Having actually taught (well TAed)in the UC Berkely math department I can say that generations of both graduate students (who have most of the contact with students) and professors have struggled to the best of their ability to teach calculus in an engaging and interesting way to their students. Now research talent and teaching talent don't always come together but there were plenty of dedicated and talented teachers. Dr. Coward is basically claiming that he is so amazingly talented (or that not one of the multitude of intro calc teachers over the years was competent) that he single handedly does the impossible and rises head and shoulders above all these other teachers.

Even though he quotes from the letter from the math department disturbingly selectively I think he gives away what is really going on in that quote:

"They also reveal some significant differences between your practices and what has been typical in our department [...] I hope and expect that you will be able to align more with our standards for the remainder of this semester and during the next academic year."

Surprise surprise, the students like the guy who doesn't make them learn (those in 16A/B aren't continuing on in a technical field but only take the course to satisfy requirements and/or because their counselors stress the importance of having math on your transcript).

If this isn't suggestive enough consider his statistics: his classes have 400+ students enrolled but the supposedly equivalent class taught by a faculty member only has 100. If he isn't cherry picking an 8am lecture (in which case we should be even more distrustful) this difference is so drastic as to be extremely suspicious. My experience TAing these very courses was that students were quite willing to put up with a bad lecturer (or poor TA in my case) to have a nicer schedule (leave earlier, avoid trudging back and forth etc..) but they were very cogniscent of even minor differences in supposed ease of grading and subject matter.

Besides, anyone who rights an open letter like this while supposedly appealing a deciscion is an ass who would be a nightmare to work with. Even if you (unwisely) believe he was unjustly terminated delibrately impugning the motives and integrity of the people he supposedly wishes to remain colleagues with is just a super asshole move.

I've met great teachers who were very dedicated to improving mathematics education. Every one of them avoided self-aggrandizement and did their best to share their approaches and experience with other educators. The mathematics department at UC Berkeley would be ecstatic if someone figured out how to teach intro calc content in a way that invigorated the students. Hell, it's almost a holy grail their as generation after generation of grad students (and professors) burn themselves out against students whose experiences in highschool have created an instinctive dislike of mathematics and the unshakable belief that math is about formulas and procedures (meaning they instinctively panic if a problem requires creativity...which is sadly what makes math interesting and fun).

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Look, I have big issues with the way UC Berkeley (and most other universities) teach intro calculus courses. It's the 21st century and no one is served by forcing uninterested students to learn computational techniques by rote any computer mathematics system can easily accomplish. Either you are going to go into a technical discipline where having a conceptually grasp of integrals matters or you can just blindly plug them into a computer.

So give up making students memorize the various tests for series convergence, tricks for integrating etc.. Hell give up teaching computations at all in 16A/B. Slow it way the hell down and just do basic qualitative reasoning about functions, derivatives and integrals, e.g., focus on things like if we know the derivative is positive here what does that tell us about the function.

However, that choice to abandon the established curriculum is rightly something that needs to be handled by the department as a whole. Indeed, I suspect it would have long since been adopted if other courses (like intro econ...yet again not really for econ majors) didn't assume students had these tools. Changing the math curriculum in this way would first require other subjects change theirs...something that won't go over well and would take time.