Towards Describing Student Learning of Abstract Algebra: Insights into Learners’ Cognitive Processes from an Acceptance Survey

Joaquin Marc Veith, Philipp Bitzenbauer and Boris Girnat
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Joaquin Marc Veith: Institut für Mathematik und Angewandte Informatik, Stiftungsuniversität Hildesheim, 31141 Hildesheim, Germany
Philipp Bitzenbauer: Physikalisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
Boris Girnat: Institut für Mathematik und Angewandte Informatik, Stiftungsuniversität Hildesheim, 31141 Hildesheim, Germany

Mathematics, 2022, vol. 10, issue 7, 1-22

Abstract: In an earlier contribution to Mathematics , we presented a new teaching concept for abstract algebra in secondary school mathematics, and we discussed findings from mathematics education research indicating that our concept could be used as a promising resource to foster students’ algebraic thinking. In accordance with the Design-Based Research framework, the developed teaching concept is now being revised in several iteration steps and optimised towards student learning. This article reports on the results of the formative assessment of our new teaching concept in the laboratory setting with N = 9 individual learners leveraging a research method from science education: The acceptance survey. The results of our study indicate that the instructional elements within our new teaching concept were well accepted by the students, but potential learning difficulties were also revealed. On the one hand, we discuss how the insights gained in learners’ cognitive processes when learning about abstract algebra with our new teaching concept can help to refine our teaching–learning sequence in the sense of Design-Based Research. On the other hand, our results may serve as a fruitful starting point for more in-depth theoretical characterization of secondary school students’ learning progression in abstract algebra.

Keywords: algebra; groups; secondary school; mathematics education (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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