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.
A nation that does not read much does not know much. And a nation that does not know much is more likely to make poor choices in the home, the marketplace, the jury box, and the voting booth. And those decisions ultimately affect the entire nation...the literate and illiterate.
Organizing facts in terms of principles and ideas from which they may be inferred is the only known way of reducing the quick rate of loss of human memory.
From that moment on, the world was hers for the reading. She would never be lonely again.
For books I want to keep reading, it's definitely the voice. It must be a voice I've never heard before, and it must have its own particular intelligence. By 'voice,' I don't mean vernacular. It has to have its own particular history and world that it inhabits.
Books can be passed around. They can be shared. A lot of people like seeing them in their houses. They are memories. People who don't understand books don't understand this. They learn from TV shows about organizing that you should get rid of the books that you aren't reading, but everyone who loves books believes the opposite. People who love books keep them around, like photos, to remind them of a great experience and so they can revisit and say, "Wow, this is a really great book."
Instead of being presented with stereotypes by age, sex, color, class, or religion, children must have the opportunity to learn that within each range, some people are loathsome and some are delightful.
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