Word Problems: Research and Curriculum Reform

Research by cognitive psychologists and mathematics educators has often been compartmentalized by departmental boundaries. Word Problems integrates this research to show its relevance to the debate on the reform of mathematics education.

Beginning with the different knowledge structures that represent rule learning and conceptual learning, the discussion proceeds to the application of these ideas to solving word problems. This is followed by chapters on elementary, multistep, and algebra problems, which examine similarities and differences in the cognitive skills required by students as the problems become more complex. The next section, on abstracting, adapting, and representing solutions, illustrates different ways in which solutions can be transferred to related problems. The last section focuses on topics emphasized in the NCTM Standards and concludes with a chapter that evaluates some of the programs on curriculum reform.

Table of Contents

Contents

Preface

1 Introduction

Part I Knowledge structures

    2 Learning Rules

    3 Conceptual Understanding

Part II Problems

    4 Elementary Problems

    5 Multistep Problems

    6 Algebra Problems

Part III Transfer

    7 Abstracting Solutions

    8 Adapting Solutions

    9 Representing Solutions

Part IV Important topics in the NCTM standards

    10 Wor(l)d Problems

    11 Estimation and Functions

    12 Curriculum Reform

References

Subject Index