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

数学草图：将数学笔式计算应用于大范围课堂

• 批准号: 7406904
• 负责人: Donald P Carney
• 金额: $ 10万
• 依托单位: FLUIDITY SOFTWARE, INC.
• 依托单位国家: 美国
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-04-10 至 2009-04-09
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7406904
• 关键词: Address; Americas; Attention; Chairperson; Class; Complex; Comprehension; Computer software; Computers; Data Analyses; Education; Educational Curriculum; Educational process of instructing; Electronics; Evaluation; Evaluation Reports; Family; Feasibility Studies; Federal Government; Feedback; Floor; Foundations; Goals; Grant; Graph; Hand; Handwriting; Instructional Technology; Laboratories; Learning; Marketing; Mathematics; Methodology; Paper; Phase; Phase I Clinical Trials; Physics; Pilot Projects; Preparation; Procedures; Process; Research; Research Project Grants; Resources; Schedule; Schools; Science; Small Business Funding Mechanisms; Small Business Innovation Research Grant; Small Business Technology Transfer Research; Solutions; Staging; Students; System; Tablets; Techniques; Technology; Testing; Time; TimeLine; Universities; Vision; Visualization software; Washington; Work; Writing; abstracting; animation; base; concept; design; fluidity; grasp; high school; improved; innovation; instructor; novel; prototype; science education; simulation; stem; teacher; tool; usability; virtual

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.

描述（由申请人提供）：该项目的总体目标是通过将 FluidMath（我们新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、虚拟操作和动态图表的形式变得生动起来。当看到早期的原型时，一组试点教师一致表示，FluidMath 可以改变数学在课堂上的呈现方式，并且可以在吸引学生注意力和加深学生理解方面发挥关键作用。特别是，他们观察到 FluidMath 提供了快速有效地探索 2D 和 3D 函数的潜力，而学生常常难以掌握这些函数，他们认为现有技术无法实现这些函数。由于 FluidMath 底层识别技术的可行性已作为 NSF STTR 项目的一部分得到成功论证，因此第一阶段 SBIR 的研究挑战是为教师如何使用 FluidMath 实现其课堂愿景制定详细的蓝图。该过程将向选定的一小群教师部署 FluidMath 原型，然后剖析他们的使用场景、方法和代表性示例。此外，此过程将需要快速对 FluidMath 进行原型扩展，专门满足每位教师对其课程和课堂工作流程的新功能要求。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，其中同一名教师将在使用和不使用 FluidMath 的情况下教授不同的课程。该 SBIR 的第二阶段将以第一阶段的结果为基础，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：该项目中进行的研究将有助于开发数学和科学教育的有效教学技术，并将为探索数学素描概念如何改善学习过程提供基础。