Second, if there is cognitive load devoted to understanding the words, that is energy not devoted to understanding the concepts. Friends in those classes in college spent extra time outside of class with tutors and study groups than those with good teachers because they knew the tests didn't change.

Third, the lack of variance means the teachers don't make a difference in general. Perhaps there is a greater question to ask there.

Another problem that you mention, and that was also very real, was that some of the teachers literally could not be understood. I use 'literally' literally -- I took an automata theory class from a guy that seemed to have been speaking his own native tongue and not English. That class was an absolute delight, as you might imagine. Most of my teachers had strong accents, and I could deal with it, but some were incomprehensible and had no business teaching in am American university.

Acting like these are problems that don't exist, and that complaints are just small-mindedness or excuse-making, is just as bad as going the other way and throwing a fit when you have to 'endure' an unfamiliar accent. Everything's a matter of degree.

Are there? We thought the same thing about our "worst" professors/TAs. Yet students ability to differentiate/integrate seemed unaffected.

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).

In the former case it suggests teacher quality don't matter much. In the latter case it suggests teachers are completely unnecessary and our usage of them should be reduced. This experiment at MIT is promising:

http://phys.org/news/2014-09-online-classes.html

...there's more to being a good or bad teacher than the numeric outcome of the class, which ought to be a familiar argument by this time.

This is a familiar platitude. I've never seen an actual argument that didn't appeal to invisible dragons.

http://www.godlessgeeks.com/LINKS/Dragon.htm

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.

These two claims contradict each other.

If you want to argue that the exams couldn't measure anything at all, go ahead. You can find examples here: http://cims.nyu.edu/~stucchio/classes/fall2008/index.html

I'll submit that the intellectual world is larger than integration and differentiation.

Calculus 1 and 2 are not. I don't see a reason why the non-simple problems you describe can't be put on an exam, apart from the fact that it's not part of Calc 1. I've also never observed a group of students from any professor who could reliably do it, so I suspect that your "order of magnitude" better teachers are a rarity.

How's that for an invisible dragon?

Are you seriously asserting that outcomes beyond reproduction are not measurable?

The university I finally chose did pay competitively to the field, most loved teaching and their research. Yes there were still a few with an accent which pronounced my name wrong, but they've had at least some speech therapy on the side to get better.

I think that foreign professors that teach should take part in a speech therapy program for the benefit of the university students. It truly is a cognitive load, and I already have difficulty in hearing and comprehending words as it is without any particular accent.

a year or so ago I went to a research conference, with a lot of people from Europe presenting. Generally, everyone there had a good handle on the language (as you might when presenting a bunch of stuff in English all the time), but about halfway through an American came on stage to present her work.

The instant she started talking I realised that listening to her was so much easier than listening to anyone else talk. I "confirmed" this from other talks by americans compared to european talks.

Not the most scientific thing but generally I think there is extra work happening in the brain when listening to a foreigner talk, and that it can be the point that makes something hard to deal with.

[1] I mean this with as little animosity as possible. Having the courage to learn a foreign language and then present in it is extremely commendable.