Proving and Knowing in Public: What Counts as Proof in a Classroom

Patricio Herbst (1, 2) , Nicolas Balacheff (3)

1 School of Education
2 University of Michigan [Ann Arbor]
3 LIG - Laboratoire d'Informatique de Grenoble

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.

Mots clés: Mathematical proof; Mathematics education; Teaching mathematical proof

Domaines: Histoire et perspectives sur les mathématiques [math.HO]

Patricio Herbst, Nicolas Balacheff. Proving and Knowing in Public: What Counts as Proof in a Classroom. Maria L. Blanton; Despina A. Stylianou. Teaching and learning proofs across the Grades. A K-16 perspective, Routledge, pp.40-70, 2009, Studies in Mathematical Thinking and Learning Series, 978-0-415-98984-8. ⟨hal-00998146⟩