Examining the Mathematical Knowledge for Teaching of Proving in Scenarios Written by Pre-service Teachers
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In this chapter, we examine what aspects of Mathematical Knowledge for Teaching of Proving (MKT-P) can be observed in written scenarios of classroom interactions, produced by pre-service teachers (PSTs) of mathematics. A group of 27 elementary and middle school PSTs completed an online interactive module, intended to trigger reflection on, and crystallization of their knowledge of the roles of examples in proving. To ground these processes in the context of teaching, the module engaged PSTs in analysis of several representations of practice such as a questionnaire about quadrilaterals with sample student work imbedded in it, and a classroom scenario in a storyboard format realized with cartoon characters. In addition, PSTs wrote a one-page continuation of that scenario describing how they would handle the situation if they were teaching the class. These scenarios proved to be a rich source of data on several aspects of MKT-P as well as general pedagogical knowledge.
KeywordsPre-service teachers Written scenarios Conceptions of proving The role of examples in proving Geometry
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