Effects of constructing, critiquing, and revising arguments within university classrooms

Abstract

Fifty-seven students in mathematics content and secondary mathematics methods classrooms at four universities participated in an instructional sequence to communally generate criteria defining a valid proof. Participants were asked to complete a proof-related task before class, work together in small groups to evaluate fellow students’ arguments, communally agree upon criteria for evaluating said arguments based on their evaluations, and then rate and revise their original argument to satisfy the communal criteria after class. We used a modified analytical categorization of arguments to compare students’ before-class and after-class work. Results demonstrated that students’ self-rating aligned positively with the argument categories, but two critical challenges were also observed: (1) students’ self-rating of their arguments was not positively correlated with the class-acceptance rate of those arguments indicating that individual and communal perceptions of proof varied; and (2) students struggled to revise their arguments to align with the communal criteria.