Web is rapidly becoming the standard vehicle for delivering instruction nowadays. In formulating an effective web-based instruction, some of necessary ingredients are user-interface design, bandwidth efficiency and robust multimedia standard, just to name a few. One software development tool that stands out qualifying all of these attributes is Flash, a ubiquitous web standard by Macromedia. Although there still is a strong tendency among the developers to use Java Applets in the web-based mathematics instruction, Flash enjoys the advantages over Java Applet in many respects as the Flash-based mathlets presented in this article demonstrate.
This article contains a collection of Flash movies ready for use in a classroom, displaying various Flash-based instructional models on Mathematics and Mathematica learning. They range from a movie-type animation to the sophisticated programmatic approach. The animation type consisting of a sequence of pictures as in a cartoon is most appropriate when the target mathematical concept is inherently in a visual form, as found in such a subject as Geometry, Calculus, and Linear Algebra. Another visual approach is Mathematica user-interface simulation that simply explains in a visual manner a sequence of Mathematica commands to accomplish a task. This is ideal in a situation where both visualization and hands-on approach are called for.
One important type in visualizing the mathematical concepts is visual representation, where an abstract mathematical concept takes a visual form conjured up by the author.
Among many types of visual approach,the most notable and promising one would be the programmatic approach, where Mathematica kernel is harnessed from within a Flash movie. A rich set of Flash functionality can be coupled with intelligent capability of Mathematica to yield a synergy of a computer-assisted instruction beneficial for the students, not just for the authors.
Each type of visualization discussed has its own unique functionality and characteristic and the effective instruction is the one that employs them in an eclectic manner considering the given instructional setting.
This article was written with the grant for the Object-oriented Courseware Development System project from Korea Research Foundation. The author also wishes to thank Wolfram Research Inc. for its help in this research.