IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i5p703-d756972.html
   My bibliography  Save this article

What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics

Author

Listed:
  • Joaquin Marc Veith

    (Institut für Mathematik und Angewandte Informatik, Stiftung Universität Hildesheim, 31141 Hildesheim, Germany)

  • Philipp Bitzenbauer

    (Physikalisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany)

Abstract

In this paper, we present a novel concept for an abstract algebra course at the secondary school level. Against the backdrop of findings from mathematics education research, we discuss benefits that arise from teaching abstract algebra to secondary school students. We derive suitable content items as well as educational ideas on how to implement them into mathematics classrooms. We build on frameworks from mathematics education research to design a teaching-learning sequence that enables a beneficial learning trajectory across three units—the result is a coherent teaching concept that encompasses Magmas in a hands-on way. It can be used for either extra-curricular activities or advanced courses in mathematics classes, and can be of benefit for mathematics learners.

Suggested Citation

  • Joaquin Marc Veith & Philipp Bitzenbauer, 2022. "What Group Theory Can Do for You: From Magmas to Abstract Thinking in School Mathematics," Mathematics, MDPI, vol. 10(5), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:703-:d:756972
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/5/703/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/5/703/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nataly Pincheira & Ángel Alsina, 2021. "Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Joaquin Marc Veith & Philipp Bitzenbauer & Boris Girnat, 2022. "Towards Describing Student Learning of Abstract Algebra: Insights into Learners’ Cognitive Processes from an Acceptance Survey," Mathematics, MDPI, vol. 10(7), pages 1-22, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:703-:d:756972. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.