Constructing Communal Criteria for Proof through Critiquing the Reasoning of Others

Fifty-seven students in mathematical content and secondary mathematics methods courses from four U.S. universities participated in an instructional sequence to generate communal criteria defining mathematical proof within their respective classrooms. Participants completed a proof-related task before class, worked together in small groups to evaluate instructor-selected arguments, communally agreed upon criteria for evaluating a proof based on their evaluations, and then revised their original argument to meet the communal criteria after class. Similar criteria were constructed across the four classrooms. Moreover, the four authors coded and compared students' initial and revised arguments with respect to proof schemes to identify specific shifts in students' work after the instructional sequence. Results indicated a majority of students' proof schemes changed in their revised argument with specific trends aligning with their class-based criteria for proof. [For the complete proceedings, see ED583608.]