Meanwhile, the average students seemed unscathed. Those who had been randomly assigned to the new mixed-level class had test scores in 11th grade that were no worse than those who had learned Algebra 1 separately.
Some diversion advocates argue that everyone benefits from mixed-ability classes, but in this experiment there was no increase in test scores for the highest-achieving students. The vast majority of students in mixed-ability classrooms would have been assigned to Algebra 1 anyway and relatively few were low achievers. There may come a point where the concentration of students with low scores becomes so high that it negatively affects their peers, the researchers said.
Between the senior students and the regular Algebra 1 students, there was an intermediate group of students who scored just below the cutoff for placement in Algebra 1 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 a single dose of algebra in a mixed-level class. They were less likely to pass geometry in 10th grade, but did not appear to be worse off in 11th grade. “One interpretation is that this was a fairly successful experiment for most students, but if you combined it with more instructional time, it would be even more effective,” Huffaker said. It would also be more expensive, he said.
The Sequoia Union High School district, where this experiment took place, educates a wide range of students. It includes wealthy neighborhoods in Redwood City, Menlo Park and East Palo Alto, and 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 one-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 geometry or algebra 2 classes. A handful of extremely accelerated freshmen were in precalculus.
That allowed this limited diversion experiment to avoid the community upheaval that had engulfed San Francisco, where advanced students had been prevented from taking algebra in eighth grade and were all placed in the same ninth-grade math class.
Tom Dee, a Stanford education professor who conducted the math study with his former graduate student Huffaker, said this study shows that there are smaller things schools can do between the two extremes of requiring all students to take advanced courses or bar any student from advanced courses in the name of equity. “If we speed everyone up,” Dee said, “it could be detrimental to kids who aren’t fully prepared for that acceleration. And if we slow everyone down, it can potentially be detrimental to the achievement of higher-achieving kids and limit the kinds of things they could do.”
“But it’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 have to be replicated elsewhere before recommending the elimination of high school remedial math classes as a national policy.
Inside the classroom
It is difficult to say what could have been the key to the success of this experiment. It is possible that half of the remedial students never actually needed remedial and were incorrectly placed because of their high school math scores. At the same time, the district changed the way it taught in these mixed-ability classes, and it could be those changes that made the difference. Better teachers could have volunteered to teach them. These teachers received additional training and were given an additional non-teaching period each day.
The school handled mixed abilities in an unusual way. Instead of differentiating instruction by giving different practice problems to different students, which is a common approach in American classrooms, teachers were trained to give the same problems to all students. Victoria Dye, director of curriculum and professional development at Sequoia Union, told me that the district selected open-ended writing problems that even a student with low skills could solve, but that also challenged stronger students. (An analogy would be a game with simple rules, like Othello, which is still a challenge for expert players.) Dye said these “low floor, high ceiling” problems were selected to complement the district’s curriculum, which emphasized procedural fluidity. and calculations.
Classroom mathematics discussions took center stage so that students could discuss each other’s analyses. In one exercise, each student wrote down their reasoning and reviewed it several times. “It’s great because any kid can start doing it and get better,” Dye said.
To allow time for problem solving and discussion, teachers simplified the curriculum to emphasize key concepts. That meant eliminating some algebra topics. Teachers made their own decisions about how to incorporate a review of the high school concepts that students needed for algebra. Dye described this review as being done briefly and “just in time,” not as a repeat of an entire unit.
Today, remedial math has been eliminated in the district’s major high schools and nearly all students are in ninth grade algebra or a more advanced class, except for students with severe disabilities. Eliminating recovery math doesn’t solve everything. Many struggling students are still failing the class and need more help. And it does not reduce the huge disparities in math achievement within school buildings. But it could help a large portion of the children furthest behind, and that’s particularly relevant after the pandemic, when even more teenagers are woefully behind in math.
