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The role of the partitioning and coset algorithm quotient group partial meanings in comprehending the First Isomorphism Theorem and its proof

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Abstract

In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a study of student activity as they work to comprehend the First Isomorphism Theorem and its proof. We analyze, using an onto-semiotic lens, the ways that students’ meanings for quotient group both support and constrain their comprehension activity. Furthermore, we suggest that the relationship between understanding concepts and proof comprehension can be reflexive: understanding of concepts not only influences comprehension activity, but engaging with theorems and proofs can serve to support students in generating more sophisticated understanding of the concepts involved.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. All names are pseudonyms.

  2. For ease, we use this notation to indicate our codes of semiotic shifts that either occurred or were invited by the instructor.

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Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1836559. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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  1. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Kathleen Melhuish, Lino Guajardo, Paul C. Dawkins, Holly Zolt & Kristen Lew

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  1. Kathleen Melhuish
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  2. Lino Guajardo
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  3. Paul C. Dawkins
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  5. Kristen Lew
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Correspondence to Kathleen Melhuish.

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Melhuish, K., Guajardo, L., Dawkins, P.C. et al. The role of the partitioning and coset algorithm quotient group partial meanings in comprehending the First Isomorphism Theorem and its proof. Educ Stud Math 113, 499–517 (2023). https://doi.org/10.1007/s10649-023-10207-2

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