Examining the potential of rehearsal interjections to support the teaching of mathematical practice: the case of mathematical defining

This study investigates the potential of rehearsal interjections to provide opportunities for novice teachers and teacher educators to discuss topics related to teaching the practice of mathematical defining. Through analysis of video recordings of seven elementary novice teachers' rehearsals about geometric definitions, we identified the problems of practice that initiated rehearsal interjections, the topics discussed during rehearsal interjections, and relations between initiating problems of practice and topics discussed. We found that initiating problems of practice focused overwhelmingly on pedagogical issues, with most related to aspects specific to the teaching of mathematical defining. Likewise, discussions during interjections tended to focus on definitional pedagogical topics. Although epistemic topics were mentioned, they were only conveyed implicitly and at times in conflicting manners. Moreover, few opportunities arose for novices to make sense of student thinking about definitions and the mathematics of shape. Our results illustrate ways in which the goal of improving pedagogy, although important, can overshadow learning of other aspects for teaching mathematical practice.