What is Mathematrics?
For several years now, I have invited groups of homeschooled kids to meet at my house for Math Club – a relaxed, mind-stretching time of games and hand-on activities. And each year, when a new group comes, I try to gauge their expectations by asking them, "What is math?"
One answer that consistently ranks at the top of the charts and usually the first thing my students say is, "Numbers!"
If we took a nation poll, I think we'd find that most adults agree with my Math Club students: Mathematics is numbers. Math is arithmetic. Adding, subtracting, multiplying, dividing. Fractions and decimals and percents and ratios. Numbers, numbers and more numbers. Of course math is numbers. What else could it be?
In my workshops, I try to broaden students' ideas of math. There's a whole lot more than numbers out there. Mathematics can be beautiful: shape, symmetry, perspective, tessellations…or mathematics can be history: Euclid, Archimedes, Newton, Gauss….Or mathematics can be science, baseball statistics, logical puzzles or just plain fun.
As my Math Club kids discover every year, math is a great way to spend an afternoon with friends.
In the same way, in my workshops for homeschool parents, I want to help people see the variety and richness of math. I encourage parents to look beyond their textbook – a useful tool, but such a limited one – and explore the adventure of creatively logical thinking. If we give our children a good taste of that "Aha!" feeling, the thrill of working through a challenging puzzle and solving it, then we won't be able to keep them away from math.
Math books ruin mathematics for most people, distorting a discipline that is half art and half sport by turning it into boring lecture and drill. Imagine a piano teacher who insisted her students spend six years on scales and exercises of gradually increasing difficulty before she let them attempt a piece of actual music. Or a football coach who made his team run laps and do sit-up every day, but only let them play two or three games a year – and scrimmage games at that. How many people would become bored with music or learn to hate football under such instructions? As every coach knows, skill grows through practice, practice, practice. But practice is meaningless unless the team has a real game to play. And the best practice takes advantage of the benefits of cross training by emphasizing variety rather repetitive drill.
Real mathematics is an exploration of patterns and mysterious connections. School math is page after page of arithmetic. Real math is an M.C. Escher drawing of interlocked fish splashing across a page. School math is long division by hand. Mathematical cross training is games and puzzles – the fun stuff that textbooks look down on, but real mathematicians see as the heart of their subject.
Real mathematics is mental play. This is the essence of creative problem solving. This is what we need to teach our children – more important than fractions or decimals or even the times tables. Math is not just rules and rote memory. Math is a game, playing with ideas.
"A teacher of mathematics has a great opportunity," wrote mathematician George Polya. "If he fills his allotted time with drilling his students in routine operations, he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students, he may give them a taste for, and some means of, independent thinking."
When we wonder how best to teach mathematics, it helps to consider how we teach reading. Of course, phonics is important – but is it the whole story? Not a chance! We help our children learn to read by filling their world with interesting words: riddles, good stories, and letters from Grandma. We let them see us flipping through the newspaper, diving into the latest homeschool magazine and dragging stacks of books home from the library. This combination of providing a rich environment and setting a good example helps build a life-long love for reading.
Likewise, we can teach children to love mathematics by filling their worlds with intriguing ideas and math toys. But environment isn't enough. Before we can show our kids how to play with math, we much recapture that "Aha!" feeling for ourselves. And to do that, we have to put the textbooks and teacher's manuals away, at least for a while, and learn to do real mathematics. We have to forget the way we were taught and launch ourselves into the unknown.
We teachers need to learn how to play math.
And when we find something fun, our children will want to try it too. "Hey, look what I found!" is a fantastic motivator.