Secondary prospective mathematics teachers learning to notice: The need for a dual perspective of teaching

The Association of Mathematics Teacher Educators recommends that well-prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics teachers (PMTs) participate in six teaching cycles of peer taught lessons, we analyzed lesson debriefings of PMTs' questions and comments to determine what PMTs notice over the course of the semester and how their noticing changed based on their role as a teaching or peer PMT. Analysis of these data reveals that participating in both roles as student and teacher provided PMTs with different opportunities to connect the teaching elements (i.e., curriculum, mathematics, and pedagogy). Using these data, we present an observed learning trajectory for secondary PMTs that mathematics teacher educators can use as they design learning activities within their methods class to promote PMTs to begin to notice the dual (student/teacher) perspective.