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On the spontaneous discovery of a mathematical relation during problem solving
Author(s) -
Dixon James A.,
Bangert Ashley S.
Publication year - 2004
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1207/s15516709cog2803_6
Subject(s) - parity (physics) , abstraction , schema (genetic algorithms) , computer science , mathematical model , theoretical computer science , mathematical structure , mathematical theory , mathematics , machine learning , statistics , epistemology , philosophy , physics , mathematics education , particle physics , quantum mechanics
People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear‐system problems as part of a game. Although none of the participants initially used a mathematical representation, many discovered a parity‐based, mathematical strategy during problem solving. Two accounts of the spontaneous discovery of mathematical strategies were tested. According to the automatic schema abstraction hypothesis, experience with multiple, unique problem exemplars facilitates extraction of the parity relation. According to the comparison‐based abstraction hypothesis, explicitly comparing gear pathways that have different number, but the same parity, should result in extraction of parity. An event history analysis showed that accumulation of experiences with different‐number, same‐parity comparisons predicted discovery of parity; accumulation of unique exemplars did not. Results suggest that comparison‐based abstraction processes can lead to the discovery of a mathematical relation.