Natural Mathematics



PHILADELPHIA - If someone offered you $1 million to complete a calculus problem or add a group of fractions, and you know you'd walk away with empty pockets, a well-known mathematician says don't be too hard on yourself.

Our brains aren't well equipped to grasp those kinds of advanced mathematics - and most people who can do such abstract number twisting don't even understand what they're doing at first, said Stanford University mathematician and National Public Radio's "Math Guy" Keith Devlin.

Unlike what Devlin calls "natural mathematics," such as counting, algebra, geometry and simple arithmetic that the brain does naturally, "formal mathematics," such as adding fractions and calculus, seems counter to common sense to our brains.

Because natural and formal math require different kinds of thinking, teachers may want to look for ways to teach them differently too, said Devlin, who was speaking at the annual meeting of the National Council of Teachers of Mathematics. The four-day conference of about 17,000 math teachers started Wednesday in Philadelphia.

So how does one learn formal math? Fake it till you make it - and not everyone does because it can take years of frustrating, repetitious and rote rule-following, Devlin said.

"You have to be psychologically willing and able to just follow the formal rules, play the game and not try to make sense of it. Eventually, for some people, the meaningless game will eventually become meaningful," he said.

Devlin said it was not until he was a graduate student that he really understood what he was doing. "I learned to play the game first ... to manipulate the symbols to get the right answer, and the understanding came later," he said.

Maybe formalized math should be taught in a manner similar to the immersion method used for teaching language, in which a teacher just starts speaking in a foreign tongue and students eventually start figuring out what's being said, Devlin said. But not all students learn language that way - and not all students will master formal mathematics, he said.

"We shouldn't be surprised that there are parts of mathematics that the brain isn't suited for," Devlin said. "But if we're aware of the problem, then we can find ways around it and the strategies to deal with it."

The conference is slated to feature more than 1,000 sessions, workshops and classes - all emphasizing how to strengthen instructor skills and teaching methods for the students of the 21st century.

That also includes more bottom-line ideas such as having enough money for teacher training and equipment, and trying to get parents not to pass their insecurity and negativity about math to their children, said Johnny Lott, president of the National Council of Teachers of Mathematics.

"When you think of the stereotype of math and science - the geeky thing - that's the image many parents have, and it's a perception we're working to change," he said. "Parents read to their children from a young age, and we're trying to instill that they can do math with their children too."

Founded in 1920, the council has 100,000 members and seeks to improve mathematics education for students from pre-kindergarten through 12th grade.