Purpose: This article explores the relative influence over schoolwide policy and leadership activities of teachers certified by the National Board for Professional Teaching Standards. Interest centers on teacher leadership activities and... more
Purpose: This article explores the relative influence over schoolwide policy and leadership activities of teachers certified by the National Board for Professional Teaching Standards. Interest centers on teacher leadership activities and perceived influence over schoolwide policy and decision making. In particular, the study asks whether National Board Certified Teachers (NBCTs) are engaged in leadership and influence that may be attributable to board certification. Method: Data come from a survey of the entire teaching faculties in 47 elementary schools in two states ( N = 1,282). Teacher perceived influence over schoolwide policy and participation in leadership activities were regressed on NBCT status, demographic and assignment characteristics, and inclination toward teacher leadership, controlling for schools with fixed effects. Findings: NBCTs engage in more leadership activities at both the school and district levels than their non-board certified peers. Yet, NBCTs do not repo...
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While it has been found that teacher knowledge affects mathematics student achievement, to date, little research has explored how professors affect preservice elementary teacher’s mathematical knowledge. This study explores future... more
While it has been found that teacher knowledge affects mathematics student achievement, to date, little research has explored how professors affect preservice elementary teacher’s mathematical knowledge. This study explores future teachers ’ learning in undergraduate mathematics classes. Our data includes pre and post tests from over 1000 students in classes of 41 instructors at 17 institutions in four states as well as teacher survey data from those 41 instructors. In our multilevel models, we identify three key variables that influence gain: students ’ prior knowledge, use of specifically designed textbooks, and the methods the professor uses to teach the course.
DRAFT: Please do not cite or quote without the author’s permission The Mathematical Education of Elementary Teachers (MEET) project is an NSF funded study of undergraduate mathematics classes for prospective elementary teachers in two... more
DRAFT: Please do not cite or quote without the author’s permission The Mathematical Education of Elementary Teachers (MEET) project is an NSF funded study of undergraduate mathematics classes for prospective elementary teachers in two states – Michigan and South Carolina – and in New York City. MEET researchers are investigating undergraduate mathematics classes required for elementary certification. We have collected data from mathematics departments at 57 institutions and piloted and administered over 2000 assessment forms to students at 13 schools in 58 sections of mathematics classes of 43 instructors. We have also analyzed all the published textbooks written specifically for such classes. Our data include information about who teaches the classes, what topics are covered, and what students learn. Initial analyses suggest that these classes are little influenced by policy or certification testing, but may be strongly influenced by the textbook used. Instructors are not familiar ...
Abstract. It is important for future elementary teachers to gain the mathematical knowledge necessary to teach their students. Teachers often gain such knowledge from courses taken in college. This paper reports on results of a survey of... more
Abstract. It is important for future elementary teachers to gain the mathematical knowledge necessary to teach their students. Teachers often gain such knowledge from courses taken in college. This paper reports on results of a survey of college instructors of mathematics classes for future elementary teachers, including resources they use and personal characteristics. Data suggest that while instructors are usually quite experienced, tend to use a textbook as their primary resource, and are familiar with the NCTM standards, they do not seem to be familiar with other important policy documents, such as teacher certification standards and tests. Mathematicians, mathematics educators, and the public at large agree that teachers ’ knowledge of mathematics is a key ingredient in the mathematical achievement of K-8 students. Recent research has addressed deficiencies in the mathematical knowledge of K-8 teachers (Ball, 1990; Ma, 1998) and attempted to define and measure mathematical know...
Raven McCrory Michigan State University Purpose of the video study As part of a larger study on the knowledge teachers need to teach algebra, our research team decided to explore video of algebra teaching to seek evidence of teacher... more
Raven McCrory Michigan State University Purpose of the video study As part of a larger study on the knowledge teachers need to teach algebra, our research team decided to explore video of algebra teaching to seek evidence of teacher knowledge and how it is used in practice. After initially planning to go to classrooms and capture new video, we decided instead to seek existing video from other projects that we could use. The problem We began this research with two primary questions: 1. How can we conceptualize the knowledge teachers use when teaching algebra? 2. How can we use video data from classrooms to study teacher knowledge? The first questions is a directed at the substance of the larger project, development of a framework for studying teacher knowledge. We used video both to develop and to test the emerging framework. The second question is a methodological one. We aimed to create a stronger theoretical argument, and an articulated method, for using video to study teacher kno...
