Polya’s Problem Solving Techniques
In 1945 George Polya published the book How To Solve It which quickly became
his most prized publication. It sold over one million copies and has been translated
into 17 languages. In this book he identifies four basic principles of problem solving.
Polya’s First Principle: Understand the problem
This seems so obvious that it is often not even mentioned, yet studens are often
stymied in their efforts to solve problems simply because they don’t understand it
fully, or even in part. Polya taught teachers to ask students questions such as:
•Do you understand all the words used in stating the problem?
•What are you asked to find or show?
•Can you restate the problem in your own words?
•Can you think of a picture or diagram that might help you understand the
problem?
•Is there enough information to enable you to find a solution?
Polya’s Second Principle: Devise a plan
Polya mentions that there are many reasonable ways to solve problems. The skill
at choosing an appropriate strategy is best learned by solving many problems. You
will find choosing a strategy increasingly easy. A partial list of strategies is included:
•Guess and check •Look for a pattern
•Make an orderly list •Draw a picture
•Eliminate possibilities •Solve a simpler problem
•Use symmetry •Use a model
•Consider special cases •Work backwards
•Use direct reasoning •Use a formula
•Solve an equation •Be ingenious
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