Assessing Engineering Students’ Abilities at Generating and Using Mathematical Models in Capstone Design

Jennifer Cole; Robert Linsenmeier; Esteban Molina; Matthew Glucksberg; Ann McKenna

doi:10.18260/1-2--17517

Assessing engineering students’ abilities at generating and using mathematical models in capstone designAbstractEngineering capstone design offers students an opportunity to apply their previous engineeringknowledge to develop unique solutions to open-ended and analytically complex problems. Often,the expectation is that a thorough or rigorous solution to a capstone level problem would includecomputational or mathematical analysis appropriate to that discipline. However, engineeringstudents often struggle in recognizing when and how to apply the mathematical analysisencountered in prior coursework to their particular design solutions. The ultimate aim of thisstudy is to better understand how to develop students’ computational fluency in generating,applying, and interpreting mathematical models in the process of engineering design.The current study is a continuation of an earlier project in which we explored how studentsinterpreted the concept of “modeling,” and how they decided what parameters of a physicalsituation should be represented mathematically, all in the context of developing design solutions(reference author, 2010). In the phase of the study described here, we wanted to understandstudents’ abilities in the generation and implementation of the mathematical model. Previouswork identified a set of steps for what mathematical modeling should include. The stepsassessed in the current study include: generating the mathematical relationships for physicalphenomena, making simplifications, performing mathematical manipulations, and interpretingmodel output.Like our previous work, the study was conducted in a biomedical engineering capstone designcourse. Data collection was conducted using a scenario that included specific questions related togenerating the mathematical equations for the model and interpreting model outputs as applied toan actual design problem used in previous courses. The problem used in the scenario was thedesign of a phototherapy device for treating neonatal jaundice in developing countries, with afocus on how to deliver the correct dosage of phototherapy light to the infant’s skin. All studentswere assumed to have the same basic math skills based on their exposure to light and optics intheir undergraduate physics course; however, none of the students had worked on designsinvolving light. Part of the assignment was done as homework, and part as independent work inclass.The results showed that students are not comfortable with several aspects of creating and usingmathematical models. Of the 38 students participating in the study, only six were able togenerate a model using some form of mathematical equations necessary to model the system inthe scenario, even though an equation for one element of the system was given in class. Whenstudents were asked to state assumptions they would use to simplify the system they planned tomodel, 34% failed to state even one assumption. In fact, less than 20% of students statedassumptions that were relevant to the creation of the mathematical model. However, ourinvestigation also found that most students (78%) were able to interpret model results. Thisindicates that once data from a model is provided, students were more proficient in their dataanalysis abilities.Data from this stage of our research has shed further light on where students struggle in the areasof creating and using a mathematical model. This research has provided some insight into howto revise instruction in order to improve engineering students’ abilities in mathematical modelingin the context of design.

Assessing Engineering Students’ Abilities at Generating and Using Mathematical Models in Capstone Design

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