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Using non-Euclidean Geometry to teach Euclidean Geometry to K-12 teachers


"The Oregon Mathematics Leadership Institute (OMLI) is an NSF-funded partnership aimed at increasing mathematics achievement of students in partner K-12 schools through the creation of sustainable leadership capacity. OMLI's 3-week summer institute offers content and leadership courses for in-service teachers. We report here on one of the content courses, entitled Comparing Different Geometries, which enhances teachers' understanding of the (Euclidean) geometry in the K-12 curriculum by studying two non-Euclidean geometries: taxicab geometry and spherical geometry. By confronting teachers from mixed grade levels with unfamiliar material, while modeling protocol-based pedagogy intended to emphasize a cooperative, risk-free learning environment, teachers gain both content knowledge and insight into the teaching of mathematical thinking."