Adds Up At CCNY Teacher Training Program
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
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
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 5th and 6th 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.
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
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.”#
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
Update, Inc., P.O. Box 20005, New York, NY 10001.
Tel: (212) 481-5519. Fax: (212) 481-3919.Email: firstname.lastname@example.org.
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