Proof, Proving, and Teacher-Student Interaction: Theories and Contexts

Abstract

This chapter focuses on the teachers’ role in teaching proof and proving in the mathematics classroom. Within an over-arching theme of diversity (of countries, curricula, student age-levels, teachers’ knowledge), the chapter presents a review of three carefully selected theories: the theory of socio-mathematical norms, the theory of teaching with variation, and the theory of instructional exchanges. We argue that each theory starts by abstracting from observations of school mathematics classrooms. Each then uses those observations to probe into the teachers’ rationality in order to understand what sustains those classroom contexts and how these might be changed. Here, we relate each theory to relevant research on the role of the teacher in the teaching and learning of proof and proving. Our review offers evidence and support for mathematics educators meeting the challenge of theorising about proof and proving in mathematics classrooms across diverse contexts worldwide.