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M athematicians have a unique opportunity to influence elementary teachers’ mathematical knowledge. Nearly all future teachers are required to take mathematics courses in their undergraduate education, and many take courses specifically... more
M athematicians have a unique opportunity to influence elementary teachers’ mathematical knowledge. Nearly all future teachers are required to take mathematics courses in their undergraduate education, and many take courses specifically required for elementary certification. Even in this era of alternative certification, a majority of teachers come to their first job from a four-year teacher certification program in which one or more mathematics courses are required. According to the Conference Board of the Mathematical Sciences (CMBS) 2005 survey of U.S. mathematics departments, 87% of mathematics departments in the United States are in institutions that certify elementary teachers, and of these, 86% offer a special course or sequence of mathematics courses for K –8 teachers (Lutzer, Rodi, Kirkman, & Maxwell, 2007, pp. 49–50). Mathematics departments design and teach these courses and thus can make a huge difference across the United States in what is offered to, and expected of, f...
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This paper explores how extensions of the number system from whole number to fractions are discussed in mathematics courses for prospective elementary school teachers (PSTs). First, we explain four ways of extending the number system... more
This paper explores how extensions of the number system from whole number to fractions are discussed in mathematics courses for prospective elementary school teachers (PSTs). First, we explain four ways of extending the number system found in the historical development of fractions: part-whole-based, measurement-based, division-based, and settheoretical approaches. Second, we analyzed fraction lessons taught by six instructors of such courses, focusing on whether and how the instructors made extensions. Results show these instructors covered some aspects of extensions, discussing them implicitly rather than explicitly. Finally, we argue that knowledge of mathematical extensions may be beneficial to PSTs when they become teachers, for they will need to help their K-8 students understand fractions as part of a coherent number system. WHOLE NUMBERS TO FRACTIONS
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This study focuses on two instructors who taught a mathematics course designed for prospective elementary teachers and explores which interpretations of fractions they addressed and how they used visual representations when discussing... more
This study focuses on two instructors who taught a mathematics course designed for prospective elementary teachers and explores which interpretations of fractions they addressed and how they used visual representations when discussing fraction multiplication. Our findings indicate that the distinct interpretations of rational numbers can turn out to be quite intertwined during actual practice. As a result, it might be challenging to extract meaning from the visual representations, especially when the problems are not situated in a context, unless instructors explicitly attend to the interpretations underlying those representations.
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Prospective elementary teachers must understand fraction division deeply to be able to teach this topic to their future students. This paper explores how two university instructors help prospective elementary school teachers develop such... more
Prospective elementary teachers must understand fraction division deeply to be able to teach this topic to their future students. This paper explores how two university instructors help prospective elementary school teachers develop such understanding. In particular, we examine how instructors teach the meaning of division, the concepts of unit, and the connections between multiplication and division.
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This paper reports on one aspect of a study of mathematics classes for prospective elementary teachers in three states. Here, we provide results of a survey of 57 mathematics departments in institutions that offer undergraduate elementary... more
This paper reports on one aspect of a study of mathematics classes for prospective elementary teachers in three states. Here, we provide results of a survey of 57 mathematics departments in institutions that offer undergraduate elementary teacher certification programs in these states. Results suggest that most students are required to take 2 or 3 mathematics classes, with the average of 2.18 falling below recommendations from CBMS of 3 mathematics courses (9 credits) minimum for elementary certification. States now require middle school mathematics certification and institutions are approaching the CBMS recommendation of 7 mathematics classes. We provide data about differences by type of institution, size of elementary education program, and selectivity of institution.
Prospective teachers need not waffle about developing the knowledge required to serve up appetizing justification and problem-solving methods to their elementary school students.
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this paper. 3/1/99 Wallace Proposal Page 28 http://www-personal.umich.edu/~ravenmw/wallaceproposal.pdf
Research Interests: Education and Educational
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atories. Computer skills, information demands, and level of subject knowledge vary greatly among these user populations. Addressing the needs of high school students within a general-purpose digital library particularly stresses the... more
atories. Computer skills, information demands, and level of subject knowledge vary greatly among these user populations. Addressing the needs of high school students within a general-purpose digital library particularly stresses the flexibility of our underlying architecture. The UMDL must support services quite distinct from those that other digital libraries and the World Wide Web offer. Many researchers and policy groups argue that students should engage in sustained inquiry to develop an in-depth understanding of science. Digital libraries provide an outstanding opportunity to vitalize science education in public schools through inquiry-based education. However, we must avoid the inflated expectations typical of technology in the schools. Technology is only one element of a complex educational environment. Students, teachers, and curriculum planners must work together for a digital classroom library to succeed. We are addressing the UMDUs ambitious scale and heterogeneity require
Prospective elementary mathematics teachers should be able to understand how their future students understand number concepts. A difficult concept is that of rational numbers. Rational numbers often have complicated means of... more
Prospective elementary mathematics teachers should be able to understand how their future students understand number concepts. A difficult concept is that of rational numbers. Rational numbers often have complicated means of representation, signifiers and signifieds, making them difficult for students to understand and teach. In this paper, we describe how one teacher integrates a theory of semiotics when instructing prospective elementary school teachers about rational numbers. We propose that by teaching prospective teachers about semiotics, connections between signs and units are made explicit and prospective teachers will be more equipped to approach the instruction of rational numbers to future students. Background on Obstacles to Understanding Rational Numbers Lamon (2007) suggests that fractions are a subset of rational numbers, in that fractions are notational and are ―non-negative rational numbers‖ (p. 635). We are interested in how to instruct preservice elementary school ...
