Teaching Mathematical Thinking through Space Exploration

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* 9550493 Feurzeig The goal of this three-year project is to develop four curriculum units to replace or supplement current classroom materials on key topics in algebra, geometry, calculus, and topology. These units will introduce some of the most fundamental and central ideals of modern mathematical thinking to a broad population of high-school students and teachers through a series of highly graphic and interactive computer-assisted explorations, experiments and games. The first three units can be used separately within the standard algebra, geometry or calculus courses. Taken as a whole, they prepare the way for a series of exploratory journeys in the world of one-, two-, and three-dimensional space forms, which comprise the specific subject matter of the last unit. As another alternative, units can be joined to provide a one-semester course, either in place of pre-calculus or as an optional fourth-year college preparatory course. The four units will support from 10 to 18 weeks of instruction. The first year of the project will focus on development and informal trials of the activities and supporting software; the second year on continued materials development, staff development, classroom implementation, pilot trials, and formative evaluation; the third year on teacher development, field testing, evaluation, and dissemination. Local high schools will participate in the pilot trials and field tests. The research, development, and teaching will be carried out by an interdisciplinary team of mathematicians and mathematics education consultants with expertise in curriculum development and evaluation. The project team will work closely with the developers of ARISE, the NSF Comprehensive high-school curriculum project underway by the Consortium for Mathematics and its Applications (COMAP), to publish project materials in the widely distributed series, High-school Mathematics and its Applications (HiMAP.) ***