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|Title:||The Context of Proving||Contributor(s):||Livingston, E (author)||Publication Date:||2006||DOI:||10.1177/0306312705053055||Handle Link:||https://hdl.handle.net/1959.11/311||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||Statistics to Oct 2018:||Visitors: 19
|Appears in Collections:||Journal Article|
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