Both the mathematics and physics approaches have their advantages. As already stated, themathematics approach adapts more readily to generic situations without much symmetry,whereas the physics approach excels in situations with lots of symmetry. We do not wishto see one approach replaced by the other. But the current situation is that the approachestend to be taught without overlap by different departments; this “vector calculus gap” mustbe eliminated. We do note with pleasure that some “reform” calculus texts do indeed emphasize the geometric interpretation; this is a step in the right direction. We would add to this a treat-ment of elementary orthogonal bases, specifically those adapted to spherical and cylindricalcoordinates. In any case, we strongly advocate that any introductory course in vector calculus clearly indicate the existence of both approaches, and the types of problems each is suitable to.How much detail in each case should depend on local circumstances, but this will typicallyrequire incorporating supplemental material which is not in existing textbooks.