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.
I think we should stop asking people in their 20s what they 'want to do' and start asking them what they don't want to do. Instead of asking students to 'declare their major' we should ask students to 'list what they will do anything to avoid.' It just makes a lot more sense.
I view it as one of the greatest crimes to shadow the minds of the young with these gloomy superstitions, and with fears of the unknown and the unknowable to poison all their joy in life.
A professor can never better distinguish himself in his work than by encouraging a clever pupil, for the true discovers are among them, as comets amongst the stars.
Indeed the general natural Tendency of Reading good History, must be, to fix in the Minds of Youth deep Impressions of the Beauty and Usefulness of Virtue of all Kinds, Publick Spirit, Fortitude.
I do my precalc homework, and then when I'm done I actually sit with the textbook for like three hours and try to understand what I just did. That's the kind of weekend it is--the kind where you have so much time you go past the answers and start looking into the ideas.
I like my job because it involves learning. I like being around smart people who are trying to figure out new things. I like the fact that if people really try they can figure out how to invent things that actually have an impact.
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