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

描述（由申请人提供）：该项目的总体目标是通过调整FluidMath来改善数学和科学教育，FluidMath是我们数学素描新概念的体现，适用于高中数学和科学课程。使用FluidMath，学生和教师可以使用配备手写笔的计算机（例如Tablet PC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使用户符号成为交互式动画，虚拟操作和动态图形。当看到早期的原型时，一组试点教师一致表示，FluidMath可以改变课堂上数学的呈现方式，并且在吸引学生注意力和加深学生理解方面都是至关重要的。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，学生通常很难掌握这些功能，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成功地证明了作为NSF STTR项目的一部分，本阶段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。这个过程将是部署FluidMath原型到一个选定的，一小群教师，然后剖析他们的使用场景，方法和代表性的例子。此外，这一过程将需要快速原型扩展到FluidMath，专门解决每个教师的课程和课堂工作流程的新兴功能需求。在第一阶段结束时，将在一所或两所学校进行受试者之间评估程序的试点测试，以衡量FluidMath的教育效果，在这些学校中，同一名教师将使用和不使用FluidMath教授不同的课程。该SBIR的第二阶段将建立在第一阶段的结果，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第一阶段的使用蓝图。项目叙述：本研究将有助于开发有效的数学和科学教育教学技术，并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.