Proving and Knowing in Public: What Counts as Proof in a Classroom
Abstract
We take on the question of what counts as proof in a classroom by arguing that a descriptive theory of public mathematical knowing over time needs at least three meanings for the word proof. These include a vague, habitual notion of proof that articulates a set of preferences for making general, necessary statements, a precise, conception-specific notion of proof that serves as the ultimate regulatory structure for the control of solutions to problems, and a metaphorical notion of proof that permits the lifting and application of conception-specific proofs onto different conceptions. We argue that such triad of notions of proof can help dissolve the theoretical deadlock regarding proof in mathematics education research.
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2009 Herbst et Balacheff - Proof and proving in public - authors version (1).pdf (491.49 Ko)
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