The Group Theory Concept Assessment: a Tool for Measuring Conceptual Understanding in Introductory Group Theory

Abstract

Introductory group theory provides the foundational course on algebraic structures. Yet, we know little about students’ underlying conceptual understandings. In this paper, I introduce the Group Theory Concept Assessment (GTCA), a measure created for the purpose of conducting large-scale studies of student conceptual understanding in group theory. The GTCA measures this understanding divorced from proof construction ability. I outline the design process and share results from various stages of analysis and refinement. I then present an item-level analysis of the GTCA including a detailed look at four items. These items focus on subgroups, inverses, quotient groups, and kernels, respectively. I conclude by reflecting on the GTCA’s potential usage as a research tool and practitioner tool.