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