Designing Learning Environments for Developing Understanding of Geometry and Space

(Studies in Mathematical Thinking and Learning)

  Richard Lehrer, Daniel Chazan

Lawrence Erlbaum | 1998 | 520 páginas | rar -  pdf | 25 Mb

link (password: matav)

Conteúdos:

Prefácio ix
I - WHY TEACH GEOMETRY? 1
A Role for Geometry in General Education 3
E. Paul Goldenberg , Albert A. Cuoco , June Mark
From a Different Perspective: Building on Students' Informal Knowledge 45
Koeno P. Gravemeijer
Charting a Course for Secondary Geometry 67
Daniel Chazan e Michal Yerushalmy
Chaos in the Classroom 91
Robert L. Devaney
II - STUDIES OF CONCEPTUAL DEVELOPMENT 105
Interpreting Student Understanding in Geometry: A Synthesis of Two Models 109
John Pegg e Geoff Davey
Longitudinal Study of Children's Reasoning About Space and Geometry 137
Richard Lehrer, Michael Jenkins, Helen Osana
Developing Understanding of Geometry and Space in the Primary Grades 169
Richard Lehrer, Cathy Jacobson, Greg Thoyre, Vera Kemeny, Dolores Strom, Jeffrey Horvath, Stephen Gance, Matthew Koehler
Development of Geometric and Measurement Ideas 201
Douglas H. Clements, Michael T. Battista, Julie Sarama
Students' Understanding of Three-Dimensional Cube Arrays: Findings From a Research and Curriculum Development Project 227
Michael T. Battista e Douglas H. Clements
Sixth-Grade Students' Conceptions of Stability in Engineering Contexts 249
James A. Middleton e Robert Corbett
Interconnecting Science and Mathematics Concepts 267
Kalyani Raghavan, Mary L. Sartoris, Robert Glaser
Geometric Curve-Drawing Devices as an Alternative Approach to Analytic Geometry: An Analysis of the Methods, Voice, and Epistemology of a High-School Senior 297David Dennis e Jere Confrey
Conjecturing and Argumentation in High-School Geometry Students 319Kenneth R. Koedinger
III DEFINING A NEW SEMANTICS OF SPACE: COMPUTERS, SOFTWARE, AND THE ELECTRONIC WORLD 349
What Is Dynamic Geometry?
E. Paul Goldenberg e Albert A. Cuoco 351
An Alternative Approach to Proof in Dynamic Geometry 369
Michael de Villiers
Opportunities to Explore and Integrate Mathematics with the Geometer's Sketchpad 395
John Olive
Mapping the Classroom Using a CAD Program: Geometry as Applied Mathematics 419
Daniel Lynn Watt
An Introduction to Geometry Through Anchored Instruction 439
Linda Zech, Nancy J. Vye, John D. Bransford, Susan R. Goldman, Brigid. J. Barron, Dan L. Schwartz, Rachelle Kisst-Hackett, Cynthia Mayfield-Stewart e the Cognition and Technology Group
Teachers and Students Investigating and Communicating About Geometry: The Math Forum 465
K. Ann Renninger, Stephen A. Weimar e Eugene A. Klotz
EPILOGUE 489
Organization and Freedom in Geometry Learning and Teaching
Rina Hershkowitz