By Steve Hill
It seems that old saying, “as easy as 1-2-3″ might not be so easy after all.
The UW’s Elham Kazemi, an assistant professor in the College of Education, says different students go through different thought processes when completing even the simplest math computations. Adding, say, 2 plus 2 to get 4, can be a process as different as the students in the classroom. Educators’ understanding of the different strategies students use, Kazemi argues, is critical if math education in this country is to improve.
“To teach math well, you need to know what your students understand and how these understandings develop,” she said. To do that teachers need to delve into an individual student’s mind, not merely look for right or wrong answers. That is Kazemi’s motivation for a project that is drawing positive reviews from educators in six area school districts – Bellevue, Lake Washington, Mercer Island, Northshore, Seattle and Shoreline.
Expanding the Community of Mathematics Learners (ECML) is a five-year $3.9 million National Science Foundation-funded project that is expected to serve about 2,500 teachers in the region by spring of 2004. Ramesh Gangolli, a professor of mathematics, is the principal investigator on the project. Kazemi is a co-principal investigator along with Christopher Fralie, from the Lake Washington School District; Nathalie Gehrke, director of the teacher education program in the College of Education; June Morita, an associate professor of interdisciplinary arts and sciences at UW Bothell; Rosemary Sheffield, director of Center Connect in the College of Education; research associate Virginia Stimpson; and Ginger Warfield, a senior math lecturer.
Those eight currently support 270 teacher leaders who facilitate seminars for other math teachers interested in expanding their teaching repertoire. During the seminars participants read and discuss cases written by real teachers about real student interactions. Those cases highlight the different ways students solve math problems. The teachers also do some math problems together and finally, they do their own case studies and bring them back to the group for further discussion.
It’s a process that is radically different from most teacher training.
“They’re not coming to the seminars to learn how to teach any particular curriculum and they’re not necessarily getting a whole set of activities to do in their classrooms,” Kazemi said. “The seminars instead are there to help teachers develop a much deeper understanding of the mathematics the kids are doing and how their ideas develop.”
An original crop of about 70 teachers went through the first of five different seminars during the 1999-2000 academic year. Diane Kane, a teacher at Lake Washington’s Bell Elementary, was one of a handful of teachers who helped facilitate the seminars for the first group of teachers.
“There’s a change that happens in people,” she said, recalling what she went through in her own training and what she witnessed in the teachers she later trained. “It’s so vastly different from how we were taught to teach math and vastly different from the experience each of us had as students. You have to make a real paradigm shift.”
What Kane and other teachers were taught was the so-called right way to teach math. It focused on teaching the most efficient method for solving problems then drilling the students on that particular method. The ECML seminars, however, encourage teachers to find out what students are thinking when performing mathematical computations.
Once teachers develop an understanding of the student’s thought process, they are encouraged to build from that base. They are taught to ask questions that might push the student toward another, often more efficient, way to complete the problem. But in the end, the more right ways a student learns to perform a problem, the better, according to Kane.
“You are taught there’s one way to do addition, there’s one way to do subtraction, one way to do multiplication and one way to do division,” she said. “But in the seminars you’re taught that there’s more than one way and furthermore, the more ways a student knows how to solve a problem, the better their understanding.”
Principals in the Bellevue and Lake Washington districts have been so impressed with the project that they’re now requiring all elementary school teachers to take the first of five seminars. It deals specifically with the base-10 numbering system. The other seminars cover basic operations like addition, subtraction, division and multiplication; working with data; measurement; and geometry.
If the project can better students’ understanding of math it won’t happen too soon. Consider performances in the mathematics portion of the Washington Assessment of Student Learning (WASL), for example. Just 43 percent of fourth-graders and an abysmal 27 percent of seventh-graders met the state standard during the 2000-2001 round of testing. What’s worse, according to Kazemi, is what that might mean down the road.
“Math is really a gatekeeper,” she said. “If kids do well in elementary school math, it sets them up to do well down the road in all kinds of subjects. If they do poorly, they tend to struggle.”
And many elementary school students are getting their instruction from teachers who don’t necessarily identify with math, she says. Kane, for example, struggled teaching the subject prior to participating in the seminars.
“The students didn’t seem to like it at all. I was so frustrated,” she remembered. “It made me feel very inadequate as a teacher.”
That’s why Kazemi said one of the important aspects of the project is to support the teachers as they attempt to make what can be a huge shift in their classroom practice.
“The demands on teachers are already very high,” Kazemi said. “So one of the challenges of this project is to support teachers as they try to create conditions in the classroom that they probably never experienced themselves.”