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.
I'm a very introverted person. Nothing that's happened has changed that, but one of the reasons I write for teens is it's a real privilege to have a seat at the table in the lives of young people when they're figuring out what matters to them.
Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.
Education, the great mumbo jumbo and fraud of the age purports to equip us to live and is prescribed as a universal remedy for everything from juvenile delinquency to premature senility.
The humanities are like the great old Paris Flea Market where, amidst masses of junk, people with a good eye found cast away treasures...They are like a refugee camp where all the geniuses driven out of their jobs and countries by unfriendly regimes are idling.
If you have a 2 or 3 year old who is not talking, you must start an early intervention program. The worst thing you can do with an autistic 3 year old is to do nothing.
As the soil, however rich it may be, cannot be productive without cultivation, so the mind without culture can never produce good fruit
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