SBIR Phase I: A Standards-based High School Symbolic Geometry System

This Small Business Innovation Research Phase I research project will investigate the feasibility of developing an interactive symbolic geometry system that integrates algebra and geometry and focuses on high school mathematics. A general mathematical equation involving several variables is interpreted as expressing a relationship among the variables. Which variables are considered as independent and which are dependent is not always clear and, even with a given geometry, there may be several possibilities. To develop a software system that adequately handles such sophistication is a non-trivial challenge. The project addresses the extension of real variable algebra to real-valued functions of real variables where those functions are arbitrary, not an instance of such a function. This goal poses an almost self-contradictory, challenge. Since the system will be visual, such functions will be displayed and hence some specific function must exist. However, to the user, they must seem arbitrary. The goal is the visual integration of algebra and geometry. The National Council of Teachers in Mathematics (NCTM) Standards include the visualization of three-dimensional figures and the mapping between certain three-dimensional surfaces and their two-dimensional unfolding on the plane. The project addresses user interface and algorithms for 3D symbolic geometry. The American Institutes for Research have recently re-examined data from major studies (TIMSS and PISA) and determined that the performance of US students, relative to their International peers, is worse than had previously been thought. In particular, US student performed poorly in geometry. The National Mathematics Advisory Panel stresses the need for 'solid math skills' not just for those students that are college bound but also for those going directly into the workforce. Additionally, this panel has also placed a special focus on the learning of algebra. This research project addresses these societal issues, by focusing on algebra and geometry, and linkages between the two, which a central theme of the NCTM standards. The integration of technology itself within the learning of mathematics is one of the six key principles of school mathematics. The research 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.