## Fractals, Graphics, and Mathematics EducationFractal geometry is a recent addition to the collection of mathematical tools for describing nature and the works of Man. It made possible for the first time a national study of roughness. Fractals are encountered in mathematics and many natural sciences, but also in finance and in art, music and literature most often without being consciously included by anyone. Therefore, fractals interconnect the arts and the natural and social sciences in many intrinsic ways. Rarely, if ever, are students exposed to anything like this in mathematics and science classes. This book collects essays about fractal's role in mathematics and science education. In the first four chapters, the editors address general issues. The next twelve chapters are invited case studies authored by educators who began years ago to use fractal geometry in classes that range from second grade elementary school, through public and private high schools, to state universities and private colleges. Some contributors survey literature and software they have used, others present detailed sample lessons. The chapter for Florida Atlantic University reports on a program training teachers in Florida. Many teachers developed fractals courses on their own in isolation from one another. This book is a token of how widespread such courses have become. The common themes that appear throughout mark the coming of age of this subject. - Publisher. |

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### Contents

Some Reasons for the Effectiveness of Fractals in Mathematics Education by Benoit B Mandelbrot Michael Frame | 3 |

Unsolved Problems and StillEmerging Concepts in Fractal Geometry by Benoit B Mandelbrot | 11 |

Fractals Graphics and Mathematics Education by Benoit B Mandelbrot | 21 |

Mathematics and Society in the 20th Century by Benoit B Mandelbrot | 29 |

CLASSROOM EXPERIENCES | 33 |

Teaching Fractals and Dynamical Systems at The Hotchkiss School by Melkana Brakalova David Coughlin | 35 |

Considering Change in the Undergraduate Mathematics Major John A Dossey Editor | 45 |

Scaling the Heights Deborah Nolan Editor | 46 |

A Report on Evaluation Efforts and National Impact from 1988 to 1998 Susan L Ganter | 56 |

Resources for Professional Development Matthew Delong and Dale Winter | 57 |

Fractals Graphics and Mathematics Education Benoit Mandelbrot and Michael Frame Editors | 58 |

Assets for Undergraduate Mathematics David Carlson Charles R Johnson David C Lay and A Duane Porter Editors | 59 |

Periods of the Bulbs by Robert L Devaney | 61 |

FractalsEnergizing the Mathematics Classroom by Vicki Fegers Mary Beth Johnson | 69 |

Other Chaos Games by Sandy Fillebrown | 105 |

a Personal Experience by Michel Lapidus | 111 |

Innovative Programs Using Technology Susan Lenker Editor | 47 |

Writing in the Teaching and Learning of Mathematics John Meier and Thomas Rishel | 48 |

Assessment Practices in Undergraduate Mathematics Bonnie Gold Editor | 49 |

Exploring ODEs with Modern Technology Michael J Kallaher Editor | 50 |

An International Perspective Victor J Katz Editor | 51 |

Resources for Undergraduate Instructors Thomas L Moore Editor | 52 |

Papers in Applied Geometry Catherine A Gorini Editor | 53 |

A Guide for New Mathematicians Thomas W Rishel | 54 |

Issues That Matter and Strategies That Work Elizabeth C Rogers Barbara E Reynolds Neil A Davidson and Anthony D Thomas Editors | 55 |

Exploring Fractal Dimensions by Experiment by Ron Lewis | 117 |

Fractal Themes at Every Level by Kenneth G Monks | 139 |

Artistic Explorations of Natural SelfSimilarity by Brianna Murratti Michael Frame | 149 |

a First College Course in Quantitative Reasoning Based on Fractals and Chaos by David Peak Michael Frame | 157 |

200901 1 12 | 164 |

A Software Driven Undergraduate Fractals Course by Douglas C Ravenel | 171 |

The Fractal Ring from Art to Art through Mathematics Finance and the Sciences | 179 |

About the Editors and Other Contributors | 201 |

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