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

本SBIR一期项目研究了一类新的交互式数学软件，并开发了一个基于手势的数学应用程序来进行符号推导。该项目的目标受众广泛，包括学生、教育工作者、科学家和工程师。该应用程序提供了一个新颖的，基于触摸的用户界面，允许用户和数学之间前所未有的连接。研究将集中于开发一种应用程序，该应用程序将围绕人们如何实际学习和做数学而从头开始构建。该项目为基础数学的发现式学习开发了一个应用环境，通过将运动记忆与数学运算相结合来提高记忆力。它是可扩展的，以适应科学家和工程师的高级数学，并围绕专业人员用笔和纸进行分析推导的方式构建。该项目更大的社会影响是向学生展示数学是一项互动活动，并通过将人情味引入数学来揭示方程的动态之美。对于专业人员来说，应用程序提高了工作效率，减少了人为错误，并增强了协作。它创造了一个新的市场类别，与已经蓬勃发展的计算机代数系统行业密切相关，并解决了市场对纸笔和现有计算机代数系统之间空白地带的数学工具的需求。平板电脑和智能手机等现代触控设备的出现，为符号操作的全新交互式数学软件类别铺平了道路。通过将手势与数学运算配对，可以完全避免使用传统的语法繁重的命令行界面。新的界面保留了现有计算机代数系统的许多计算优势，同时让用户一步一步地控制推导，就像他们用笔和纸一样。专注于基本的逐步算法，核心数学引擎可以是轻量级和快速的。这不仅确保了交互界面的响应性，而且还允许应用程序以极具竞争力的价格出售。在消除无谓的人为错误的同时，数学应用程序也把学习数学变成了动态和互动的游戏。第一阶段的目标是开发一个概念验证版本，使用现代游戏引擎，充分利用先进的图像功能和跨平台功能。注意优化用户界面，允许快速，直观，逐步操作方程。研究将集中于构建一个可扩展的核心数学引擎，允许未来集成更高级的数学功能。

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.