Mathematics is not a spectator sport!
Interpretation
Mathematics requires active participation and engagement, rather than passive observation.
The quote by George Polya emphasizes the importance of actively engaging with mathematical concepts instead of simply watching others perform calculations or problem-solving. It suggests that true understanding and mastery of mathematics come from hands-on practice, exploration, and participation, akin to how one must actively play a sport to appreciate and excel in it.
In practice
In a classroom setting, a teacher might say this quote to encourage students to participate in problem-solving activities.
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 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.
We need to have a course in school that teaches about ecology and gastronomy. I could imagine that all children could eat at school for free and that the cafeteria would become part of the school's curriculum.
Then I celebrated my Wall of Books. I counted the volumes on my twenty-foot-long modernist bookshelf to make sure none had been misplaced or used as kindling by my subtenant. βYouβre my sacred ones,β I told the books. βNo one but me still cares about you. But Iβm going to keep you with me forever. And one day Iβll make you important again.β I thought about that terrible calumny of the new generation: that books smell.
Gold, silver, jewels, purple garments, houses built of marble, groomed estates, pious paintings, caparisoned steeds, and other things of this kind offer a mutable and superficial pleasure; books give delight to the very marrow of one's bones. They speak to us, consult with us, and join with us in a living and intense intimacy.
High School is the place where poetry goes to die.
I walk around the school hallways and look at the people. I look at the teachers and wonder why they're here. If they like their jobs. Or us. And I wonder how smart they were when they were fifteen. Not in a mean way. In a curious way. It's like looking at all the students and wondering who's had their heart broken that day, and how they are able to cope with having three quizzes and a book report due on top of that. Or wondering who did the heart breaking. And wondering why.
On the average, five times as many people read the headlines as read the body copy.
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