Chapter 13: Representations and Cognitive Objects in Modern School Geometry

It is widely recognized that Dynamical Geometry Environments (DGEs) such as the Geometer’s Sketchpad (GSP) (Jackiw, 1995) and Cabri (Baulac, Bellemain, & Laborde, 1994) are powerful tools for learning and doing geometry. However, DGEs also can play an important role in research on students’ geometry learning. As an additional medium for geometric reasoning, DGEs provide to researchers a new window for viewing students’ learning. This window can be especially valuable for investigating the nature of the representations and cognitive objects that students use in geometric thought. The goal of this chapter is to highlight some of the critical issues involved in understanding the objects and representations utilized in geometric reasoning, first in general, then for DGEs.