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.
Interpretation
Teachers and students must focus on key questions and analyze problems from multiple perspectives.
This quote by George Polya emphasizes the importance of critical thinking and thorough investigation in both teaching and learning. It suggests that for effective problem-solving, educators should be aware of the unknowns and the essential data involved, while students are encouraged to examine problems attentively and from different angles to deepen their understanding.
In practice
Educators can use this quote in a workshop about effective teaching strategies.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
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.
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.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal, and the facts from the fiction.
I think the next thing I publish will be for children, but I don't really want to be held to that because I also know what my next book for adults will be, and I really like that, too, so it depends. I've always had more than one thing going.
There is not human being from whom we cannot learn something if we are interested enough to dig deep.
We don't care really about children as a society and television reflects that indifference to children as human beings.
Books are the perfect Time Machine. By the simple act of opening a book you can, in an instant, be travelling up a jungle river without once being bitten by mosquitoes, or you can almost die of thirst in the desert while holding a cold drink in your hand, or dine in the finest restaurants and never have to worry about paying the bill, or ride the wild country of our western frontier and never worry about losing your scalp to a raiding party.
I went to college because I didn't have anywhere else to go and it was a fabulous hang. And while I was there I was exposed to this world that I didn't know was possible.
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