Assessing engineering students' mathematical modeling abilities in capstone design

In engineering capstone design, students need to use their previous knowledge to develop solutions to open-ended problems. A thorough solution to a capstone level problem often includes an appropriate computational or mathematical analysis. However, faculty are often disappointed in engineering students" ability to recognize when and how to apply mathematical analysis to their particular design solutions. This study assessed the capability of senior engineering students to apply mathematical modeling to design, and began the process of testing classroom interventions to rectify certain weaknesses. This research was constructed around a framework that identifies 6 steps in mathematical modeling1. Students were given a scenario and asked to assist a hypothetical design team by creating a mathematical model that could be used in making decisions about the design of a phototherapy device to treat neonatal jaundice. The problem was posed in four iterations over the academic term, with each iteration requiring students to perform different steps in the modeling process. In an earlier paper we explored how students interpreted the concept of "modeling," and how they decided what parameters were relevant. Most students had difficulty with these essential first steps of model creation, In subsequent iterations, students also demonstrated difficulty in representing a physical situation in equations, and in stating and justifying simplifications and assumptions. The last stages of modeling involve interpretation of the model, and here students proved to be better. They could, in general, relate graphical results from the mathematical model to experimental data obtained from a physical model. They were also able to use the model outputs to make design decisions, or explain why the existing model was inadequate for this purpose. In the second year of the study, there was more instruction and review of students" performance after they worked on each stage of the problem. This improved performance. In the first year only 16% of students were able to generate equations (even incorrect ones), even though an equation for one element of the system had been given in class. In the second year this number increased to 29%. When students were asked to state assumptions they would use to simplify the system they planned to model, only 35% of students in the first year of the study stated assumptions that were relevant, but this number increased to 80% in the second year. We conclude that even though students are exposed to certain aspects of modeling in earlier engineering courses, they may not recognize how to perform some of the required steps in an open-ended situation such as design. This prevents or constrains their use of modeling in this important context. Specific instruction in the steps of model creation can improve students" abilities. More work remains to optimize this instruction, and to determine whether the improvement resulting from instruction transfers from the scenario we created to the students" actual design projects.