## 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.