The Math Problem
Nov. 15, 2007
Arithmetic and algebra haven't changed for centuries. So why do kids - and adults - have such a hard time with math?
One mathematician says he thinks he knows the answer.
"We see how people are being taught. We see the math that's going on, and it's insane," says Wayne State University math professor Steve Kahn.
Kahn says there are atrocities being committed in math classrooms everywhere.
Take fractions. Kahn says fractions give most kids and some adults the heebie-jeebies. And he says you don't have to look any farther than the definition of a fraction to figure out why.
The standard definition most teachers give, Kahn says, is that a fraction is a part of a whole.
"But if you think about it, what the hell is that? Part of a whole? OK, let's think about it," says Kahn.
"My hand is part of the whole arm. My arm is part of the whole body. The top of this table is part of the whole table. This floor is part of the whole room. The room is part of the whole building. The building is part of the whole campus. The campus is part of the whole city. Everything is part of a whole. Everything!"
Kahn says it's no wonder kids struggle with fractions, "because they're thinking OK, how do I add a hand to the top of this table."
Kahn says kids would be a whole lot less stumped if they got the definition he gave his own son when he started asking about fractions.
"I said, they're just numbers, little guy. They're just numbers," says Kahn.
"You know, like, remember how you learned a hundred and then a thousand, and you were so excited when you learned a million? Like those big giant numbers? You know, the bigger and bigger, the more exciting? I said, these are just little guys. They're just little numbers."
And Kahn says it's the same with things like arithmetic. Thick textbooks introduce addition ten different ways: how to add fractions. How to add decimals. How to add polynomials. How to add complex numbers.
But in Kahn's curriculum that he's developed for middle school students, everything students need to know about addition is in these two lines:
"The main principle of addition is that the only things you can ever add are the same things, and when you add the same things, you get the same things," says Kahn. "If you want to add dogs to dogs, fine! That's it! Two dogs plus three dogs is five dogs! If you want to add dogs to cats, no. Two dogs plus three cats is two dogs plus three cats!"
And Kahn's ideas don't just exist on paper, or in his hyperbolic proclamations. They've also been tested - in the real world, on real kids.
Steve Kahn's laboratory is University Preparatory Academy in Detroit.
For the past four years, the charter school has partnered with Wayne State to run its middle school math program.
Monica McLeod heads the program. She says her sixth grade students come to school with second- and third-grade math skills. So they start there: with adding, subtracting, multiplying and dividing whole numbers.
"And it just builds real nicely, step by step, and students start to see the power and the language of mathematics," McLeod says. "They see themselves as mathematicians. It's a discipline they understand, it's not foreign, they're not scared of it anymore."
Every week, mathematician Len Boehm visits classrooms at UPA to introduce students to math that's way beyond arithmetic.
Boehm uses the Socratic Method to get kids thinking and interested in high-level math ideas. There aren't any wrong answers. Students are encouraged to help each other through tough spots. They give hand signals to indicate encouragement, or agreement or disagreement.
Boehm says the immediate objective is to get students engaged in serious mathematical discussions, and to have fun with math.
"And the long-term goal is that, when it's all over, they'll walk away with the knowledge that hey, you know, I'm an able thinker," says Boehm. "I can do this stuff. I can do high-power conceptual mathematics."
But the road to high-level mathematics is paved with homework assignments. And the math department at UPA takes their homework very seriously.
Steve Kahn recalls one student who scored 90s all the way through his course, and a hundred on the final exam.
"And we flunked him, because he was missing too many homeworks," Kahn says.
Parents are called every time a student misses a homework assignment. And no one is allowed into any math class late.
Kahn says high standards and high expectations - backed up with repercussions for not meeting them - are cornerstones of the program.
That created some friction at UPA. Kahn says parents and teachers didn't appreciate it when students were refused entry to math class because they were late. Students might have been working on a project for another class, or they might have come to school late because of bad weather. But Kahn says those rules are important.
"And I think they're more important when you realize that's probably the most important thing that's lacking in many inner city schools," says Kahn. "Not much is expected of our kids in inner cities."
In the most recent class of kids who took three years of math at UPA, a little more than 80 percent of them entered the ninth grade ready for algebra. And two-thirds of them entered high school with at least a semester of algebra under their belts.
Tayona Cleary is an eighth grader at UPA. She says she was one of the kids who struggled with math.
"Oh, I was real bad at math when I was in elementary school - until I came here," says Cleary. "I used to hate math, but when I got here I started to like math. It started to be my best subject."
But when it comes to the state standardized test, UPA's scores were still below state averages. That could be because Kahn's team jettisoned instruction of the geometry and statistics topics that appear on the test.
"We've made choices," Kahn says, "and the core of mathematics is arithmetic and algebra. That's the road down the middle."
But UPA founder Doug Ross says the school has to live in the real world - where the state requires students to know some statistics and geometry before high school.
Next year, the Wayne State math program won't be running at UPA. The grant that paid for it ran out a year ago. UPA officials say they plan to use the curriculum Kahn has developed - but also include topics that appear on the state test.
Kahn says he doesn't consider the end of the UPA partnership to be a sad ending to the story.
He says what he and his colleagues have developed is the math equivalent of being on the verge of a cure for Alzheimer's.
"And so, if you come away from your experiment, and from your lab school, with a potential cure, you can't feel too bad. It's like, OK. Let's go."