{"pk":26449,"title":"An Information-Processing Account of Representation Change:International Mathematical Olympiad Problems are Hard not only for Humans","subtitle":null,"abstract":"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.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[{"word":"problem solving; information-processing model;insight; representation change"}],"section":"Papers","is_remote":true,"remote_url":"https://escholarship.org/uc/item/6ps6f4gm","frozenauthors":[{"first_name":"Takuya","middle_name":"","last_name":"Matsuzaki","name_suffix":"","institution":"Nagoya University","department":""},{"first_name":"Munehiro","middle_name":"","last_name":"Kobayashi","name_suffix":"","institution":"University of Tsukuba","department":""},{"first_name":"Noriko","middle_name":"H.","last_name":"Arai","name_suffix":"","institution":"National Institute of Informatics","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"2016-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/26449/galley/16085/download/"}]}