Bridging the Vector Calculus Gap

点击翻译按钮获取中文摘要

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".