A Longitudinal Study Of Mathematical Reasoning

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Affect and Mathematics Education

Author : Markku S. Hannula
Publisher : Springer
ISBN 13 : 3030137619
Total Pages : 437 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Affect and Mathematics Education by : Markku S. Hannula

Download or read book Affect and Mathematics Education written by Markku S. Hannula and published by Springer. This book was released on 2019-06-03 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book, inspired by the ICME 13 topic study group “Affect, beliefs and identity in mathematics education”, presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling. In the final chapter, the editors look ahead to future directions in the area of mathematics-education-related affect. It is a timely resource for all those interested in the interaction between affect and mathematics education.

Symbolizing and Communicating in Mathematics Classrooms

Author : Paul Cobb
Publisher : Routledge
ISBN 13 : 1135677824
Total Pages : 439 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Symbolizing and Communicating in Mathematics Classrooms by : Paul Cobb

Download or read book Symbolizing and Communicating in Mathematics Classrooms written by Paul Cobb and published by Routledge. This book was released on 2012-11-12 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of a symposium on discourse, tools, and instructional design at Vanderbilt University in 1995 that brought together a small international group to grapple with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. The participants invited to develop chapters for this book--all internationally recognized scholars in their respective fields--were selected to represent a wide range of theoretical perspectives including mathematics education, cognitive science, sociocultural theory, and discourse theory. The work is distinguished by the caliber of the contributors, the significance of the topics addressed in the current era of reform in mathematics education, and the diversity of perspectives taken to a common set of themes and issues. The book is intended for those who are seeking to expand their understanding of the complexity of learning in order to enhance the learning experiences students have in schools, primarily researchers, instructional designers, and graduate students in mathematics education, as well as those in other fields including science education, instructional design in general, discourse theory, and semiotics.

The Cambridge Handbook of Cognition and Education

Author : John Dunlosky
Publisher : Cambridge University Press
ISBN 13 : 1108245102
Total Pages : 1130 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis The Cambridge Handbook of Cognition and Education by : John Dunlosky

Download or read book The Cambridge Handbook of Cognition and Education written by John Dunlosky and published by Cambridge University Press. This book was released on 2019-02-07 with total page 1130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement.

Mathematical Reasoning

Author : Raymond Nickerson
Publisher : Taylor & Francis
ISBN 13 : 1136945393
Total Pages : 597 pages
Book Rating : 4.1/5 (369 download)

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Book Synopsis Mathematical Reasoning by : Raymond Nickerson

Download or read book Mathematical Reasoning written by Raymond Nickerson and published by Taylor & Francis. This book was released on 2011-02-25 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Researching and Using Progressions (Trajectories) in Mathematics Education

Author :
Publisher : BRILL
ISBN 13 : 9004396446
Total Pages : 255 pages
Book Rating : 4.0/5 (43 download)

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Book Synopsis Researching and Using Progressions (Trajectories) in Mathematics Education by :

Download or read book Researching and Using Progressions (Trajectories) in Mathematics Education written by and published by BRILL. This book was released on 2019-02-04 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.

Mathematical Reasoning of Children and Adults

Author : Alina Galvão Spinillo
Publisher : Springer Nature
ISBN 13 : 303069657X
Total Pages : 324 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Mathematical Reasoning of Children and Adults by : Alina Galvão Spinillo

Download or read book Mathematical Reasoning of Children and Adults written by Alina Galvão Spinillo and published by Springer Nature. This book was released on 2021-05-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.

Combinatorics and Reasoning

Author : Carolyn A. Maher
Publisher : Springer Science & Business Media
ISBN 13 : 9400706154
Total Pages : 226 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Combinatorics and Reasoning by : Carolyn A. Maher

Download or read book Combinatorics and Reasoning written by Carolyn A. Maher and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.

Tep Vol 29-N4

Author : Teacher Education and Practice
Publisher : Rowman & Littlefield
ISBN 13 : 1475832516
Total Pages : 143 pages
Book Rating : 4.4/5 (758 download)

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Book Synopsis Tep Vol 29-N4 by : Teacher Education and Practice

Download or read book Tep Vol 29-N4 written by Teacher Education and Practice and published by Rowman & Littlefield. This book was released on 2016-10-11 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teacher Education and Practice, a peer-refereed journal, is dedicated to the encouragement and the dissemination of research and scholarship related to professional education. The journal is concerned, in the broadest sense, with teacher preparation, practice and policy issues related to the teaching profession, as well as being concerned with learning in the school setting. The journal also serves as a forum for the exchange of diverse ideas and points of view within these purposes. As a forum, the journal offers a public space in which to critically examine current discourse and practice as well as engage in generative dialogue. Alternative forms of inquiry and representation are invited, and authors from a variety of backgrounds and diverse perspectives are encouraged to contribute. Teacher Education & Practice is published by Rowman & Littlefield.

