„Teachers need to be trained on how children learn, not only how to solve mathematical problems. They must know how to make learners well understand the New Math and enable them to solve mathematical problems.“

Teacher

Adopted from Wikiquote. Last update Nov. 26, 2020. History
Sukavich Rangsitpol photo
Sukavich Rangsitpol31
Thai politician 1935

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„From the computer application point of view the primary problem [of Computer-Aided Design] is not how to solve problems, but how to state them.“

—  Douglas T. Ross American computer scientist 1929 - 2007

Source: Computer-Aided Design: A Statement of Objectives (1960), p. iii; Abstract.

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„Our country must be strong enough to solve problems, and that means we must learn how to work together again.“

—  Gabrielle Giffords American politician 1970

Comment after winning re-election — [Giffords wins re-election to U.S. House; Kelly says voters have spoken, Sierra Vista Herald, Arizona, November 6, 2010, Bill Hess]

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„If people don't think they have the power to solve their problems, they won't even think about how to solve them.“

—  Saul D. Alinsky American community organizer and writer 1909 - 1972

Source: Rules for Radicals: A Pragmatic Primer for Realistic Radicals

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„In mathematics the art of asking questions is more valuable than solving problems.“

—  Georg Cantor mathematician, inventor of set theory 1845 - 1918

Doctoral thesis (1867); variant translation: In mathematics the art of proposing a question must be held of higher value than solving it.
Original: (la) In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.

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„Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.“

—  Isaac Newton, book Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiae Naturalis Principia Mathematica (1687)
Context: The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.

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„What I cannot create, I do not understand.Know how to solve every problem that has been solved.“

—  Richard Feynman American theoretical physicist 1918 - 1988

on his blackboard at the time of death in February 1988; from a photo in the Caltech archives http://archives.caltech.edu/pictures/1.10-29.jpg

„Dad, how do soldiers killing each other solve the world's problems?“

—  Bill Watterson American comic artist 1958

Source: Calvin and Hobbes: Sunday Pages 1985-1995: An Exhibition Catalogue

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„Any problem solved is a new problem made.“

—  Karl Pilkington English television personality, social commentator, actor, author and former radio producer 1972

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„After 25 years of buying and supervising a great variety of businesses, Charlie and I have not learned how to solve difficult business problems. What we have learned is to avoid them.“

—  Warren Buffett American business magnate, investor, and philanthropist 1930

1989 Chairman's Letter http://www.berkshirehathaway.com/letters/1989.html
Letters to Shareholders (1957 - 2012)
Context: After 25 years of buying and supervising a great variety of businesses, Charlie and I have not learned how to solve difficult business problems. What we have learned is to avoid them. To the extent we have been successful, it is because we concentrated on identifying one-foot hurdles that we could step over because we acquired any ability to clear seven-footers.

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„What happens when a brain is educated in problems? It can never solve problems; it can only create more problems. When a brain that is trained to have problems, and to live with problems, solves one problem, in the very solution of that problem, it creates more problems.“

—  Jiddu Krishnamurti Indian spiritual philosopher 1895 - 1986

Source: 1980s, That Benediction is Where You Are (1985), p. 18
Context: From childhood we are trained to have problems. When we are sent to school, we have to learn how to write, how to read, and all the rest of it. How to write becomes a problem to the child. Please follow this carefully. Mathematics becomes a problem, history becomes a problem, as does chemistry. So the child is educated, from childhood, to live with problems — the problem of God, problem of a dozen things. So our brains are conditioned, trained, educated to live with problems. From childhood we have done this. What happens when a brain is educated in problems? It can never solve problems; it can only create more problems. When a brain that is trained to have problems, and to live with problems, solves one problem, in the very solution of that problem, it creates more problems. From childhood we are trained, educated to live with problems and, therefore, being centred in problems, we can never solve any problem completely. It is only the free brain that is not conditioned to problems that can solve problems. It is one of our constant burdens to have problems all the time. Therefore our brains are never quiet, free to observe, to look. So we are asking: Is it possible not to have a single problem but to face problems? But to understand those problems, and to totally resolve them, the brain must be free.

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