I am presently teaching phyllotaxis in my "discovering math" class. Phyllotaxis is the study of pattern formation in plants. The most striking and prevalent kind of patterns observed is configurations of spirals. Two families of spirals are usually observed, winding in oposite directions. The number of spirals in each of the families are very often a successor in the Fibonacci series. The class is structured as labs that I am developing on the web as I go (http://www.math.smith.edu/~phyllo/phyltutor.html), based on interractive JAVA applets written by a group of colleagues and students. We had written these programs originally to support our mathematical research on Phyllotaxis.