In mathematics, definitions are an integral part of understanding concepts and students often face obstacles in developing a deep understanding on how to apply definitions in mathematical proofs and problem-solving situations. In the context of geometry, research shows that by observing properties and making conjectures in non-Euclidean geometry, students can better develop their understanding of concepts and definitions in Euclidean geometry. For this ongoing project, Taxicab geometry (defined by Taxicab distance, or the 𝐿1 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 students to a real-life problem situated in Taxicab geometry. This presentation will provide 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.
Immediately after the talk all students are welcome to join Dr. Kemp and MESA for an informal conversation via Zoom
Zoom link: https://zoom.us/j/94392132706