.08 38.92 37.28 45.8 48.94 54.66 54 Exint 16 14.57 12.42 21 17.07 18.83 23.09 28.26 18.33 18.5 ID 59 60 61 62 63 64 65 66 67 68 Catalog name RON Ron2 Contin 455 455 HF HF Cal Techn Cal Tech TRW52 Age 16-19 16-19 19-22 23+ 23+ 22+ 22+ 22+ 22+ 31= Date 9001 9001 9101 9201 9201 9201 9201 9001 9001 8601 Education Level 14 14 13 15 15 16 16 15 15 13 Version no. 2 2 3 3 3 3 3 3 3 1 Test 1 1 1 1 1 1 1 1 1 1 Criterion Internati onal Relations Internati onal Relations freshman college teachers teachers Business, teachers Business, teachers junior/senior seniors Electronic Gender 1 2 1 1 2 1 2 1 2 1 Sample size 12 12 18 3 15 37 57 26 38 28 Ps30 (Psa) 13.56 12.88 13.75 13.84 13.73 14.68 13.99 Pslap 15.92 15.67 16.28 16.17 16.3 17.14 16.74 Pssp 14.92 13.67 15.11 15.34 15.07 16.53 15.37 683 Dif 9.58 10.33 9.31 9.25 9.32 8.17 8.95 Perceptual 39.34 37.32 44.44 44 44.52 42.8 46.58 40.92 45.26 28.5 Conceptual 29 29.34 26.88 15.32 29.2 30.42 28.06 41.38 33.84 29.42 Motor 31.5 33 45.32 56 43.2 39.08 43.36 28.6 35.36 34.56 Analytical 53.34 43 26.76 30.66 26 43.08 33.36 38 37.52 40.84 Social 28.34 41 54.34 50.66 55.06 35.94 46.98 39.92 41.36 29.7 Control/Str. 44 44.34 78.44 49.32 84.26 78.36 79.08 54.6 78 37.14 Flex 34.82 30.66 51.54 54.66 50.92 50.38 52.36 50.92 44 37.14 Exint 20.42 19 16 2.67 18.67 7.48 10.98 11.88 14.47 11.85 ID 69 70 71 72 73 74 75 76 77 78 Catalog name TRW 522 TRW-1 TRW-2 TRW57 TRW36 TRW590 TRW5902 TRW790-1 TRW79 0-1 TRWimg Date 8601 8803 8803 8812 8911 9005 9005 9007 9007 9100 Age 31+ 31+ 31+ 31+ 31+ 31+ 31+ 31+ 31+ 31+ Education Level 13 14 14 14 14 14 14 14 14 14 Version no. 1 2 2 2 2 3 3 2 3 3 Test 1 1 1 1 1 1 1 1 1 1 Criterion junior/se nior analyst analyst analyst analyst analyst analyst analyst analyst analyst Gender 2 1 2 1 1 1 2 1 1 1 Sample size 7 26 13 57 36 34 16 41 12 14 Ps30 (Psa) 13.61 12.98 12.79 12.85 13.98 14.03 13.71 12.98 12.93 Pslap 14.62 13.8 13.28 13.8 15.79 15.93 15.28 15.41 12.78 Pssp 15.65 14.81 14.68 14.56 15.81 15.84 15.54 14 15.21 Dif 9.87 10.7 11.02 10.82 9.2 9.12 9.59 10.3 11.01 Perceptual 30.28 43.52 47.38 42.44 44 44.34 43.5 40.96 48.34 36.52 Conceptual 25.7 34.3 35.06 31.12 31.72 38.34 29.74 30.58 23.16 26.56 Motor 31.42 36.52 33.52 39.36 38.88 30.94 40.12 38.48 47.82 43.56 Analytical 36 46.22 38.46 42.7 38.6 43.34 39 44.18 39.16 38.7 Social 34.84 31.92 39.06 37.42 41.5 37.82 40.5 33.8 38 39.42 Control/Str. 37.14 60.3 55.68 54.58 55.32 68.7 76.5 59.9 77.34 52 Flex 44.56 49.68 52.32 51.28 48 60.82 61 48.18 45.66 51.42 Exint 13.71 12.62 20.16 14.67 13.83 9.82 11.75 