In teaching, this gleam in the eye always gives me the greatest pleasure. This is the same joy which comes when the fire in the oven, which we are trying to revive, at last flames up. There are teachers who try to teach mathematics by the memorization of rules and by developing a mechanical routine. They are bunglers, and such teaching is not worth much. The real teacher is concerned most with making the student understand; he tries to teach him how to think. Whoever learns only recipes, instead of really understanding what he learns, will not be able to use these recipes correctly.
"Galileo" ala Alfred Renyi
Dialogues on Mathematics, 1967, p. 71