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BOALER: The reform method computes.
Linda A. Cicero/News Service |
In one classroom, a teacher
stands beside a whiteboard, pointing to equations and
intoning “X minus 4” and “X minus
5.” Students are slumped at their desks, some
with their heads down.
Fast-forward to a video of another classroom. Here,
four kids are working together on a poster that represents
the elusive X as a graph, as a T table and as a shape.
The chatter around the table is electric. No one is
dozing off.
“One of the things teachers say when they watch
the second video is that not only are the kids engaged,
but they’re so motivated,” says associate
professor of education Jo Boaler. “Even when they’re
completely stuck, they don’t move off task. They
keep talking to each other about how to move forward.”
Boaler, a specialist in mathematics education, filmed
the two classrooms to illustrate two very different
approaches to teaching math—traditional textbook-based
teaching versus a “reform-oriented” approach
that involves “complex instruction.” In
a five-year study funded by the National Science Foundation,
she followed 700 students at three Bay Area high schools:
an urban, ethnically diverse school offering reform
classes, and two more affluent schools that took a conventional
approach.
Boaler found that those at the school offering mixed-ability,
reform classrooms outperformed those in tracked, traditional
classes. What’s more, students in the reform classes
liked math more, with almost 40 percent of them saying
they wanted to be mathematicians, compared to 5 percent
in the traditional rooms. The proof was in their course
schedules: by 12th grade, more than 40 percent of the
reform students were taking calculus, compared to about
27 percent in the traditional classrooms.
Reform mathematics instruction is characterized by teachers
who eschew textbooks in favor of designing their own
curricula. They work collaboratively, teach math as
a whole—not broken into separate courses such
as algebra and geometry—and require their students
to work as teams. “[The teachers] have a rule
that you’re not allowed to move on to the next
problem until everyone understands,” Boaler says.
“And they grade the group discussion. They value
asking good questions, rephrasing problems and sharing
methods.”
Although students at the urban school were the weakest
in math when they entered high school, within two years
they were scoring better than their counterparts at
the traditional-approach schools on tests designed by
the study, and performing well on district exams. However,
they did poorly on state standardized tests. Boaler
says that’s largely because the state exams test
language comprehension in addition to mathematical competency.
Some students, she relates, emerged from the standardized
exams saying things like, “What’s a soufflé?”
Brad Osgood, a professor of electrical engineering with
a courtesy appointment in education, told Stanford
Report he does not question Boaler’s results.
But, he said, it may be necessary to find a middle ground
between the state standards and the reform-instruction
approach. “You need technical skills, there’s
no doubt about that,” he said. “But no curriculum
is a replacement for inspired teaching. If this helps
teachers get excited, that’s a good thing.”
Indeed, the results of the study have convinced Boaler
that teachers can create environments in which different
learning styles are valued and rewarded. “We know
a fair amount about good teaching,” she says.
“Now, real work needs to be done in getting these
changes into schools.”
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