Abstract

Abstract algebra is a challenging subject because it requires a deep understanding of algebraic structures such as groups, rings, and fields. Many students struggle with grasping abstract concepts and constructing mathematical proofs, often leading to systematic errors. This study aims to identify the types of errors made by students in solving abstract algebra problems, analyze their underlying causes, and provide recommendations for improving the learning process. A qualitative approach was employed, using error analysis on students’ exam and assignment responses focused on group and ring theory. Data were collected from three mathematics education students and categorized into conceptual, procedural, and technical error patterns. The findings reveal that the most common errors include: (1) misconceptions related to the definitions of normal subgroups and homomorphisms; (2) logical flaws in proving ring properties; and (3) carelessness in performing algebraic operations. The root causes of these errors include weak intuitive understanding, limited practice in proof construction, and confusion in applying theorems. Students’ errors in abstract algebra are systematic and strongly linked to the depth of conceptual understanding. Moreover, the use of Wolfram Alpha has proven effective in identifying gaps in understanding and stimulating students’ reflection on their mathematical thinking processes. The Wolfram Alpha integration allows for determining the nature of the fault, rather than just its existence. By juxtaposing the logic students apply with the step-by-step derivations that the tool generates, it can identify where the reasoning deviates, either due to a misunderstanding of definitions, a neglected burden of proof, or a symbolic fallacy. This improves the reliability of the fault classification and provides concrete feedback targets for each student. The pedagogical implications highlight the need for more interactive teaching approaches, increased practice in mathematical proof-writing, and the use of concrete examples to aid the visualization of abstract structures.