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On the spontaneous discovery of a mathematical relation during problem solving

dc.contributor.authorDixon, James A.en_US
dc.contributor.authorBangert, Ashley S.en_US
dc.date.accessioned2010-06-01T21:28:56Z
dc.date.available2010-06-01T21:28:56Z
dc.date.issued2004-05en_US
dc.identifier.citationDixon, James A.; Bangert, Ashley S. (2004). "On the spontaneous discovery of a mathematical relation during problem solving." Cognitive Science 28(3): 433-449. <http://hdl.handle.net/2027.42/74539>en_US
dc.identifier.issn0364-0213en_US
dc.identifier.issn1551-6709en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/74539
dc.description.abstractPeople 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.en_US
dc.format.extent330972 bytes
dc.format.extent3109 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.publisherLawrence Erlbaum Associates, Inc.en_US
dc.publisherBlackwell Publishing Ltden_US
dc.rights2004 Lawrence Erlbaum Associates, Inc.en_US
dc.subject.otherSchema Abstractionen_US
dc.subject.otherDiscoveryen_US
dc.subject.otherMathematical Relationsen_US
dc.subject.otherComparisonen_US
dc.subject.otherStructure Mappingen_US
dc.subject.otherProblem Solvingen_US
dc.titleOn the spontaneous discovery of a mathematical relation during problem solvingen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelNeurosciencesen_US
dc.subject.hlbtoplevelHealth Sciencesen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationotherDepartment of Psychology, 406 Babbidge Road, Unit 1020, University of Connecticut, Storrs, CT 06269-1020, USAen_US
dc.contributor.affiliationotherDepartment of Psychology, 525 East University, Ann Arbor, MI 48109-1109, USAen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/74539/1/s15516709cog2803_6.pdf
dc.identifier.doi10.1207/s15516709cog2803_6en_US
dc.identifier.sourceCognitive Scienceen_US
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dc.owningcollnameInterdisciplinary and Peer-Reviewed


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