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

- Takuya Matsuzaki,
*Nagoya University, Nagoya, Aichi, Japan*
- Munehiro Kobayashi,
*University of Tsukuba*
- Noriko H. Arai,
*National Institute of Informatics*

## Abstract

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.

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