Exploring Learning Difficulties in Abstract Algebra: The Case of Group Theory

Abstract

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.

Keywords

• algebra
• group theory
• secondary school
• mathematics education