In the previous chapter the distinction was made between Isomorphic problems that had identical solutions, but different stories, and Similar problems that had identical stories, but different solutions. Both types of problems require the two basic operations for the successful use of analogy--finding a good analogous problem and mapping the objects and relations in the analogous solution to the test problem. However, the relative difficulty of these two operations differs across the two types of problems. It was seen that the most challenging requirement in solving Isomorphic problems is realizing that two apparently different problems share the same solution. Students often do fairly well in finding corresponding objects and relations in the two problems after they realize that the problems are isomorphic. In contrast, the most challenging requirement in solving Similar problems is adapting those relations that are not identical to the ones in the analogous solution.
This chapter begins with the issue of selecting a helpful solution. Because students often judge similarity of problems on the basis of story content, it is natural for them to use story content when selecting a helpful analogy. If given a homework problem that requires mixing two solutions, they are likely to look for example problems that involve mixing two solutions. But what if they find two examples, one of which is more complex than their homework problem and one of which is less complex than their homework problem. Which should they choose as being more helpful?
The chapter then turns to the second operation, mapping objects and relations. The difficulty here is that some of the relations between the two problems are not identical and students often have difficulty modifying