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.
Liberating education consists in acts of cognition, not transferrals of information
We do not trust educated people and rarely, alas, produce them, for we do not trust the independence of mind which alone makes a genuine education possible.
We live in a moment and a culture when reading is really endangered. There's simply no way to write well, though, if you're not reading well.
It is easier for a tutor to command than to teach.
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.
A man is not learned until he can read, write and swim.
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