Are there? We thought the same thing about our "worst" professors/TAs. Yet students ability to differentiate/integrate seemed unaffected. That's a data point w

Are there? We thought the same thing about our "worst" professors/TAs. Yet students ability to differentiate/integrate seemed unaffected. That's a data point worth paying attention to. However, I'll submit that the intellectual world is larger than integration and differentiation. I'll further suggest that there is a world of difference between understanding enough calculus to integrate and differentiate, and understanding calculus in sufficient depth to apply its principles to problems and in settings that do not afford simple template matching -- I wrote an integration/differentiation package in Scheme my freshman year, but would not claim that it understands calculus. This is one of the ways in which a good teacher and a bad teacher can vary by an order of magnitude. You might counter that your tests were so rigorous that any such differences would fall out in the data. Perhaps you have achieved this apex of testing methodology, but I'm suspicious. Now this suggests one of two things. First, that there really are no "worst" professors/TAs. Second, that students have the ability to replace a $3-4,000 class with reading a $50-150 book (+ Khan academy, etc). Or that your measurements are not sufficiently granular, as described above. This is a familiar platitude. I've never seen an actual argument that didn't appeal to invisible dragons. Many parents produce children who survive long enough to successfully reproduce themselves. By one of the most fundamental biological heuristics that's a rip-roaring success, and yet presumably you would aspire to more with your own children. How's that for an invisible dragon? EDIT: figured out how to make quotes italicized.