Revisiting the functions of proof in mathematics classrooms: A view from a theory of instructional exchanges

Abstract

We consider the functions of proof in mathematics from the perspective of the work of the mathematics teacher. The work of proving and the time spent on proving, what can a teacher account it to? How can he or she justify it? We frame that problem in a descriptive theory of teaching and place within that frame the work of scholars who have inquired on the function of proof in mathematics. We argue that the multiple functions that proof plays in mathematics are resources that a teacher could use to account for the work of proving. We describe how the functions of proof identified in the literature can assist the work of the teacher and illustrate the role these functions of proof can play using classroom scenarios that showcase the work of proving. Since the teacher is not only accountable to mathematics but also accountable to students’ learning of that mathematics some times work is valuable because it helps represent important mathematical knowledge, sometimes because it helps students acquire, or demonstrate they have, knowledge. The existence of these different sources of value is not only a resource for the teacher to value diverse work but also permits to anticipate management dilemmas concerning the different ways of accounting for the work of proving.