Abstract

Diagnostic assessment in understanding students’ mathematical reasoning is crucial yet challenging, often requiring navigation through the “black box” of the student’s mind without making erroneous assumptions about their thought processes. This article examines the challenges that National Curriculum (Vocational) Level 2 students at Technical Vocational Education and Training colleges face in factorization, analyzing twelve students’ final examination scripts using Donaldson’s error analysis model, which is defined and exemplified in the section on the nature of misconceptions, before suggesting pedagogical interventions. The model categorizes errors into executive, structural, and arbitrary types, providing insights into students’ understanding and application of mathematical concepts. The investigation reveals a significant prevalence of structural and executive errors, with a notable absence of arbitrary errors, indicating that students’ struggles with factorization stem from systematic misunderstandings and misapplications rather than random mistakes. This study reveals a predominance of structural errors (76%) over executive errors (22%) and highlights the need for targeted pedagogical strategies to improve conceptual understanding and procedural accuracy. This finding points to the need for teaching strategies that emphasize both procedural practice and a deep understanding of mathematical concepts to address the root causes of students’ errors effectively. The study recommends implementing pedagogical interventions that promote conceptual clarity alongside procedural fluency, aiming to improve mathematical proficiency among vocational education students. By focusing on these systematic misunderstandings, educators can offer more targeted support, potentially improving vocational mathematics education outcomes and enhancing students’ confidence and competence in algebraic factorization.