# Word Problems: Research and Curriculum Reform

By Stephen K. Reed | Go to book overview

CHAPTER
7
Abstracting Solutions

The three chapters in this section of the book discuss transfer of solutions to solve related problems. Table 7.1 shows an example problem and four test problems ( Reed, 1987). The classification of the test problems shows what is meant by a related problem. The classification is based on whether the example problem and test problem share a common story context and a common solution procedure (equation). One would expect that students would do the best when the two problems share both. I label these problems as Equivalent and include them in my research as a measure of how well students have learned the solution to the example problem. It would be unfair to expect students to transfer a solution to modified problems if they haven't learned the solution to the example. Fortunately, students usually do fairly well in solving Equivalent problems.

Another relation between problems that has received much attention in examining transfer is what most researchers refer to as Isomorphic problems. Isomorphic problems have different story contexts but share a common solution. A practical issue is how different do the story contexts have to be in order to classify two problems as Isomorphic rather than as Equivalent. I consider the story context of algebra word problems to be different if the two problems fall into different categories in the taxonomies ( Hinsley, Hayes, & Simon, 1977; Mayer, 1981) that were discussed in the previous chapter. For example, the Isomorphic problem in Table 7.1 would be classified as a motion problem in Mayer's ( 1981) taxonomy, although it can be solved the same way as the example. This chapter examines transfer to Isomorphic problems.

Chapter 8 examines transfer to Similar problems. These problems share a story context but require modifying the solution of the example to solve

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Word Problems: Research and Curriculum Reform

• 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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