Nicholas Jackiw, Chief Technology Officer, KCP Technologies

In considering the geometric figure, Kant distinguishes between image--the traditional visual diagram--and schemata, the generalized concept of that diagram that "can never exist anywhere except in thought." Dynamic Geometry figures produced by software such as The Geometer's Sketchpad bridge this divide through flexible, "rubbery" diagrams that (under manipulation) transform into any valid realization of their defining geometric constraints, but at any instant retain the immediacy and tangibility of specific images. In this talk, Sketchpad's author explores the implications of Dynamic Geometry visualization on mathematical inquiry and pedagogic practice in the context of school (6-12) mathematics, and describes implementation concerns in the design and development of Dynamic Geometry software.