The participants started a rainy day 3 of the Math Forum Advanced Summer Institute in connections, and then on individual projects.
Following Dave's session, Bob Panoff demonstrated some the Shodor Foundation's work. Project Interactivate (http://www.shodor.org/interactivate/) explores fractals by iterating line deformations, providing a tool for teaching pattern recognition and self-similarity (http://www.shodor.org/interactivate/applets/). The Project Interactivate lessons are organized into three segments: "What?" asks questions to be investigated; "How?" explains the how to use the applet; and "Why?" develops other applications. In addition, there are lessons linked to the table of contents of several math texts (http://www.shodor.org/interactivate/toc.html). He began with a paper and pencil exercise, where participants drew a line with a simple "kink" in it and then successively replaced each segment with the same kink to the scale of that segment. Bob noted that this exercise becomes tedious quickly and thus defined the point where using applets becomes beneficial. In one example, Bob demonstrated three fractals, each of which differed only slightly from the other at the outset; when iterated, however, they resulted in very different images -- the perimeter of the first approaching infinite length but enclosing finite area, the second copying over itself, the last one increasingly space-filling. He drew qualitative parallels from these three illustrations of "sensitivity to initial conditions" to the regeneration of healthy skin, the growth of a benign tumor, and the spread of a malignant tumor, respectively. Bob requested feedback on the pages, particularly on how to expand and clarify the "What?" and "Why?" segments. The participants suggested adding information that links the explorations to real world uses (such as the three examples above), developing exercises that require more participation from the students (similar to Sketchpad), and organizing feedback with annotations so that others may view some participant results.
In the next session, Nicole and Tushar introduced displaying Mathematica, Maple, and Mathview notebooks on the Web (http://forum.swarthmore.edu/spimsow/). Users can rotate graphs and change equations to experiment with graphs already created. Of the three, Mathview, which requires a plug-in (http://www.maplesoft.com/www/mathview.html), is the least powerful, but also the least expensive and most interactive. To put a Maple notebook on web pages, generate the notebook in Maple and save it as an HTML file. Maple will then create three Maple HTML files and a graphics file, which must be uploaded through FTP. To see Mathematica on the web, download the application helper Math Reader (http://www.wolfram.com). Nicole and Tushar noted that with Maple and Mathematica notebooks, it is not possible to create an interactive environment. For more on implementing math software on the web, view their example notebooks (http://forum.swarthmore.edu/spimsow/notebooks.html), read their synopsis of comparisons (http://forum.swarthmore.edu/spimsow/synopsis.html), or e-mail them directly at <email@example.com> and <firstname.lastname@example.org>, respectively.