In Michigan, talking your way to a solution
Teri Keusch, a sixth-grade math teacher at Portland Middle School in Michigan, is fired up over her math class - and her students are getting into it, too.
"Okay, I have one square pan of brownies that costs $27," Ms. Keusch begins, laying out a problem to students in groups around the room. "They're selling pans of brownies, and we want to find out how much to charge for the brownies that are left."
She and her kids use a textbook from the Connected Mathematics Project, a math-reform program developed at Michigan State University in nearby East Lansing. It emphasizes learning in groups, using calculators, and real-life problems. Portland became a "pilot" school in the 1990s for the program. Hanging on the wall is a sheet with pockets that reads "calculator caddy." It's empty. Kids have their calculators, even though today's lesson on fractions doesn't use them.
Keusch tells the children only 2/3 of one pan of brownies remains. But the man at the bake sale only bought 1/2 of what is left. So what fraction of the full pan did he buy? How much did he pay?
"Try it by yourself at first," she calls out over a murmur of group discussions. "If you're having trouble, you've got people you're sitting with who can help."
At a cluster of student desks, Jenna, Adrienne, and Tony begin debating the issue.
Adrienne: "I have 1/2 of a pan of 2/3, so can I multiply here? Do I have a multiplication problem?
Tony: No. You've got to make a fraction of a fraction. I think that means you have to divide.
Just then Ms. Keusch chimes out to the class: "When you multiply whole numbers the answers get bigger. Is that what happens when you multiply fractions?"
Jenna looks lost. Tony has a puzzled expression on his face. And Adrienne decides to multiply anyway. She gets 1/3.
"What I did was cut the pan into thirds," Adrienne explains to her partners. "I knew one 1/3 was already eaten. And that they had 2/3 left. So I think if they split it in half, then they have just 1/3 left."
On a different problem where 2 1/4 pans of brownies are left, Tony explains his route: "I divided my pan of brownies into 16. The guy at the bake sale wants to buy exactly 1/2 of what's left and 1/8 is easier for me to work with."
Jenna splits her pans into 1/8ths, estimates how many 1/8ths, then counts out two even stacks of nine units each.
These are the sorts of wrestlings that warm Keusch's heart. State test scores seem to back up her faith in the program.
"I love this class," she says. "The focus is much more on the teacher. It's critical for them to listen to each other. People misinterpret these classes. They're not about algorithms, they're about understanding fractions."
(c) Copyright 2000. The Christian Science Publishing Society