USE OF ANALOGIES AND SPATIAL TRANSFORMATIONS BY EXPERTS

Since Polya, Wertheimer, and Hadamard's descriptions of qualitative reasoning strategies used by scientists and mathematicians, very little data has been collected on whether these strategies are actually used by experts. This study used video-taped thinking aloud interviews to examine the problem solving strategies of professors and advanced graduate students in technical fields. Evidence fram these interviews documents the use of analogies, visual transformations, extreme cases, and other plausible reasoning strategies used by experts. In the case of analogies, it was found that there is more than one method for generating analogies, and that in addition, the process of critically evaluating the analogy is very important. 1 2 Considering helpful analogous cases and extreme cases, breaking problems into analyzable parts, and performing simplifying spatial transformations are key reasoning processes in solving non-trivial problems. These processes allow talented scientists to attack problems outside the domain of familiar problems for which'they have established algorithmic procedures. They allow thern to attack problems they have never seen before, giving them a degree of problem solving power and scope that is truly impressive. Previous reports [I, 2, 3, 4J have documented the fact that these qualitative reasoning processes are used by expert scientists in solving physics problems. This paper examines the possibility that empir ical evidence for these processes can also be found in the case of experts ' solutions to mathematics problems. I will first describe results from the earlier physics p~oblem study, and then describe those from the current mathematical problem study