STUDENT PERCEPTIONS OF RELATEDNESS AMONG MATHEMATICAL VERBAL PROBLEMS

In his writings on mathematical problem solving, Polya (1957, 1962, 1965) has suggested a series of heuristic precepts that might be useful in the solution of a mathematical problem. For example, Polya has suggested that, when one is devising a plan for solving a problem, it is often useful to "think of a related problem." Indeed, it is reasonable to assume that many mathematics teachers suggest such advice to their students. But how do students respond to the suggestion? How have students categorized the vast number of problems that they have encountered so that they can retrieve a related problem when the suggestion is made? The answers to such questions may provide insight into the psychological implications of Polya's reasonable suggestion. In fact, the answers may help to provide an increased understanding of the modes of information processing and retrieval that students use in mathematical problem solving. Consider a person's mathematical problem-solving experience. The problems that have been solved previously have almost certainly been classified in a certain way. A person's ability to make good use of Polya's related problem heuristic advice is, at least partially, a function of the criteria that have been used in forming the categories. The criteria reveal the dimensions along which the person views problems as similar. That individuals may differ in their perceptions of the important features of common stimuli is well known. Evidence is available from many fields of study, including visual pattern processing (Garner, 1974); medical anthro-