An Information-Processing Account of Representation Change: International Mathematical Olympiad Problems are Hard not only for Humans


We present a new information-processing model of math problem solving in which representation change theory can be implemented. The problem representation process is divided into two. One is to translate a problem into a formula in a conservative extension of Zermelo-Fraenkel's set theory, and the other is to interpret the translated formulas in local mathematical theories. A ZF formula has several interpretations, and representation change is thus implementable as a choice of an interpretation. Adopting the theory of real closed fields as an example of local theory, we develop a prototype system. We use more than 400 problems from three sources as benchmarks: exercise books, university entrance examination, and the International Mathematical Olympiad problems. Our experimental results suggest that our model can serve as a basis of a quantitative study on representation change in the sense that the performance of our prototype system reflects difficulties of the problems quite precisely.

Back to Table of Contents