Introducing Students and Prospective Teachers to the Notion of Proof in Mathematics

• In Event: Student Mathematics Learning Pre-K–12

Abstract

Despite the importance of "proof" in mathematics, little is known about what it might involve to introduce students and prospective teachers to proof. In this theoretical paper we propose a learning trajectory for students’ and prospective teachers’ introduction to proof, and we use data from two multi-year design experiments to illustrate what it looked like when an intervention aimed to promote the learning trajectory in two contexts. The learning trajectory comprises two milestones: (1) seeing a need to learn about proof and (2) developing an operationally functional conceptualization of proof. The “need” in milestone 1 entails an aspect of epistemological justification applicable to both students and prospective teachers and a further aspect of pedagogical justification applicable to prospective teachers.

Authors

• Gabriel J. Stylianides, University of Oxford

• Andreas J. Stylianides, University of Cambridge