9660861 Jackiw This Small Business Innovation Research Phase I project builds on the success of The Geometer's Sketchpad, a piece of educational software that has had an important impact on the teaching and learning of mathematics in secondary schools. The research will prototype a next generation of this software--3-D Sketchpad--an integrated exploratory environment for creating, analyzing, and investigating three- and higher-dimensional mathematics. The Geometer's Sketchpad allows users to carry out geometric constructions using standard 2-D tools and transformations (Euclid's compass and straightedge tools augmented by reflection, rotation, and dilation). At any time, users may drag one or more objects in the sketch using the computer's mouse, and all of the other objects will dynamically adjust their position and size to maintain the constructed relationships. This simple idea has profound implications in the teaching and learning of mathematics. Generalized to three dimensions, the revolution in geometry education brought about by Sketchpad has the opportunity to broaden the geometry curriculum and to extend its relevance to other areas in mathematics and science. The objectives of this Phase I research project are to design and prototype critical elements of 3D Sketchpad and to describe and prototype the support materials that will ease its introduction into classrooms. The Geometer's Sketchpad has enjoyed substantial commercial success. If the proposed research meets its goals, the resulting software and support materials will have even greater application in middle schools, secondary schools, and colleges.
