Word Problems: Research and Curriculum Reform

By Stephen K. Reed | Go to book overview

Preface

The purpose of this book is to try to bring together ideas from the fields of cognitive psychology, mathematics education, and educational technology to achieve a better theoretical and practical understanding of how students attempt to solve word problems. I am a cognitive psychologist who has used algebra word problems in my research over the past 15 years. But like most other cognitive psychologists, my research interests have not focused as much on how students solve algebra word problems, as on more general theoretical issues such as how students transfer a solution from one problem to another problem. Algebra word problems just happened to be a convenient source of problems for my research, in large part because students have so much trouble solving them.

Nonetheless, when I began working with algebra word problems I naively thought that my work would be of some interest to professionals in the field of mathematics education. After all, I was working with word problems and transfer has always been a central issue for educators as well as for psychologists. But my work has had little influence on mathematics education, and work in mathematics education has had little influence on my work. Unfortunately, this is typical. Look at the reference section of any article published by a cognitive psychologist on mathematical problem solving and you will see mostly references to the work of other cognitive psychologists. Look at the reference section of any article published by a mathematics educator on mathematical problem solving and you will see mostly references to the work of other mathematics educators. The odds are not improved much by looking at the references of papers presented at the Psy

-ix-

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Word Problems: Research and Curriculum Reform
Table of contents

Table of contents

  • The Studies in Mathematical Thinking and Learning Series Alan Schoenfeld, Advisory Editor ii
  • Title Page iii
  • Contents vii
  • Preface ix
  • Chapter 1: Introduction 1
  • Part I Knowledge Structures 13
  • Chapter 2: Learning Rules 15
  • Chapter 3: Conceptual Understanding 28
  • Part Ii Problems 43
  • Chapter 4 Elementary Problems 45
  • Chapter 5: Multistep Problems 62
  • Chapter 6: Algebra Problems 76
  • Part III Transfer 99
  • Chapter 7: Abstracting Solutions 101
  • Chapter 8: Adapting Solutions 116
  • Chapter 9: Representing Solutions 134
  • Part Iv Important Topics in the Nctm Standards 149
  • Chapter 10: Wor(l)d Problems 151
  • Chapter 11: Estimation and Functions 166
  • Chapter 12 Curriculum Reform 184
  • References 203
  • Author Index 213
  • Subject Index 217
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