PROBLEM SOLVING STRATEGIES FROM GEORGE POLYA
George Polya (1887 – 1985) was one of the most famous mathematics educators of the 20th
century (so famous that you probably never even heard of him). Dr. Polya strongly believed
that the skill of problem solving could and should be taught – it is not something that you are
born with. He identifies four principles that form the basis for any serious attempt at problem
solving:
1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back (reflect)
1. Understand the problem
· What are you asked to find out or show?
· Can you draw a picture or diagram to help you understand the problem?
· Can you restate the problem in your own words?
· Can you work out some numerical examples that would help make the problem more
clear?
2. Devise a plan
A partial list of Problem Solving Strategies include:
Guess and check Solve a simpler problem
Make an organized list Experiment
Draw a picture or diagram Act it out
Look for a pattern Work backwards
Make a table Use deduction
Use a variable Change your point of view
3. Carry out the plan
· Carrying out the plan is usually easier than devising the plan
· Be patient – most problems are not solved quickly nor on the first attempt
· If a plan does not work immediately, be persistent
· Do not let yourself get discouraged
· If one strategy isn’t working, try a different one
4. Look back (reflect)
· Does your answer make sense? Did you answer all of the questions?
· What did you learn by doing this?
· Could you have done this problem another way – maybe even an easier way?
[Taken from PSS Teaching and problem Solving, the attached Document, which you don't need to read unless you really want to]