Download Expanding Visions of Geometry: Learning and Teaching Approaches and more Lecture notes Geometry in PDF only on Docsity! Contents Preface ................................................................................................ xi I. Expanding Visions of Geometry ..................................................1 1. What Is Geometry? ..............................................................................3 Joseph Malkevitch City College of New York—York College, Jamaica, New York 2. Enumerating Symmetry Types of Rectangle and Frieze Patterns: How Sherlock Might Have Done It ....................................................17 Doris Schattschneider Moravian College (Emerita), Bethlehem. Pennsylvania 3. Möbius Concepts: Strips and Tori ......................................................33 Yuichi Handa California State University—Chico, Chico, California David A. James University of Michigan—Dearborn, Dearborn, Michigan Thomas Mattman California State University—Chico, Chico. California 4. Exploring Curvature with Paper Models ...........................................49 Howard T. Iseri Mansfield University of Pennsylvania, Mansfield, Pennsylvania 5. Prairie Plants: Exploring Fractals in Nature .....................................63 Dane Camp New Trier Township High School—Winnetka Campus, Winnetka, Illinois Erich Hauenstein College of DuPage, Glen Ellyn, Illinois 6. Folding Polygons to Convex Polyhedra .............................................77 Joseph O’Rourke Smith College, Northampton, Massachusetts II. Learning Geometry ....................................................................89 7. Highlights of Research on Learning School Geometry .......................91 Michael T. Battista Ohio State University, Columbus, Ohio vi Contents 8. Prototypes and Categorical Reasoning: A Perspective to Explain How Children Learn about Interactive Geometry Objects .............................................................................................109 Paul Yu Grand Valley State University, Allendale, Michigan Jeffrey Barrett Illinois State University, Normal, Illinois Norma Presmeg Illinois State University, Normal, Illinois 9. Conceptions of Angle: Implications for Middle School Mathematics and Beyond .................................................................127 Christine Browning Western Michigan University, Kalamazoo, Michigan Gina Garza-Kling Western Michigan University, Kalamazoo, Michigan 10. Developing the Spatial Operational Capacity of Young Children Using Wooden Cubes and Dynamic Simulation Software ...........................................................................................141 Jacqueline Sack Rice University, Houston, Texas Retha van Niekerk University of the Witwatersrand, Johannesburg, Johannesburg, South Africa 11. Fostering Geometric Thinking in the Middle Grades: Professional Development for Teachers in Grades 5–10 .....................................................................................155 Mark Driscoll Education Development Center, Inc., Newton, Massachusetts Michael Egan Augustana College, Rock Island, Illinois Rachel Wing DiMatteo Education Development Center, Inc., Newton, Massachusetts Johannah Nikula Education Development Center, Inc., Newton, Massachusetts Contents of the CD-ROM Section I: Expanding Visions of Geometry 1. What Is Geometry? • Art Gallery Problem (Blackline master) • Folding Boxes (Blackline master) 2. Enumerating Symmetry Types of Rectangle and Frieze Patterns: HowSherlock Might Have Done It • Frieze pattern worksheet 1 (Blackline master) • Frieze pattern worksheet 2 (Blackline master) 4. Exploring Curvature with Paper Models • Curvature template for figure 4.4 (Blackline master) • Curvature template for figure 4.6 (Blackline master) • Curvature template for figure 4.7 (Blackline master) • Curvature template for figure 4.9 (Blackline master) • Curvature template for figure 4.10 (Blackline master) 6. Folding Polygons to Convex Polyhedra • Folding a Latin cross to make a tetrahedron (Blackline master) • Folding a square into an octahedron (Blackline master) • Folding a triangle into a tetrahedron (Blackline master) Section II: Learning Geometry 9. Conceptions of Angle: Implications for Middle School Mathematics and Beyond • Link to Smile Math and Logo Light 10. Developing The Spatial Operational Capacity of Young Children Using Wooden Cubes and Dynamic Simulation Software • Construction box (Video clip) • Extended construction box (Video clip) • Geocadabra installation 11. Fostering Geometric Thinking in the Middle Grades: Professional Development for Teachers in Grades 5–10 • Link to Web site • Do Math sessions 4 and 5 — Session 4: Dissecting Shapes (PDF) — Session 5: Analyze Student Work (PDF) x Contents Section III: Teaching Geometry for Understanding 12. Teaching Geometry for Conceptual Understanding: One Teacher’s Perspective • Law of sines worksheet (Blackline master) 13. Defining in Geometry • Geometer’s Sketchpad files 15. Using Interactive Geometry Software to Teach Secondary School: Geometry: Implications from Research • Video clips 19. Using Circle-and-Square Intersections to Engage Students in the Process of Doing Geometry • Geometer’s Sketchpad files 20. Area Formulas with Hinged Figures • Interactive figures 21. An Integrated Approach to Teaching and Learning Geometry • Mathematics 2 Course (PDF) • Link to Phillips Exeter Academy Web site 23. Looking Forward to Interactive Symbolic Geometry • Sample lessons • Files with Geometry Expressions reader
