Friday, May 13, 2016

Got Polya?

During the twenty years I taught mathematics, I observed a variety of strategies that students used to solve problems.  One of the most widely used and least successful methods was to immediately try to solve the problem.  Time and again I watched as students would dive into a math problem, wrestle with it for a while, and then declare "I can't do it."  Of course, I was confident that my students could triumph over any math problem they faced; a great deal of my teaching was helping them realize it.

The key to solving a math problem - or most any other problem - was elegantly stated by George Polya:  "Understand the problem."  I used to tell my students that everything they needed to solve the problem was right there in front of them.  But they had to allow the problem to "speak" to them and gradually reveal its solution.

"Get to know the problem," I would say.  "Find out about it.  What does it look like?  Where does it live?  Who is it friends with?  Where does it like to go for lunch?"
My students would laugh and say that the problem likes tacos and pizza; but they would also get the point and approach the problem from a fresh perspective.

Mathematics is built into the fabric of the universe; we all have natural math instincts if we get in touch with them.  "Understand the problem."  The problem knows what it needs and will help you find a solution.  Especially if you buy it tacos for lunch.