An Analysis of Prospective Teachers' Dual Roles in Understanding the Mathematics of Change: Eliciting Growth With Technology

We analyze the interrelations between prospective and practicing teachers' learning of the mathematics of change and the development of their emerging understanding of effective mathematics teaching. The participants in our study, who were all interested in teaching secondary mathematics, were mathematics majors who had significant formal knowledge of the fundamental concepts of calculus prior to taking our courses, but who often experienced and expressed procedural orientations toward the teaching of mathematics. To address this difficulty, we developed novel computer-based activities to challenge the participants' mathematical understandings and required them to use technology during short teaching episodes they conducted with younger students. To analyze our participants' understandings, we developed a framework that juxtaposes the roles of the participants as students and teachers, and their understanding of mathematics and of pedagogical strategies. Our analysis of the participants' views from these different perspectives enabled us to see simultaneously the intertwined development of subject matter insights and specific views of teaching.

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