Word Problems: Research and Curriculum Reform

By Stephen K. Reed | Go to book overview

CHAPTER
9
Representing Solutions

Transfer may occur at a more general level than transferring the details of a specific solution. Sometimes you may notice that the general method you used to solve a previous problem may also apply to the problem you are now trying to solve. Novick ( 1990) referred to the transfer of general methods as representational transfer to distinguish it from the analogical transfer of specific solutions. Analogical transfer is concerned with the transfer of specific steps in the solution, such as modifying the equation for a work problem in which two workers work the same amount of time to fit a problem in which one worker works longer than the other worker. Representational transfer is concerned with the transfer of a general method. The method may be a very general one, such as use of a diagram, or a more specific one, such as use of a Venn diagram.

Representational transfer, like analogical transfer, can be broadly divided into noticing that two problems can be solved by the same general method and applying that method to a test problem. It was discussed previously that noticing similarities among problems can be studied by asking people to sort problems into categories based on identical solutions ( Silver, 1981) or common principles ( Chi, Glaser, & Rees. 1982). This technique can also be used to investigate whether people can categorize problems according to general solution methods ( Schoenfeld & Hermann, 1982). Applying general methods can be studied by pointing out the analogous problem and then measuring students' success in using the same method to solve a test problem. Novick and Hmelo ( 1994) used this technique to study whether students would transfer the use of an appropriate diagram from one prob-

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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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