Freshman year, I took Math 21C (one of four in the engineering calculus series) with Prof. Alexander Coward. I was unfamiliar with proofs, so I emailed him asking for help: "Thanks for helping me work through the proof of the limit comparison test today. While it was definitely helpful, I still feel woefully incompetent when it comes to proving a theorem. What I want to know is if you have any suggestions for ways to improve on proofs. Obviously I can systematically go through the book and prove every theorem we cover, but I was wondering if there's some way I can make such a task more productive/educational."
I have never again had a professor respond the way that he did. He didn't reply to my email. Instead, at the next lecture, he asked if I was in class. He explained the question that I had asked. He explained that proofs are intrinsically hard and that no procedure exists for proving or disproving every possible statement. He told us stories about struggling for years with a single problem, having some very good ideas, but being unable to solve his problem. It was an unparalleled educational experience.
A few weeks ago, I sent him a friend request on Facebook. He accepted. Tonight, he posted a link to an article he wrote titled BLOWING THE WHISTLE ON THE UC BERKELEY MATHEMATICS DEPARTMENT. I highly recommend that you read it as it speaks to my own personal experiences with faculty avoiding pressures to become better teachers.
I also stumbled across this letter he wrote to his students back in 2013. While the whole letter is worth reading, the following is essential:
"In order for you to navigate the increasing complexity of the 21st century you need a world-class education, and thankfully you have an opportunity to get one. I don't just mean the education you get in class, but I mean the education you get in everything you do, every book you read, every conversation you have, every thought you think.
You need to optimize your life for learning.
You need to live and breath your education.
You need to be *obsessed* with your education."
His teaching statement is also worth reading.