2021 Research in Undergraduate Mathematics Education Reports
2021
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The Circle Schema: An Example of Schema Interaction in College Geometry
Page: 147
There is a need to address student understanding of the role of definitions in undergraduate mathematics, and research is needed to determine pedagogical strategies that facilitate development of this understanding. In geometry, research shows students can better develop their understanding of concepts and their definitions by observing properties and making conjectures in non-Euclidean geometry. In this study, students learned concepts in Taxicab geometry in a College Geometry course in which theory in Euclidean geometry is the primary focus. The triad of stages of schema development and a model of schema interaction were used as frameworks in the analysis of student responses to a questionnaire and follow-up interview about the definition of circle in Taxicab and Euclidean geometry. As a representative illustration of a level of schema interaction, insight into the thinking of one student is presented in this report. Pedagogical suggestions are provided as a result of this data analysis.