NSF Proposal Summary DUE-0321032
4/03–3/07; $217,039

Tevian Dray & Corinne A. Manogue

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 some engineers due to its central role in the description of electricity and magnetism.

The two basic underpinnings of this proposal 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 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 others, at several institutions.

It is the goal of this Full Development proposal to “bottle” our success by training other faculty in the use of our materials. We intend to offer workshops for those using these materials, and to write an Instructor's Guide containing information about this geometric approach to vector calculus, advice on using small group activities effectively, and tips on the individual activities. Four institutions have so far agreed to beta test these materials.

Enhancing students' geometric understanding of vector calculus will help to bridge the “vector calculus gap”.

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