July 24, 2009

Teachers learn new way to help kids figure out math

by K.C. Jaehnig

CARBONDALE, Ill. -- Now that your little boy can walk, it’s time to sign him up for a five-mile road race.

If you can spot the flaw in that thinking, you’ll get the idea behind a Southern Illinois University Carbondale project that aims to change the way elementary school teachers teach math.

“It’s about understanding the developmental progression in math -- the stages children go through in learning mathematics,” says Jennifer L. Prusaczyk, a doctoral student in SIUC’s College of Education and Human Services and one of the coaches for the three-year, $946,431 project funded by the Illinois Board of Higher Education.

“Teachers listen to the students talk about how they solved their math problems, fit the existing knowledge into the progression and then design new problems that build on that knowledge and move them up to the next level of thinking.”

Most teachers do OK with math’s basics. Put two apples on a desk, then plunk down one more or take one away and bingo! The kids now know addition and subtraction. The next level should still involve some sort of visual aid to help kids see how to reach a solution, but too often, teachers leap directly from apples to algorithms.

“The teacher gets up with chalk in hand, writes some figures on the blackboard, explains what she’s doing and then says, ‘Everybody get that?’” says Susanne C. Ashby, who wrote the grant application and oversees the project.

“It’s all teacher talk -- ‘Let me show you how to do it’ -- but the students are clueless about why they’re doing it.”

Adds Prosaczyk, herself a former middle school math teacher, “The problem is, that’s a memorization tool. Some students will do well with that, but many will not. If there’s no understanding tied to it, it’s easy to forget later which tool goes with which procedure.”

The SIUC project homes in on that middle step. Sets of “manipulatives” -- brightly colored or oddly shaped little objects -- can stand in for the apples, but many children choose to draw their own symbols on their worksheets as they attempt to visualize, for example, how two-fifths of six and a quarter might look.

A document reader allows teachers to project each worksheet so the whole class can see it. As children explain the thinking behind their solutions, they clarify and imbed the knowledge in their own minds while showing the other kids that you can arrive at an answer by many different routes.

“The emphasis is on the thinking, not on the procedure,” Ashby says.

“It also takes out that idea that there’s only one way -- the teacher’s way -- to do something,” Prusaczyk says.

Elementary and middle schoolteachers -- the targets of this particular project -- generally don’t major in math, and most of them learned what they do know the old-fashioned way.

“They’ve had to change the ways they think about and teach math, leave their comfort zones and embrace a new mindset,” Prusaczyk said. “That’s hard.”

To use the new method effectively, teachers have to devise problems that build on the base of what their students already know while moving them further along. If the students don’t “get it,” teachers must figure out where the kids are going off track and how to redirect their thinking so the concept becomes clear.

“There’s no roadmap,” Ashby says. “We’re asking the teachers to be thinking on their feet all the time.”

It turns out that teachers learn this new style best by seeing it done, an insight that came during the project’s second year when 10 teachers from Mounds asked to take part. Ashby and Prusaczyk had given the 35 original participants all the “bookwork” first, but because the Mounds group was a year behind, they jumped right in to classroom demonstrations, figuring they’d follow up with theory later. The Mounds teachers found their students’ latent abilities astounding.

“The resistance you always get is, ‘My students can’t do that -- it will never work in my classroom,’” Ashby says.

“We proved to them in their own classrooms with their own students that it can work before they ever got any theory. That’s just how powerful teaching can be when it’s done appropriately. We call that our biggest lesson learned.”

In the project’s final year, which will start with the fall semester, the coaches will step back, allowing the teachers to move to the front of the room. The coaches will limit themselves to observing, offering feedback and helping the teachers think their way to solutions for classroom problems that may crop up. In a lot of ways, it’s like the new way of teaching math.

“We don’t go in and say, ‘Here it is, do it this way,’” said Prosaczyk.

Adds Ashby, “We like to say that the person doing the learning is the person doing the talking.”