Students’ Cognitive Processes in Solving Group Theory Problems: An Analysis Based on Bloom’s Taxonomy

Abstract

Abstract algebra requires students to coordinate formal definitions, algebraic properties, and proof structures rather than rely on procedural recall alone. This study describes the cognitive processes demonstrated by fifth-semester mathematics education students when solving introductory group theory problems, using the first four categories of the revised Bloom’s taxonomy as an analytical lens. The study employed a qualitative descriptive approach at the Mathematics Education Study Programme, Alkhairaat University, from 15 September to 6 November 2025. Four students (LF, WS, AR, and N), selected purposively from students enrolled in the algebraic structures course, completed two written tasks and participated in interviews used to clarify their responses. The first task examined students’ definitions of a group, while the second required them to state and prove a theorem about group properties. All four students recalled central elements of the group definition, although the precision of their explanations varied. In the proof task, LF produced a coherent argument for the uniqueness of the identity element, whereas WS, AR, and N attempted to use familiar group properties but showed difficulties in theorem selection, property identification, or the logical ordering of operations. Across the four cases, remembering was consistently supported, whereas evidence of understanding was partial for several participants, and applying and analyzing were most clearly demonstrated in LF’s proof. These findings suggest that assessment of group theory learning should distinguish the recall of definitions and properties from the ability to coordinate them within a valid proof.