Proceedings of the Annual Meeting of the Cognitive Science Society

This paper is part of an effort to extend research on mathematical problem solving beyond the traditional focus on formal procedures (both in the classroom and in problem solving research). W e are beginning to investigate students' inductive discovery-oriented strategies and the interaction between these and formal deductive strategies. In contrast to typical classroom problems in math and science which demand the application of a learned formal procedure (e.g., prove X), we gave students more open-ended problems (e.g., is X true?) for which the formal deductive procedure is useful, but other, possibly informal or inductive, strategies are also potentially useful. The normative approach for solving these problems, in fact, requires the use of both a deductive strategy, which is definitive only when X is true, and an inductive search for examples, which is definitive only when X is not universally true. When presented with these problems we found that geometry students have some limited facility to perform the deductive strategy (though, less so in this context than when they are directly asked to vwite a proof) and use a degenerate version of the inductive strategy. Instead of considering multiple examples and looking for a counter-example, students tend to read off the conclusion from the single example (or model) we provided.