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George Polya Quotes
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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. (George Polya Quotes)
Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements. (George Polya Quotes)
Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. (George Polya Quotes)
Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements (George Polya Quotes)
A mathematics teacher is a midwife to ideas (George Polya Quotes)
Geometry is the science of correct reasoning on incorrect figures (George Polya Quotes)
The principle is so perfectly general that no particular application of it is possible (George Polya Quotes)
Mathematics is not a spectator sport! (George Polya Quotes)
Mathematics consists in proving the most obvious thing in the least obvious way (George Polya Quotes)
Beauty in mathematics is seeing the truth without effort (George Polya Quotes)
My method to overcome a difficulty is to go round it (George Polya Quotes)
The best of ideas is hurt by uncritical acceptance and thrives on critical examination (George Polya Quotes)
The open secret of real success is to throw your whole personality into your problem (George Polya Quotes)
There are many questions which fools can ask that wise men cannot answer (George Polya Quotes)
If you cannot solve the proposed problem try to solve first some related problem (George Polya Quotes)
An idea which can be used once is a trick. If it can be used more than once it becomes a method (George Polya Quotes)
I am too good for philosophy and not good enough for physics. Mathematics is in between (George Polya Quotes)
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 (George Polya Quotes)
We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building (George Polya Quotes)
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 Polya Quotes)
In order to solve this differential equation you look at it until a solution occurs to you (George Polya Quotes)
A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise (George Polya Quotes)
The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeatedly, and from from various sides (George Polya Quotes)
Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them (George Polya Quotes)
It is better to solve one problem five different ways, than to solve five problems one way (George Polya Quotes)
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important (George Polya Quotes)
Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better (George Polya Quotes)
Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side (George Polya Quotes)
When introduced at the wrong time or place, good logic may be the worst enemy of good teaching (George Polya Quotes)
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems (George Polya Quotes)
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