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.

中文翻译：

---

团体理论概念评估：介绍性团体理论中用于衡量概念理解的工具

群体概论提供了代数结构的基础课程。但是，我们对学生的基本概念理解知之甚少。在本文中，我介绍了群体理论概念评估（GTCA），这是一种旨在对群体理论中的学生概念理解进行大规模研究的措施。GTCA衡量了这种与证明构建能力脱节的理解。我概述了设计过程，并分享了分析和完善各个阶段的结果。然后，我介绍了GTCA的项目级分析，包括对四个项目的详细介绍。这些项目分别关注子组，逆，商组和内核。最后，我总结了GTCA作为研究工具和实践者工具的潜在用途。