(733f) Understanding What Makes Mathematical Modeling Hard for Capstone Design Students

Cole, J., Northwestern University

Mathematical modeling is a practical skill from which engineering students can benefit.  This is especially true in capstone design, where open-ended, analytically complex problems are often solved by innovatively applying engineering fundamentals from previous coursework.  Ideally students would break down the components or systems within a proposed design solution into distinct elements.  The fundamental relationships between the elements could be examined, manipulated, and put into mathematical representation.  The resulting mathematical models would then be used to test assumptions about the components or find the limitations of the system. 

However, in our experience and in our research we have found that students are not adept at applying mathematical engineering fundamentals to open-ended design problems.  More often students take a “trial and error” approach, preferring to match up their open-ended design problem to several somewhat similar problems encountered in previous coursework until they get an answer that seems to provide a reasonable solution.  Little effort is made by the students to understand the fundamental behaviors governing the elements in their system or what a reasonable output looks like.  Instructors often see this when students use process modeling software, such as Aspen.  Students may enter process conditions and constraints that may not make sense but lead to a converged solution.    

This project investigated students’ abilities to generate mathematical models that they can use in the development of innovative design solutions to open-ended problems. In particular, we studied how students’ approached creating, solving, and interpreting mathematical models in a chemical engineering capstone design course.  Two modeling problems were analyzed in this study.  The first was a simple optimization problem and the second was a simulation of a distillation column in Aspen HYSYS.  The instruction and the modeling problems were broken down into steps, from defining the model elements to generating the mathematical equations and interpreting model outputs.  Student performance was measured on each of these steps, in order to determine what aspects of mathematical modeling were the most difficult.

Our research has shown that students struggle with creating, manipulating, and critiquing mathematical models to assist in the design of a product or process.  The results of this work will be presented in this paper and will be used to revise instruction in order to improve students’ abilities in mathematical modeling in the context of design.