George Pólya describing methods of problem solving. First, you have to understand the problem. If this technique fails, Pólya advises: “If you can’t solve a problem, then there is an easier problem you can solve: find it. Or: “If you cannot solve the proposed problem, try to triz problem solving examples first some related problem.
Could you imagine a more accessible related problem? Understand the problem” is often neglected as being obvious and is not even mentioned in many mathematics classes. Yet students are often stymied in their efforts to solve it, simply because they don’t understand it fully, or even in part. 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 understand all the words used in stating the problem? Do you need to ask a question to get the answer?
The teacher is to select the question with the appropriate level of difficulty for each student to ascertain if each student understands at their own level, moving up or down the list to prompt each student, until each one can respond with something constructive. 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. Applying these rules to devise a plan takes your own skill and judgement.