Discursive differences in written feedback of individuals with varied teaching experiences: Towards validating knowledge of content and teaching specific to proof

Fostering student engagement with mathematical reasoning and proving requires a special kind of teacher knowledge – Mathematical Knowledge for Teaching Proof (MKT-P). One important component of MKT-P is Knowledge of Content and Teaching specific to Proof (KCT-P), which is knowledge of pedagogical practices for supporting student learning of proof. Providing effective feedback on students' mathematical arguments is one of the key aspects of KCT-P. This study examined the qualitative differences in written feedback of secondary teachers, undergraduate mathematics and computer science majors, and pre-service teachers participating in a capstone course focused on mathematical reasoning and proving. The discursive distinctions in the groups’ feedback, along with changes in the feedback of prospective teachers, provide empirical support for the construct of KCT-P as knowledge unique to teachers, which develops with experience.