Fractal Geometry: Summer Workshops and Other Outreach

Yale University, New Haven CT

Investigators

Abstract

For each of the next four years, the investigators will continue and expand an ongoing and successful series of two successive summer workshops on Fractal Geometry at Yale University, and develop related outreach efforts. The intended workshop participants are high school, community college, and college teachers interested in offering fractal geometry courses for non-science students. Such a course has been run very successfully at Yale since 1993. Fractal geometry presents these students with a branch of mathematics that is recent, is visual, is computer-based, has real mathematical content (in contact with the works of eminent living mathematicians), and encourages student exploration and discovery. In addition, the tremendous range of applications of fractal geometry extends beyond science and engineering to arts and humanities. The applications outside science make the course most attractive to liberal arts students. Generally, students come out of this course with a feeling that mathematics is something they can approach, is alive and well, and is relevant to their own interests. Yet teaching this course is quite challenging. The very applications that make it so appealing are outside the training of most mathematicians. The purpose of the workshops is to survey fractal geometry and some applications in detail sufficient to enable other teachers to incorporate this material in their own courses. This lesson planning will be aided by a support infrastructure. These ideas will be spread to a wider area through other outreach activites, including establishing similar workshops at satellite sites and producing a videotape illustrating these courses. In addition, the proposers have prepared a webpage http://classes.yale.edu/math190a/Fractals/Welcome.html to support the workshops and to be a resource for the participants in their courses. The proposers' main goal is to build on what has already been achieved. Specifically, (i) to refine these workshops, draw participants from a larger area, and establish a support infrastructure, (ii) to expand and elaborate the above-mentioned website for use as the basis for Distance Learning courses on fractal geometry, (iii) to develop and grow another website that emphasizes the uses of fractals and extends the brief "Panorama" chapter of the forthcoming book "Fractals, Graphics, and Mathematics Education," MAA 2002. A preliminary version of this site already is online at http://classes.yale.edu/math190a/Fractals/Panorama/Welcome.html (iv) to prepare a lab manual of simple experiments and classroom activities, illustrating basic concepts of fractal geometry, and (v) to develop an outreach network for growing these workshops at other locations and disseminating these ideas through other media, including a videotape.