Recurring errors in integration by substitution: the need for pedagogical innovation based on mathematical decision support

Integration by substitution is a fundamental technique in integral calculus that frequently poses difficulties for students in higher education. Although this technique is taught systematically, many students continue to make recurring errors, particularly in the selection of appropriate substitution variables and the management of differentials. This phenomenon indicates that the difficulties encountered are not merely procedural in nature but are closely related to weaknesses in students’ conceptual mathematical decision-making. Therefore, this study aims to discuss the forms of recurring errors in integration by substitution and to argue for the need for pedagogical innovation based on mathematical decision support. The discussion is grounded in a review of recent literature and reflections on calculus teaching experience. The findings indicate that teaching approaches that focus primarily on procedural memorisation are insufficient to help students understand the mathematical rationale underlying the substitution technique. Accordingly, pedagogical innovations that provide structured and visual decision support are proposed to reduce recurring errors and to enhance students’ conceptual understanding and confidence in learning calculus.