The influence of teachers' knowledge of mathematics in their classroom interactions
Fox, Ryan David
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This study examined how two Advanced Placement Calculus teachers used their own knowledge of mathematics in their classroom interactions. In particular, this study focused on teachers’ responses to unanticipated or unplanned student questions during a normal lesson. Each teacher was observed for one unit of instruction of at least ten hours. Field notes and audio recordings were taken during the observations. Throughout the unit of instruction, four interviews were conducted with each teacher to explore how they used their own knowledge. In this study, the teachers tended to use four types of responses: posing counterexamples, acknowledging challenging responses, asking simpler or related questions, or following through with the student’s comment. Through the four responses, teachers could respond to the students’ comments by addressing the comment separately, interweaving a response with the planned activity, or coordinating a response with planned activity. Future research could explore teachers’ responses and patterns of responses for longer observations or earlier mathematics courses.