This book offers a critique of two major themes of the modern reform movement in mathematics education: problem solving and the applications of mathematics to the «real world». In examining the educational fallacy inherent in the impulse to move unflinchingly from «problem» to «problem solving», Stephen I. Brown demonstrates the potential of mathematical reflection to reveal aspects of self and society that have been suppressed in curriculum. He then argues that in seeking connections between mathematics and the «real world», we have tended to reduce their relationship to one of modeling. Furthermore, in constructing what is «real» in an overly concrete way, we have lost sight of the wonder of what is «real» in both mathematics and the world. Brown explores alternative text formats, including that of the novel and the Talmud, as vehicles to rejuvenate the educational potential of problems and of real world connections.

The experience and knowledge acquired in teacher education courses should build important fundamentals for the future teaching of mathematics. In particular, experience in mathematical problem solving, and in planning lessons devoted to problem solving, is an essential component of teacher preparation. This book develops a problem solving approach and is intended to be a text used in mathematics education courses (or professional development) for preservice or inservice middle and secondary school teachers. It can be used both in graduate and undergraduate courses, in accordance with the focus of teacher preparation programs. The content of the book is suited especially for those students who are further along in their mathematics education preparation, as the text is more involved with mathematical ideas and problem solving, and discusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as an introduction to mathematics education (a first course), but rather as a second, or probably, third course. The book deals both with general methodology issues in mathematics education incorporating a problem solving approach (Chapters 16) and with more concrete applications within the context of specific topics – algebra, geometry, and discrete mathematics (Chapters 713). The book provides opportunities for teachers to engage in authentic mathematical thinking. The mathematical ideas under consideration build on specific middle and secondary school content while simultaneously pushing the teacher to consider more advanced topics, as well as various connections across mathematical domains. The book strives to preserve the spirit of discussion, and at times even argument, typical of collaborative work on a lesson plan. Based on the accumulated experience of work with future and current teachers, the book assumes that students have some background in lesson planning, and extends their thinking further. Specifically, this book aims to provide a discussion of how a lesson plan is constructed, including the ways in which problems are selected or invented, rather than the compilation of prepared lesson plans. This approach reflects the authors’ view that the process of searching for an answer is often more important than the formal result.

Unique in offering a multidisciplinary perspective on key issues of alternative epistemologies in education, this collection includes contributions from scholars in family therapy, epistemology, and mathematics, science, and language education. These respected researchers were brought together to develop the theme of constructivism as it applies to many diversified fields. This book examines key distinctions of various constructivist epistemologies, comparing and contrasting the various paradigms. Each section provides both keynote positions on a particular alternative paradigm as well as critical comments by respondents regarding that position. Several chapters also present a synthesis of the alternative epistemological perspectives.

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathemati

The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem posing (such as where problems come from, what to do with them, and the like) from the "other" to themselves and offers a broader conception of what can be done with problems. Special features include: an exploration of the logical relationship between problem posing and problem solving; sketches, drawings, and diagrams that illustrate the schemes proposed; and a special section on writing in mathematics. In the updated third edition, the authors specifically: *address the role of problem posing in the NCTM Standards; *elaborate on the concept of student as author and critic; *include discussion of computer applications to illustrate the potential of technology to enhance problem posing in the classroom; *expand the section on diversity/multiculturalism; and *broaden discussion of writing as a classroom enterprise. This book offers present and future teachers at the middle school, secondary school, and higher education levels ideas to enrich their teaching and suggestions for how to incorporate problem posing into a standard mathematics curriculum.

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Bring the principles and practice of the acclaimed Mathematics Recovery Programme to whole-class teaching! WHY INVEST IN THE NEW EDITION? In full-colour with a revised layout for clearer navigation More up-to-date tasks, activities and real classroom examples Learning trajectories for guiding instruction and tracking progress on key topics Extra resources online on the companion website Part of the best-selling Maths Recovery series, this practical, step-by-step guide to classroom instruction takes an inquiry-based approach to assess children's knowledge and build on this to develop a firm foundation of understanding and confidence in mathematics. Topics covered range from beginning number and early counting strategies to multi-digit addition and subtraction right through to multiplication and division. An invaluable resource for use on pre-service teacher training courses and for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors, as well as learning support personnel, primary mathematics advisors, numeracy consultants and educational psychologists. WHAT EXTRAS ARE ON THE COMPANION WEBSITE? Downloadable extra chapter resources like print-out grids, worksheets, cards and much more A Facilitator’s Guide that can be used either individually or in group study to help you get the most out of the material In-class video demonstrations to clearly show how the instructional activities in the book are used in the classroom Webinar discussing the key points in the book and how it supports your teaching Visit the companion website at https://study.sagepub.com/wrighttnc "Research informs practice in this easy to access resource. Each chapter gives educators practical, bite-sized assessments, linked to a host of activities that helps them target teaching and develop the firm foundations which are so vital for confident and competent mathematicians." - Jill Piotrowski, Numeracy Consultant, Wigan Local Authority, UK "'The Classroom Instructional Framework in Early Number is research-based and provides a roadmap of not only the what, but the when and the how to teach all aspects of early number." - Vicki Nally, Mathematics Consultant at Catholic Education Office, Melbourne "The structured approach offers a wealth of rich and easily implemented classroom-based activities that work - thousands of teachers in Ireland attest to this!" - Noreen O'Loughlin, Director Maths Recovery and Maths Education Lecturer, Mary Immaculate College, Limerick, Ireland

This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways: * It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area. * It is future oriented, presenting recommendations for practice and policy and identifying areas for further research. * It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling. As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.

'Book Review Index' provides quick access to reviews of books, periodicals, books on tape and electronic media representing a wide range of popular, academic and professional interests. More than 600 publications are indexed, including journals and national general interest publications and newspapers. 'Book Review Index' is available in a three-issue subscription covering the current year or as an annual cumulation covering the past year.

The monograph series is published by NCTM as a supplement to the Journal for Research in Mathematics Education (JRME). Each monograph has a single theme related to the learning or teaching of mathematics. Number 11 in the JRME monograph series, this monograph attempts to clarify what we mean by everyday and academic mathematics, to provide empirical analyses of what happens when we bring particular aspects of everyday practises into classrooms and to consider how workplace practises relate to school mathematics.