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Title: The Context of Proving
Contributor(s): Livingston, E  (author)
Publication Date: 2006
DOI: 10.1177/0306312705053055
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Abstract: Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper’s central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.
Publication Type: Journal Article
Source of Publication: Social Studies of Science, 36(1), p. 39-68
Publisher: Sage Publications
Place of Publication: United Kingdom
ISSN: 0306-3127
Field of Research (FOR): 169999 Studies in Human Society not elsewhere classified
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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