8 5.67 14.28 684 ID 79 80 81 82 83 84 85 86 87 88 Catalog name agr Agrf Psy403 psy403 Ad544 m Ad544f Ve3 m Vers3f Ver3M B Ver3MBf Age 35+ 35+ 23+ 23+ 23+ 23+ 31+ 31+ 22+ 22+ Date 8501 8501 8707 8707 8703 8703 9101 9101 9502 9502 Education Level 16 16 15 15 15 15 14 14 15 15 Version no. 1 1 1 1 1 1 3 3 3 3 Test 1 1 1 1 1 1 1 1 1 1 Criterion Agr Ag Teachers Teachers Work Work Work Work Bus Bus Gender 1 2 1 2 1 2 1 2 1 2 Sample size 33 25 8 21 6 8 68 72 79 87 Ps30 (Psa) 13.54 13.29 12.94 12.67 12.75 11.81 14.01 13.65 13.32 13.15 Pslap 14.75 14.42 14.87 13.26 13.83 13.5 15.97 16.11 15.31 15 Pssp 15.45 15.12 14.19 14.45 14.34 12.63 15.78 14.99 14.73 14.55 Dif 9.9 10.23 10.47 11.15 10.92 11.94 9.13 9.45 9.98 10.23 Perceptual 35.42 36 43.5 43.62 41.32 45 41.4 46.22 44.3 41.78 Conceptual 27.16 27.04 36.74 35.22 30 33.24 30.82 30 29.58 30.02 Motor 33.6 31.84 34.24 37.04 37.66 36.5 39.1 41.5 40.32 40.66 Analytical 35.6 37.76 30.74 27.62 40.66 35 45.18 33.8 41.96 34.88 Social 44.22 41.44 36.5 42.38 31.32 36.5 33.02 46.5 36.4 44.68 Control/Str. 45.14 48.32 50 53.14 53.34 54 60.3 70.26 73.56 74.42 Flex 38.62 41.44 54.5 55.62 44 53.5 48.88 52.76 47.12 47.74 Exint 18.22 18.56 24.5 21.23 13.67 21.5 8.23 13.04 6.87 11.59 ID 92 93 94 95 96 97 98 99 100 101 Catalog name 403m 403f Nnypl Nnypl Kir Kir Syl Sylm Gregm Bill70m Date 8707 8707 8503 8505 9811.09 9811.09 Age 23+ 23+ 14-17 14-17 15-17 15-17 12 12 16 14-17 Education Level 15 15 11 11 11 7 7 7 11 11 Version no. 2 2 1.5 1 2 2 1 2 1 1 Test 1 1 1 1 1 1 1 1 1 1 Criterion Grad Grad Incarc Incarc Students Students Students Stud Stud Stu Gender 1 2 2 1 1 2 2 1 1 1 Sample size 8 22 15 83 57 44 18 18 28 30 Ps30 (Psa) 12.94 12.67 11.07 11.04 12.18 12.01 11.06 11.96 11.6 12.53 685 8501 Pslap 14.87 13.26 9.96 10.46 13.46 13.18 12.06 11.83 12.23 14.13 Pssp 14.19 14.45 12.91 12.59 13.38 13.18 11.83 13.75 12.84 13.73 Dif 10.47 11.15 13.56 13.47 11.58 11.83 13.06 12.21 12.46 11.07 Perceptual 43.6 43.4 40.8 40.14 39.72 41.64 41.33 42.67 41.76 31.07 Conceptual 35.2 36.6 32.04 32.14 34.67 30.73 37.56 36.89 34.32 31.47 Motor 37 34.2 37.12 36.65 43.86 47.36 42.22 44 34.96 34.67 Analytical 27.6 30.6 35.4 35.33 42.25 33.73 38.44 39.56 35.84 47.33 Social 42.2 36.4 35.48 35.3 40.63 49.64 47.33 45.78 34.24 33.87 Control/Str. 53 50 49.44 49.01 36.91 36.45 44.44 39.78 44.48 34.13 Flex 54.2 54.4 38 39.18 39.16 37 42.89 40.67 40.32 32.4 Exint 21.2 24.5 15.2 14.27 19.37 21.91 20.89 17.22 15.84 18.67 ID 102 103 104 105 106 107 108 111 112 Catalog name Bill70f Ptpi305 Ptpi305f Wool Wolleyf