Adults' Mathematical Thinking and Emotions

Author : Jeff Evans
Publisher : Routledge
ISBN 13 : 1135701911
Total Pages : 313 pages
Book Rating : 4.1/5 (357 download)

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Book Synopsis Adults' Mathematical Thinking and Emotions by : Jeff Evans

Download or read book Adults' Mathematical Thinking and Emotions written by Jeff Evans and published by Routledge. This book was released on 2002-01-04 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The crisis around teaching and learning of mathematics and its use in everyday life and work relate to a number of issues. These include: The doubtful transferability of school maths to real life contexts, the declining participation in A level and higher education maths courses, the apparent exclusion of some groups, such as women and the aversion of many people to maths. This book addresses these issues by considering a number of key problems in maths education and numeracy: *differences among social groups, especially those related to gender and social class *the inseparability of cognition and emotion in mathematical activity *the understanding of maths anxiety in traditional psychological, psychoanalytical and feminist theories *how adults' numerate thinking and performance must be understood in context. The author's findings have practical applications in education and training, such as clarifying problems of the transfer of learning, and of countering maths anxiety.

A Practical Guide to Transforming Primary Mathematics

Author : Mike Askew
Publisher : Routledge
ISBN 13 : 131781326X
Total Pages : 185 pages
Book Rating : 4.3/5 (178 download)

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Book Synopsis A Practical Guide to Transforming Primary Mathematics by : Mike Askew

Download or read book A Practical Guide to Transforming Primary Mathematics written by Mike Askew and published by Routledge. This book was released on 2015-07-30 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practical Guide to Transforming Primary Mathematics offers inspiration and ideas for all training and practising teachers committed to making mathematics enjoyable, inclusive, engaging and successful. The companion to Mike Askew’s bestselling book, Transforming Primary Mathematics, this practical guide focuses on showing you how to unlock the powerful potential of a small set of consistent principles and practices, known as the teaching tripod, to develop a coherent approach to teaching mathematics. Organised around the major strands of the curriculum - number, calculations, shape and space, measures, and data handling – it offers an accessible introduction to the teaching tripod, a careful choice of tasks, supported by a range of tools that extend our natural abilities and held together by careful attention to classroom talk. A range of classroom tasks, each including key learning outcomes, clear links to the framework, links to relevant research, and suggestions for making the tasks easier or harder, are offered for every topic, helping you plan units of work for meaningful learning. A Practical Guide to Transforming Primary Mathematics offers all teachers a vision, rationale and ideas for how teaching can support better learning of mathematics but also encourage learners to see themselves as being capable of learning mathematics, and wanting to learn it.

Mathematics Education in the Early Years

Author : Christiane Benz
Publisher : Springer
ISBN 13 : 3319782207
Total Pages : 305 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Mathematics Education in the Early Years by : Christiane Benz

Download or read book Mathematics Education in the Early Years written by Christiane Benz and published by Springer. This book was released on 2018-06-29 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives insight in the vivid research area of early mathematics learning. The collection of selected papers mirror the research topics presented at the third POEM conference. Thematically, the volume reflects the importance of this relatively new field of research. Structurally, the book tries to guide the reader through a variety of research aims and issues and is split into four parts. The first two parts concentrate on teacher professional development and child learning development; the third part pools research studies creating and evaluating designed learning situations; and the fourth part bridges focuses on parent-child-interaction.

Handbook of International Research in Mathematics Education

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1135192839
Total Pages : 830 pages
Book Rating : 4.1/5 (351 download)

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Book Synopsis Handbook of International Research in Mathematics Education by : Lyn D. English

Download or read book Handbook of International Research in Mathematics Education written by Lyn D. English and published by Routledge. This book was released on 2010-04-02 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition continues the mission of bringing together important new mathematics education research that makes a difference in both theory and practice. It updates and extends the Handbook’s original key themes and issues for international research in mathematics education for the 21st century, namely: priorities in international mathematics education research lifelong democratic access to powerful mathematical ideas advances in research methodologies influences of advanced technologies. Each of these themes is examined in terms of learners, teachers, and learning contexts, with theory development being an important component of all these aspects. This edition also examines other catalysts that have gained increased import in recent years including a stronger focus on the teacher and teacher practice, a renewed interest in theory development, an increased focus on the mathematics needed in work place settings, and a proliferation of research designs and methodologies that have provided unprecedented opportunities for investigating (and ultimately improving) mathematical teaching and learning. This edition includes ten totally new chapters; all other chapters are thoroughly revised and updated.

