Full Development of Visualization Tools for 3D

数学科学（21）.该项目正在开发一个塑料操作工具“套件”，用于制作三维参考框架，以支持三维数学对象的构建，研究和实验。组件将包括塑料杆来表示矢量，大理石来表示点，管道清洁器来表示曲线。研究人员认为这些物理工具可以提高学生在三维空间中将点、面、平面、曲线、轮廓和向量等概念可视化的能力。例如，当向学生介绍多变量函数时，这些物理对象的操作可以证明比将三维投影到二维屏幕上更有效。该项目还建立在使用原型的这些操纵在precalculus课程的工程师，介绍了功能的两个变量的precalculus。来自不同机构的教师顾问委员会，包括国家支持的研究机构，私立四年制学院，社区学院和中学，正在帮助PI和同事完善这些工具的设计，并制作随附手册的草稿，以帮助多变量微积分和代数的教师使用该工具包。

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.