An APOS Analysis of Student Learning of Congruence in Taxicab Geometry

Abstract

Non-Euclidean geometries are commonly used in the education of college geometry students to enhance their understanding of Euclidean geometry. Of these geometries, Taxicab geometry can be introduced to help students generalize their current understandings of specific concepts in Euclidean geometry. Of these concepts, Taxicab geometry perturbs students’ definition of congruence. This research project is part of a larger research project that aims to encourage students to define congruence with respect to isometries. Using the APOS framework, data collected from classroom participation was analyzed to investigate how students would develop this definition in Taxicab geometry.