# Word Problems: Research and Curriculum Reform

By Stephen K. Reed | Go to book overview

CHAPTER 5
Multistep Problems

The previous chapter focused on elementary story problems that could be solved with a single arithmetic operation. Students had to decide whether to add, subtract, multiply, or divide. More complex arithmetic problems can be solved by formulating a plan for combining these elementary operations. Consider the following problem:

Julie had a budget of \$1,200 to furnish her new apartment. She found a five-piece living room set on sale for \$625. She also found a queen-sized bed for \$350 and a dresser for \$195. How much money, if any, will Julie have left to buy various odds and ends for her apartment?

Note that this is basically a Change problem. Julie started with \$1,200 and the student needs to find how much she had left after her purchases. But the amount of change has to be calculated by finding the total cost of her purchases. This is a Combine problem.

This chapter examines how multistep problems are solved by combining the elementary operations that were discussed in the previous chapter. Research on multistep problems has usually been conducted on computer systems that can coach students in constructing plans for solving these problems. This has both practical and theoretical advantages. The practical advantage is that there now exists computer coaches that can assist students in solving multistep problems. The theoretical advantage is that constructing solutions on the computer makes it easy to study the planning process that students use to solve these kinds of problems.

Three different systems that have been used to support and analyze solutions for multistep problems are compared and contrasted below. The

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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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