A Structured AHP-Based Approach for Effective Error Diagnosis in Mathematics: Selecting Classification Models in Engineering Education

Abstract

Identifying and classifying mathematical errors is crucial to improving the teaching and learning process, particularly for first-year engineering students who often struggle with foundational mathematical competencies. This study aims to select the most appropriate theoretical framework for error classification by applying the Analytic Hierarchy Process (AHP), a multicriteria decision-making method. Five established classification models—Newman, Kastolan, Watson, Hadar, and Polya—were evaluated using six pedagogical criteria: precision in error identification, ease of application, focus on conceptual and procedural errors, response validation, and viability in improvement strategies. Expert judgment was incorporated through pairwise comparisons to compute priority weights for each criterion. The results reveal that the Newman framework offers the highest overall performance, primarily due to its structured approach to error analysis and its applicability in formative assessment contexts. Newman’s focus on reading, comprehension, transformation, and encoding addresses the most common errors encountered in the early stages of mathematical learning. The study demonstrates the utility of the AHP as a transparent and replicable methodology for educational model selection. It addresses a gap in the literature regarding evidence-based criteria for designing diagnostic instruments. These findings support the development of targeted pedagogical interventions in mathematics education for engineering programs.