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Enrique Ortiz

University of Central Florida, School of Teacher Education, Faculty Member

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Enrique Ortiz received his Doctor of Education degree in mathematics education from Louisiana State University in 1987. He received his Bachelor of Science degree in mathematics education from Inter-American University, Puerto Rico, in 1976, and his Master of Arts degree in mathematics supervision from Phoenix University in 1981. For over 30 years, Enrique Ortiz has been involved in mathematics education as a middle school teacher, supervisor, instructor, writer or curriculum developer in Puerto Rico, Louisiana, and Florida. Since 1989, he has been an assistant professor (1989-1994), associate professor (1994-2020) and professor (August, 2020-present) at the University of Central Florida. He has taught mathematics methods, curriculum development, problem solving, assessment, technology and action research courses. His topics of interest include brain-based research, teaching goals, use of technology for teaching, teaching mathematics for social justice, algebraic thinking, action research, creativity, art education, TeachLive simulations, diagnosis of mathematics strengths and misconceptions, cognitive learning levels and fraction concept development. He has stayed very active in the profession by volunteering his services to organize conferences, reviewing manuscripts for possible publication, presenting papers and workshops locally, nationally and internationally, and publishing articles and books.
Phone: 407-823-5222

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Papers by Enrique Ortiz

The Problem-Solving Process in a Mathematics Classroom

Transformation, 2016

Problem Solving in Mathematics

Preservice elementary teachers need to be given the experiences of integrating mathematics with o... more Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how mathematics and science can be integrated with one another. Problem solving involves more than just solving word problems presented in a textbook. As NCTM (2000) suggests: Students can learn about, and deepen their understanding of, mathematical concepts by working through carefully selected problems that allow applications of mathematics to other contexts. Many interesting problems can be suggested by everyday experiences, such as reading literature or using cellular telephones, in-line skates, kites, and paper airplanes. Instruction should take advantage of the expanding mathematical capabilities of students to include more-complex problem...

Pre-Service Teachers' Conceptions and Misconceptions of Physical and Virtual Manipulatives

Pre-Service Teachers’ Implementation of Physical and Virtual Manipulatives

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

Issues in the Undergraduate …, 2007

From the Classroom: Memorable Menu Math: The Journey from Teaching Procedurally to Teaching Conceptually

Teaching Children Mathematics, 2007

Menus may seem an unlikely topic for a mathematics unit. Over the years, however, restaurant menu... more

From the Classroom: Memorable Menu Math: The Journey from Teaching Procedurally to Teaching Conceptually

Teaching Children Mathematics, 2007

Menus may seem an unlikely topic for a mathematics unit. Over the years, however, restaurant menu... more

Use of Neuroimaging to Clarify How Human Brains Perform Mental Calculations

The purpose of this study was to analyze participants’ levels of hemoglobin as they performed ari... more The purpose of this study was to analyze participants’ levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information, including mental calculation. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental calculations. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). It is well known that near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). By illumination the surface of the brain with near-infrared light of two speci...

Use of Neuroimaging to Clarify How Human Brains Perform Mental Calculations

The purpose of this study was to analyze participants’ levels of hemoglobin as they performed ari... more The purpose of this study was to analyze participants’ levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information, including mental calculation. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental calculations. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). It is well known that near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). By illumination the surface of the brain with near-infrared light of two speci...

The Shape of Art: Mathematics Connections

Mathematics Teacher: Learning and Teaching PK–12, 2021

How the brain's performance during mathematics and reading fluency tests compare

The purpose of this study was to analyze how participants’ levels of hemoglobin as they performed... more The purpose of this study was to analyze how participants’ levels of hemoglobin as they performed mathematics fluency and reading fluency (reading comprehension) compare. We used Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS) to measure levels of brain activity. A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental activities. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). Near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). Changes in the concentrations of oxyand deoxyhem...

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

Preservice elementary teachers need to be given the experiences of integrating mathematics with o... more Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how mathematics and science can be integrated with one another. Problem solving involves more than just solving word problems presented in a textbook. As NCTM (2000) suggests: Students can learn about, and deepen their understanding of, mathematical concepts by working through carefully selected problems that allow applications of mathematics to other contexts. Many interesting problems can be suggested by everyday experiences, such as reading literature or using cellular telephones, in-line skates, kites, and paper airplanes. Instruction should take advantage of the expanding mathematical capabilities of students to include more-complex problem...

