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Investigating Engineering Students’ Mathematical Modeling Abilities In Capstone Design

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2010 Annual Conference & Exposition


Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010



Conference Session

Engineering Design: Implementation and Evaluation

Tagged Division

Educational Research and Methods

Page Count


Page Numbers

15.812.1 - 15.812.16



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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. Dr. Cole’s primary teaching is in Capstone Design, and her research interest are in engineering design education.

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Robert Linsenmeier Northwestern University


Ann McKenna Northwestern University

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Ann McKenna is the Director of Education Improvement in the Robert R. McCormick School of Engineering and Applied Science at Northwestern University. She holds a joint appointment as Research Associate Professor in the Department of Mechanical Engineering and the School of Education and Social Policy. She also serves as co-director of the Northwestern Center for Engineering Education Research (NCEER). Dr. McKenna’s research focuses on understanding the cognitive and social processes of design teaching and learning, the role of adaptive expertise in design and innovation, and teaching approaches of engineering faculty. Dr. McKenna received her B.S. and M.S. degrees in Mechanical Engineering from Drexel University and Ph.D. in Engineering, Science and Mathematics Education from the University of California at Berkeley.

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Matthew Glucksberg Northwestern University

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Matthew Glucksberg is the Department Chair in Biomedical Engineering in the Robert R. McCormick School of Engineering and Applied Science at Northwestern University. Dr. Glucksberg’s research interests are in pulmonary mechanics and lung liquid transport, blood pressure and flow in the retinal circulation, and non-invasive sensing of blood flow and analytes.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Investigat abilities in capstone design Abstract

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.


Mathematical modeling is essential to engineering practice and a valuable tool for engineering design. Engineers who generate mathematical models or use mathematical and conceptual

Dossey1 defines quantitative literacy of mathematics to fruitfully understand, predict, and control relevant factors in a variety of these aspects, and operation sense, measurements, variables and relations, geometric shapes and spatial The education of future engineers must prepare them to approach

Cole, J., & Linsenmeier, R., & McKenna, A., & Glucksberg, M. (2010, June), Investigating Engineering Students’ Mathematical Modeling Abilities In Capstone Design Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--16271

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