Development of First-Year Engineering Teams' Mathematical Models through Linked Modeling and Simulation Projects
The development and use of mathematical models and simulations underlies much of the work of engineers. Mathematical models describe a situation or system through mathematics, quantification, and pattern identification. Simulations enable users to interact with models through manipulation of input variables and visualization of model outputs. Although modeling skills are fundamental, they are rarely explicitly taught in engineering. Model-eliciting activities (MEAs) represent a pedagogical approach used in engineering to teach students mathematical modeling skills through the development of a model to solve an authentic problem. This study is an investigation into the impact of linking a MEA and a simulation-building project on students’ model development. The purpose of this research is to further address the need for developing effective curricula to teach students’ mathematical modeling skills and begin to address the need to teach students about simulations. The data for this study were 122 first-year engineering student teams’ solutions to both a MEA and a subsequent simulation-building project set in the context of a nanotechnology topic, specifically quantum dot solar cells. The teams’ mathematical models submitted at the end of the MEA and the simulation project were analyzed using two frameworks to assess the quality of the mathematical models and the level of simulation completeness. Three teams’ works with the feedback they received were analyzed in a case study. The analysis of the 122 teams’ mathematical models showed that many teams selected particular aspects of their final MEA models for further development in their simulations. Based on the components of the models that were consistent in the MEA and project submissions, teams either improved, did not change, or weakened aspects of their models. Twenty-six teams improved the functionality of their model. Six teams increased the input variable handling of their models. Two teams improved the efficiency of their models; eight teams made their models less efficient through poor programming decisions. Based on an analysis of the 122 teams’ simulations, 62 percent were complete simulations (i.e. backed by a model and front-ended with user-input and output visualization capabilities). The case study enabled a more detailed analysis of how select teams’ mathematical models changed across their submissions and the evidence of potential deeper learning about their models across their submissions. The findings of this study suggest that model development continued through simulation development enables student teams an opportunity to either further improve or explore their models. These sequential projects provide teams with low quality models with more time for development and application within a simulation. They provide teams with high quality models an opportunity to explore ideas beyond the original scope of the MEA.
Diefes-Dux, Purdue University.
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