Despite a long intellectual history dating back to the origins of civilization and a recent resurgence as cutting edge mathematics, geometry and spatial visualization in school are often compressed into a caricature of Greek geometry, generally reserved for the second year of high school. The resulting impoverished view of the mathematics of space rebounds throughout schooling to generally diminish student (and adult) understanding of mathematics. Rather than looking to high school geometry as the locus - and all too often, the apex - of geometric reasoning, the contributors to this volume suggest that reasoning about space can and should be successfully integrated with other forms of mathematics, starting at the elementary level and continuing through high school. Reintegrating spatial reasoning into the mathematical mainstream - indeed, placing it at the core of K-12 mathematics environments that promote learning with understanding - will mean increased attention to problems in modelling, structure and design, and reinvigoration of traditional topics like measure, dimension and form. Geometry education should include contributions to the mathematics of space that were developed after those of the Greeks. This volume reflects an appreciation of the interactive roles of subject matter, teacher, student and technologies in designing classrooms that promote understanding of geometry and space. Although these elements of geometry education are mutually constituted, the volume is organized to highlight: first, the editors' vision of a general geometry education; second, the development of student thinking in everyday and classroom contexts; and third, the role of technologies.

Table of Contents:

Contents: Preface. Part I: Why Teach Geometry?E.P. Goldenberg, A.A. Cuoco, J. Mark, A Role for Geometry in General Education. K. Gravemeijer, From a Different Perspective: Building on Students' Informal Knowledge. D. Chazan, M. Yerushalmy, Charting a Course for Secondary Geometry. R.L. Devaney, Chaos in the Classroom. Part II: Studies of Conceptual Development.J. Pegg, G. Davey, Interpreting Student Understanding in Geometry: A Synthesis of Two Models. R. Lehrer, M. Jenkins, H. Osana, Longitudinal Study of Children's Reasoning About Space and Geometry. R. Lehrer, C. Jacobson, G. Thoyre, V. Kemeny, D. Danneker, J. Horvath, S. Gance, M. Koehler, Developing Understanding of Space and Geometry in the Primary Grades. D.H. Clements, M.T. Battista, J. Sarama, Development of Geometric and Measurement Ideas. M.T. Battista, D.H. Clements, Students' Understanding of Three-Dimensional Cube Arrays: Findings From a Research and Curriculum Development Project. J.A. Middleton, R. Corbett, Sixth Grade Students' Conceptions of Stability in Engineering Contexts. K. Raghavan, M.L. Sartoris, R. Glaser, Interconnecting Science and Mathematics Concepts: Area and Volume. D. Dennis, J. Confrey, Geometric Curve-Drawing Devices as an Alternative Approach to Analytic Geometry: An Analysis of the Methods, Voice, and Epistemology of a High School Senior. K.R. Koedinger, Conjecturing and Argumentation in High School Geometry Students. Part III: Defining a New Semantics of Space: Computers, Software, and the Electronic World.E.P. Goldenberg, A.A. Cuoco, What Is Dynamic Geometry? M. de Villiers, An Alternative Approach to Proof in Dynamic Geometry. J. Olive, Opportunities to Explore and Integrate Mathematics With the Geometer's Sketchpad. D.L. Watt, Mapping the Classroom Using CAD Program: Geometry as Applied Mathematics. L. Zech, N.J. Vye, J.D. Bransford, S.R. Goldman, B.J. Barron, D.L. Schwartz, R. Kisst-Hackett, C. Mayfield-Stewart, The Cognition and Technology Group at Vanderbilt, An Introduction to Geometry Through Anchored Instruction. K.A. Renninger, S.A. Weimar, E.A. Klotz, Teachers and Students Investigating and Communicating About Geometry: The Math Forum.