Toward a Unified Theory of Problem Solving: Views from the Content Domains

By Mike U. Smith | Go to book overview

5
A VIEW OF MATHEMATICAL PROBLEM SOLVING IN SCHOOL

James G. Greeno Stanford University and the Institute for Research on Learning


INTRODUCTION

The information-processing view of problem solving has achieved several major successes. Among them is the analysis of cognitive processes and knowledge structures involved in solving problems in school mathematics. This paper will begin with a brief review of results that have been obtained in these analyses, considering both the contributions to cognitive science that have been achieved, and some ways in which the resulting theoretical results are beginning to be used in educational practice. We now have clear theoretical pictures of the knowledge that text problems require, and these can be used to teach that problem-solving knowledge more effectively.

We can also use these clear theoretical pictures to ask whether the knowledge needed for text problems is what we want students to learn. In my view, the answer is that knowledge required for solving text problems is unacceptably limited. I will present this opinion and sketch an alternative view of mathematical knowing as an activity, rather than as a set of cognitive structures and processes. If we want students to become knowers of mathematics in this sense, the goals and methods of

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Toward a Unified Theory of Problem Solving: Views from the Content Domains
Table of contents

Table of contents

  • Title Page *
  • Contents *
  • Preface *
  • 1 - A View from Biology 1
  • Acknowledgment 17
  • References 17
  • 2 - A View from Chemistry 21
  • References 32
  • 3 - A View from Medicine 35
  • References 43
  • 4 - A View from Programming 45
  • Acknowledgements 63
  • References 63
  • 5 - A View of Mathematical Problem Solving in School 69
  • Acknowledgements 95
  • References 95
  • 6 - A View from Physics 99
  • References 113
  • 7 - A View from Trouble-Shooting 115
  • References 148
  • Author Index 155
  • Subject Index 161
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