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Comment from S. Pollock (CU Boulder, visiting OSU and teaching Paradigm “Vector Fields), Nov 2009:

Did this activity Lecture #7, same day that we had “derived” Biot-Savart from the definition of the vector potential (which in turn was obtained in direct analogy to the integral formula for the scalar electric potential). We had roughly 25 minutes for this activity, and I simply asked them to find the B field at all points. Since we had just worked on the vector potential activity (the two previous classes) they understood their task and immediately got to work. Most groups now zipped past a lot of the old issues (e.g. they figured out how to write down $I dl'$, and started finding $\hat\phi'$ in Cartesian coordinates, and were working on the required cross product in the numerator, within minutes. I was impressed with their performance, this was evidence to me that the previous activity had been effective. By the end of 25 minutes, most groups had worked out the cross product, and were thinking about how to do the various integrals. They were not yet invoking symmetry arguments on their own (and were sometimes struggling with related issues to that, i.e. ways to simplify the integrals before evaluating them), and this is what I took up in the whole-class discussion that followed.