Reflecting upon 30 Years of STEM Partnerships between Industry, University, and Public Schools: Past Lessons, Current Successes, and Future Dreams

by Enrique Ortiz and Lisa Dieker

Education Sciences

The importance of partnerships is critical in educational arenas, but information on how partners... more The importance of partnerships is critical in educational arenas, but information on how partnerships form with the involvement of corporations, districts, and universities working in harmony is limited in the current literature. The teacher preparation program described in this paper is a “built-to-last” partnership model with over 650 teachers prepared to be teacher-leaders in science, technology, engineering, and mathematics (STEM) education. The authors provide a history of the program’s development, the sustainability of the program over time, the content of the various components of the partnership, and the evolution of the program, including its current status.

A Comparison of a Computer Programming Approach to a Textbook Approach in Teaching the Mathematics Concept "Variable" to Sixth Graders

The p u rp o s e o-f t h i s s tu d y was t o i n v e s t i g a t e w h e th er t h e r e was a s... more The p u rp o s e o-f t h i s s tu d y was t o i n v e s t i g a t e w h e th er t h e r e was a s i g n i f i c a n t d i f f e r e n c e in u n d e r s t a n d in g th e c o n c e p t o f v a r i a b l e and i n a t t i t u d e s to w a rd m a th e m atic s among s i x t h g r a d e s t u d e n t s who programmed LOGO g r a p h ic s , s tu d e n ts who used te x b o o k -b a s e d a c t i v i t i e s , and s tu d e n ts who r e c e iv e d no i n s t r u c t i o n on t h e c o n c e p t o f v a r i a b l e . The s u b j e c t s w ere 8 9 s i x t h g r a d e s t u d e n t s <47 fe m a le , 42 m a le ) fro m two m id d le s c h o o ls in t h e E a s t Baton Rouge P a r is h School S ystem . The T e s t o f L o g ic a l T h in k in g (T O L T ) , R o b u s tn e s s S e m a n t ic D i f f e r e n t i a l (R S D ) , and C om prehensive T e s t o f Eiasic S k i l l s (CTBS) w ere a d m in is t e r e d as p r e t r e a t m e n t t e s t s . The s tu d y was c o n d u c te d i n two p h ...

Optical Topography of Evoked Brain Activity during Mental Tasks Involving Whole Number Operations

Students start to memorize arithmetic facts from early elementary school mathematics activities. ... more Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants’ levels of brain activation and possible reasons for these levels as they solved arithmetic exercises mentally. It used Optical Topography an imaging technique that measures brain changes in blood flow using near-infrared light. Twelve undergraduate and graduate students participated in scanning sessions and follow-up interviews. Different levels of brain activity were found during tasks: low, moderate and high. Answers during interviews indicated that differences in brain activation were related to students’ effectiveness in solving exercises and prior experiences with memorization of facts. These findings indicate that especial attention should be placed on how facts are memorized, which could have effects on how efficiently ...

An Analysis of Middle School Mathematics Pre-Service Teachers' Development of Teaching Goals

International Journal for mathematics teaching and learning, 2011

This longitudinal study analyzes middle school mathematics pre-service teachers‟ development of t... more This longitudinal study analyzes middle school mathematics pre-service teachers‟ development of teaching goals. The Teaching Goals Inventory (TGI) (Angelo & Cross, 1993) was administered on four occasions: preand posttest summer 1, end posttest end of spring, and posttest end of summer 2. The data were analyzed for consistency and changes from one administration to another. The participants were part of a teacher preparation and master‟s degree program. Most selected the higher order thinking skills as their essential goal cluster, and demonstrated some changes in their goal selection from one administration to the other. Implications for pre-service teacher preparation programs were included.

Physical and Virtual Manipulative Framework Conceptions of Undergraduate Pre-Service Teachers

x x x virtual-Concrete x x virtual-Pictorial x x virtual-Abstract x x

It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers

Mathematics Teaching in the Middle School, 2015

Modeling using mathematics and making inferences about mathematical situations are becoming more ... more Modeling using mathematics and making inferences about mathematical situations are becoming more and more prevalent in most fields of study. When we want to generalize about a population or make predictions of what could occur, we cannot use descriptive statistics. Instead, we turn to inference. Simulation and sampling are essential in building a foundation for statistical inference.

