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.
For the mind does not require filling like a bottle, but rather, like wood, it only requires kindling to create in it an impulse to think independently and an ardent desire for the truth.
I now understand what Nelle Morton meant when she said that one of the great tasks in our time is to "hear people to speech." Behind their fearful silence, our students want to find their voices, speak their voices, have their voices heard. A good teacher is one who can listen to those voices even before they are spoken-so that someday they can speak with truth and confidence.
It does not seem to me that I have the right to foist a story on people, most of whom are children who should be learning all the time, unless I am learning from it too.
The goal of education is the advancement of knowledge and the dissemination of truth.
One of the most important things that teachers teach students is you, you can work harder. You are mentally tougher than you think.
You know, you can make a small mistake in language or etiquette in Britain, or you could when I was younger, and really be made to feel it, and it's the flick of a lash, but it would sting, and especially at school where there's not much privacy, and so on. You could, yes, undoubtedly be made to feel crushed.
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