PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Exploring college geometry students’ understandings of taxicab geometry
Page: 847
Non-Euclidean geometries are commonly used in college geometry courses to highlight aspects of Euclidean geometry. Scholars have theorized that working in non-Euclidean geometries requires thinking at the highest van Hiele level of geometric thinking, which was developed by investigating students’ learning of Euclidean geometry, but few have pursued this empirically. This empirical study seeks to develop levels of geometric thinking for students in Taxicab geometry, which is the non-Euclidean geometry that is closest in structure to Euclidean geometry. Students in a college geometry course that included prospective secondary teachers were audio-recorded in group discussions as they completed tasks about congruence and transformations in taxicab geometry, and their written work was collected. Portraits of participants’ thinking about Taxicab geometry were developed, leading to a proposed structure for the levels of geometric thinking for Taxicab geometry.