Are self-constructed and student-generated arguments acceptable proofs? Pre-service secondary mathematics teachers' evaluations

This study examined 14 pre-service secondary mathematics teachers' productions and their evaluations of self-constructed and student-generated arguments in the domains of algebra, geometry, and number theory. Pre-service secondary mathematics teachers' (PSMTs) evaluations of their own arguments indicate if they considered self-productions as proofs from a learner perspective. Similarly, PSMTs' evaluations of student-generated arguments indicate if they decided given students' productions could be counted as proofs from a teacher perspective. Our results show that the majority of PSMTs suspected that their invalid productions did not qualify as proofs. Furthermore, the PSMTs who were confident with their work and claimed that they had constructed a proof were more likely to make a correct judgment on four of the six studentgenerated arguments. We discuss implications of these findings for supporting PSMTs' learning of proof and future research on the construction-evaluation activity.