Agriman Agri Unk Unk Date 8501 Age 14-17 22+ 22+ 15-17 15-17 35+ 35+ Education Level 11 12 12 11 11 14 14 Version no. 2 1 2 1 1 1 1 Test 1 1 1 1 1 1 1 Criterion Studs Work Work Stud Stud Mgr. Gender 1 1 2 1 2 1 2 Sample size 40 96 111 71 43 43 42 146 187 Ps30 (Psa) 12.16 12.7 12.73 10.67 11.08 13.53 13.29 12.97 0.84 Pslap 13.75 14.69 14.63 10.06 11.05 14.76 14.42 14.36 1.6 Pssp 13.19 13.81 13.89 12.06 12.39 15.44 15.12 14.5 0.99 Dif 11.53 10.75 10.74 13.94 13.28 9.9 10.23 10.57 1.22 Perceptual 35 41.33 42.38 28.62 30.57 35.43 36 39.6 8.34 Conceptual 29.7 31.63 30.22 31.69 34.24 27.18 27.04 31.84 4.32 Motor 32.2 37.78 40.55 34.65 34.43 33.6 31.84 36.59 4.88 Analytical 35.7 38.29 32.43 34.62 28.38 35.6 37.76 36.97 5.76 Social 40.5 39.65 47.55 33.24 40.76 44.23 41.44 39.86 6.02 Control/Str. 42.4 60.79 66.09 36.96 35.33 45.14 48.32 56.08 12.93 Flex 35 50.3 51.25 37.07 40.76 38.63 41.44 46.24 10.63 Exint 18.7 12.93 16.26 13.49 18.76 18.23 18.56 15.57 4.71 686 Sample Characteristics: The next Table 88 indicates the general ages, gender, and dates of the samples collected with the data re-analyzed under the present theory. Demographic Characteristics of Studies Name of sample Date Sample size Age Age SD Range Min Max Gender cat 1000-1491-m 8901 96 23.33 9.9 38 14 52 1 cat 1 1491-2000-m 8801 140 26.13 8.87 38 16 54 1 cat 2 males-m 8401 416 33.09 13.02 57 10 57 1 cat 3 males-m 8801 464 34.11 12.06 17 19 74 1 cat 4 males-m 8801 427 40.07 10.74 45 19 64 1 cat 4 males-m 9001 195 41.4 8.5 55 19 74 1 cat 5 males-m 8901 80 34 10.81 54 13 67 1 ca1 1-400-f 8401 148 22.85 8.76 44 15 59 2 cat 401-700-f 8601 57 20.77 8.74 49 7 58 2 cat 701-1000-f 9101 39 25.71 11.21 48 12 56 2 cat 1000-1491-f 8901 119 23.33 9.9 38 14 52 2 cat 1 1491-2000-f 9001 250 26.13 8.87 38 16 54 2 cat 2 females-f 8401 291 33.09 13.02 57 10 57 2 cat 3 females-f 8801 530 34.11 12.06 17 19 74 2 cat 4 females-f 8801 152 36.46 9.5 33 22 55 2 cat 4 females-f 9001 71 38.77 7.63 44 22 66 2 cat 5 females-f 8901 140 34 10.81 54 13 67 2 LSI rating 5-6 -f 8801 71 5.5 0.32 2 5 6 2 LSI ratings 5-6-m 8801 48 5.5 0.32 2 5 6 1 LSI (0a) -m 8-9 8801 15 8.26 0.46 1 8 9 1 687 LSI (0a) -f 8-9 8801 13 8.26 0.46 1 8 9 2 LSI (1)-f 8-9 8901 28 8.5 0.76 1 8 9 2 LSI (1)-m 8-9 8901 41 8.5 0.46 1 8 9 1 LSI (2) -m 9-10 (Hvidson) 9201 32 9.5 0.28 1 9 10 1 LSI (2) -f 9-10 (Hvidson) 9201 46 9.5 0.28 1 9 10 2 LSI (3) -m 9-10 (Denise) 9201 22 9.5 0.48 1 9 10 1 LSI (3) -f 9-10 (Denise) 9201 24 9.5 0.48 1 9 10 2 LSI (4) -m 12 (Laurie) 9001 38 12 0 0 12 12 1 LSI (4) -f 12 (Laurie) 