ABSTRACT
In this chapter, we describe two episodes from elementary classrooms where children are learning through design. The focus and goal of the design vary across these cases, but the episodes share an emphasis on modeling and on the related issue of mathematizing the theoretically important elements of a problem as one route toward constructing a solution. In the first classroom case, second graders are working to design combinations of Lego cars and downhill “racetracks” (inclined planes) so that the cars will traverse a fixed distance either “really fast” or “really slow.” In the second case, third-grade children are designing experiments to explore the factors that affect the growth rate of Wisconsin “Fast Plants.” These design cases are presented as a backdrop against which we illustrate the importance of inscription and symbolization for teaching and learning mathematics and science.