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ABSTRACT Learners use software for different reasons and with differentskills and motivations than other users. Using concepts of learner-centered design (LCD), we developed a user interface for supporting learners as they use digital... more
ABSTRACT Learners use software for different reasons and with differentskills and motivations than other users. Using concepts of learner-centered design (LCD), we developed a user interface for supporting learners as they use digital information resources in inquiry-based science classrooms. Learner needs are categorized in five areas: content knowledge, technology knowledge, strategic and metacognitive lmowledge, and motivation Results of research on problems encountered by students as they engage in information seeking are used as the basis for applying LCD, by identifying some specific problem areas learners encounter engaging in a process, generating search terms, staying on task, and evahmting information. Solutions offered through the Artemis interface are described.
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Many interactive learning environments (ILEs) offer on-demand help, intended to positively influence learning. Recent studies report evidence that although effective help-seeking behavior in ILEs is related to better learning outcomes,... more
Many interactive learning environments (ILEs) offer on-demand help, intended to positively influence learning. Recent studies report evidence that although effective help-seeking behavior in ILEs is related to better learning outcomes, learners are not using help facilities effectively. This selective review (a) examines theoretical perspectives on the role of on-demand help in ILEs, (b) reviews literature on the relations between help seeking and learning in ILEs, and (c) identifies reasons for the lack of effective help use. We review the effect of system-related factors, of student-related factors, and of interactions between these factors. The interaction between metacognitive skills and cognitive factors is important for appropriate help seeking, as are a potentially large space of system-related factors as well as interactions among learner- and system-related factors. We suggest directions for future research.
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Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, an analysis of video, interviews with teachers, and an... more
Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, an analysis of video, interviews with teachers, and an analysis of textbooks, the authors define categories of knowledge and practices of teaching for understanding and assessing teachers' knowledge for teaching algebra. They argue that the combination of categories and practices must be covered in assessments of teacher knowledge, if the assessments are to be used in research that investigates the presumed links among teachers' content preparation, their knowledge, their practice, and student learning.
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ABSTRACT Research shows that students, and sometimes teachers, have trouble with fractions, especially conceiving of fractions as numbers that extend the whole number system. This paper explores how fractions are addressed in... more
ABSTRACT Research shows that students, and sometimes teachers, have trouble with fractions, especially conceiving of fractions as numbers that extend the whole number system. This paper explores how fractions are addressed in undergraduate mathematics courses for prospective elementary teachers (PSTs). In particular, we explore how, and whether, the instructors of these courses address fractions as an extension of the whole number system and fractions as numbers in their classrooms. Using a framework consisting of four approaches to the development of fractions found in history, we analyze fraction lessons videotaped in six mathematics classes for PSTs. Historically, the first two approaches—part–whole and measurement—focus on fractions as parts of wholes rather than numbers, and the last two approaches—division and set theory—formalize fractions as numbers. Our results show that the instructors only implicitly addressed fraction-as-number and the extension of fractions from whole numbers, although most of them mentioned or emphasized these aspects of fractions during interviews.
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Digital libraries offer a unique and unprecedented resource through which teachers can facilitate student inquiry. In the recent National Research Council publication quoted above, National Science Education Standards, emphasis on inquiry... more
Digital libraries offer a unique and unprecedented resource through which teachers can facilitate student inquiry. In the recent National Research Council publication quoted above, National Science Education Standards, emphasis on inquiry is pervasive. Yet, when it ...
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Research Interests: Computer Architecture, Information Retrieval, Stress, Resource Allocation, Mediation, and 14 moreUser Interface, Databases, Digital Library, Software Agents, Interoperability, User interfaces, Information Sources, Library Service Quality, Resource Management, Open Systems, Software Agent, Secondary School, Distributed Agents, and Computer
Inquiry into authentic questions generated from student experiences is the central strategy for teaching science. Such inquiry requires access to serious information resources. The article discusses that how Internet as an information... more
Inquiry into authentic questions generated from student experiences is the central strategy for teaching science. Such inquiry requires access to serious information resources. The article discusses that how Internet as an information resource supports student inquiry. In its ...
OBJECTIVES Teaching assistants (TAs) play a vital role in undergraduate mathematics instruction. Acting as sole instructors, recitation instructors, tutors, or homework graders, they are in frequent contact with undergraduate students in... more
OBJECTIVES Teaching assistants (TAs) play a vital role in undergraduate mathematics instruction. Acting as sole instructors, recitation instructors, tutors, or homework graders, they are in frequent contact with undergraduate students in the lower division mathematics ...