9001 44 12 0 0 12 12 2 LSI (5) -m 13 (Ann) 8901 33 13 0 0 13 13 1 LSI (5) -f 13 (Ann) 8901 49 13 0 0 13 13 2 LSI (5a) -m (Beth) 9201 25 14 0.26 1 13 14 1 LSI (5a) -f (Beth) 9201 32 13.94 0.41 1 13 14 2 LSI (6) -m 14-17 (Ila) 8701 22 14.61 0.62 3 14 17 1 LSI (6) -f 14-17 (Ila) 8701 31 14.72 0.62 3 14 17 2 Gifted (7) -m 14-18 (Deno) 9001 50 16 1.96 4 14 18 1 Gifted (7) - f 14-18 (Deno) 9001 49 16 1.96 4 14 18 2 LSI (8) -m 14-18 (Wolley) 8801 42 16 1.48 4 14 18 1 LSI (8) -f 14-18 (Wolley) 8801 49 16 1.48 4 14 18 2 LSI (9) -m 14-18 (Nony) 8801 161 16 1.95 4 14 18 1 LSI (10) -m 14 -18 (Nony) 8801 172 16 1.53 4 14 18 1 Bill's Study-m 8501 30 15.5 0.5 2 15 16 1 Bill's Study-f 8501 40 15.5 0.5 2 15 16 2 Miko's Study-m 8501 60 16.5 0.93 5 13 18 1 Miko's study -f 8501 31 16.5 0.93 5 13 18 2 Cote's study-m 9201 26 17 0.86 2 16 18 1 Cote's Study-f 9201 14 16.34 0.86 2 16 18 2 Spat's -m 9001 19 16.51 0.58 2 15 17 1 Spats -f 9001 11 16.51 0.58 2 15 17 2 544 Data Collection 8901 108 16.33 1.69 7 15 22 1 688 544 Data Collection 8901 42 16.42 3.44 7 15 22 2 Jour-45 m 8701 11 16.36 0.8 2 15 17 1 Jour-45 f 8701 34 16.35 0.77 2 15 17 2 Continuation group -m 9001 6 21.02 2.56 4 19 23 1 Continuation group -f 9001 6 21.02 2.56 4 19 23 2 Ron's Group-m 9001 12 24.6 3.67 6 18 27 1 Ron's Group -f 9001 12 24.5 3.47 6 18 27 2 Continuation group2-m? 9101 18 33.11 8.28 29 21 50 1 455-m group with demographic 9201 3 30.27 7.45 26 23 50 1 455-f group 9201 15 30.27 7.45 26 23 50 2 Human Factors-m 9201 37 29 6.99 1 Human Factors-f 9201 57 33 8.89 2 Cal Tech-m short version 9001 26 21.34 2.99 1 Cal Tech-F short version 9001 38 22.65 4.74 2 TR 52 w/ Survey m 8601 28 24.39 5.21 1 TR 52 w/ Survey f 8601 7 21.85 1.21 2 TR sodata40 m 8803 26 33 6.61 26 23 49 1 TR sodata 40 f 8803 13 28.38 7.05 26 23 49 2 TR -m 57 8812 57 33 7.05 1 TR -m 36 8911 36 33 7.05 1 TR 50-590 M 9005 34 44 7.05 1 TR 50-590 f 9005 16 44 7.05 2 TR 7/90/ 10+ m 9007 41 33 7.05 1 TR 7/90/ 10+ m 9007 12 33 7.05 2 TR Image 14 -m 9100 14 33 7.05 1 Agri-m 8501 33 33 2.03 1 Agri-f 8501 25 25 2.4 Psy 403 m 8707 8 27 5.23 1 Psy 403 f 8707 21 27 5.23 2 Adoles 544 m 8703 6 35.08 9.56 689 2.03 37 2 22 59 1 Adoles 544 f 8703 8 35.08 9.56 37 22 59 2 Version 3 m 9101 68 29 11.5 35 15 50 1 Version 3 f 9101 72 29 11.5 35 15 50 2 Version 3 Mary Buck-m 9502 79 27 6.5 29 18 47 1 Version 3 Mary Buck -f 9502 87 24 6.4 27 18 38 2 LSI Version Jim Cox-m 9506 91 11 2 2 11 13 1 LSI Version Jim Cox-f 9506 83 11 2 2 11 13 2 PTPI Nurses 7704 70 11 2 2 11 13 2 PTPI Vet Students 7706 140 11 2 2 11 13 2 PTPI Miss. State Students. 