Oral Language Needs: Making Math Meaningful

Teaching Children Mathematics, 2015

A Game Involving Fraction Squares

Teaching Children Mathematics, Dec 1, 2000

The Problem-Solving Process in a Mathematics Classroom

Transformation, 2016

Problem Solving in Mathematics

Preservice elementary teachers need to be given the experiences of integrating mathematics with o... more Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how mathematics and science can be integrated with one another. Problem solving involves more than just solving word problems presented in a textbook. As NCTM (2000) suggests: Students can learn about, and deepen their understanding of, mathematical concepts by working through carefully selected problems that allow applications of mathematics to other contexts. Many interesting problems can be suggested by everyday experiences, such as reading literature or using cellular telephones, in-line skates, kites, and paper airplanes. Instruction should take advantage of the expanding mathematical capabilities of students to include more-complex problem...

Pre-Service Teachers' Conceptions and Misconceptions of Physical and Virtual Manipulatives

Pre-Service Teachers’ Implementation of Physical and Virtual Manipulatives

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

Issues in the Undergraduate …, 2007

From the Classroom: Memorable Menu Math: The Journey from Teaching Procedurally to Teaching Conceptually

Teaching Children Mathematics, 2007

Menus may seem an unlikely topic for a mathematics unit. Over the years, however, restaurant menu... more

From the Classroom: Memorable Menu Math: The Journey from Teaching Procedurally to Teaching Conceptually

Teaching Children Mathematics, 2007

Menus may seem an unlikely topic for a mathematics unit. Over the years, however, restaurant menu... more

Use of Neuroimaging to Clarify How Human Brains Perform Mental Calculations

The purpose of this study was to analyze participants’ levels of hemoglobin as they performed ari... more The purpose of this study was to analyze participants’ levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information, including mental calculation. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental calculations. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). It is well known that near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). By illumination the surface of the brain with near-infrared light of two speci...

Use of Neuroimaging to Clarify How Human Brains Perform Mental Calculations

The purpose of this study was to analyze participants’ levels of hemoglobin as they performed ari... more The purpose of this study was to analyze participants’ levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information, including mental calculation. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental calculations. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). It is well known that near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). By illumination the surface of the brain with near-infrared light of two speci...

The Shape of Art: Mathematics Connections

Mathematics Teacher: Learning and Teaching PK–12, 2021

How the brain's performance during mathematics and reading fluency tests compare

The purpose of this study was to analyze how participants’ levels of hemoglobin as they performed... more The purpose of this study was to analyze how participants’ levels of hemoglobin as they performed mathematics fluency and reading fluency (reading comprehension) compare. We used Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS) to measure levels of brain activity. A central issue in cognitive neuroscience involves the study of how the human brain encodes and manipulates information. Recently, functional neuro-imaging studies have begun to clarify how the human brain performs mental activities. fNIRS is an imaging technique capable of measuring changes in the relative concentration of hemoglobin the in the cerebral cortex of the brain (Hoshi & Tamura, 1993; Villringer et al., 1993; Koizumi et al., 2003). Near-infrared light of a wavelength between 650 nm and 950 nm can penetrate living tissue where it is specifically absorbed by hemoglobin (Strangman et al., 2002). Changes in the concentrations of oxyand deoxyhem...

Using Science to Promote Preservice Teacher Understanding of Problem Solving in Mathematics

Preservice elementary teachers need to be given the experiences of integrating mathematics with o... more Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how mathematics and science can be integrated with one another. Problem solving involves more than just solving word problems presented in a textbook. As NCTM (2000) suggests: Students can learn about, and deepen their understanding of, mathematical concepts by working through carefully selected problems that allow applications of mathematics to other contexts. Many interesting problems can be suggested by everyday experiences, such as reading literature or using cellular telephones, in-line skates, kites, and paper airplanes. Instruction should take advantage of the expanding mathematical capabilities of students to include more-complex problem...

