Meanwhile, the middle schoolers seemed unscathed. Those who were randomly assigned to the new mixed-grade class had test scores in 11th grade that were no worse than those who learned Algebra 1 separately.
Some proponents of detraction argue that everyone benefits from mixed-ability classes, but in this experiment there was no increase in test scores for higher-achieving students. The majority of students in mixed-ability classrooms would have been assigned Algebra 1 anyway, and relatively few were low performers. There may be a point at which the concentration of low-achieving students becomes so high that it negatively affects peers, the researchers said.
Between the lowest performing students and regular Algebra 1 students was a middle group of students who scored just below the Algebra 1 placement cutoff and were traditionally assigned to a double dose of algebra in ninth grade. The results were more ambiguous for those students whose instructional time was cut in half by being given just one dose of algebra in a mixed-level class. They were less likely to pass geometry in 10th grade, but did not seem to get worse later in 11th grade. “One interpretation is that this is a fairly successful experiment for most students, but if you pair it with more instructional time, it will 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 affluent neighborhoods in Redwood City, Menlo Park and East Palo Alto, as well as low-income neighborhoods. Approximately a one third of the students in the district are poor enough to qualify for the federal subsidized lunch program and 15 percent are categorized as English Language Learners. Almost half of the students are a spanish11 percent are Asianand a third are white.
This experiment did not include more advanced students who had already studied algebra in eighth grade or earlier. More than a third of the 2,000 ninth-graders continued to take separate classes in geometry or Algebra 2. A handful of extremely accelerated freshmen were in a preliminary course.
This allowed this limited experiment to remove tracking to be avoided community excitement which had engulfed San Francisco, where advanced students were prevented from taking eighth-grade algebra and all were 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 there are smaller things schools can do between the two extremes of forcing all students to advanced courses or banning all students from advanced courses in the name of equity. “If we speed everyone up,” Dee said, “it can be harmful to kids who aren’t fully prepared for that speed up. And if we slow everyone down, that could be potentially detrimental to the achievement of higher-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 the results would need to be replicated elsewhere before recommending eliminating high school remedial math 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 remedial students never needed remediation and were misclassified because of their high school math scores. At the same time, the district changed the way it taught in these mixed-ability classes, and perhaps those changes made the difference. Better teachers may volunteer to teach them. These teachers had additional training and received an additional non-teaching period each day.
The school dealt with 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, Sequoia Union’s director of professional development and curriculum, told me the district chose open-ended word problems that even a low-skill student could try, but that also challenged stronger students . (An analogy would be a game with simple rules, like Othello, that still presents a challenge to experienced players.) Dye said these “low-floor, high-ceiling” problems were chosen to complement the district’s curriculum, which emphasizes procedural fluency and calculations.
Mathematical classroom discussions take center stage so that students can discuss each other’s analysis. In one exercise, each student writes down their reasoning and revises it several times. “It’s great because any kid can start this and improve,” Dye said.
To allow time for problem solving and discussion, teachers streamlined the curriculum to emphasize key concepts. This meant cutting some algebra topics. Teachers made their own decisions about how to weave in a review of middle school concepts that students needed for algebra. Dye describes this review as happening briefly on a “just-in-time” basis, rather than re-teaching an entire module.
Today, remedial math has been eliminated in the district’s core high schools, and almost all students are in ninth grade algebra or more advanced, except for students with severe disabilities. Removing remedial math doesn’t fix everything. Many struggling students are still failing the subject and need more help. And that doesn’t diminish the huge differences in math achievement across school buildings. But it could help a large proportion of children who are lagging behind, and this is especially important after the pandemic, when even more teenagers are falling far behind in math.
