About the Course

This course, a directed independent study for the Center for Technology and Teacher Education at the University of Virginia, is designed to explore potential educational uses of Macromedia Flash, especially as it may relate to mathematics and mathematical visualization.

Macromedia Flash has developed from a simple animation tool into a development environment for very advanced and robust internet applications. Most powerfully, it is used for the design of interfaces for data-driven and dynamic web applications; most commonly, it is used for demonstrative multimedia animations and slide presentations; less commonly, though no less usefully, it may also be used to create freestanding applications for distribution via CD or the web. (This may be particularly useful for situations in which a teacher gets resources from the web but cannot count on connectivity under all circumstances.)

Both the Flash "movie clips" which form the facades for innumerable web sites and the Flash development environment in which they are built can be quite interesting in their own right. To begin with, certain mathematical topics, especially those related to computation, may be very fully represented by the algebraic and geometric skills that development requires. So both the exploration of the program and the design of web materials (representing ideas of widely varying levels of complexity), may in themselves lead to new and highly personalized understandings of patterns, data, data representation, and mathematical utility for students and teachers alike.

Some mathematical topics lend themselves easily and naturally to computers and computer graphics -- especially trigonometry and, somewhat by extension, vectors. (For purposes of scalability and compression, Macromedia's Flash group pioneered the widespread use of vector graphics on the web.) These topics alone have much potential. There are, furthermore, many other topics which may be explored in the Flash development environment and/or explained with multimedia: motion over time (velocity); discrete arrangements of elements (both in graphics and in the abstract, as in object-oriented programming); and elements of number theory related to computation.

Students in the course are Ph.D. candidates in mathematics education at the University of Virginia.