Investigating prospective teachers’ skills of predicting and identifying significant student reasoning instances and deciding how to respond to those instances

The importance of constructing mathematical arguments and critiquing the reasoning of others has been emphasized as a key component for deep mathematical understanding. As a result, acknowledging proof as an essential tool to comprehend mathematics at all grade levels has been suggested by many researchers as well as reform initiatives. To do so, both teachers and prospective teachers should be able to predict how students reason mathematically, identify significant student reasoning instances and decide how to respond productively to those instances. The participants consisted of eleven prospective teachers who enrolled in a teacher education program at a public university in Turkey. All participants enrolled in a two-credit mathematics education course about teaching reasoning and proving in the middle grades taught by the author. The results of this study demonstrated that the participating prospective teachers were able to predict student reasoning productively. However, the results regarding to the participants' levels of identifying significant student reasoning instances were less successful. This study also documented that majority of the participants listed guiding questions. Although the elective course was not structured toward promoting participants' noticing skills, all these results could suggest that the course might have influenced the participants' prediction, identifying, and responding skills.