The objective measure of a teacher's success must be what the class ended up learning regardless of what was or wasn't taught and all other random factors involved.
With that definition in mind, as a former pure math student, the best teaches I had were those who were
- oddly enough, good story tellers! By which I mean, they sounded very much interested in what they were telling me. Their narratives always had at least a few mini-mysteries going on just like in a good story. They used one thing leading to another kind of explanations rather than stating unrelated facts one after the other. The narratives always seemed to have a underlying theme even when that theme was sort of irrelevant to the lesson at hand.
- did not answer my question unless they properly understood what I was asking and why I was asking it. I hate it when I ask X and the teacher answers Y. The good teachers always went to great lengths to understand my questions.
- good mentors and guides and could help your career along if you deserved it. the best ones would go out of the way to make the system reward the deserving.
I think those were the two crucial factors. I have had awesome teachers on all sides of the arrogance, style, humourous, lenience, liberal, demanding, thorough/good enough at the subject matter, popular, good natured/asshole spectra.
Ummm... Not all the good teachers did this, but I very much liked the ones who actually tested what I had learnt rather than whether I was paying attention in the class or taking good notes or pretty much was even present in the class or not.