June 24, 2017
June 24, 2017
June 28, 2017
This research paper presents new findings about first-year engineering students’ approaches for visualizing models within the Models and Modeling Perspective theoretical framework. The results are primarily discussed in the full paper, but the motivation, background, implications, and future directions for research are briefly described in this abstract.
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. Since models are embedded in many engineering courses, it is beneficial to help students develop modeling skills early on in their engineering education. Model-eliciting activities (MEAs) represent a pedagogical approach implemented and researched in engineering to teach students mathematical modeling skills through the development of a model to solve an authentic problem. Model-adaptation activities (MAAs) were created within the same theoretical framework in mathematics education, but they are scarcely implemented and researched within engineering.
This study is a part of a larger investigation into the impact of implementing a linked MEA and MAA within a first-year engineering course at a large Midwestern university. 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 started with 122 student teams’ submissions at the end of a MEA and a MAA. Within the MEA, teams had to develop one mathematical model to create a solar panel with various materials based on provided data and some relevant equations. Within the MAA, teams had to develop one simulation per a student on the team based on the model from their MEA and other models they found on nanoHUB.org or other resources. The teams developed their simulations with graphical-user interfaces using MATALB. The nature of the mathematical models was analyzed in a previous study and the relevant findings are tied throughout this study. The teams’ simulations submitted at the end of the MAA were analyzed using a framework to assess the level of simulation completeness based on the presence of interaction, an underlying model, and visualization. Based on an analysis of the 122 teams’ 383 simulations, 62 percent were complete simulations (i.e. backed by a model and front-ended with user-input and output visualization capabilities). All of the 237 complete simulations were further analyzed using grounded theory in this study to understand the types of visualizations that students used and how they related to their underlying mathematical models. There was a large range of ways that students decided to incorporate visualization into their simulations. Most teams visualized an output of their model, but some chose to display values that users input into the models. The most common types of visualization consisted of bar charts, pie charts, and line graphs. Some teams implemented 3-D objects, but these appeared to be beyond the capability of students because they did not display any meaningful information. These findings are described quantitatively and qualitatively in greater detail in the full paper.
The goal of this study was to gain further insight into students’ thought-process of the meaning of their models. This understanding can help researchers better investigate potential misconceptions, misunderstandings, and opportunities to help students learn about mathematical models. The findings of this study also help inform practioners of ineffective and effective types of visualizations that students used in developing simulations to help them give more informed feedback throughout implementation of similar projects.
Rodgers, K. J., & Dala, N. J., & Madhavan, K. (2017, June), How First-Year Engineering Students Develop Visualizations for Mathematical Models Paper presented at 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. 10.18260/1-2--28446
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