The focus of this research was the conduct and analysis of six hours of clinical interviews with sixth and ninth grade students to investigate how they learn geometry in light of the van Hiele model. In chapter 1 an overview of the project and its four major goals is given. The theoretical model is described in chapter 2. In chapter 3 the development and detailed description of the project's research tool, Instructional Modules 1, 2, and 3 (Properties of Polygons, Angle Measurement and Angle Sum for Polygons, and Area of Polygons) are set forth. Chapter 4 follows with the project's formulation of the van Hiele model and level descriptors with sample student responses to questions or activities in the instructional modules. In chapters 5, 6, and 7, the individual performances of 32 students are analyzed and discussed and the findings are summarized. The performances of eight preservice and five inservice teachers on selected activities from the instructional modules are analyzed and reported in chapter 8. An analysis of the geometry strand in three United States mathematics textbook series, grades K-8, is set forth in chapter 9. Implications of the project's study as well as questions for further research are discussed in chapter 10. (PK)