The Journal of Mathematical Behavior | 2021
Ways secondary mathematics teachers apply definitions in Taxicab geometry for a real-life situation: Midset
Abstract
Abstract Definitions in mathematics are an integral part of understanding concepts and are often not used correctly by students in mathematical proofs and problem-solving situations. Research shows that by observing properties and making conjectures in non-Euclidean geometry, students can better develop their understanding of concepts in Euclidean geometry. For this study, Taxicab geometry (defined by Taxicab distance, or the L 1 norm) was introduced to students enrolled in a College Geometry course at a university. Action-Process-Object-Schema (APOS) Theory was used as a guiding framework in the data analysis of responses from eleven secondary mathematics teachers to a real-life problem situated in Taxicab geometry. This report provides illustrations of the conceptual understanding of midset (known as a perpendicular bisector in Euclidean geometry) found among participants and suggestions for teaching material to help facilitate development of a deeper understanding of definitions in geometry.