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The Context of Proving.
- Source :
- Social Studies of Science (Sage Publications, Ltd.); Feb2006, Vol. 36 Issue 1, p39-68, 30p
- Publication Year :
- 2006
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03063127
- Volume :
- 36
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Social Studies of Science (Sage Publications, Ltd.)
- Publication Type :
- Academic Journal
- Accession number :
- 19983547
- Full Text :
- https://doi.org/10.1177/0306312705053055