According to extensive evaluations, elementary and middle school students are failing to learn basic geometric concepts and geometric problem solving, and are woefully underprepared for the study of more sophisticated geometric concepts and proof. The most critical barrier to students' successful learning of geometry is the failure of standard geometry curricula to systematically facilitate students' progression from basic intuitions and simple concepts to higher levels of geometric thought. To overcome this barrier, mathematics educators need to know specific conceptual constructions they make, and how such progression can be facilitated in the classroom. It has become apparent in our current NSF-supported curriculum development project that the original levels of geometric thought described by Piaget and van Hiele are useful but not completely adequate for understanding children's geometric thinking or designing and fine-tuning instructional treatments. Thus, the major goal of the proposed project is to construct more elaborate, precise, and powerful descriptions and models of children's development of geometric thinking. Such descriptions and models have strong potential to impact on theories of learning geometry. In fact, a by- product of the proposed research project will be further refinement and field-testing of the Logo-based geometry curriculum that we are currently developing ( which we consider to be one implementation of the NCTM Standards for teaching geometry.)
