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Four Steps to Work a Math Problem

Hungarian Mathematician, George Pólya’s Four Step Process.

George Pólya (December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education.

I used to teach 7th and 8th grade math several years ago. In one of the chapters, they mentioned the Pólya’s Four Step Process. I had my students cite this in class whenever they got stuck on a problem, or if they had ideas on how to solve a problem.

I included the comments next to each step as I explained it to my students.

1. Understand the Problem. (Read it, restate it, write down variables, etc.).

2. Devise a Plan. (Use the general problem solving strategy process below, figure out a strategy).

3. Carry out the Plan. (Once you have figured out a way to solve it, then do it).

4. Look Back. (Look at your answer, analyze the process that you completed).

General Problem Solving Strategies

1. Use a variable.
2. Complete a Table.
3. Consider a special case.
4. Look for a pattern.
5. Guess and test.
6. Draw a Picture.
7. Draw a Diagram.
8. Make a list.
9. Solve a simpler, related problem.
10. Use reasoning.
11. Solve an equivalent problem.
12. Work backward.
13. Solve an equation.
14. Look for a formula.
15. Use coordinates.

Note: Initial information cited from Wikipedia (http://en.wikipedia.org/wiki/George_P%C3%B3lya).

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