Prior research has shown how incorporating group theory into upper secondary school or undergraduate mathematics education may positively impact learners’ conceptual understanding of mathematics in general and algebraic concepts in particular. Despite a recently increasing number of empirical research into student learning of introductory group theory, the development of a concept inventory that allows for the valid assessment of a respective conceptual understanding constitutes a desideratum to date. In this article, we contribute to closing this gap: We present the development and evaluation of the Concept Inventory of Introductory Group Theory—the CI2GT. Its development is based on a modern mathematics education research perspective regarding students‘ conceptual mathematics understanding. For the evaluation of the CI2GT, we follow a contemporary conception of validity: We report on results from two consecutive studies to empirically justify that our concept inventory allows for a valid test score interpretation. On the one hand, we present N=9 experts‘ opinions on various aspects of our concept inventory. On the other hand, we administered the CI2GT to N=143 pre-service primary school teachers as a post-test after a two weeks course into introductory group theory. The data allow for a psychometric characterization of the instrument, both from classical and probabilistic test theory perspectives. It is shown that the CI2GT has good to excellent psychometric properties, and the data show a good fit to the Rasch model. This establishes a valuable new concept inventory for assessing students’ conceptual understanding of introductory group theory and, thus, may serve as a fruitful starting point for future research into student learning of abstract algebra.

In an earlier contribution to Education Sciences we presented a new concept inventory to assess students’ conceptual understanding of introductory group theory—the CI2GT. This concept inventory is now leveraged in a pretest-post-test design with N=143 pre-service teachers to enrich this body of work with quantitative results. On the one hand, our findings indicate three recurring learning difficulties which will be discussed in detail. On the other hand, we provide a summative evaluation of the Hildesheim Teaching Concept and discuss students’ learning gain in different sub-domains of group theory. Together, the results allow for an empirical perspective on educational aspects of group theory and thus bridge the gap between qualitative and quantitative research in this field which constitutes a desideratum to date.

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.

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Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students' affective characteristics within a two-weeks course program-the Hildesheim teaching concept. In our study, this concept was used to introduce preservice primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.