Mathematical Knowledge for Teaching Proof: Comparing Secondary Teachers, Pre-Service Secondary Teachers, and Undergraduate Majors

The calls for reasoning and proof to have a prominent place in secondary mathematics classrooms raise the question of knowledge that teachers need to support student learning of reasoning and proof. Several conceptualizations of Mathematical Knowledge for Teaching Proof (MKT-P) have been proposed over the years, yet some key questions about the nature of MKT-P remain unclear, such as whether MKT-P is a special kind of knowledge specific to teaching or whether it is just common mathematics knowledge. Another question is whether MKT-P can be improved through targeted intervention. Our study attempts to respond to both questions. An MKT-P questionnaire was administered to in-service secondary teachers, undergraduate mathematics and computer science (M&CS) majors, and pre-service secondary teachers before and after taking a capstone course Mathematical Reasoning and Proving for Secondary Teachers. The results suggest that MKT-P is indeed a specialized type of knowledge, which can be improved through targeted intervention.