Understanding authority in small-group co-constructions of mathematical proof

Abstract

Authority becomes shared in mathematics classrooms when perceived sources of valid mathematical knowledge extend beyond the teacher/textbook and allow both students and disciplinary modes of reasoning to hold authority. The goal of this research is to better understand classroom situations that are intended to facilitate shared authority over proof, namely small-group episodes where students are granted authority (Gerson & Bateman, 2010) to co-construct mathematical proofs. We sought to better understand the content of undergraduate students’ attention during group proving and the sources of legitimacy for students. Using Stylianides’ (2007) definition of proof as an analytical frame, we found that student discourse focused primarily upon the mode of argumentation, followed by the mode of argument representation, and then the set of accepted statements. We identified four themes with respect to the sources of authority students relied upon in their group proving: (1) the course rubric, (2) peers’ confidence, (3) form and symbols, and (4) logical structure. Implications for research and practice are presented.