Math Adds Up At CCNY Teacher Training Program
By Kim Brown

It takes a suspension of disbelief to participate in “Mathematics in the City.” In one City College classroom Professor Catherine Twomey Fosnot is wearing a sailor’s jacket and standing on a table. Colored cubes are scattered on the floor; the class of teachers and graduate students is gathered around her.

But here there is more than meets the eye. If you were a participant you would know the cubes represent swimmers; Fosnot is the captain of a boat. And the teachers are trying to figure out what pattern is formed by the bathers that are a safe distance away.

The teachers talk among themselves, but they want more facts. “Is that the real height of the captain’s perch?” One student asks.

“Yes,” Professor Fosnot answers, and then she laughs, “And I am the real captain.” The students are convinced. They are submerged in a mathematics environment where math is not a foreign language but the posing and solving of problems.

Mathematics in the City is a nationally recognized project in mathematics education reform developed by Professor Fosnot and Maarten Dolk. Both wanted to help mathematics teachers base their instruction on how students learn. Professor Fosnot is a former mathematics teacher herself and the developer of the Center for Constructivist Teaching. At the center she helped teachers see the big ideas their students were struggling with. But she wanted to combine the ideas with didactics—or the development of mathematical learning.

In the late 80’s she began to bring groups of teachers to the Netherlands for one-week intensive workshops at the Freudenthal Institute organized by Dolk and his colleagues.

In 1993 Fosnot took a position at CUNY’s City College and began to build a large in-service program involving five school districts in New York City known as Mathematics in the City. The project was funded by the National Science Foundation and the Exxon Educational Foundation and began in 1995.

During they next five years they worked with over 450 elementary school teachers in New York City and attempted to deepen teachers’ knowledge of the mathematics they teach. They also wanted to help them see themselves as mathematicians willing to raise questions. Throughout the project they interviewed teachers, analyzed children’s work, and videotaped lessons. The result is a course that “teaches teachers to teach better,” according to Professor Fosnot.

Professor Fosnot can be an imposing figure as she explains the theories behind the Institute and looks out from behind rectangular glasses. “We start with real world problems that are meaningful to learners,” she says, “then we investigate how children learn and go back to teach this way.”

And the program seems to work. Rocky Metzger is one of six teachers who traveled to New York from North Dakota to participate in the Institute. He teaches 5^th and 6^th grades and was a high school dropout himself. He explains passionately that part of the reason he left school was because he didn’t learn the way teachers were asking him to learn.

“Here we’re learning to allow children to explore,” he said, “just understanding rules doesn’t enable you to do the math. Children need to understand the meaning behind the math.”

The approximately 90 students in the summer institute are broken up into six groups. In one classroom they are opening cubes to investigate how many two-dimensional shapes can be formed. Students exchange ideas as they trace shapes on graph paper. “Oh, so you mean if you move one of these pieces you’ll still get a cube?” one student asks.

In another room iMacs hum softly. Christina Bookout, an elementary teacher in Park Slope, Brooklyn says the Institute has given her “innovative ideas,” that she will use in her class. In a third room, staff member Dawn Selnes is using colored tiles to help teachers see what happens to the area of a shape as the perimeter is changed.

In her own classroom Dr. Fosnot is transformed from a scholarly professor to an energetic teacher with bare feet and a baseball cap. Faces light up at the conclusion of her lesson. “So what you’re saying is this triangle here is similar to this triangle here,” she points to shapes that students drew on the blackboard. “Can kids do this?” she asks. The teachers nod.

She explains that teachers used to start by proving the triangles were similar. But now they are starting with real world problems, like the swimmers that might have been hit by the boat. “Mathematics is about ongoing observation of the world around you,” she says, “It’s about teaching a discipline that’s alive.”#

For more information about Mathematics in the City call Dawn Selnes 212-650-8148 or Pablo Carvajal 212-650-6346 or go to www.mitccny.org

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