Polya's Problem Solving Techniques
Step 1: Understand the problem
It is not enough to read the problem once. You must always read it the first time for a general understanding. For the second or third time that you read the problem, you need to ask yourself questions like:
- What do I know? What do I not know?
- What do I need to find out?
- Do I have enough information to proceed?
Make it a habit to underline key words and ensure that you fully understand what the question is asking for before you carry on to the next step.
Step 2: Devise a Plan
Once you have fully understand the problem, you need to think of a way to solve the problem. Some methods may include:
- Guess and check
- Making a systematic list
- Draw a picture
- Look for a pattern
- Use a model
- Working backwards
- Restating the problem in another way.
Step 3: Carry it out
For this step, you simply just carry out what you have chosen from Step 2. You just need to be careful in your workings and ensure you transfer the correct numbers onto your paper.
Always persist through with the plan that you have chosen earlier. If it does not work after you have tried it, then choose another plan and carry it out. Be willing to try new methods. Do not stick to only one method of solving problems.
Step 4: Check/Reflect
After completing a problem, do take the time and look at what you have done and reflect. This will allow you to think about what worked and what did not. By doing this in your daily work, it will enable you to learn to predict what method to use to solve future problems.
Also, make it a habit to check whether your answer is reasonable or not. This will help you make sense of your answer and make mathematics more meaningful for you too.