Investigating engineering students' mathematical modeling abilities in capstone design

Engineering capstone design is a culminating experience that is intended to provide an opportunity for students to apply their previous engineering knowledge to develop solutions to open-ended problems. Capstone design problems are often analytically complex, and their solutions integrate several disciplinary fundamentals, as well as more general design process knowledge. Often, the expectation is that a thorough or rigorous solution to a capstone level problem would include some type of computational or mathematical analysis appropriate to that discipline. However, engineering students often struggle in recognizing when and how disciplinary knowledge (e.g. mathematical analysis inherent in many engineering fundamentals) applies to their particular design solutions. This paper describes the strategy for and initial results of a study exploring how students use mathematical reasoning when developing design solutions. Specifically, we want to understand where students struggle in the development and implementation of a mathematical model. We conducted our study in a biomedical capstone (senior) design course. We presented students with a scenario based on a design problem in using phototherapy to treat jaundice, and asked specific questions relating to mathematical modeling in the solution to this problem. We developed the scenario and corresponding assignments based on previous work that identified six steps for what mathematical modeling should include. We staged the activities over a four-week period such that students addressed two of these steps at each time interval, or assignment stage. This report analyzes results from the first two activities, which focused on identifying the real-world phenomenon and simplifying or idealizing it. We found that in an open-ended statement of the problem, no students proposed using a mathematical model to assist in designing the device. When we specifically asked for a mathematical model in a second activity, only five students of thrity-eight proposed a purely mathematical model, and another two proposed experiments that would lead to predictive equations. When asked to identify parameters that would be important to model, 37% of students chose ones that were part of the design requirements, and therefore fixed, and only 35% correctly chose parameters that could be adjusted to meet the design requirements. These results show a gap in using modeling skills in design, and suggest that educational interventions are needed to improve these capabilities.