The "Symmetry, Patterns and Designs" seminar was intended to introduce the Fellows to new areas of mathematics with classroom appeal as well as to the potential uses of computers in the classroom. Although most of the Fellows were mathematics teachers, there were also teachers from art, social studies and computer science.
The seminar grew out of a Junior/Senior level course on symmetry and design that I have taught in the Department of Art at UH. Just as in the Art Department class, I emphasized geometry, visualization and a “hands on” approach to symmetry and patterns rather than a symbolic algebraic approach. (I find most of the “college algebra” courses and associated syllabi painfully boring and unmotivated).
Part of the seminar involved Fellows using some software I have developed, Prism, to design and color various planar symmetric patterns. The patterns produced by the seminar participants are displayed on my seminar web page (see the URL http://www.math.uh.edu/~mike/PATTERNS/). I regarded this part of the seminar as a vital way of building confidence and showing the possibilities for creativity in a Mathematics (or Art, Social Studies) class -- Mathematicians can have (productive) fun!
A side benefit of the time spent in the computer lab was that Prism software uses methods based on chaos and fractals and this led to possibilities for curriculum units based on fractals and chaos. In addition, Fellows were also encouraged to experiment with commercial software packages such as Kevin Lee's tessellation programs and drawing packages (such as software produced by Adobe).
I understand that in other teachers’ institutes, there have been relatively few seminars given in the past on mathematics -- especially pure (as opposed to applied) mathematics. Unlike, perhaps, seminars in the humanities and even some of the sciences, I believe that the communication of new ideas and concepts is basic and essential to a seminar in mathematics. It is not so easy to hold ‘opinions’ in the field of mathematics and this must affect the way the seminar is presented. I believe that this communication can be done in an interesting and stimulating way and, at the same time, a core of basic mathematical ideas can be communicated both to the Fellows and, most importantly, to their students in the high schools and middle schools.
As it turned out, in spite of acute scheduling and time-tabling difficulties the first time around, I was delighted with efforts of the Fellows in my seminar. I am sure that these curriculum units will be of use to other teachers, and a benefit to their students as well. Bravo! I am looking forward to my next seminar.