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

这个SBIR第一阶段项目研究了一种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，用于进行符号推导。该项目面向由学生、教育工作者、科学家和工程师组成的广泛受众。该应用程序提供了一个新颖的、基于触摸的用户界面，允许用户与数学之间建立前所未有的联系。研究将专注于开发一种从头开始围绕人们实际如何学习和做数学而构建的应用程序。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配对来提高记忆力。它是可扩展的，以适应科学家和工程师的高级数学，并围绕专业人士用纸笔进行分析推导的方式进行构建。该项目更大的社会影响是向学生展示数学是一种互动活动，并通过将人性化的触觉带入数学来揭示方程的动态之美。对于专业人士来说，该应用程序可提高工作效率、减少人为错误并增强协作。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，并满足了市场对数学工具的需求，这些工具位于纸笔之间的空白地带和现有的计算机代数系统之间。平板电脑和智能手机等现代触摸式设备的出现，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，可以完全避免对传统语法繁重的命令行界面的需要。新的界面保留了现有计算机代数系统的许多计算优势，同时让用户能够像用笔和纸一样逐步控制推导。核心数学引擎专注于基本的、逐步的算法，可以是轻量级的、快速的。这不仅确保了交互界面的响应性，还允许应用程序以极具竞争力的价位出售。在消除无关紧要的人为错误的同时，数学应用程序还将学习数学变成了动态和互动的游戏。第一阶段的目标包括开发编程的概念验证版本，使用现代游戏引擎，并充分利用先进的图形功能和跨平台功能。注意优化用户界面，允许快速、直观、逐步地处理公式。研究将专注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.