How to solve math problems

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Polya's 4 phase approach to problem solving

The questions and suggestions listed in the 4 phases prompts the pupil to engage in "mental operations typically useful in problem solving". (Polya elaborated on these mental operations and others in the section titled "Short Dictionary of Heuristic". Heuristics are general strategies or methods for solving problems)

Although presented as 4 phases, problem solving is actually a recursive process (especially for the more challenging or complex problems). The pupil's ideas and concepts about the problem may change again and again as he progresses and gathers more information. He may, among other things, discover a better approach, get stuck, realize that his approach was wrong or realize that he had missed out some information and need to re-examine the initial data.

Attributes of a good problem solver

Polya's list of questions and suggestion under the 4 phases can be seen as a framework for problem solving. However, having a good framework is not enough. Before he can be good at solving math problems, the pupil should also have:

• - good understanding of mathematical concepts
• - skills in mathematical computation
• - knowledge of the various problem solving heuristics
• - metacognition: the ability to monitors one's own thinking
• - good attitudes: perseverance, confidence, patience, willingness to think and figure things out, etc.

Another very important aspect to having good problem solving skills is lots of practise. The pupil cannot be a good problem solver by just reading about math concepts and heuristics. To excel in math (or any other things such as sudoku puzzles), he needs to put in sufficient practise. This is especially true if he wants to perform well under the pressure of examination where speed, correctness and accuracy are required.

As I had mentioned in "More math practise = better math grades?", parents should impose on their children to develop good habits and attitudes. As children learn by imitation and practise, we can be role models of Polya's problem solving strategy for our child by audibly asking ourselves the questions and suggestions when the opportunity arises. We should let our child see us solving problems and figuring things out. When helping our child, we should not spoonfeed them but try to "just indicate a general direction and leave plenty" for them to do.

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