[Math Lair] Ten Commandments for Teachers

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In George Polya's book Mathematical Discovery (volume II, page 114), he gives the following "Ten Commandments for Teachers":

  1. Be interested in your subject.
  2. Know your subject.
  3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.
  4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.
  5. Give them not only information, but "know-how," attitudes of mind, the habit of methodical work.
  6. Let them learn guessing.
  7. Let them learn proving.
  8. Look out for such features of the problem at hand as may be useful in solving the problems to come—try to disclose the general pattern that lies behind the present concrete situation.
  9. Do not give away your whole secret at once—let the students guess before you tell it—let them find out by themselves as much as is feasible.
  10. Suggest it, do not force it down their throats.