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.”
