Advanced tools and appropriate activities for thinking visually and experimentally in mathematics will be designed and will be used to demonstrate how such an environment can 1) dramatically change how students pose, explore, and solve problems, and 2) make accessible more complex and varied problems than students can handle in the traditional symbolic world of classroom mathematics. This project will: o select topics in traditional and contemporary mathematics that lend themselves to visual approaches (including but not restricted to topics arising naturally from the study of fractal forms), and appropriately related science content; o investigate how visually-based options for problem-posing, reasoning ("visual proofs"), and mathematical research in selected domains can result in fundamental changes in students' active engagement in and positive perception of mathematics; o identify the components and features of a learning environment using interactive computer graphics tools and supporting teaching materials, that will best support and enhance students' investigations of the selected mathematical domains; o give insight into the mathematical capabilities of 7th through 12th graders when they are availed of powerful, interactive graphics tools with which to experiment, explore, and tinker with mathematical objects and processes concretely and to reason visually; and o show that visual/experimental approaches to mathematics generalize well enough over a variety of domains to form the basis for realistic future curriculum development.
