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.
Our priests and presidents, our surgeons and lawyers, our educators and newscasters need worry less about satisfying the demands of their discipline than the demands of good showmanship.
For every fresh stage in our lives we need a fresh education, and there is no stage for which so little educational preparation is made as that which follows the reproductive period.
The idea of education has been so tied to schools, universities, and professors that many assume there is no other way, but education is available to anyone within reach of a library, a post office, or even a newsstand.
If most writers are honest with themselves, this is the difference they want to make: before, they were not noticed; now they are.
My mother was a schoolteacher and very, very encouraging. She understood what it meant when I said I wanted to be a writer; both me and my brother wrote.
When you wish to instruct, be brief; that men's [children's] minds take in quickly what you say, learn its lesson, and retain it faithfully. Every word that is unnecessary only pours over the side of a brimming mind.
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