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.
Let there be nothing harmonious about our children's playthings, lest they grow up expecting peace and order, and be eaten alive.
If you're curious, you'll probably be a good journalist because we follow our curiosity like cats.
Young film makers should learn how to deal with the money and learn how to deal with the power structure. Because it is like a battle.
All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
Each close you use should be an educational process by which you are able to raise the value in the prospect's mind.
Pretending is not just play. Pretending is imagined possibility. Pretending, or acting, is a very valuable life skill and we do it all the time.
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