Geometry Turned On: Dynamic Software in Learning, Teaching, and Research

Overview

This volume is a collection of articles about dynamic geometry: active, exploratory geometry carried out with interactive computer software. This software has had a profound effect on classroom teaching wherever it has been introduced. Unconstrained parts of the configurations are moveable - they can literally be grabbed with a cursor (using a mouse) and be dragged or stretched - and as they move, all other objects in the configuration automatically self-adjust, preserving all dependent relationships and ...

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Brand new. We distribute directly for the publisher. Dynamic geometry is active, exploratory geometry carried out with interactive computer software. It has had a profound effect ... on classroom teaching wherever it has been introduced and has become an indispensable research tool for mathematicians and scientists. The papers in this volume give a good idea of the ways in which the software can be used, and some of the effects it can have. It is clear that the software raises various questions for teaching and research, and its continuing evolution raises questions on the design of the software itself.With the use of interactive computer software, the focus in teaching sifts form students laboriously making constructions by hand to verify a stated fact in a text (for which there seems little reason to produce a proof) to a focus on students carrying out experiments, quickly producing many accurate sketches from which they conjecture properties that seem to be "always" true.The latest dynamic geometry software takes advantage of current computer hardware with mouse interface for graphics and great speed. What is most exciting about the software is its dynamic nature. Thus, after a geometric configuration is drawn, any unconstrained parts of the configuration (arbitrary segments or points for example), that are not dependent on any other objects are moveable-they can literally be grabbed with a cursor (using the mouse) and can be dragged or stretchedand as they move, all other objects in the configuration automatically self-adjust, preserving all dependent relationships and constraints.Although this volume is printed in a conventional manner, and every paper has illustrations, most of the illustrations beg to be played with. We want you to be able to experience some of the explorations described by out authors. To make that possible, dynamic sketches that use Geometer's Sketchpad or Cabri II have been made available by several of the authors and are posted on a Web page maintained by the Mathematics Forum. Read more Show Less

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Overview

This volume is a collection of articles about dynamic geometry: active, exploratory geometry carried out with interactive computer software. This software has had a profound effect on classroom teaching wherever it has been introduced. Unconstrained parts of the configurations are moveable - they can literally be grabbed with a cursor (using a mouse) and be dragged or stretched - and as they move, all other objects in the configuration automatically self-adjust, preserving all dependent relationships and constraints. The software has also become an indispensable research tool for mathematicians and scientists. This book gives many examples of the ways in which it can be used, and some of the effects it can have. It raises various questions for teaching and research. Some articles address the basic question, 'What is dynamic geometry good for?' as they discuss: accuracy of construction, visualization, exploration and discovery, motivating proof, transformations, tracing loci, simulation, and creating microworlds.

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Product Details

  • ISBN-13: 9780883850992
  • Publisher: Mathematical Association of America
  • Publication date: 7/1/1997
  • Series: Notes Series
  • Edition description: New Edition
  • Pages: 275
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.51 (d)

Table of Contents

Part I. Personal Reflections On Investigation, Discovery, and Proof: 1. Discovery and dissection of a geometric gem Douglas R. Hofstadter; 2. The role and function of proof in dynamic geometry: some personal reflections Michael de Villiers; 3. Dynamic geometry renews interest in an old problem Dan Bennett; 4. Dynamic geometry as a bridge from Euclidean geometry to analysis Albert A. Cuoco and E. Paul Goldenberg; Part II. Dynamic Geometry In The Classroom: 5. Dynamic visualization from middle school through College James Morrow; 6. Geometer's sketchpad in the classroom Tim Garry; 7. Students discovering geometry using dynamic geometry software Michael Keyton; 8. Moving triangles; 9. Experiences with geometer's sketchpad in the classroom Kathryn W. Boehm; 10. Beyond elementary constructions: selected exercises Arnold Perham and Bernadette H. Perham; 11. Interactive generation, manipulation, and application of loci Heinz Schumann; 12. Calculus with dynamic geometry Catherine A. Gorini; 13. Beginning geometry at college Tony Hampson; 14. Identifying transformations by their orbits James M. Parks; 15. Dynamic proofs that use similarities James King; 16. Visualization of group theory concepts through dynamic geometry Doris Schattschneider; 17. Using the geometer's sketchpad with preservice teachers Zhonghong Jian and Edwin McClintock; 18. Fish in the pond: inquiry with dynamic geometry Fadia Harik; Part III. Dynamic Visualization In History, Perception, Optics and Aerodynamics: 19. Drawing logarithmic curves with geometer's sketchpad: a method inspired by historical sources David Dennis and Jere Confrey; 20. Lost in the funhouse: an application of dynamic projective geometry Susan Addington and Stuart Levy; 21. The use of dynamic geometry software in teaching and research in optometry and vision science Benjamin T. Backus; 22. Creating airfoils from circles: the Joukowski transformation John Olive; Part IV. The Worlds Of Dynamic Geometry: Issues In Design And Use: 23. Drawing worlds: scripted exploration environments in the geometer's sketchpad R. Nicholas Jackiw; 24. Dynamic geometry and declarative geometric programming Richard J. Allen and Laurent Trilling.

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