I'm always shocked to see how many college-level students can't string coherent sentences together. In a third-year class (I went to a five-year school) I once handed a paper I'd written that day. It was crap, and I knew it, so I was shocked when it came back with an A. The professor spent the first half of the class lecturing that a thesis paper must have a thesis statement, supporting evidence, documentation, and a conclusion. I went to her afterwards, apologized for my poor paper, and suggested that my grade be changed to a B or a C (I thought it deserved a C.) She told me that she was keeping it as an A, since I'd written the best paper in the class, and that she wanted to see improvement with the rest of my work. I finished that class with an A, but I felt I'd earned it by the end.

Back to the subject of Math: after reading this, I'm now kicking myself for not complaining to my university about two very poor Math teachers I had, both of whom did not speak English as a first language and didn't know how to teach. I dropped both classes rather than complain, because I'd been raised with the idea that The Teacher is Always Right. This friend of yours got the short end of the stick, which is awful because it sounds like he was a good teacher, which is what every university in the country needs more of.

I've worked as a Calculus Tutor and spent a year editing Math textbooks, and I think the biggest problem with Math teachers is that the people who are good at Math tend to skip steps in problems because they do them in their heads. For those of us who aren't so good at Math, this is a problem because we don't make those intuitive connections and get lost easily. So in my opinion, the definition of a good teacher is one who goes over every step of every process.