On the spontaneous discovery of a mathematical relation during problem solving

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 omparison-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 di...

• Type: Journal
• Year: 2004
• Where: COGSCI
• Authors: James A. Dixon, Ashley S. Bangert
• Keywords: Abstraction, COGSCI 2004, Mathematical Representation, Omparison-based Abstraction Hypothesis