Polya Method

According to Polya, kids are often stymied in their efforts to solve problems simply because they

don’t understand it fully, or even in part. Pólya would like kids to ask 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 a diagram that might help you understand the problem? Is there enough information to enable you to find a solution? Do you need to ask a question to get the answer?

Second principle: Devise a plan

Pólya 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
• Make an orderly list
• Eliminate possibilities
• Use symmetry
• Consider special cases
• Use direct reasoning
• Solve an equation

Also suggested:

• Look for a pattern
• Draw a picture
• Solve a simpler problem
• Use a model
• Work backward
• Use a formula
• Be creative
• Use your head

 Third principle: Carry out the plan

This step is usually easier than devising the plan. All you need is care and patience, given that

you have the necessary skills. Persist with the plan that you have chosen. If it continues not to

work discard it and choose another. Don’t be mislead, this is how mathematics is done, even by professionals.

Fourth principle: Review/extend

Pólya mentions that much can be gained by taking the time to reflect and look back at what you

have done, what worked and what didn’t. Doing this will enable you to predict what strategy to

use to solve future problems, if these relate to the original problem.