Mathematical Sketching: Adapting mathematical pen-computing for broad-scale class

描述（由申请人提供）：本项目的总体目标是通过将FluidMath（我们新颖的数学素描概念的体现）应用于高中数学和科学课程来改善数学和科学教育。使用FluidMath，学生和教师可以使用配备手写笔的计算机（例如平板电脑或电子白板）自然地输入符号数学表达式和支持图表。通过自动识别这些手写符号并推断相关关联，FluidMath使用户符号以交互式动画、虚拟操作和动态图形的形式活跃起来。当看到早期的原型时，一个由教师组成的试点小组一致表示，他们认为FluidMath可以改变数学在课堂上的呈现方式，在吸引学生注意力和加深学生理解方面可能起到关键作用。特别是，他们观察到FluidMath提供了快速有效地探索2D和3D功能的潜力，这些功能学生通常难以掌握，他们认为现有技术无法实现。由于FluidMath的底层识别技术的可行性已经成功地作为NSF STTR项目的一部分进行了演示，因此第一阶段SBIR的研究挑战是为教师如何使用FluidMath来实现他们的课堂愿景制定详细的蓝图。这个过程将是将FluidMath原型部署到选定的一小群教师中，然后剖析他们的使用场景、方法和代表性示例。此外，这个过程将需要快速原型扩展到FluidMath，专门解决每个教师对他们的课程和课堂工作流程的新功能需求。在第一阶段结束时，将在一到两所学校进行科目间评估程序的试点测试，以衡量FluidMath的教育效果。在这些测试中，同一名教师将使用或不使用FluidMath来教授不同的课程。第二阶段的SBIR将建立在第一阶段的结果上，与更广泛的教师群体一起对FluidMath进行扩展的教学评估。这些教师可能会依赖于第一阶段的使用蓝图。项目叙述：在这个项目中进行的研究将有助于为数学和科学教育开发有效的教学技术，并将为探索数学素描概念如何改善学习过程提供基础。

DESCRIPTION (provided by applicant): The overarching goal of this project is to improve math and science education by adapting FluidMath, an embodiment of our novel concept of mathematical sketching, for high school math and science curricula. Using FluidMath, students and teachers can naturally enter symbolic mathematics expressions and supporting diagrams using a stylus-equipped computer (e.g. Tablet PC or electronic whiteboard). By automatically recognizing these handwritten notations and inferring relevant associations, FluidMath makes user notations come alive as interactive animations, virtual manipulatives, and dynamic graphs. When presented with early prototypes, a pilot group of teachers uniformly professed to a vision that FluidMath could transform the way mathematics is presented in their classrooms, and could be pivotal in both engaging student attention and deepening student comprehension. In particular, they observed that FluidMath offered a potential for rapidly and effectively exploring 2D and 3D functions, which students often have difficulty grasping, that they did not feel was attainable with existing technologies. Since the feasibility of FluidMath's underlying recognition technology has been successfully demonstrated as part of an NSF STTR project, the research challenge of this Phase I SBIR is to develop a detailed blueprint for how teachers can use FluidMath to achieve their classroom visions. The process will be to deploy FluidMath prototypes to a select, small group of teachers and then to dissect their usage scenarios, methodologies, and representative examples. Additionally, this process will require rapidly prototyping extensions to FluidMath that specifically address each teacher's emerging functional requirements for their curriculum and classroom workflow. Toward the end of Phase I, pilot tests of between-subjects evaluation procedures for gauging the educational efficacy of FluidMath will be conducted at one or two schools in which the same instructor will teach different classes with and without using FluidMath. Phase II of this SBIR will build upon the Phase I results to perform an expanded didactic evaluation of FluidMath with a wider group of teachers. These teachers will likely rely on the usage blueprints derived from Phase I. Project Narrative: The research conducted in this project will help to develop effective instructional technologies for mathematics and science education and will provide a foundation for exploring how the mathematical sketching concept can improve the learning process.