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.
Interpretation
Effective teaching requires a teacher to connect emotionally with their subject.
In this quote, George Polya emphasizes the importance of a teacher's emotional engagement with their subject matter. He suggests that a teacher who genuinely feels enthusiastic about what they are teaching can better inspire their students, conveying the vitality and importance of the material. This emotional connection is essential for fostering a similar enthusiasm in students and effectively communicating the message.
In practice
A teacher might use this quote during a faculty meeting to encourage colleagues to engage deeply with their subjects.
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.
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.
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
You have learnt something. That always feels at first as if you had lost something.
Let schoolmasters puzzle their brain, With grammar, and nonsense, and learning, Good liquor, I stoutly maintain, Gives genius a better discerning.
Democracy has to be born anew every generation, and education is its midwife.
Now of the difficulties bound up with the public in which we doctors work, I hesitate to speak in a mixed audience. Common sense in matters medical is rare, and is usually in inverse ratio to the degree of education.
I cannot imagine the type of sinister fiend who would be against the library. A library essentially says, 'Look, here is some free information that will enrich your life. Read it on your own time. I trust that you will bring it back when you are finished.' It might be the most civilized, forward-thinking institution in America. Perhaps the only one, in fact.
I always knew from that moment, from the time I found myself at home in that little segregated library in the South, all the way up until I walked up the steps of the New York City library, I always felt, in any town, if I can get to a library, I'll be okay. It really helped me as a child, and that never left me. So I have a special place for every library, in my heart of hearts.
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