Handbook of Child Psychology and Developmental Science, Cognitive Processes

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118953851
Total Pages : 1120 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Handbook of Child Psychology and Developmental Science, Cognitive Processes by :

Download or read book Handbook of Child Psychology and Developmental Science, Cognitive Processes written by and published by John Wiley & Sons. This book was released on 2015-03-31 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential reference for human development theory, updated and reconceptualized The Handbook of Child Psychology and Developmental Science, a four-volume reference, is the field-defining work to which all others are compared. First published in 1946, and now in its Seventh Edition, the Handbook has long been considered the definitive guide to the field of developmental science. Volume 2: Cognitive Processes describes cognitive development as a relational phenomenon that can be studied only as part of a larger whole of the person and context relational system that sustains it. In this volume, specific domains of cognitive development are contextualized with respect to biological processes and sociocultural contexts. Furthermore, key themes and issues (e.g., the importance of symbolic systems and social understanding) are threaded across multiple chapters, although every each chapter is focused on a different domain within cognitive development. Thus, both within and across chapters, the complexity and interconnectivity of cognitive development are well illuminated. Learn about the inextricable intertwining of perceptual development, motor development, emotional development, and brain development Understand the complexity of cognitive development without misleading simplification, reducing cognitive development to its biological substrates, or viewing it as a passive socialization process Discover how each portion of the developmental process contributes to subsequent cognitive development Examine the multiple processes – such as categorizing, reasoning, thinking, decision making and judgment – that comprise cognition The scholarship within this volume and, as well, across the four volumes of this edition, illustrate that developmental science is in the midst of a very exciting period. There is a paradigm shift that involves increasingly greater understanding of how to describe, explain, and optimize the course of human life for diverse individuals living within diverse contexts. This Handbook is the definitive reference for educators, policy-makers, researchers, students, and practitioners in human development, psychology, sociology, anthropology, and neuroscience.

The Nature of Mathematical Thinking

Author : Robert J. Sternberg
Publisher : Routledge
ISBN 13 : 1136487433
Total Pages : 353 pages
Book Rating : 4.1/5 (364 download)

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Book Synopsis The Nature of Mathematical Thinking by : Robert J. Sternberg

Download or read book The Nature of Mathematical Thinking written by Robert J. Sternberg and published by Routledge. This book was released on 2012-10-12 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why do some children seem to learn mathematics easily and others slave away at it, learning it only with great effort and apparent pain? Why are some people good at algebra but terrible at geometry? How can people who successfully run a business as adults have been failures at math in school? How come some professional mathematicians suffer terribly when trying to balance a checkbook? And why do school children in the United States perform so dismally in international comparisons? These are the kinds of real questions the editors set out to answer, or at least address, in editing this book on mathematical thinking. Their goal was to seek a diversity of contributors representing multiple viewpoints whose expertise might converge on the answers to these and other pressing and interesting questions regarding this subject. The chapter authors were asked to focus on their own approach to mathematical thinking, but also to address a common core of issues such as the nature of mathematical thinking, how it is similar to and different from other kinds of thinking, what makes some people or some groups better than others in this subject area, and how mathematical thinking can be assessed and taught. Their work is directed to a diverse audience -- psychologists interested in the nature of mathematical thinking and abilities, computer scientists who want to simulate mathematical thinking, educators involved in teaching and testing mathematical thinking, philosophers who need to understand the qualitative aspects of logical thinking, anthropologists and others interested in how and why mathematical thinking seems to differ in quality across cultures, and laypeople and others who have to think mathematically and want to understand how they are going to accomplish that feat.

Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline

Author : Matthew Inglis
Publisher : World Scientific
ISBN 13 : 1786340704
Total Pages : 204 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline by : Matthew Inglis

Download or read book Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline written by Matthew Inglis and published by World Scientific. This book was released on 2016-09-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.

Understanding Emotions in Mathematical Thinking and Learning

Author : Ulises Xolocotzin
Publisher : Academic Press
ISBN 13 : 0128024895
Total Pages : 476 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Understanding Emotions in Mathematical Thinking and Learning by : Ulises Xolocotzin

Download or read book Understanding Emotions in Mathematical Thinking and Learning written by Ulises Xolocotzin and published by Academic Press. This book was released on 2017-05-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place

Second Handbook of Research on Mathematics Teaching and Learning

Author : Frank K. Lester
Publisher : IAP
ISBN 13 : 160752709X
Total Pages : 1380 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Second Handbook of Research on Mathematics Teaching and Learning by : Frank K. Lester

Download or read book Second Handbook of Research on Mathematics Teaching and Learning written by Frank K. Lester and published by IAP. This book was released on 2007-02-01 with total page 1380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.