be to direct student behavior to ensure success, limit the amount of resources for the project, and make the teacher’s management of the activity easier. This treatment of “constraints” is typical of many curricula we reviewed.

Modeling

We defined “modeling” as any graphical, physical, or mathematical representation of the essential features of a system or process that facilitates engineering design. Our analysis suggests that modeling is represented by a thin, varicolored thread running through most of the beads. The colors represent the different uses of modeling in engineering activities and in the teaching and learning process.

Engineers use models to help visualize potential solutions to design problems and/or as an interim step in the development of working prototypes. In many of the curricula, modeling is defined the same way. For example, in one unit in the “Engineering is Elementary” curriculum, a model is defined as “a small representation, usually built to scale, that serves as a plan.” In the “Design and Discovery” materials, a model is defined as a “visual representation of a total design (or some aspect of the design) that is nonfunctional.” In those same materials, a prototype is defined as a “working model used to demonstrate and test some aspect of the design or the design as a whole.” In the Gateway to Technology unit of the “Project Lead the Way” curriculum, modeling is defined as “the process of creating three-dimensional representations of design solutions.” Computer modeling is defined as “the use of computer software applications that allows the user to visualize an idea in a three-dimensional format.”

As these characterizations suggest, most of the curricula engage students in making things, usually from everyday materials, to help them visualize their designs and present them to others. For example, in Building Structures with Young Children, students construct towers and enclosures using building blocks. In “Children Designing and Engineering,” elementary students construct models of lighthouses and habitats for koalas. “Engineering is Elementary” projects engage students building models of windmills, water filters, paper bridges, alarm systems, and other objects. In “A World in Motion” projects, students construct and test toy vehicles (e.g., motorized cars, gliders). Gateway to Technology involves modeling cranes, magnetic-levitation trains, automated devices, airfoils, and rockets. “Material World Modules” involve the construction and testing of models of concrete roofing tiles, composite fishing poles, and humidity sensors. In “The Infinity Project”



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