As a professor at Berkley in 1945, Hungarian mathematician George Polya, published a book, How to Solve It. In his book, he outlined the following problem solving strategy techniques for mathematicians. Today, these same techniques are universally applied across all disciplines whenever a situation or problem is presented.
Problem Solving Strategy
First: Understand the problem. Read and reread the problem. Highlight the key words. What does the problem ask you to find? (This is the unknown.)
What data does the problem give you?
What are the requirements or conditions?
⇒Hint: Draw a figure or picture. Make a table or model.
⇒Hint: Introduce helpful symbols.
Second: Make a plan. Have you solved other problems like this one before?
What steps will you take to get from the data to the unknown?
Does your plan use all of the important data?
⇒Stuck? Tactic: Is there a similar problem which is simpler?
⇒Stuck? Tactic: Could you solve part of the problem?
⇒Stuck? Tactic: Could you restate the problem?
⇒Stuck? Tactic: Would other data help you find the unknown?
⇒Stuck? Tactics: Use one of the following methods: look for a pattern, work backwards, guess and check (or trial and error), make an orderly list, draw a picture or use a model, eliminate possibilities, solve a simpler problem, use direct reasoning (or logical deduction), use a formula, solve an equation -OR- be ingenious and creative!
Third: Carry out your plan.
Check each step.
Can you see clearly that the step is correct?
Fourth: Look back. Reread the problem.
Did you answer the question that was asked?
Was more than one question asked?
Is your answer reasonable?
Can you check the result? Can you think of an easier way to solve the problem?
Source: Adapted from Princeton University Press: G. Polya, “How to Solve It”, 2nd ed., Princeton University Press, 1957, For details check: http://www.pupress.princeton.edu/titles/669.html
