Analyzing conceptual and procedural errors in solving routine problems on gradients and straight-line equation among prospective mathematics teachers

This study examines the types of errors made by prospective mathematics teachers in solving routine problems involving gradients and linear equations, which are fundamental to Analytic Geometry. Employing a qualitative descriptive methodology, the research involved 35 mathematics education students who completed a semi-structured written test designed to assess both conceptual comprehension and procedural proficiency. Eleven responses containing incomplete or incorrect solutions were purposively selected for detailed analysis. Data were analyzed using Miles and Huberman’s interactive model, encompassing stages of data reduction, presentation, and conclusion derivation. Errors were systematically categorized into conceptual, procedural, and other types, with further refinement into 18 specific misconception subtypes. The findings revealed persistent misconceptions in gradient interpretation, improper application of linear equation forms, and frequent procedural errors in algebraic simplification and negative sign operations. Several students exhibited overlapping error types, indicating a strong correlation between conceptual gaps and procedural breakdowns. These results emphasize the significance of designing instructional interventions that simultaneously enhance conceptual and procedural proficiency.