From David Mamet's Redbelt:
Chet Frank: Ah, but you train people to fight.
Mike Terry: No, I train people to prevail.
From David Mamet's Spartan:
Scott: What they gotcha teachin' here, young sergeant?
Jackie Black: Edged weapons, sir. Knife fighting.
Scott: Don't you teach 'em knife fighting. Teach 'em to kill. That way, they meet some sonofabitch who studied knife fighting, they send his soul to hell.
I like the idea in both of these quotes that what it appears you are teaching, what you think you are teaching, what you think are are learning, is not the real thing. The real thing you should be teaching is something else, something more fundamental. I wonder if when I teach writing I am really teaching something more basic, like thinking.