I received the following e-mail response from Michael Keyton to the Forum's recent discussion summary of Polya's common-sense questions, and post it with his permission thinking the group might find it of interest:
I am a great Polya fan and enjoy your summary here. Recently, I purchased the biography of Polya by H. and L. Taylor (Dale Seymour, 1993) and have enjoyed re-examining his ideas. In his book Mathematical Discovery (1962), he gives 10 commandments for teaching which formed the basis for much of my teaching approach: 1) Be interested in your subject (and I add anything that can be in the least attached to it; thus baseball for geometry, baseball for pre-calculus; etc.) 2) Know your subject (always a problem, for in WIttgenstein's view, do we ever know anything well?) 3) Know about the ways of learning: The best way to learn anything is to discover it by yourself. (A paradigm that should be engraved on the inner eyelid of every "teacher".) 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. (cake eating also, brownies, or even oreos) 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 their throats.
MICHAEL KEYTON ______________
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