A Design-Based Approach to Teaching Differential Equations Through Digitally Integrated Modeling

This study addresses the need for innovative instructional design in engineering mathematics by proposing a digitally integrated modeling approach for teaching differential equations. Grounded in theories of mathematical modeling and technology-enhanced learning, the study conceptualizes modeling in a digital context as a learning design in which students use digital tools such as MATLAB, GeoGebra, and simulation environments to construct, analyze, and validate mathematical models of engineering phenomena. Based on this perspective, a six-phase instructional design aligned with the mathematical modeling cycle is developed, integrating digital technologies throughout the learning process, from problem identification and model construction to solution, interpretation, and refinement. To evaluate the effectiveness of the proposed design, a pedagogical experiment was conducted with two groups of mechanical engineering students (n = 80) using a pre- and post-research design, supported by multiple data sources, including modeling competence tests, questionnaires, classroom observations, and interviews. The results demonstrate statistically significant improvements in students’ mathematical modeling competence, particularly in model formulation, interpretation, and validation, as well as notable gains in critical thinking and collaborative skills. These findings highlight the role of digitally supported modeling as an effective instructional design for fostering design-oriented learning processes in engineering mathematics. The study contributes to design education by providing a structured instructional design framework that integrates mathematical modeling and digital technology, with practical implications for curriculum innovation.