Many people find mathematics daunting. If true, this piece is for you. If not, this piece is still for you.
What do you think of when you think about mathematics? Perhaps you think about x's and y's, intractable fractions, or nonsensical word problems.
Math Pólya’s way
For many reasons, not the least of which is that Pólya died in 1985, you will meet him as I did – through his wildly successful 'How to Solve It.'
As a mathematician, Pólya worked on a wide range of problems, including the study of heuristics, or how to solve problems.
When you read 'How to Solve It,' it feels like you're taking a guided tour of Pólya's mind.
Pólya's problem solving plan breaks down to four simple steps:
Make sure you understand the problem.
Make a plan to solve the problem.
Carry out the plan.
Check your work to test your answer.
There it is. Problem solving in the palm of your hand – math reduced to four steps.
Here's a classic problem from research on mathematics education done by Jean Lave.
John is a mathematician and problem solver.
First, he understood the problem: He needed ¾ of what the recipe called for, which was 2/3 cup.
Then, he made a plan, most likely visualizing in his head how he would measure and divide the cottage cheese. Finally, he carried out the plan.
Another approach
Would this solution work with different foods or serving sizes? So long as a person could divide that serving into quarters, yes, the plan would work.
Could we solve the problem another way with the same result? Sure — there are many ways to solve this problem, and they should all result in the same halfcup answer.
These messages are especially important for parents helping children learn mathematics.
If you understand the problem you're trying to solve, you're well on your way to solving it.
And you, yes you, are a problem solver.
We all know it's not always so simple to solve problems. Pólya did too.
That's the glory of it – the messy, wonderful, powerful adventure.
