PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
The transfer and application of definitions from Euclidean to taxicab geometry: Circle
Page: 324
Research shows that definitions in mathematics are often not used correctly by students in mathematical proofs and problem-solving situations. By observing properties and making conjectures in non-Euclidean geometry, students can better develop their understanding of these concepts. In particular, Taxicab geometry is suggested to be introduced before other non-Euclidean geometries since it is a considerably simpler space. To further investigate this, APOS Theory is used as the framework in this analysis of responses to a real-life situation from students enrolled in a College Geometry course at a university. Through the perspective of APOS Theory, this report provides two representative illustrations of the conceptual understandings found among these students in relation to the definition of circle. By adapting and applying their knowledge of definitions from Euclidean geometry to Taxicab geometry, these students provided insight as to how Taxicab geometry concepts are assimilated into their existing understanding of concepts in geometry.