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

基于笔的计算有可能大大改善我们学生在STEM学科方面的教育，从而培养出一支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范式，它为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结合来制作和探索动态插图的过程。这项拟议的研究将开发新的数学素描工具，以改善学生在STEM中的学习。将探索理解数学草图的高级语义识别技术(手写问题描述、数学表达式和绘图的组合)，以确保适当的交互反馈，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推理静力学和动力学的策略，当用户在解决问题的过程中没有直接指定运动方程时，找到合适的动画的过程。鉴于数学草图对基于识别的交互的依赖，可用性研究将研究用户如何受到识别反馈和准确度水平的影响。这些研究将提供有用的指导方针，以确保数学素描界面可供教师和学生使用。两项教育研究也将探索数学素描如何影响教与学。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，从而推动笔式用户界面的发展。更广泛的影响：这项建议将笔式用户界面的研究与STEM教育联系起来，STEM教育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有机会与中佛罗里达大学S EXCEL项目合作进行这项研究，该项目是美国国家科学基金会的一个分步资助的项目，帮助学生在大学的头两年在数学和科学方面取得成功，在那里数学素描范例直接适用。PI将通过佛罗里达州高科技走廊委员会techCAMP计划进行演示和演讲，将数学草图带给非裔美国人和西班牙裔高中的教师和学生。拟议的研究将整合到笔式用户界面的研究生课程中，从而加强对未来-S笔式用户界面设计师和研究人员的教育。最后，本科课程将讲授人机交互(HCI)和交互系统的设计，这些课程与研究生课程一起，将成为UCF人机交互的教育基础。

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.