Reflective Apprenticeship for Teaching and Learning Mathematical Proof

This article explores teacher learning in a graduate-level analysis course for teachers. Drawing from the frameworks of extreme apprenticeship and Peer-Assisted Reflection (PAR), the course created authentic learning experiences for the teachers that served as models that they could use in their own classrooms. This paper describes how the teachers developed across the four dimensions of extreme apprenticeship. While this paper is grounded in mathematics, the extreme apprenticeship and PAR frameworks are cross-disciplinary, and thus there are implications for teaching and learning in all of the STEM disciplines.