“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 New Aspect of Mathematical Method, describes four powerful principles of problem solving of great value to anybody. The most direct value from this methodology accrues to anyone tackling problems of the mathematical variety.
Pólya’s first key insight relates to the primary but oft-neglected step in dealing with a dilemma of any sort: understanding the problem:
“First of all, the verbal statement of the problem must be understood… the student should be able to state the problem fluently. The student should also be able to point out the principal parts of the problem, the unknown, the data, the condition.
“The student should consider the principal parts of the problem attentively, repeatedly, and from various sides… There is another question which may be useful in this preparatory stage provided that we do not expect a definitive answer but just a provisional answer, a guess: Is it possible to satisfy the condition?”
Basically, the first step in solving a problem–mathematical or otherwise–is to understand what the problem really is. Anyone taking standardized tests should take this advice to heart: if you don’t know what a question really asks, your chances of intentionally getting it right are infinitesimal.
Mike Bergin