Fractals, Graphics, and Mathematics Education

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Cambridge University Press, Jun 20, 2002 - Computers - 206 pages
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Fractal 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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