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.
What I wanted to do was use literature and different kinds of stories and poems as a springboard, tapping into the creativity of our teens - I wanted teenagers to come up with their own creative responses to literature - using books themselves as a starting point.
In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience.
Good writing, and this is especially important in a subject such as economics, must also involve the reader in the matter at hand. It is not enough to explain. The images that are in the mind of the writer must be made to reappear in the mind of the reader, and it is the absence of this ability that causes much economic writing to be condemned, quite properly, as abstract.
History shows that it does not matter who is in power or what revolutionary forces take over the government, those who have not learned to do for themselves and have to depend solely on others never obtain any more rights or privileges in the end than they had in the beginning.
The academic bias against subjectivity not only forces our students to write poorly ("It is believed...," instead of, "I believe..."), it deforms their thinking about themselves and their world. In a single stroke, we delude our students into believing that bad prose turns opinions into facts and we alienate them from their own inner lives.
How can our kids really understand the moral complexities of being alive if they are not allowed to engage in those complexities outdoors?
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