Engineering students’ difficulties in solving mathematical modelling tasks: the case of linear algebra

Abstract

This study examines the challenges first-year engineering students encounter when solving a mathematical modelling task in a Linear Algebra course. A qualitative methodology based on design-based research was employed, comprising three phases: experimental preparation, implementation of a sustainability-contextualized modelling task, and retrospective analysis. A total of 62 students from Construction Engineering and Civil Engineering programs participated and were organized into 17 work groups. Data collection involved the evaluation of written protocols with an analytical rubric, administering a student perception questionnaire, and conducting researcher observations. The results indicate three primary difficulties: applying appropriate mathematical tools; interpreting results within the real-world context of the problem; and coordinating group work during task resolution. These challenges were consistently evident in both student perceptions and written work, which demonstrated conceptual errors in the use of matrices and insufficient connection between numerical results and their contextual meaning. This study provides empirical evidence of the specific challenges students encounter when solving mathematical modelling tasks, laying the foundation for designing pedagogical interventions to enhance these competencies in early engineering education.