This research aims to characterize the overlap as well as distinctness between engineering design thinking, on the one hand, and engineering model-based reasoning, on the other hand. The 1990s witnessed the rise of a transformative wave to the engineering curricula, where the “engineering science” model became dominant in engineering curricula. In this model, the focus in the first two years of the curriculum is placed on the “engineering sciences,” or, alternatively, “analysis,” with the expectation that students would apply the learned scientific principles to solve technical problems. However, a segregation problem between “design” and “analysis” started to emerge. The problem was caused not only by lack of appreciation for the complexities associated with design teaching and learning, but also by lack of students’ fluency to apply their learned mathematical modeling skills in complex, open-ended design problems. In this paper, we develop a “representations framework” to study the relationship between engineering design thinking and engineering model-based reasoning. It is the focus of this study to understand the role of multiple representations in problem solving, in order to characterize the overlaps and the distinctiveness in the use of the term “representation” in the contexts of mathematical modeling and design processes. Engineering design is a systematic, intelligent process that aims to solve ambiguous problems. Design pedagogy is enhanced through project-based learning (PBL), where students engage in real-life projects that motivate learning by doing. The original PBL pedagogy featured two unique themes: (1) design-oriented projects which focused on the know-how of synthesizing knowledge from different disciplines, and (2) problem-oriented projects which focused on the know why of solving theoretical problems through relevant knowledge. These two themes point to early attention in the design pedagogy to the relationship between design and analysis. Modeling efforts attempt to translate natural phenomenon or real-world problems into representation systems, including mathematical and computational models. In educational settings, the process of is called model-eliciting activity. The process aims to train students in the “process” of creating models while practicing model-based reasoning. In the majority of current engineering education curricula, a major emphasis is placed on the traditional view where prerequisite ideas are taught in decontextualized situations. While students in their courses interact with models in varying contexts, teaching focuses on algorithmic steps to find a solution. Although there are studies that indicated the importance of mathematical modeling as one representation in design; others focused on visual synthesis in representation; and others studied language as representation of knowing, studies are lacking on integrating the different levels of representation. In this paper, we develop a framework to understand how representation is described, taught and learned in analysis-focused classes and in design-focused classes.
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