Pre-service teachers developing and using mathematical knowledge for teaching proof

This paper explores pre-service teachers’ development of mathematical knowledge for teaching proof in a practice-based setting. Proof is challenging for both students and teachers but is crucial for meaningful mathematical learning. We design an instructional sequence based on core practices, tasking pre-service teachers with planning, implementing, and presenting proving activities. Analyzing six presentations on the process, we select two cases of maximal variation to explain and illuminate how pre-service teachers report on and utilize mathematical knowledge for teaching proof. The results suggest that a minimum level of common content knowledge for proof might be necessary for developing other forms of mathematical knowledge for teaching proof. This highlights the need for further research into the relationship between categories of mathematical knowledge for teaching proof in relation to designing instructional sequences.