Reflecting upon 30 Years of STEM Partnerships between Industry, University, and Public Schools: Past Lessons, Current Successes, and Future Dreams

by Enrique Ortiz and Lisa Dieker

Education Sciences

The importance of partnerships is critical in educational arenas, but information on how partners... more The importance of partnerships is critical in educational arenas, but information on how partnerships form with the involvement of corporations, districts, and universities working in harmony is limited in the current literature. The teacher preparation program described in this paper is a “built-to-last” partnership model with over 650 teachers prepared to be teacher-leaders in science, technology, engineering, and mathematics (STEM) education. The authors provide a history of the program’s development, the sustainability of the program over time, the content of the various components of the partnership, and the evolution of the program, including its current status.

A Comparison of a Computer Programming Approach to a Textbook Approach in Teaching the Mathematics Concept "Variable" to Sixth Graders

The p u rp o s e o-f t h i s s tu d y was t o i n v e s t i g a t e w h e th er t h e r e was a s... more The p u rp o s e o-f t h i s s tu d y was t o i n v e s t i g a t e w h e th er t h e r e was a s i g n i f i c a n t d i f f e r e n c e in u n d e r s t a n d in g th e c o n c e p t o f v a r i a b l e and i n a t t i t u d e s to w a rd m a th e m atic s among s i x t h g r a d e s t u d e n t s who programmed LOGO g r a p h ic s , s tu d e n ts who used te x b o o k -b a s e d a c t i v i t i e s , and s tu d e n ts who r e c e iv e d no i n s t r u c t i o n on t h e c o n c e p t o f v a r i a b l e . The s u b j e c t s w ere 8 9 s i x t h g r a d e s t u d e n t s <47 fe m a le , 42 m a le ) fro m two m id d le s c h o o ls in t h e E a s t Baton Rouge P a r is h School S ystem . The T e s t o f L o g ic a l T h in k in g (T O L T ) , R o b u s tn e s s S e m a n t ic D i f f e r e n t i a l (R S D ) , and C om prehensive T e s t o f Eiasic S k i l l s (CTBS) w ere a d m in is t e r e d as p r e t r e a t m e n t t e s t s . The s tu d y was c o n d u c te d i n two p h ...

Optical Topography of Evoked Brain Activity during Mental Tasks Involving Whole Number Operations

Students start to memorize arithmetic facts from early elementary school mathematics activities. ... more Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants’ levels of brain activation and possible reasons for these levels as they solved arithmetic exercises mentally. It used Optical Topography an imaging technique that measures brain changes in blood flow using near-infrared light. Twelve undergraduate and graduate students participated in scanning sessions and follow-up interviews. Different levels of brain activity were found during tasks: low, moderate and high. Answers during interviews indicated that differences in brain activation were related to students’ effectiveness in solving exercises and prior experiences with memorization of facts. These findings indicate that especial attention should be placed on how facts are memorized, which could have effects on how efficiently ...

An Analysis of Middle School Mathematics Pre-Service Teachers' Development of Teaching Goals

International Journal for mathematics teaching and learning, 2011

This longitudinal study analyzes middle school mathematics pre-service teachers‟ development of t... more This longitudinal study analyzes middle school mathematics pre-service teachers‟ development of teaching goals. The Teaching Goals Inventory (TGI) (Angelo & Cross, 1993) was administered on four occasions: preand posttest summer 1, end posttest end of spring, and posttest end of summer 2. The data were analyzed for consistency and changes from one administration to another. The participants were part of a teacher preparation and master‟s degree program. Most selected the higher order thinking skills as their essential goal cluster, and demonstrated some changes in their goal selection from one administration to the other. Implications for pre-service teacher preparation programs were included.

Physical and Virtual Manipulative Framework Conceptions of Undergraduate Pre-Service Teachers

x x x virtual-Concrete x x virtual-Pictorial x x virtual-Abstract x x

It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers

Mathematics Teaching in the Middle School, 2015

Modeling using mathematics and making inferences about mathematical situations are becoming more ... more Modeling using mathematics and making inferences about mathematical situations are becoming more and more prevalent in most fields of study. When we want to generalize about a population or make predictions of what could occur, we cannot use descriptive statistics. Instead, we turn to inference. Simulation and sampling are essential in building a foundation for statistical inference.

Oral Language Needs: Making Math Meaningful

Teaching Children Mathematics, 2015

A Game Involving Fraction Squares

Teaching Children Mathematics, Dec 1, 2000