I sat in an introductory physics course at my university and the professor was explaining Gauss's Law. While I was in there I noticed he was incorrectly teaching the mathematics of surface integrals. For example: The professor stated that for a sphere centered at the origin, the area element dA was found as follows. Since, for a sphere the surface area is A=4πr2 it follows that dA=8πrdr. He gave similar arguments for cylindrical and other symmetries. So far, this has not affected the examples since most of them have symmetries which have the E field constant on the surfaces in question so that it reduces to just an integral over dA. Normally, I don't mind correcting a professor if there is a simple error, but this shows there is a severe lack of fundamental understanding of the math required. Never was there mention of parameterizing the surface and obtaining the correct area element by means of the vector product of partial derivatives. Even worse, the fact that he is integrating over r on the surface of the sphere is bothersome. I feel awkward correcting him because this is such a fundamental requirement for surface integrals. I don't know what I should do.