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.
You can't just declare that you have a growth mindset. Growth mindset is hard.
No bubble is so iridescent or floats longer than that blown by the successful teacher.
I was a voracious reader and the library fed my curiosity, imagination and my soul. I read by the shelf - biographies, fantasy - all and everything fed my dreams. Then as an adult whenever I would go on location the first thing we would do as a family is sign up at the closest library. Not only would we find books, but what was happening in that town, because the library is the head of the community.
Competitive sports may be where exercise becomes 'fun' for children who are good at it, but for those who are less talented, it is where exercise becomes not only physically demanding but also emotionally painful and socially humiliating.
I think that the best way to solve problems and to fight against war is through dialogue. For me the best way to fight against terrorism and extremism... just a simple thing: educate the next generation.
I am not in the business of suppressing books.
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