SBIR Phase II: A Standards-Based High School Symbolic Geometry System

This Small Business Innovation Research (SBIR) Phase II project will develop an interactive symbolic geometry system that integrates algebra and geometry and focuses on high school mathematics. The absence of such a system has led to a technology gap in mathematics education between the geometry year in high school and the college level calculus sequence. The result of this project will be a software system along with learning materials which fills that gap. The National Council of Teachers of Mathematics (NCTM) standards include the visualization of three-dimensional figures and the mapping between certain three-dimensional surfaces and their two-dimensional unfolding or projection onto the plane. To address this, the project will create a three dimensional symbolic geometry system and in the process will break new ground both from an algorithmic and a user interface perspective. The creation of geometric models dependent on discrete but possibly indeterminate parameters, for example, a general n-gon, is an important pedagogic device for the study of the limits of geometrical figures. Such a facility poses new design and user interface challenges ranging from the definition of the general form of the dependence to the display of a geometrical figure with an indeterminate number of primitives. This Phase II project addresses the need for solid mathematics skills required for college-bound students and for those going directly into the workforce. Specifically, this project focuses on the learning of algebra, and its linkages with geometry. To date, no application exists that integrates algebra and geometry. The integration of technology itself within the learning of mathematics is one of the NCTM's six key principles of school mathematics. The project will incorporate geometrical constraints in addition to geometrical constructions and hence, unlike any other current educational system, directly address the workforce/professional requirements of a geometry system.