When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
More Quotes from George Polyá:
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work.... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted. One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.George Polyá
Mathematics consists of proving the most obvious thing in the least obvious way.
George Polyá
There are many questions which fools can ask that wise men cannot answer.
George Polyá
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and to turn his back to the class. He writes a, he says b, he means c but it should be d. Some of his sayings are handed down from generation to generation. 'In order to solve this differential equation you look at it till a solution occurs to you.' 'This principle is so perfectly general that no particular application of it is possible.' 'Geometry is the science of correct reasoning on incorrect figures.' 'My method to overcome a difficulty is to go round it.' 'What is the difference between method and device A method is a device which you used twice.'
George Polyá
Epitaph on Newton Nature and Nature's law lay hid in night God said, 'Let Newton be,' and all was light. added by Sir John Collings Squire It did not last the Devil shouting 'Ho. Let Einstein be,' restored the status quo Aaron Hill's version O'er Nature's laws God cast the veil of night, Out blaz'd a Newton's soul and all was light.
George Polyá
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