New Perspectives in Science Education

This paper examines the impact of implementing a continuous supervised problem-solving methodology in a foundational linear algebra course for first-year engineering students at the Technical Salesian University in Cuenca, Ecuador. The research compares two consecutive cohorts: one taught using traditional lecture-based instruction, and a subsequent cohort taught under a redesigned approach emphasizing in-class, instructor-guided problem-solving and formative feedback.

Quantitative analysis reveals statistically significant improvements in students’ ability to apply mathematical concepts and solve complex problems, with an average increase of 5 points in procedural application and 8 points in problem-solving scores (out of 35). In contrast, scores in the conceptual understanding domain remained stable, suggesting that traditional lectures may suffice for factual knowledge, but active problem engagement is essential for developing higher-order cognitive skills.

The intervention was designed to be scalable and cost-effective, requiring no technological infrastructure, and was implemented across large sections without altering core curricular content. Qualitative feedback from instructors indicated increased student motivation, participation, and persistence.

The findings reinforce the pedagogical value of sustained active engagement and continuous formative assessment in enhancing mathematics learning, especially in engineering education. This study contributes to the growing body of evidence advocating for the integration of supervised practice into STEM curricula and offers recommendations for broader adoption in higher education contexts.