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Part I. Introductory Essays: 1. Some reasons for the effectiveness of fractal geometry in mathematics education Benoit B. Mandelbrot and Michael Frame 2. Unsolved problems and still emerging concepts Benoit B. Mandelbrot 3. Fractals, graphics and mathematics education Benoit B. Mandelbrot 4. Mathematics and society in the twentieth century Benoit B. Mandelbrot Part II. Classroom Experiences: 5. Teaching fractals and dynamical systems at the Hotchkiss school Melkana Brakalova and David Coughlin 6. Reflection on Wada basins: some fractals with a twist Dane Camp 7. Learning and teaching about fractals Donald M. Davis 8. The fractal geometry of the Mandelbrot set Robert L. Devaney 9. Fractals - energizing the mathematics classroom Viki Fegers and Mary Beth Johnson 10. Other chaos games Sandy Fillebrown 11. Creating and teaching undergraduate courses in fractal geometry: a personal experience Michel Lapidus 12. Exploring Fractal dimensions by experiment Ron Lewis 13. Fractal themes on all levels Kenneth G. Monks 14. Art and fractals: artistic explorations of natural self-similarity Brianna Murati and Michael Frame 15. Order and chaos, art and magic: a first college course in quantitative reasoning based on fractals and chaos David Peak and Michael Frame 16. A software driven undergraduate fractals course Douglas C. Ravenel Part III. A Final Word: 17. The fractal ring from art to art through mathematics, finance and the sciences Benoit B. Mandelbrot Part IV. Appendices: 18. Panorama of fractals and their uses. An alphabetic workbook-index Michael Frame and Benoit B. Mandelbrot 19. Reports of some field experiences.