Learning and Teaching Differential and Integral Calculus: A Case Study in Portugal

Students entering engineering programs often exhibit insufficient mathematics knowledge and considerable variability in prior training, which can create learning gaps and challenges for higher education integration. This study aims to characterize students’ mathematics proficiency at the Coimbra Institute of Engineering and to develop strategies to address these gaps. A diagnostic test was designed based on the Portuguese primary and secondary education syllabus and the guidelines of the European Society for Engineering Education. Data were collected from students enrolling in engineering degrees between the 2013/14 and 2021/22 academic years. Based on the diagnostic results, a targeted intervention was implemented to motivate students and enhance their learning in mathematics. This intervention includes complementary teaching methodologies applied to Differential and Integral Calculus, a mandatory first-year course across all engineering programs. The analysis demonstrates that the combined approach of diagnostic assessment and targeted support improves student engagement and addresses disparities in prior knowledge. This study contributes to the development of evidence-based strategies that support equitable learning opportunities in engineering education and offers a model for integrating diagnostic assessment with active learning practices in foundational STEM courses.