Polya’s approach to teaching math

The following phrase by CSS expert Lea Verou, excerpted from CSS Secrets, “… I’ve tried to describe the thinking behind every technique in detail, as I believe that understanding the process of finding a solution is far more
valuable than the solution itself
… ” has impressed me because of their universality. It applies everywhere and particularly to teaching math. The (thinking) process is far more important than the result.

In fact, it remembers me George Polya’s approach to teaching maths and problem solving.

Hungarian mathematician George Pólya (1887–1985) is well known by his book How to Solve it (1945), where he describes several of his own problem solving techniques.

Polya was very much interested about teaching. The following are some of Polya’s guidelines when teaching students (Complex Variables, 1974, p. v-vi):

Start from something that is familiar, useful, or challenging-from some connection with the world around us, from the prospect of some application, or from an intuitive idea.
Do not be afraid of using colloquial language when it is more suggestive than the conventional precise terminology. In fact, do not introduce technical terms before the student can understand the need for them.
Do not enter too early or too far into the heavy details of a proof. First, give a general idea or just the intuitive germ of the proof.
Generally, realize that the natural way to learn is to learn by stages.
First, we want to see an outline of the subject in order to perceive a concrete source or a possible use. Then, gradually, as we can see use, connections, and interest, we accept more willingly the responsibility of filling in the details.

Teaching is hard. Even harder when you are a math teacher.

Sometimes, we forget simple but useful advice about teaching: motivate, communicate, explain the big idea, then, details step by step.

I just wanted to remember it publicly.