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Care to Compare : Eliciting Mathematics Discourse in a Professional Development Geometry Course for K-12 Teachers

This article describes how the idea of comparing Euclidean geometry with two nonEuclidean geometries (taxicab and spherical) provides participants with engaging mathematical tasks in a professional development geometry course for K-12 teachers. We illustrate with three different examples how the combination of rich mathematical activities centered on comparison, well-orchestrated group work, and skilled facilitators makes for productive classroom discourse and provides the teacher participants with a model to be emulated in their own classrooms. This model demonstrates for the teacher participants the process of generating and supporting student learning through mathematics discourse in the classroom.