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

  • Kathleen MelhuishEmail author
  • Joshua Fagan
Chapter
Part of the Research in Mathematics Education book series (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.

Keywords

Group theory Functions Binary operations Backward transfer 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsTexas State UniversitySan MarcosUSA

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