The Future of Education
Diagnostic Analysis of Students’ Errors in Integral Calculus: Method Selection as a Source of Difficulty in Undergraduate Mathematics
Siditë Duraj, University of Shkodra ”Luigj Gurakuqi" (Albania)
Lekë Pepkolaj, University Metropolitan Tirana, Department of Computer Science (Albania)
Abstract
Many first-year university students are unable to execute basic integration procedures; however, they encounter significant difficulties when required to select an appropriate method for a given problem. This study aims to examine students’ errors in solving integrals, with particular emphasis on method selection and on the conceptual understanding of integral structure, while also seeking to identify targeted instructional interventions to address these difficulties. The study adopts a diagnostic approach to be implemented with first-year students enrolled in an introductory calculus course at the University of Shkodra “Luigj Gurakuqi”, focusing on the transition from procedurally oriented strategies developed in pre-university education to the more flexible and structurally grounded reasoning expected at the tertiary level. It is anticipated that the analysis will reveal a tendency among students to apply familiar techniques without adequately assessing their appropriateness and, in some cases, to persist with unproductive methods despite the absence of progress. The expected findings suggest that these difficulties are primarily associated with limited structural understanding of integrals and with weaknesses in decision-making during method selection. The study highlights the importance of engaging students in the comparison of alternative solution strategies and of integrating diagnostic tasks to systematically address these deficiencies.
Keywords: Integral calculus; students’ errors; method selection; diagnostic assessment; mathematical understanding
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