A Design of Teacher Principles for the Development, Diffusion, and Appropriation of Students’ Mathematical Knowledge

This study documents and describes results of a classroom design study that investigated middle school mathematics classrooms where students were introduced to new mathematical tools, tool-related practices, concepts, facts, and problem solving strategies through the sharing of student-initiated ideas throughout the classroom. A resulting product of this design study is a set of multi-revised principles for mathematics teachers to use to promote the development, diffusion, and exchange of innovative mathematical knowledge in classrooms where students work collaboratively on problem-based mathematical tasks. The implementation principles were designed using the established research framework of diffusion theory (da Ponte, 2013; Rogers, 2003) and are intended to guide teachers in modifying the classroom environment to promote the sharing, spread, and exchange of mathematical ideas, facts, concepts, problem solving strategies, and tool usages.. Utilizing a pattern coding method to analyze student interaction and work samples, the principles underwent four testing iterations in a design experiment. The final set of constructed principles provide implications for middle school mathematics teacher education.