7808 140 11 2 2 11 13 2 690 Appendix E Hierarchical Decision-Making Tree Assumes a hierarchical model of solving problems with cognition at the top, followed by abstract reasoning, the speed of processing, personality, and then career decision-making found within each subgroup 1 IPS System 2 ¦--General Problem Solver 3 ¦ ¦--high arithmetic 4 ¦ ¦ °--high 5 ¦ ¦ °--highspeed 6 ¦ ¦ ¦--Flex 7 ¦ ¦ ¦ ¦--conceptual 8 ¦ ¦ ¦ ¦ ¦--Analytical 9 ¦ ¦ ¦ ¦ ¦ ¦--7 10 ¦ ¦ ¦ ¦ ¦ °--25 11 ¦ ¦ ¦ ¦ ¦--analytical 12 ¦ ¦ ¦ ¦ ¦ °--social 13 ¦ ¦ ¦ ¦ ¦ ¦--13 14 ¦ ¦ ¦ ¦ ¦ °--31 15 ¦ ¦ ¦ ¦ °--Social 16 ¦ ¦ ¦ ¦ ¦--1 17 ¦ ¦ ¦ ¦ °--19 18 ¦ ¦ ¦ °--motor 19 ¦ ¦ ¦ ¦--Analytical 20 ¦ ¦ ¦ ¦ ¦--9 21 ¦ ¦ ¦ ¦ °--27 22 ¦ ¦ ¦ ¦--analytical 23 ¦ ¦ ¦ ¦ °--social 691 24 ¦ ¦ ¦ ¦ ¦--15 25 ¦ ¦ ¦ ¦ °--33 26 ¦ ¦ ¦ ¦--social 27 ¦ ¦ ¦ ¦ ¦--3 28 ¦ ¦ ¦ ¦ °--21 29 ¦ ¦ ¦ °--conceptual 30 ¦ ¦ ¦ ¦--Analytical 31 ¦ ¦ ¦ ¦ ¦--8 32 ¦ ¦ ¦ ¦ °--26 33 ¦ ¦ ¦ ¦--analytical 34 ¦ ¦ ¦ ¦ °--social 35 ¦ ¦ ¦ ¦ ¦--14 36 ¦ ¦ ¦ ¦ °--32 37 ¦ ¦ ¦ °--Social 38 ¦ ¦ ¦ ¦--2 39 ¦ ¦ ¦ °--20 40 ¦ ¦ °--Structure 41 ¦ ¦ ¦--conceptual 42 ¦ ¦ ¦ ¦--Social 43 ¦ ¦ ¦ ¦ ¦--4 44 ¦ ¦ ¦ ¦ °--22 45 ¦ ¦ ¦ ¦--Analytical 46 ¦ ¦ ¦ ¦ ¦--10 47 ¦ ¦ ¦ ¦ °--28 48 ¦ ¦ ¦ °--analytical 49 ¦ ¦ ¦ °--social 50 ¦ ¦ ¦ ¦--16 51 ¦ ¦ ¦ °--34 52 ¦ ¦ °--motor 692 53 ¦ ¦ ¦--conceptual 54 ¦ ¦ ¦ ¦--social 55 ¦ ¦ ¦ ¦ ¦--5 56 ¦ ¦ ¦ ¦ °--23 57 ¦ ¦ ¦ ¦--Analytical 58 ¦ ¦ ¦ ¦ ¦--11 59 ¦ ¦ ¦ ¦ °--29 60 ¦ ¦ ¦ °--analytical 61 ¦ ¦ ¦ °--social 62 ¦ ¦ ¦ ¦--17 63 ¦ ¦ ¦ °--35 64 ¦ ¦ ¦--social 65 ¦ ¦ ¦ ¦--6 66 ¦ ¦ ¦ °--24 67 ¦ ¦ ¦--Analytical 68 ¦ ¦ ¦ ¦--12 69 ¦ ¦ ¦ °--30 70 ¦ ¦ °--analytical 71 ¦ ¦ °--social 72 ¦ ¦ ¦--18 73 ¦ ¦ °--36 74 ¦ °--Differential Problem Solver 75 ¦ 76 ¦ 77 ¦ °--average arithmetic °--high °--average high speed 78 ¦ ¦--Flex 79 ¦ ¦ ¦--conceptual 80 ¦ ¦ ¦ ¦--Analytical 81 ¦ ¦ ¦ ¦ ¦--7 693 82 ¦ ¦ ¦ ¦ °--25 83 ¦ ¦ ¦ ¦--analytical 84 ¦ ¦ ¦ ¦ °--social 85 ¦ ¦ ¦ ¦ ¦--13 86 ¦ ¦ ¦ ¦ °--31 87 ¦ ¦ ¦ °--Social 88 ¦ ¦ ¦ ¦--1 89 ¦ ¦ ¦ °--19 90 ¦ ¦ °--motor 91 ¦ ¦ ¦--Analytical 92 ¦ ¦ ¦ ¦--9 93 ¦ ¦ ¦ °--27 94 ¦ ¦ ¦--analytical 95 ¦ ¦ ¦ °--social 96 ¦ ¦ ¦ ¦--15 97 ¦ ¦ ¦ °--33 98 ¦ ¦ ¦--social 99 ¦ ¦ ¦ ¦--3 100 ¦ ¦ ¦ °--... 1 node w/ 0 sub 101 ¦ ¦ °--... 1 node w/ 11 sub 102 ¦ °--... 1 node w/ 45 sub 103 °--... 1 node w/ 190 sub > 694

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Problem Solving: The Integration of Personality, Cognition, and Interest Subgroups around Verbal, Numerical, and Spatial Problems Using Machine Learning

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