The best math teachers I have had were in high school and one university lecturer I had for linear algebra in my second year. These teachers turned the traditional math classroom into a conversation and an opportunity for both students and teacher to benefit from the dialogue. There was humour, there were debates, there was interaction. It made all the difference in attempting to learn complicated topics and at the end of the day, it turned these topics into something engaging and exciting to learn.
The not-so-great math teachers I have had focused on meaningless activities that had no real benefit to learning, wasted student (and teacher) time, and furthermore stagnated the passion or interest that students had for their topic. Memorization for the memorization, discussion for the sake of discussion, and other activities lacking reason or motivation or meaning are all top contenders in my experience for math lessons and math teachers that did not know how to engage or interact with their students. The 'proof' is in the pudding so to speak when nearly an entire class fails a test or completely misunderstands a topic (this is a lived experience, many times over).
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