How urban high schoolers got math

Jo Boaler

Jo Boaler

A group of disadvantaged Bay Area high school students who learned mathematics by discussing open-ended problems in mixed-ability groups outperformed wealthier teenagers placed in tracked, traditional classes, according to a new School of Education study. Their performance on state-mandated tests, however, was less encouraging.

Jo Boaler, an associate professor of education, followed about 700 students in three Bay Area high schools from 1999 to 2004 as they studied mathematics from 9th through 12th grade. Boaler, a specialist in mathematics education, wanted to learn how different teaching methods affected student learning. The National Science Foundation supported the five-year project.

The results surprised Boaler. Students from a school called "Railside," a pseudonym for an urban school with a 77 percent Latino, African American and Asian/Pacific Islander population, entered freshman year achieving at significantly lower levels in mathematics than students at the other two Bay Area schools, according to the study's tests. These more affluent schools included "Hilltop," the pseudonym for a rural school with a half white, half Latino population, and "Greendale," a school in a coastal community with an almost all-white student body. Unlike Railside, where teachers had designed a reform-oriented program, students at Hilltop and Greendale were placed in tracked classes mostly using conventional teaching methods involving demonstration and individual practice, she said.

Within two years, Boaler said, Railside students were "significantly outperforming" the students at the other two schools in tests designed by the study. By junior year, 54 percent of Railside students said they enjoyed math "all or most of the time," compared to 29 percent of students at the other schools, she said. Furthermore, although white students at Railside performed at higher levels than Latinos at the start of freshman year, this disparity disappeared by the end of sophomore year.

The study found no gender differences in performance in any of the tests the students took at any level. Female students made up half of the advanced classes at Hilltop, 48 percent at Greendale and 59 percent at Railside. By 12th grade, 41 percent of all Railside students were taking calculus, Boaler said, compared with about 27 percent of seniors at the other two schools.

Keith Devlin, a consulting professor in mathematics, said the study's results do not surprise him. "Good teaching is not just about teaching the tools, but teaching students how to use the tools," he said. "Learning math is about developing our mental capacity to a point [that] when faced with a new problem involving mathematical thinking, we know how to go about solving it. You can't get away from drill, rote and practice, but then you have to develop the skills for using the tools well."

Boaler attributes Railside's success to reform-oriented instruction and teachers dedicated to promoting equity. "The more [teachers] opened up the ways of being mathematical, the more kids were able to contribute," she said. "Put simply, when there are many ways to be successful, many more students are successful."

Boaler noted the results include a caveat: Although Railside students performed well on the study's tests as well as end-of-year exams administered by the high school district, they fared relatively poorly on the state's standardized tests.

"Indeed, the performance of the Railside students on the state tests is closer to the schools decided by the state to be 'similar schools' in demographics than it is to the other more wealthy schools in our study," Boaler wrote in a paper delivered last July at the International Conference on Mathematical Education. "This phenomenon speaks more to the biased nature of the tests than it does to any inadequacy in the students' understanding, in my view."

Boaler argues that the state tests gauge English-language comprehension as much as mathematical competency. "The tests use complicated terminology, terms that kids have never heard of and, when you put them into schools like this one with [English] language learners and minority kids, they don't do well," she said. "For example, kids came out of these tests asking, 'What's a soufflé?'"

Brad Osgood, a professor of electrical engineering with a courtesy appointment in education, does not question Boaler's results. However, he added, if the study's findings do not match up with the state's, each party may have to find middle ground. "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."

In Boaler's view, the greatest outcome is that Railside's teaching methods are leaving lasting results. Out of 105 seniors interviewed at the end of the study, all said they wanted to pursue mathematics courses in college—compared with 67 percent of the students who learned traditional math. In addition, 39 percent of Railside students said they planned a future in mathematics compared with just 5 percent of those from the other schools. "The mathematics teachers at Railside achieved something important that many other teachers could learn from—they gave students from disadvantaged backgrounds a great chance of success in life and taught them to love mathematics," she said. "That's very important because there is a critical shortage of people who are mathematically qualified."

How Railside succeededAccording to the study, Railside students succeeded for a variety of reasons:

  • Students of mixed abilities were placed in classes together. While Hilltop and Greendale split students into algebra, remedial algebra and geometry, Railside placed all incoming students into heterogeneous algebra classes.
  • The teachers used an approach designed at Stanford called "complex instruction," to ensure that group work succeeded while countering social and academic status differences. "What you [often] see in schools in California is a lot of group work that doesn't work well—one student does all the work and the others sit there," Boaler said. That did not happen at Railside.
  • The teachers created working environments where many dimensions of mathematical work were valued, allowing for several possible paths to a solution. Students were given several ways to contribute to solving problems. In addition to achieving high grades for correct answers, they were graded for asking good questions, rephrasing problems, explaining ideas, being logical, justifying methods and bringing different perspectives to a problem.
  • Railside uses block scheduling, developing 90-minute-long lessons for courses that last half a school year instead of a full academic year with hour-long classes. In most U.S. high schools, Boaler explained, math courses take one year, beginning with algebra, followed by geometry, advanced algebra and pre-calculus. If students fail at any point they are knocked out of that sequence and have to retake a course, which limits their options before graduating. In contrast, Railside students can take two mathematics classes a year if they want to.
  • "This organizational decision has a profound impact upon the students' opportunities to take higher-level mathematics courses," Boaler said. "[It's] part of the reason that significantly more students at Railside took advanced-level classes than students at the other two schools."

    Obstacles to broader reformAccording to Boaler, teachers in California are pressured by state standards they must cover in class and tests that assess those standards. "The most efficient way to cover everything is to tell kids how all the methods work, have them practice and move on," she said. "Students don't have time to discuss the ideas. We know many students are turned off from mathematics by that approach. They don't enjoy it. They don't succeed. But still it goes on."

    Change is difficult for working teachers because usually there isn't time or money for retraining, Boaler said. As a result, the best hope for reform lies with new teachers—Boaler teaches mathematics instruction to students in the School of Education.

    Finally, Boaler said, mathematics tends to be more traditionally taught than other subjects. "Mathematics is like this Holy Grail—it gets people riled up more than anything," she said. "There's a huge movement against reform. Schools that have tried to change have faced a lot of opposition."