Teaching Mistakes in Mathematics

Perhaps the most inspiring book on mathematics teaching I've read this year is "Twenty Years before the Blackboard" by Michael Stueben.

1. Giving too many passive lectures
2. Omitting Counter examples and omitting examples of common errors.
3. Not offering suggestions toward efficient learning
4. Not giving enough problems that use mixed strategies and require recall of significant ideas
5. Not checking homework daily
6. Failing to show perspective, to show applications and to explain connections with other parts of mathematics
7. Not showing the internal motivation behind the mathematics and not answering the questions: "Why would anybody want to learn this?" and "What can we do with this knowledge or skill?"
8. Omitting discussions of the subject's history, its etymologies, and the personalities of its creators.
9. Omitting personal stories of my own experiences, my colleagues' experiences and my former students experiences in the study of mathematics.
10. Teaching only the brightest or ignoring the brightest.
11. Proving statements that are obvious to most students or giving proofs that few or none can follow.
12. Making the classroom experience equivalent to reading a textbook: definition, lemma, theorem, proof, corollary, definition, lemma, theorem, proof...
13. Taking no interest in students' difficulties in mastering the subject.