Search for: All records

Following Felix Klein, an advanced historical standpoint is here presented for teaching college geometry for teachers. Three main ways of developing an advanced historical standpoint are discussed with classroom experiments. One is building connections among geometries by developing an inquiry into definitions of geometric objects such as rhombus, their extensibility with their family relationships across Euclidean and non-Euclidean geometries. Second is on the multiplicity and extensibility of transformations as represented by two historical approaches advocated by Klein and Usiskin. The third way to develop an advanced standpoint is by developing a critical look into a geometry practice tracing its change with the reforms in school geometry. The practice of constructions to connect geometry and algebra is impacted by two historical efforts. One is a supportive effort by Hilbert on the practice of constructions by Hilbert’s Algebra of Segments dating back to 1902 to connect geometry and algebra. The other historical reform effort is by School Mathematics Study Groups (SMSG) during 1960s, which led to weakening the axiomatic foundations of the practice of constructability and exactness. The case of SMSG’s angle construction axiom is criticized in their revision of axiomatic foundations of school geometry. Three approaches to develop an advanced standpoint informing research and practice of geometry teacher education towards a more historically connected stance.