Bridging the Vector Calculus Gap

弥补矢量微积分的差距

• 批准号: 0231032
• 负责人: Tevian Dray
• 金额: $ 21.7万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-04-15 至 2007-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0231032&HistoricalAwards=false
• 关键词: Bridging; Vector; Calculus; Gap; Bridging; Vector; Calculus; Gap

There is a "vector calculus gap" between the way vector calculus is usually taught by mathematicians and the way it is used by other scientists. This material is essential for physicists and many engineers due to its central role in the description of electricity and magnetism. The two basic underpinnings of this project are the use of geometric reasoning rather than algorithmic computation (a new emphasis for lectures) and the use of open-ended small group activities (a new emphasis for recitations). We believe that our major success so far has been the identification of geometric reasoning, using the vector differential, as the common theme underlying all of vector calculus. In the previous (Proof of Concept) phase of this project, we developed small group activities based on this approach, some intended for use in a vector calculus course, and some for use in upper division physics courses on related material. These activities have been used successfully by us and by others at several institutions. This (Full Development) project will "bottle" our success by providing materials and training in the use of these materials to other faculty. The developed Instructor's Guides contain information about this geometric approach to vector calculus, advice on using small group activities effectively, and tips on the individual activities. Enhancing students' geometric understanding of vector calculus will help to bridge the "vector calculus gap".

数学家通常教授矢量演算的方式与其他科学家使用的方式之间存在“矢量计算差距”。 由于其在电力和磁性描述中的核心作用，该材料对于物理学家和许多工程师至关重要。 该项目的两个基本基础是使用几何推理而不是算法计算（讲座的新重点）和使用开放式的小组活动（对朗诵的新重点）。 我们认为，到目前为止，我们的主要成功是使用向量差异的几何推理的识别，是所有向量计算的共同主题。 在该项目的上一个（概念验证）阶段中，我们基于这种方法开发了小组活动，一些旨在用于矢量微积分课程，有些用于相关材料的上层物理学课程。 这些活动已被我们和其他机构的其他人成功使用。 这个（完整的开发）项目将通过向其他教师提供这些材料的材料和培训来“瓶装”我们的成功。 开发的讲师的指南包含有关这种几何方法的信息，以实现矢量微积分，有效地使用小组活动的建议以及有关个人活动的提示。 增强学生对矢量计算的几何理解将有助于弥合“向量计算差距”。