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RESEARCH PRODUCT

Heuristics and Memory Strategies Used by Mathematicians

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The study of the cognitive processes involved in learning and acquisition of technically complex material is a main focus of interest for basic and applied research. Our research program tries to identh memory aids and heuristic training strategies useful for improving mathematics performance. Part of the effectiveness of a course, designed by taking into account knowledge about the cognitive system, has to do with the development of an adequate relationship with the belief system of the learner. As a first step in that direction, we present a survey of the opinions of a group of mathematicians about the dd€iculty of their subjecr matter, the strategies they use spontaneously to overcome difficulties, and the involvement of heuristic strategies in the solution of problems in different mathematical fields. The purpose of the survey was to compare the beljef system developed by rhe srudent as a result of experience wirh the subject matter wich the technical knowledge about memory and reasoning gathered Erom scientific studies in psychology. Method.-The questionnaire was completed by 41 Spanish mathematicians (with master's degrees who were preparing to teach at the preuniversity level). They were attending a course on memory and study techniques, but the questionnaire was filled out at the beginning of the course. Using 5-point ratings and open answers, a questionnaire was prepared to survey how mathematicians study their subject matter, how they perceive the diEiculty of the subject matter, and the frequency of use of several heuristic strategies (Schoenfeld, 1985) that could be involved in problem-solving training. In the questionnaire subjects were asked ahour the aspects they considered most difficult in learning mathematics (amount of knowledge, dcgrce of abstractness, etc.) together wich the techniques they found best to study the marer~al We took the list of heuristics collected by Schoenfeld (1985) as useful in problem solving and asked the respondents to rate the frequency with which they used them rhroughout their learning career. These heuristics are very simple rules such as draw a graph, look at special cases, simplt€y a problem, etc. which are helpful in finding a solution. Results and ditcussion.-We examined their answers to the three parts of the questionnaire in turn: study conditions, mathematical proofs, and use of heuristics in solving. Fig. 1