Understanding geometry for a changing world

[Pt.] I. Expanding visions of geometry

1. What is geometry? / Joseph Malkevitch

2. Enumerating symmetry types of rectangle and frieze patterns : how Sherlock might have done it / Doris Schattschneider

3. Möbius concepts : strips and tori / Yuichi Handa, David A. James, Thomas Mattman

4. Exploring curvature with paper models / Howard T. Iseri

5. Prairie plants : exploring fractals in nature / Dane Camp, Erich Hauenstein

6. Folding polygons to convex polyhedra / Joseph O'Rourke

[Pt.] II. Learning geometry

7. Highlights of research on learning school geometry / Michael T. Battista

8. Prototypes and categorical reasoning : a perspective to explain how children learn about interactive geometry objects / Paul Yu, Jeffrey Barrett, Norma Presmeg

9. Conceptions of angle : implications for middle school mathematics and beyond / Christine Browning, Gina Garza-Kling

10. Developing the spatial operational capacity of young children using wooden cubes and dynamic simulation software / Jacqueline Sack, Retha van Niekerk

11. Fostering geometric thinking in the middle grades : professional development for teachers in grades 5-10 / Mark Driscoll ... [et al.]

[Pt.] III. Teaching geometry for understanding

12. Teaching geometry for conceptual understanding : one teacher's perspective / James Paniati

13. Defining in geometry / Michael de Villiers, Rajendran Govender, Nikita Patterson

14. Advancing students' understanding of quadrilaterals / Tutita M. Casa, M. Katherine Gavin

15. Using interactive geometry software to teach secondary school geometry : implications from research / Karen F. Hollebrands, Ryan C. Smith

16. Representing, modeling, and solving problems in interactive geometry environments / José N. Contreras, Armando Martínez-Cruz

17. Inventing a geometry theorem / Armando Martínez-Cruz, José N. Contreras

18. Theorems discovered by students inspire teachers' development / Antonio Quesada

19. Using circle-and-square intersections to engage students in the process of doing geometry / Stephen Blair, Daniel Canada

20. Area formulas with hinged figures / Alfinio Flores

21. An integrated approach to teaching and learning geometry / David Wilson

22. Redesigning a traditional geometry lesson as an investigative activity / Jon Davis

23. Looking forward to interactive symbolic geometry / Philip H. Todd.