PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Roles of proof in an undergraduate inquiry-based transition to proof course
Page: 376
De Villiers (1990) suggested five roles of proof important in the professional mathematics community that may also serve to meaningfully engage students in learning proof: verification, explanation, systematization, discovery, and communication. We investigate written reflections on an end-of-semester assignment from undergraduates in an inquiry-based transition to proof course, where students reflected on instances during the semester when they engaged in the five roles of proof. We present (a) student rankings of role engagement, (b) the types of activities students recalled as influential to their engagement in the roles of proof, and (c) how students perceived they engaged in the five roles. Students in this course reflected on activities distinctive of the inquiry-based environment (such as discussing, presenting, conjecturing, and critiquing) as influential to their engagement in the roles of proof. We provide student quotations highlighting these activities and offer implications for both research and practice.