Level of achievement of the mathematical modeling competence: interdisciplinary intervention study in mechanical engineering

Abstract

This research examines the attainment of mathematical modeling competence among Mechanical Engineering students through an interdisciplinary didactic intervention based on project-based learning (PBL). The intervention was conducted in the “Engineering Workshop III” course with 26 third-semester students, who worked collaboratively in eight heterogeneous groups during one academic semester. The methodology employed a qualitative design, incorporating an initial individual diagnostic assessment and analysis of final group reports to evaluate five sub-competencies of mathematical modeling competence. A specific rubric operationalized each sub-competency into evaluative criteria, using a scale from 0 to 20 points. The initial diagnostic revealed low achievement levels in simplification and validation (22.5% each), while mathematization achieved the best initial performance (59%). Collaborative work facilitated overcoming initial limitations, as six out of eight groups attained satisfactory levels in contextual understanding and critical validation. The highest-performing groups demonstrated balanced achievement across all sub-competencies, whereas lower-achieving groups continued to encounter difficulties with mathematization and interpretation. The findings suggest that interdisciplinary PBL provides an effective framework for fostering mathematical modeling competence, particularly in collaborative settings that integrate mathematical knowledge with authentic mechanical engineering problems.