Student Team Solutions to an Open-Ended Mathematical Modeling Problem: Gaining Insights for Educational Improvement
When engineers and students engage in mathematical modeling, the models they create are representational systems of real-world problem situations. These representational systems reveal modelers' interpretations of the relative importance of various real-world aspects.
This paper illustrates how interpretations of student teams' solution models (i.e., their representational systems) to a particular problem can be used to inform educational decisions.
First-year engineering teams' iterative solution models to the Travel Mode Choice Model-Eliciting Activity (MEA) were interpreted for the purpose of identifying patterns within and across teams' responses. This MEA requires the creation of a model for a client who wants to predict the mode of transportation an individual will likely take to a college campus. Teams were provided with the client's needs and sample data concerning individuals' actual travel mode and travel time, cost, and convenience for various travel modes (walk, bus, or drive).
Student teams were required to submit their intermediate and final model descriptions in narrative form. Systematic study of their models resulted in identification of four different types of models. Patterns within and across model types were then used to suggest changes to the instructional system.
When instructors study student models as representations of their interpretation of a real-world problem situation, insights gained can lead to practical proposals for improving instruction with authentic open-ended problems including revisions to tasks, implementation strategies, formative assessment strategies, and course content.