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

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Abstract

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.

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Data availability

The data that support the findings of this study are available from the corresponding author upon request.

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Authors and Affiliations

  1. Department of Mathematics, California State University, Bakersfield, 9001 Stockdale Highway, Bakersfield, CA, 93311, USA

    Aubrey Kemp

  2. Department of Mathematics and Statistics, Georgia State University, 25 Park Place, 14th Floor, Atlanta, GA, 30303, USA

    Draga Vidakovic

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  1. Aubrey Kemp
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All coauthors acknowledge their participation in conducting the research leading to the manuscript, and all agree to its submission to be considered for publication by Educational Studies in Mathematics, and all have agreed on the final version.

The work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis) and that it is not under consideration for publication elsewhere.

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Correspondence to Aubrey Kemp.

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Approval was obtained from the ethics committee of Georgia State University. The procedures used in this study adhere to the tenets of the Declaration of Helsinki.

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Freely-given, informed consent to participate in the study was obtained from participants in this study.

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The authors declare no competing interests.

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Appendix Genetic decomposition of schema interaction

Appendix Genetic decomposition of schema interaction

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Kemp, A., Vidakovic, D. Students’ understanding and development of the definition of circle in Taxicab and Euclidean geometries: an APOS perspective with schema interaction. Educ Stud Math 112, 567–588 (2023). https://doi.org/10.1007/s10649-022-10180-2

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