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.
Interpretation
Understanding the source is crucial for accurate translation, whether in language or mathematics.
George Polya's quote emphasizes the importance of comprehension in the translation process, applicable both in linguistics and mathematics. To effectively translate a sentence from one language to another or to convert verbal conditions into mathematical symbols, one must first have a thorough understanding of the original content and then be adept at the specific forms of expression used in the target language or discipline. This underscores the broader principle that deep understanding is essential in any field of knowledge for clear and accurate communication.
In practice
This quote could be used in a lecture about the importance of understanding concepts before teaching them.
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 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
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.
If high-quality content can be effectively delivered via technology, teachers can devote more time to creating innovative experiences, leading Socratic dialogs, or coaching students one-on-one in more targeted and focused interventions.
For every fresh stage in our lives we need a fresh education, and there is no stage for which so little educational preparation is made as that which follows the reproductive period.
Fundamentally, the solution to economic insecurity is economic prosperity - an achievable goal. But for anyone who has grown up without financial security, there's a shadow that lies over even those who move towards independence: lack of financial literacy.
I want a laitywho know their creed so well, that they can_x000D_ give an account of it, who know so much of history that_x000D_ they can defend it.
This applies to many film jobs, not just editing: half the job is doing the job, and the other half is finding ways to get along with people and tuning yourself in to the delicacy of the situation.
You have to know human behaviour … And the quality of your writing is absolutely capped at your understanding of human behaviour. You’ll never write above what you know about people.
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