Students' understanding and development of the definition of circle in Taxicab and Euclidean geometries: an APOS perspective with schema interaction

摘要

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of circle. In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college geometry course at a university. This report utilizes a framework describing the interaction of the Taxicab geometry and Euclidean geometry schemata to determine what components of these, and what relationships between them, were evoked when these participating students elaborated on their understanding of the circle concept. By adapting and transferring their knowledge of concepts back and forth between these two geometries, the participants demonstrated a variety of levels of schema interaction when responding to interview questions pertaining to circles. As a result, a model of schema interaction and pedagogical suggestions to help students better develop their circle schema are provided.