Full Development of Visualization Tools for 3D

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Mathematical Sciences (21). This project is developing a "kit" of plastic manipulatives to make three-dimensional reference frames that support construction, study, and experimentation with three-dimensional mathematical objects. Components would include plastic rods to represent vectors, marbles to represent points, and pipe cleaners to represent curves. The investigators see these physical tools as enhancing students' ability to visualize concepts relating to points, surfaces, planes, curves, contours, and vectors in three dimensions. For example, when introducing students multivariable functions, manipulation of these physical objects can prove more effective than a projection of three dimensions onto a two dimensional screen. The project is also building on the use of prototypes of these manipulatives in a precalculus course for engineers that introduced functions of two variables in precalculus. An Advisory Board of faculty from a diverse set of institutions including a state-supported research institution, a private four-year college, a community college, and a secondary school is helping the PI and colleagues to perfect the design of these tools and to produce drafts for accompanying manuals to help instructors of multivariable calculus and algebra use the kit.