Stages of solving mathematical problem

Nowadays, I am translating an article about the system of mathematical problem-exercise into English. In order to be aware what I am doing; first, I needed to understand the mathematical problem solving stages or strategies which is proposed by George Polya. Let me introduce this strategy to you little bit.　In order to solve a mathematical “tough” problem, ask yourself these 4 questions:

1. What do I know?

• List the facts or information given in the problem.
• Underline or circle any key words, such as factor, multiple, area, or perimeter.
• Watch out for mixed units!
• Express the facts in math symbols, if you can.

2. What do I want?

• Describe the goal, what the problem is asking you to find.
• Underline or circle any key words, such as sum, product, next, or not. (Small words are easy to miss!)
• Express the goal in math symbols, if you can.

3. What can I do?

• Combine the given facts. Can you get closer to the goal?
• Try a tool from your Problem Solving Tool Box.
• Do one little step at a time.

4. Does it make sense?

• When you get an answer, always look back at the original problem one more time.
• Does your answer make sense?
• Do you have the correct units (inches, cm², kg, etc.)?
• Can you think of a way to confirm that your answer is right?

Problem solving tool box

• Draw a diagram or picture.
• Act the problem out, step by step.
• Make a systematic list, chart, or table.
• Look for a pattern.
• Simplify the problem.
  (Try it with smaller numbers.)
• Restate the problem in another way, or look for a related problem.
• Think about “Before” and “After” situations.
• Work backwards.
• Guess and check.
  
  

Purevdorj Oyunaa (from Mongolia)