By Debra Viadero
Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced "algebra for all" policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier.
A trickle of studies suggests that in practice, though, getting all students past the algebra hump has proved difficult and has failed, some of the time, to yield the kinds of payoffs educators seek.
Among the newer findings:
• An analysis using longitudinal statewide data on students in Arkansas and Texas found that, for the lowest-scoring 8th graders, even making it one course past Algebra 2 might not be enough to help them become "college and career ready" by the end of high school.
• An evaluation of the Chicago public schools' efforts to boost algebra coursetaking found that, although more students completed the course by 9th grade as a result of the policy, failure rates increased, grades dropped slightly, test scores did not improve, and students were no more likely to attend college when they left the system.
• A 2008 paper by the Brookings Institution suggested that as many as 120,000 students nationwide were "misplaced" in algebra programs, meaning they had test scores on national exams that put them about seven grades below their peers in algebra classes. Further, it said, states with a high proportion of students taking algebra in 8th grade didn't necessarily outperform other states on national math assessments.
"Simply sticking students in courses without preparing them ahead of time for the class does not seem to work as an intervention," said Chrys Dougherty, the author of the Arkansas and Texas analysis, published last month by the National Center for Educational Achievement, in Austin, which is owned by the test publisher ACT Inc. "It seems to work with adequately prepared students, but not for the most challenged students."
The research news has not been completely bad, however.
Michigan State University researcher William H. Schmidt, in a not-yet-published study, analyzes data on 7,000 7th and 8th graders across the United States who took part in the Third International Mathematics and Science Study in 1995. He compared the performance of 8th graders with that of "feeder classes" of 7th graders from the same school to calculate how much students gained in mathematics over the course of that pivotal 8th grade school year.
Greatest Gains
An 8th grade algebra class, in other words, might be matched with a 7th grade prealgebra class, or a 7th grade general-math class paired with an 8th grade prealgebra or general-math class in which students had similar achievement levels.
What Mr. Schmidt found was that the learning gains were greatest for students who moved from either a general math class or a prealgebra class into a full-blown algebra class.
His findings are in keeping with a larger body of studies from the 1990s and early 2000s that suggested algebra was, for many students, the primary gateway to advanced-level mathematics and college. The problem was that too many students—particularly those who were poor or members of disadvantaged minority groups—were turned away at the gate, screened out by ability-grouping practices at their schools.
"There's no question that taking advanced courses boosts student achievement," said Adam Gamoran, a professor of education policy studies and sociology at the University of Wisconsin-Madison. His 2000 study on algebra and tracking helped catalyze the interest in expanding access for all students to algebra courses.
"Where the area of disagreement comes," Mr. Gamoran added, "is what should we do with students who performed poorly previously. In my judgment, the reason studies like mine show that students even with low levels of achievement do better in advanced classes is because the low-level classes are practically worthless."
"And there's no simple solution to this problem," he added, "because we also know that when tracking is eliminated, students at high levels don't gain as much as they do in high-level or [Advanced Placement] classes."
That's some of what Chicago found when it made a concerted effort to expand enrollment in college-preparatory classes, including algebra, according to the study on that district's initiative. The Consortium on Chicago School Research published the evaluation late last year.
"For the high-achieving kids, there was a big change in the classroom composition, so that changes the quality of classes," said study co-author Elaine M. Allensworth, the interim co-executive director at the consortium, an independent research group based at the University of Chicago. "That means you have to have teachers who can teach to all classes, and it also means you don't have an elite group of students who may be getting better advising in smaller classes."
"Meanwhile, the kids who weren't taking advanced classes before are taking them now," she said, "but they're not very engaged in them. They have high absence rates and low levels of learning."
As the trends became evident, the school system in 2003 began requiring 9th graders who scored below the national median on standardized math tests in 8th grade to take an algebra "support" class in addition to a regular algebra class. Students who scored higher continued to take a single period of algebra.
For the Chicago consortium's study, the researchers compared outcomes for students just above and below the cutoff for the "double dose" classes.
Worried about the potential for reintroducing tracking, the district also provided professional-development workshops and other resources to the teachers of the support classes, according to Ms. Allensworth.
"Because teachers had more time and resources, the instructional quality in those classes improved quite a bit," she said. "But the classes ended up concentrating more students with attendance and behavioral problems."
In the end, the study found, failure rates increased for both the targeted students and for their peers in single-period algebra classes. On the other hand, algebra test scores rose substantially for the students in the double-dose classes.
"The district thought [the double-dose initiative] was a failure because it did not improve pass rates, but our analysis showed that test scores improved a lot," Ms. Allensworth said.
Catching Up
Part of the problem, the Chicago researcher said, is that schools have little guidance on how to structure algebra programs to serve all students.
"Even though everyone's using double algebra periods these days, there's not a ton of research on this," Ms. Allensworth said. One exception, she noted, is studies of the Talent Development model developed by researchers at Johns Hopkins University in Baltimore, which incorporates double-dose classes as part of a broader set of reforms.
The 48,000-student Garden Grove Unified School District in Orange County, Calif., turned to a multipronged approach to increase algebra success rates in the highly diverse district.
According to Gariela Mafi, the associate superintendent for secondary education, students who are likely to struggle in a regular, single-period algebra class are directed to take either an additional "companion" algebra class or "algebra readiness," with the expectation that students in the latter course will take regular algebra the following year.
The most advanced students take either geometry or a single period of algebra. While there hasn't been a scientific evaluation of the district's algebra efforts, Ms. Mafi said, passing rates for algebra and other advanced-math courses have gone up over the past four years.
"I think the issue is that it's not one-size-fits-all," she said.
The Garden Grove district in 2004 won the Broad Prize for Urban Education, bestowed by the Los Angeles-based Eli and Edythe Broad Foundation, for its efforts at improving achievement among all student population groups.
'Basic Arithmetic'
Tom Loveless, the author of the report from the Washington-based Brookings Institution on "misplaced" math students in algebra, said the issue is even more complex.
"No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year," said Mr. Loveless, who favors interventions for struggling students at even earlier ages.
Nationwide, research findings may diverge because testing content varies—the TIMSS test has more algebra content than many state exams taken by 8th graders—and because course content varies from classroom to classroom.
"If you take what's called algebra class, and you look at the actual distribution of allocated time, you find that many of those teachers spend a very large portion of that year on basic arithmetic," said Mr. Schmidt, who is a distinguished university professor of education at Michigan State's East Lansing campus. His research on U.S. classrooms has found, in fact, that nearly a third of students studying algebra are using arithmetic books in their classes.
Likewise, Mr. Loveless' study found that "misplaced" students tended to attend large urban schools where their teachers were more likely to have less than five years of experience, less likely to hold a regular teaching certificate, and less likely to have majored in math than teachers of typical 8th grade algebra students.
"It may well have more to do with whether students have been given adequate opportunities to learn this stuff," Mr. Schmidt said of the disappointing findings that have emerged from some studies.
