CAREER: Mathematical Sketching: Pen-based Tools for Conceptual Understanding in Mathematics and Physics

职业：数学素描：用于数学和物理概念理解的笔式工具

• 批准号: 0845921
• 负责人: Joseph LaViola
• 金额: $ 45.98万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-05-01 至 2016-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0845921&HistoricalAwards=false
• 关键词: CAREER; Mathematical; Sketching; Pen; based

Pen-based computing has the potential to make a significant improvement in the education of our students in STEM disciplines so as to produce a more skilled technical workforce able to compete in the new global economy. Mathematical sketching, a pen-based interaction paradigm that is providing a new approach to STEM education, is the process of making and exploring dynamic illustrations by associating handwritten mathematics with free-form diagrams. The proposed research will develop new mathematical sketching tools to improve student learning in STEM. High level semantic recognition techniques for understanding mathematical sketches (the combination of handwritten problem description, mathematical expressions, and drawings) will be explored to ensure proper interactive feedback, facilitation of correct cognitive models, and the generation of the most appropriate dynamic visualizations for a given problem. In addition, these techniques will, in part, be used to develop strategies in inferential statics and dynamics, the process of finding appropriate animations when users do not directly specify motion equations in the problem solving process. Given the reliance on recognition-based interaction in mathematical sketching, usability studies will examine how users are affected by recognition feedback and accuracy levels. These studies will provide useful guidelines for ensuring that the mathematical sketching interface is usable by both teacher and student. Two educational studies will also explore how mathematical sketching affects teaching and learning. This work will advance the state-of-the-art in pen-based UIs through the development of techniques and exploration of user interface design issues for enriching mathematical sketching. Broader Impact: This proposal links research in pen-based UIs with STEM education, a critical application area. Thus, the work has the potential to reach thousands of students each year. The PI has the opportunity to work on this research in conjunction with the University of Central Florida?s EXCEL Program, an NSF STEP-funded project that helps students succeed in math and science during the first two years of college, where the mathematical sketching paradigm is directly applicable. The PI will give demonstrations and lectures through the Florida High Tech Corridor Council techCAMP program to bring mathematical sketching to teachers and students in African American and Hispanic high schools. The proposed research will be integrated into a graduate-level course on pen-based UIs, thus enhancing the education of tomorrow?s pen-based UI designers and researchers. Finally, undergraduate courses will be taught on human computer interaction (HCI) and design of interactive systems that, together with the graduate course, will be an educational foundation for HCI at UCF.

笔式计算有可能在STEM学科的学生教育方面取得重大进展，从而培养出能够在新的全球经济中竞争的更熟练的技术劳动力。数学素描是一种基于笔的交互模式，为STEM教育提供了一种新的方法，它是通过将手写数学与自由形式的图表相关联来制作和探索动态插图的过程。拟议的研究将开发新的数学素描工具，以提高学生在STEM的学习。高层次的语义识别技术理解数学草图（手写的问题描述，数学表达式和图纸的组合）将被探索，以确保适当的交互式反馈，促进正确的认知模型，并为给定的问题生成最合适的动态可视化。此外，这些技术将在一定程度上用于开发静态和动态推理策略，即当用户在解决问题的过程中不直接指定运动方程时，找到适当动画的过程。鉴于数学素描依赖于基于认知的交互，可用性研究将研究用户如何受到识别反馈和准确性水平的影响。这些研究将提供有用的指导方针，以确保数学素描接口是可用的教师和学生。两项教育研究还将探讨数学素描如何影响教学和学习。 这项工作将通过开发技术和探索用户界面设计问题来丰富数学草图，从而推进基于笔的用户界面的最新技术。 更广泛的影响：该提案将笔式UI的研究与STEM教育联系起来，这是一个关键的应用领域。因此，这项工作每年有可能接触到数千名学生。 PI有机会与中央佛罗里达大学合作进行这项研究吗？的EXCEL计划，一个NSF STEP资助的项目，帮助学生在大学的前两年在数学和科学方面取得成功，其中数学素描范式直接适用。PI将通过佛罗里达高科技走廊理事会techCAMP计划进行演示和讲座，为非洲裔美国人和西班牙裔高中的教师和学生带来数学素描。拟议的研究将被整合到一个研究生水平的课程笔为基础的用户界面，从而提高教育的明天？的笔式UI设计师和研究人员。最后，本科课程将教授人机交互（HCI）和交互系统的设计，与研究生课程一起，将成为UCF HCI的教育基础。