SBIR Phase I: A transformative gesture-based application for learning and doing mathematics

This SBIR Phase I Project researches a new category of interactive math software, and develops a gesture-based mathematical application for doing symbolic derivations. The project targets a broad audience consisting of students, educators, scientists, and engineers. The application provides a novel, touch-based user interface allowing for an unprecedented connection between the user and mathematics. Research will focus on developing an application that is structured from the ground-up around how people actually learn and do mathematics. The project develops an application environment for discovery-style learning of basic math that increases retention by pairing motor memory with mathematical operations. It is scalable to accommodate advanced math for scientists and engineers, and structured around the way professionals do analytic derivations with pen-and-paper. The project's larger societal impact is to show students that mathematics is an interactive activity, and to expose the dynamical beauty of equations by bringing a human touch to math. For the professional, the application increases productivity, reduces human errors, and enhances collaboration. It creates a new market category closely related to the already thriving industry of computer algebra systems, and addresses a market need for a mathematical tool lying in the empty space between pen-and-paper and existing computer algebra systems. The emergence of modern touch-based devices such as tablets and smart phones paves the way for an entire new category of interactive math software for symbolic manipulation. By pairing gestures to mathematical operations the need for the traditional syntax-heavy command-line interface can be fully avoided. The new interface retains many of the calculation advantages of existing computer algebra system, while giving users the step-by-step control to finesse a derivation as they would with pen and paper. Focusing on elementary, stepwise algorithms the core math engine can be lightweight and fast. This not only ensures that the interactive interface is responsive, but also allows the application to be sold at an extremely competitive price-point. While eliminating frivolous human errors, the math application also turns learning mathematics into dynamic and interactive play. The goal of Phase I consists of developing a proof-of-concept version programmed, using a modern game engine and taking full advantage of advanced graphics capabilities and cross-platform functionality. Care is taken to optimize the user interface allowing for rapid, yet intuitive, stepwise manipulation of equations. Research will focus on constructing a core math engine that is scalable, allowing for future integration of more advanced math functionality.