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