Considering Proofs: Pre-Service Secondary Mathematics Teachers' Criteria for Self-Constructed and Student-Generated Arguments

Abstract

In this paper, we examined 14 pre-service secondary mathematics teachers' (PSMTs) criteria used in evaluating the validity of self-constructed and student-generated arguments in the domains of algebra, geometry, and number theory. During the interviews, participants produced and analyzed their own proofs or counterexamples for the three tasks first and analyzed if six student-generated arguments could be counted as proofs next. The two criteria most frequently used by PSMTs in evaluating their own construction and a student-generated argument as a proof or not a proof were verification and clear details. Our finding showed that more PSMTs were inclined to pay attention to clear details presented in students’ work than their own productions. Our finding also showed that more PSMTs focused on the verification feature in their self-constructions than in student-generated arguments. These results suggest that the criteria–verification and clear details–do not have the same weight for PSMTs when evaluating the validity of their own work and student-generated products. This study also has implications for proof-intensive courses, as PSMTs’ conceptions of proofs are more likely affected by their instructors in those proof-intensive classes.