Tag Archives: problem solving

A problem, by definition, needs to be solved. Alas for many, effective solution methods do not include crying, complaining, or ignoring the situation. In fact, problem solving often depends on methods and approaches outside our ordinary routine. Good old George Pólya knew a thing or two about problems and solutions. His masterpiece of mathematical heuristics, How to Solve It: A New Aspect of Mathematical Method, maps out the four essential steps to solving problems. We must always start, of course, by understanding what the problem really is. How else can you solve it? But the second and perhaps most critical step is not, as many believe, to jump right in and start making things happen. Instead, take a moment to come up with a plan about how best to solve the problem: “We have a plan when we know, or know at least in outline, which calculations, computations, or constructions…

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“It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. Such foolish and sad things often happen, in and out of school…” Into every life, it is said, a little rain must fall. Farmers and firefighters may take comfort in the inevitability of precipitation, but most others see an unanticipated deluge for what it is: a problem. Everywhere you look–on tests, in school, throughout life–you find problems. Problems, by their very nature, require solving. Unfortunately, many of us don’t really have a strategy to solve problems apart from painful trial and error. Those who study heuristics, however, have a distinct advantage. A heuristic can be any practical approach to problem solving, learning, or discovery. George Pólya, the Hungarian master of heuristics, systematized problem solving with unparalleled lucidity. His influential work, How to Solve It: A…

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Albert Einstein, genius that he was, reportedly commented that, if he only had one hour to solve a problem, he would spend 55 minutes defining the problem and the remaining 5 minutes solving it. No matter that this quote is most likely apocryphal; the brilliance and truthfulness of it transcends its false origins. Any great mind can recognize how much work goes into understanding a problem before actually solving it. George Pólya certainly understood the reality of problem solving. This highly influential Hungarian mathematician is well-known for his contributions to complex analysis, mathematical physics, probability theory, geometry, and combinatorics. However, he most distinguished himself to the masses through his work on heuristics, which is to say problem solving. In 1945, Pólya wrote How to Solve It: A New Aspect of Mathematical Method, a small book with a large impact. This volume describes his four principles of problem solving, steps so…

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