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Using Instruction to Improve Mathematical Modeling in Capstone Design

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2012 ASEE Annual Conference & Exposition


San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012



Conference Session

Research Informing Teaching Practice I

Tagged Division

Educational Research and Methods

Page Count


Page Numbers

25.1428.1 - 25.1428.18



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Paper Authors


Jennifer Cole Northwestern University Orcid 16x16

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Jennifer Cole is the Assistant Chair in chemical and biological engineering in the Robert R. McCormick School of Engineering and Applied Science at Northwestern University. Cole’s primary teaching is in capstone and freshman design, and her research interest are in engineering design education.

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Robert A. Linsenmeier Northwestern University

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Robert A. Linsenmeier is a professor of biomedical engineering, neurobiology, and ophthalmology, Northwestern University, and
Director, Northwestern Center for Engineering Education Research.

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Timothy Miller Binghamton University


Matthew R. Glucksberg Northwestern University

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Matthew R. Glucksberg is a professor of biomedical engineering at Northwestern University. His technical expertise is in tissue mechanics, microcirculation, and optical instrumentation. His laboratory has developed image-based instrumentation to measure pressure and flow in the circulation of the eye, instruments to measure the response of pulmonary alveolar epithelial cells to their immediate mechanical environment, and is currently involved in developing minimally invasive optical biosensors for monitoring glucose, lactate, and other measures of metabolic function. He is a Co-founder of Northwestern’s Global Healthcare Technologies Program in Cape Town South Africa and Co-director of an M.S. program in Global and Ecological Health.

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Using instruction to improve mathematical modeling in capstone designAbstractEngineering students in capstone design have the opportunity to develop unique solutions toopen-ended and analytically complex problems, allowing them to use their knowledge fromprevious coursework. One element of design is mathematical modeling, but students oftenstruggle in recognizing when and how to apply the mathematical analysis encountered in priorcoursework 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 this study is to assess students’ ability to use models in capstone design afterbeing exposed to instruction on mathematical modeling.The current study is a continuation of an earlier project in which we explored how studentsdeveloped, used, and interpreted mathematical models. In the previous study, students weregiven instruction in the steps of mathematical modeling and a scenario in which they were asked toassist a hypothetical design team by creating a mathematical model that could be used in makingdecisions about the design. The instruction and the scenario broke down model creation andinterpretation into six stages, from defining the model parameters to generating the mathematicalequations and interpreting model outputs. Rather than teaching particular modeling software, thepurpose was to explain why modeling is done, what needs to be considered in moving from aphysical system to a model, why one should explore a parameter space, and how to interpretmodels. We found that most students had difficulty in deciding what parameters were relevant,representing a physical situation in equations, and stating and justifying simplifications andassumptions. Students performed better at interpreting the model, and relating graphical results fromthe mathematical model to experimental data obtained from a physical model. They were also ableto use the model outputs to make design decisions, or explain why the existing model was inadequatefor this purpose. In this current phase of the study we investigated how well students transferredthese skills to their own open-ended design problems.Like our previous work, the study was conducted in a biomedical engineering capstone designcourse. Data were collected from each student group’s final design report and presentation forthe capstone course. Each team had a unique open-ended design problem with a real client. Arubric was developed to assess student performance on the six stages of model creation andinterpretation. We compared the performance of students over two years. In both years, theyworked through the scenario described above, but only in the second year was their performanceon those tasks used to provide a basis for instructing them about modeling.Specific instruction in mathematical modeling was required before we saw an impact on the useof modeling in students’ own design projects. Eighty-two percent of teams were able to generatesome type of mathematical relationship between model parameters after instruction, whereas inprevious years, where no instruction occurred, only 25% of the teams developed a mathematicalrelationship to describe their system. However, the results also showed that even withinstruction, students did not utilize models to their full potential. Only 41% of all groupsadequately explored the parameter space of their model, and only 12% of teams discussed thelimitations of their model. Seventy-one percent used the model results to inform their finaldesign. This research has provided some insight into how to revise instruction in order toimprove engineering students’ abilities in mathematical modeling in the context of design.

Cole, J., & Linsenmeier, R. A., & Miller, T., & Glucksberg, M. R. (2012, June), Using Instruction to Improve Mathematical Modeling in Capstone Design Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. 10.18260/1-2--22185

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