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.
- Giving too many passive lectures
- Omitting Counter examples and omitting examples of common errors.
- Not offering suggestions toward efficient learning
- Not giving enough problems that use mixed strategies and require recall of significant ideas
- Not checking homework daily
- Failing to show perspective, to show applications and to explain connections with other parts of mathematics
- 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?"
- Omitting discussions of the subject's history, its etymologies, and the personalities of its creators.
- Omitting personal stories of my own experiences, my colleagues' experiences and my former students experiences in the study of mathematics.
- Teaching only the brightest or ignoring the brightest.
- Proving statements that are obvious to most students or giving proofs that few or none can follow.
- Making the classroom experience equivalent to reading a textbook: definition, lemma, theorem, proof, corollary, definition, lemma, theorem, proof...
- Taking no interest in students' difficulties in mastering the subject.