Using instruction to improve mathematical modeling in capstone design

Engineering students in capstone design have the opportunity to develop unique solutions to open-ended and analytically complex problems, allowing them to use their knowledge from previous coursework. One element of design is mathematical modeling, but students often struggle in recognizing when and how to apply the mathematical analysis encountered in prior coursework to their particular design solutions. Specifically, they struggle with creating, manipulating, and critiquing mathematical models to assist in the design of a product or process. The ultimate aim of our work is to improve students' ability to use models in capstone design after being exposed to instruction on mathematical modeling. This study was a continuation of an earlier project in which we explored how students developed, used, and interpreted mathematical models. In the previous study, students were given instruction in the steps of mathematical modeling and a scenario in which they were asked to assist a hypothetical design team by creating a mathematical model that could be used in making decisions about the design. The instruction and the scenario broke down model creation and interpretation into six stages, from defining the model parameters to generating the mathematical equations and interpreting model outputs. In this study, we investigated how well students transferred these skills to their own open-ended design problems. Specific instruction in mathematical modeling was required before we saw an impact on the use of modeling in students' own design projects. Eighty-two percent of teams were able to generate some type of mathematical relationship between model parameters after instruction, whereas in previous years, where no instruction occurred, only 25% of the teams developed a mathematical relationship to describe their system. However, the results also showed that even with instruction, students did not utilize models to their full potential. Only 41% of all teams adequately explored the parameter space of their model, and only 12% of teams discussed the limitations of their model. Seventy-one percent used the model results to inform their final design. This research has provided some insight into how to revise instruction in order to improve engineering students' abilities in mathematical modeling in the context of design.