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.
Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving
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 feasible.
10. Suggest it, do not force it down your throats.
I got this from the plenary talk of Bernard Hodgson titled Whither the mathematics/didactics interconnection? at ICME 12, Korea, where he highlighted the important contribution of George Polya in making stronger the interconnection between mathematics and didactics and between mathematicians and mathematics educators.
If it’s too hard to commit the 10 commandments to memory then just remember the two rules below which is also from Polya. Combine it with Four Freedoms in the Classroom and you are all set.
How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
