activities, students use simulation software to model sound-effect generators, video systems, and computer networks.

In engineering practice, physical and mathematical models are also used to obtain data as a basis for making informed decisions during the design process. An example of this can be found in Challenge Number 3, a unit of “A World in Motion,” in which eighth graders collect and graph data relating the center of gravity of a model glider to where the wing is placed and to the amount of weight in the nose of the glider. Based on the graphs, students predict optimal flight performance by determining the nose weight that locates the center of gravity closest to the centerline of the wing. Thus this curriculum has students use a physical model, the toy glider, to generate data for a simple mathematical model that represents the relationship between key variables that affect flight. The model is then used to adjust the design of the glider to achieve desired flight behavior. In a “Gateway to Technology” project, students use simulations posted on the Internet to model the effects of changing variables on the performance of rockets. Although the students interact with a mathematical model through the graphical model, the instructional materials do not call attention to the mathematical modeling.

For the most part, models are not used to represent key variables in the early stages of the design process but are presented as steps in the later stage of the design process for refining a relatively mature design solution to a problem. Thus models are used to visualize a design, take it to a higher level of refinement, and communicate its features to others. In many ways, this use of modeling is representative of industrial design rather than engineering design. Industrial design is the professional service of creating and developing concepts and specifications that optimize the function, value, and appearance of products and systems for the mutual benefit of both user and manufacturer (IDSA, 2008).

However, the reader should keep in mind that the pedagogical role of modeling is independent of its role in engineering design. Strategies to engage students in cooperative learning, such as Socratic dialogue, inquiry and design, and reflection and debriefing, typically involve making, testing, and presenting models. Modeling requires that students generate ideas, translate them into concrete form, and assess their validity. In the process, they must re-examine their assumptions, identify misconceptions and failures, refine their thinking, and develop and implement new ideas. Ultimately, models are embodiments of thought processes, insights, and discoveries in a form that communicates them to others.



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