Recall of Mathematical Problem Information: Solving Related Problems.

When solving a new problem, a successful problem solver presumably uses information, procedures, and more general notions that have been obtained from previous experience and training. Gestalt psychologists (Duncker, 1945; Luchins, 1942) have demonstrated that prior experience with related problems may have a negative effect in certain new problem-solving situations. In recent years, attention has been focused on identifying the circumstances under which positive transfer occurs. Reed, Ernst, and Banerji (1974) examined performance on the "Missionaries and Cannibals" problem and one of its homomorphs and reported that subjects exhibited positive transfer between the similar problems only when they were told of the relationship between the problems and only when they solved the more difficult problem of the pair first. Kulm and Days (1979) used an information-theoretic approach to study transfer between problems with related structures. They reported that significant transfer occurred when subjects solved an equivalent puzzle problem (Missionaries and Cannibals) but not an equivalent algebraic problem. However, significant transfer was reported when solving a similar algebraic problem but not a similar puzzle problem. The solution of related problems appeared to help subjects focus on relevant strategies, but different problem contexts appeared to interfere with transfer. Simon and Hayes (1976) also reported that the "cover story," or problem context, may have a significant effect on a subject's problem-solving performance. All the investigations cited above involved college students and, with the exception of an algebraic problem in the Kulm and Days study, all involved the solution of puzzle problems-Missionaries and Cannibals, Tower of Hanoi, and their isomorphs or homomorphs. The present study sought to extend this work by using school-age subjects and mathematical word problems of the kind usually encountered in school. Furthermore, the study looked specifically at the role of memory in transfer between related problems.