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This study focuses on bridging the gap between physics and mathematics by teaching an integrated first-year college course of physics and mathematics using Modeling Instruction (MI) and models and modeling perspective. This innovation involves redesigning the course’s content, combining teaching strategies, reshaping the classroom setting, and using technology. In this study 37 first-year engineering students were enrolled in the integrated course. The research questions were: What elements of the physical and mathematical models do students use when solving a complex real problem? How does the consistency of students’ model lead to a robust understanding of the problem? To answer these questions, students worked collaboratively on a project that involved the analysis of an extreme bungee jump. The performance of the students in this project revealed: a) students’ integration of physical and mathematical models, b) different representations used in the solution and c) robustness of students’ models. As conclusions we can state that as the students constructed more robust models, these were more helpful in their problem solving. Participating students constructed physical models that led them to mathematical models that required numerical methods. The use of numerical methods with technology as an aid in solving complex problems is part of the natural integration of physics, math and technology. Final presentations in a poster fair format provided students with the space and environment to present and share the models they constructed. Students were required to show their work and process to arrive to such solution to their peers. More importantly, the final project offered students the opportunity to realize how empowered they were in solving complex and non-familiar problems.

Closing the Gap Between Physics and Calculus: Use of Models in an Integrated Course