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Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level

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Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

Part of the book series: Research in Mathematics Education ((RME))

Abstract

The Group Theory Concept Assessment (GTCA) was developed to meaningfully capture student conceptions around fundamental concepts in introductory group theory. In this chapter, we share results from a large-scale implementation of the GTCA with 375 students across 30 undergraduate institutions in the USA. We include a breakdown of performance based on major. We pair these findings with a detailed look at several GTCA tasks with direct connections to the secondary curriculum. Student conceptions around prior content, including function and operation, often mediated student performance on group theory tasks. Functions play an essential role in student approaches to building isomorphisms, exploring consequences of homomorphisms, and identifying kernels. Binary operations play an essential role in student approaches to exploring properties (such as the associative property), finding identities and inverses, defining groups, and identifying subgroups. We share results from both the multiple-choice inventory and follow-up interviews to illustrate some of these connections. We conclude with a discussion of implications for the abstract algebra classroom, with a focus on opportunities for backward transfer to secondary content that can be embedded in conceptual explorations of group theory topics.

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Notes

  1. 1.

    Note: The GTCA survey collected data on major. However, this distinction may not cover all preservice secondary teachers at institutions where preservice teachers obtain a mathematics major.

  2. 2.

    In pilot rounds the set was {1, 2, 3}.

  3. 3.

    This change occurred because a minority of students did create a correct symbolic binary operation for the {1, 2, 3}, and the intention was to remove this option.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, San Marcos, TX, USA

    Kathleen Melhuish & Joshua Fagan

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  1. Kathleen Melhuish
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Correspondence to Kathleen Melhuish .

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Editors and Affiliations

  1. Department of Mathematics, Science and Technology, Teachers College, Columbia University, New York, NY, USA

    Nicholas H. Wasserman

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Melhuish, K., Fagan, J. (2018). Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level. In: Wasserman, N. (eds) Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99214-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-99214-3_2

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