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Summary

This book provides middle school teachers with a firm pedagogical foundation based on the manner in which students learn the mathematics being taught.

This book is written primarily for middle grade teachers who are discovering that they now want to teach in ways that create positive mathematical learning environments and instigate rich classroom discourse. Many of these teachers are finding that their mathematical preparation did not address the complexities underlying the mathematics they now want to teach.

In Part One, the authors provide a foundation for the mathematics of these grades, particularly the mathematics that grows out of concepts of number, quantity, and arithmetic operations. In Part Two, through three case studies, the authors demonstrate to teachers how a deeper understanding of the mathematics they teach can enhance classroom instruction.

The book interweaves research and classroom practice. Mathematics teacher educators, researchers, curriculum developers, textbook authors, and supervisors of mathematics programs will find this book to be useful. Teachers, both prospective and practicing, will benefit most from this book when the chapters are used as catalysts for discussion in classes or professional development programs.

Judith T. Sowder is Professor and Bonnie P. Schappelle is Research Associate in the Center for Research in Mathematics and Science Education at San Diego State University.

Table of Contents

Preface

1. Continuing the Mathematical Preparation of Middle-Grade Teachers: An Introduction

Judith T. Sowder

Part 1: Mathematics for the Middle Grades

2. Instructing for Rational Number Sense

Judith T. Sowder

3. Creating Spaces for Learning Fractions

Thomas E. Kieren

4. Critical Ideas, Informal Knowledge, and Understanding Fractions

Nancy K. Mack

5. Multiplication and Division of Fractions: The Search for Meaning

Barbara E. Armstrong Nadine Bezuk

6. Addressing the Story-Problem Problem

Larry Sowder

7. From Naive-Interpretist to Operation-Conserver

Guershon Harel

8. Ratio and Proportion: Elementary Didactical Phenomenology

Susan J. Lamon

9. Notation, Convention, and Quantity in Elementary Mathematics

Patrick W. Thompson

10. The Value of Interaction in Promoting Teaching Growth

Judith T. Sowder Randolph A. Philipp

Part II: Case Studies: Catalysts for Change

11. Instructional Effects of Knowledge Of and About Mathematics: A Case Study

Judith T. Sowder Randolph A. Philipp Alfinio Flores Bonnie P. Schappelle

12. Orchestrating, Promoting, and Enhancing Mathematical Discourse in the Middle Grades: A Case Study

Alfinio Flores Judith T. Sowder Randolph A. Philipp Bonnie P. Schappelle

13. A Responsible Mathematics Teacher and the Choices She Makes: A Case Study

Randolph A. Philipp Judith T. Sowder Alfinio Flores Bonnie P. Schappelle