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.
Keep your hands moving. Writing is rewriting.
The atmosphere of libraries, lecture rooms and laboratories is dangerous to those who shut themselves up in them too long. It separates us from reality like a fog.
The teaching of one virtuous person can influence many; that which has been learned well by one generation can be passed on to a hundred.
As a young writer, I was on guard against the Latina in me, the Spanish in me because as far as I could see the models that were presented to me did not include my world. In fact, 'I was told by one teacher in college that one could only write poetry in the language in which one first said Mother. That left me out of American literature, for sure.
I think books are like people, in the sense that they'll turn up in your life when you most need them.
There's no question that a great teacher can make a huge difference in a student's achievement, and we need to recruit, train and reward more such teachers. But here's what some new studies are also showing: We need better parents. Parents more focused on their children's education can also make a huge difference in a student's achievement.
Subscribe for the occasional hand-picked quote. No noise.