In this and other pages we'll try to give suggestions on teaching math, for both teachers and parents. This first page has some general ideas, and other pages will illustrate the general point with some very specific ideas.

     Children are like the rest of us: they tend to resist anything that looks like work, and to be beguiled by anything that amuses them.

     For many kids, math looks like work.

     So how can you -- a teacher or parent -- make math fun, amusing, and entertaining?

     Here are some suggestions to make math beguiling both for you and for your students.

FIRST: spend a short time each class period (perhaps 5 minutes) on something mathematical which is puzzling or fascinating. For example, ask a perplexing question at the end of one class, and answer it at the beginning of the next. Here are some examples in each of seven categories:

• Puzzles. What's the fewest number of colors needed to paint any map, if the rule is "no two countries sharing a boundary can be the same color"? Find a series of seven consecutive numbers none of which are prime.
• Magic. Tell a child to add 9 to his age, double the result, then subtract 15. He tells you the result, and you tell him his age.
• History of math. What were numbers like before the zero was invented? What values have been used in the past for the number pi? What is mathematical Chaos and why is it important?
• Guessing. How many seconds have you lived? If someone covered your bed with pennies without overlapping them, how much money would you have?
• Unsolved problems. Is every even number bigger than 5 the sum of two prime numbers?
• Use of artifacts. Show two loops of paper. Cut each one down the center. One will be cut into two separate loops. The other will form one big loop. (The strange loop is a Mobius strip --a loop of paper with one twist in it.)
• Play games. How many possible ways are there, in chess, for black and white each to make his opening move? If you're four squares from Boardwalk, in Monopoly, what's the chance you'll hit it on your next turn?

SECOND: Let your students help you teach. Don't force proofs or methods down their throats. Give them a lead, and then let them make suggestions.

THIRD: Teach how to solve problems. One notable method devised by George Polya uses these steps:

• Understand the problem: (what's unknown? What's given?)
• Devise a plan (Have you seen this problem, or a similar one, before? Think of a similar problem with the same unknown, and see if you can apply it.)
• Carry out the plan.
• Check the result (And see if you can find another way of finding it.)

Try to use these steps each time you solve any problem in the classroom.

FOURTH: Think of teaching as an art. There's no one way of doing it right. Every good teacher has his or her own way of holding the class's attention, and it's worthwhile developing your own style just as an actor, dancer, painter, or writer does.

There's a lot here, on our Web site, to help you make math entertaining. There's our hilarious free math newsletter, and links to other math sites, and lists of books with teaching ideas, and much more.

Of course, it's essential is that you yourself enjoy math and know the material you're teaching. If you find the subject boring, the kids will find it boring. If you don't really understand it, you won't be able to make it clear to them.

To see how these ideas can be applied, click the "Next Idea" button down below.

Sincerely,