Meanwhile, average students seemed unscathed. Those who were randomly assigned to the new mixed-level class had test scores in 11th grade that were no worse than those who learned Algebra 1 separately.
Some proponents of detracking argue that everyone benefits from mixed-ability courses, but in this experiment there was no increase in test scores for high-performing students. The vast majority of students in mixed-ability classes would have been assigned to Algebra 1 anyway, and relatively few of them were low-achieving students. It’s possible that there will be a point where the concentration of low-achieving students becomes so high that it negatively affects their peers, the researchers said.
Between the lowest and regular Algebra 1 students, there was a middle group of students who performed just below the Algebra 1 placement threshold and were traditionally assigned to a double dose of Algebra in ninth grade. The results were more ambiguous for these students, whose instructional time was cut in half by giving them only one dose of algebra in a mixed-ability class. They were less likely to pass geometry in 10th grade, but they did not appear worse off later in 11th grade. “One interpretation is that it’s a pretty successful experience for most students, but if you couple it with more instructional time, it would be even more effective,” Huffaker said. It would also be more expensive, she said.
The Sequoia Union High School district, where this experiment took place, educates a wide range of students. It includes the wealthy neighborhoods of Redwood City, Menlo Park and East Palo Alto, as well as low-income neighborhoods. About a third of the district’s students are poor enough to qualify for the federal subsidized lunch program, and 15 percent are classified as English learners. Nearly half of the students are Hispanic, 11 percent are Asian and a third are white.
This experiment did not include more advanced students who had already taken algebra in eighth grade or earlier. More than a third of the 2,000 ninth graders continued to take separate courses in geometry or algebra 2. A handful of extremely accelerated freshmen were in precalculus.
This allowed this limited experience of going haywire to avoid the community tumult that had engulfed San Francisco, where advanced students were barred from taking eighth-grade algebra and everyone was placed in the same math class. mathematics in ninth grade.
Tom Dee, a Stanford education professor who led the math study with his former graduate student Huffaker, said the study shows there are smaller things schools can do between the two extremes: force all students to take advanced courses or prohibit all students from taking advanced courses. advanced courses in the name of equity. “If we speed up everyone,” Dee said, “it could hurt kids who aren’t fully prepared for that speedup.” And if we slow everyone down, that can potentially hurt the success of high-achieving kids and limit the kinds of things they could do.
“But that’s not the only arrow in our quiver,” Dee said.
Dee emphasized that this was just one group of students in one school district and that the results would need to be replicated elsewhere before recommending the elimination of high school remedial math courses as a national policy.
Inside the classroom
It is difficult to say what might have been the key to the success of this experiment. It is possible that half of the students in remedial classes never really needed remedial classes and were misplaced because of their middle school math scores. At the same time, the district changed the way it taught in these mixed classes and it was perhaps these changes that made the difference. Better teachers could have volunteered to teach them. These teachers received additional training and had an extra rest period each day.
The school has handled mixed abilities in an unusual way. Instead of differentiating instruction by posing different practice problems to different students, which is a common approach in American classrooms, teachers were trained to pose the same problems to all students. Victoria Dye, Sequoia Union’s director of professional development and programs, told me that the district selects open-ended word problems that even a weak student could attempt, but that also provide a challenge for stronger students. (An analogy would be a game with simple rules, like Othello, which still poses a challenge for expert players.) Dye said these “low floor, high ceiling” problems were selected to complement the district’s curriculum, which emphasized mastery of procedures. and calculations.
Classroom math discussions took center stage so students could discuss each other’s analyses. During an exercise, the students each wrote down their reasoning and revised it several times. “It’s great because any kid can start and get better,” Dye said.
To allow time for problem solving and discussion, teachers streamlined the curriculum to emphasize key concepts. This meant removing some algebra topics. Teachers made their own decisions about how to incorporate a review of middle school concepts students needed for algebra. Dye described this review as occurring briefly, “just in time,” not as reteaching an entire unit.
Today, remedial math classes have been eliminated at the district’s main high schools and almost all students are in ninth-grade algebra or higher, except for students with severe disabilities. Eliminating remedial courses does not solve everything. Many struggling students still fail the subject and need more help. And it doesn’t reduce the huge disparities in math achievement within school buildings. But it could help a large portion of the kids who fall furthest behind, and it’s especially relevant after the pandemic, when even more teens are falling woefully behind in math.
