Proceedings of the Annual Meeting of the Cognitive Science Society

In this paper, we present a new information-processing modelof math problem solving in which representation change the-ory can be implemented. Specifically, we divided the problemrepresentation process into two. One is to straightforwardlytranslate problem texts into formulas in a conservative exten-sion of Zermelo-Fraenkel’s set theory, and the other is to in-terpret the translated formulas in local mathematical theories.A ZF formula has several interpretations, and representationchange is thus implementable as a choice of an appropriate in-terpretation. Adopting the theory of real closed fields as an ex-ample of local theory and its quantifier elimination algorithmsas an approximate process of searching for solutions, we de-velop a prototype system. We use more than 400 problemsfrom three sources as benchmarks: exercise books, univer-sity entrance examination, and the International MathematicalOlympiad problems. Our experimental results suggest that ourmodel can serve as a basis of a quantitative study on represen-tation change in the sense that the performance of our proto-type system reflects difficulties of the problems quite precisely.