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.
Interpretation
Learning requires active participation and engagement with challenges.
This quote emphasizes the importance of hands-on experience in the learning process. Just as a person must physically get into the water to learn how to swim, an individual must actively engage in problem-solving to develop the skills necessary for effective problem-solving. The essence of gaining knowledge or expertise lies in confronting and attempting to overcome the challenges that arise.
In practice
A teacher might use this quote to encourage students to tackle challenging math problems.
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.
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 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.
Fifty years from now if an understanding of man's origins, his evolution, his history, his progress is not in the common place of the school books we shall not exist.
How do we merge entertainment and education? We live in a world where entertainment wins, but if entertainment can have an educational heart, then we can really change people's lives.
As Olafsson showed me, White can win... It's hard to believe. I stayed up all night analysing, finally convicing myself, and, incidentally, learning a lot about Rook and Pawn endings in the process.
The one experience that I hope every student has at some point in their lives is to have some belief you profoundly, deeply hold, proved to be wrong because that is the most eye-opening experience you can have, and as a scientist, to me, is the most exciting experience I can ever have.
I studied psychology in school, and the best psychology is in literature. It's so much easier to understand a character than a theory. You can recognize yourself—or other people—in a different way.
The very concept of an Iranian university is an oxymoron. There are no free and open places of learning in that repressive theocracy. Dissenters are not given tenure; they are murdered, after first being tortured. Blasphemy, which is broadly defined, is punished. Gays are not only excluded from Iranian universities, but are imprisoned and killed.
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