The Context of Proving.  

Oleh:

Livingston, Eric

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Social Studies of Science vol. 36 no. 1 (Feb. 2006), page 39.
Topik: discovery; ethnomethodology; mathematics; proofs; reasoning
Fulltext: 39.pdf (270.41KB)

Isi artikel

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.

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