To understand how students constructs mathematical ideas in "Dynamic Geometry" environments (tools like Geometer's Sketchpad and Cabri), one needs clear characterizations of : (1) the mathematical "raw materials" embodied in the software and (2) how students use these "raw materials." What are the mathematical objects and allowable transformations? Which do they notice and attend to? How do they interpret what they notice? Through interviews with developers, and through our won analyses, we will investigate the tools' mathematical and pedagogical potential. Experiments and clinical interviews with students well lead to a preliminary epistemology of concepts related to the defining feature of this software: dynamic "dragging." focussed experiments will then reexamine these results and hone them, to derive implications for learning and teaching, and for the design of materials. Thus the project will establish empirical and theoretical foundations for an epistemology of dynamic geometry.
