Average students, on the other hand, seemed unscathed. Those who were randomly assigned to the new mixed-level class had no worse 11th grade test scores than those who studied Algebra 1 independently.
Although some proponents of course correction argue that everyone benefits from mixed-ability classes, this experiment did not show an increase in test scores for high-achieving students. In any case, the majority of students in the mixed ability classroom were assigned to Algebra 1, and relatively few students were low performers. Researchers said there may be a point at which students with low scores become so focused that they have a negative impact on other students.
Between the lowest-ranking students and the regular Algebra 1 students, there was a middle group that was just below the Algebra 1 placement cut-off and was traditionally assigned two doses of Algebra in 9th grade. For these students, taking algebra just once in a mixed-level class cut their class time in half, and the results were even more ambiguous. Although students were less likely to pass geometry in 10th grade, their performance did not seem to worsen in the second half of 11th grade. “Some interpretations are that this was a very successful experiment for most students, but it would be even more effective if combined with more instructional time,” Huffaker said. It would also be expensive, she said.
The Sequoia Union High School District, where this experiment was conducted, serves a wide range of students. This includes affluent and low-income neighborhoods in Redwood City, Menlo Park, and East Palo Alto. About one-third of the district’s students are poor enough to qualify for the federal subsidized school lunch program, while 15 percent are classified as English language learners. Almost half of the students are Hispanic, 11% are Asian, and one-third are white.
This experiment did not include advanced students who had already taken algebra in eighth grade or earlier. More than a third of the 2,000 ninth-graders continued to be taught in separate classes in Geometry or Algebra 2. A handful of extremely accelerated freshmen were in the pre-calculus stage.
This limited course-correction experiment thus avoided the community unrest that engulfed San Francisco. In San Francisco, advanced students were not allowed to take algebra in 8th grade and were all placed in the same 9th grade math class.
Tom Dee, a Stanford education professor who conducted the math study with Huffaker, a former graduate student, said the study falls between the two extremes of forcing all students to take advanced classes and banning students from academic studies. He said this shows that there is little the school can do. Take advanced coursework in the name of fairness. “If we accelerate everyone, that could have a negative impact on kids who are not adequately prepared for that acceleration,” Dee said. And slowing everyone down can have a negative impact on the performance of higher-achieving children and can put limits on the actions they are likely to take. ”
“But that’s not the only arrow in our quiver,” Dee said.
Dee emphasized that this is just one group of students in one school district, and that the results would need to be replicated elsewhere before national policy could recommend eliminating high school remedial math.
Inside the classroom
It is difficult to know what was the key to the success of this experiment. It’s possible that half of the remedial students didn’t actually need remedial work, but were wrongly placed because of their middle school math grades. At the same time, the district changed the way it taught in these mixed-ability classes, and those changes may have made a difference. A better teacher might have volunteered to teach me. These teachers received additional training and were given additional non-instructional time each day.
This school dealt with mixed abilities in an unusual way. Rather than differentiating instruction by giving different practice problems to each student, which is a common approach in U.S. classrooms, teachers were trained to give all students the same problems. Victoria Dye, Sequoia Union’s director of professional development and curriculum, said the district chose open-ended word problems that would challenge less-skilled students, but also challenge stronger students. . (An analogy would be a game with simple rules, like Othello, but still challenging for experienced players.) Dye says these “low floor, high ceiling” problems are a challenge to procedural fluency. He said it was chosen to complement the district’s curriculum, which he emphasized. And calculation.
Mathematics discussions took center stage in the classroom, allowing students to discuss each other’s analyses. In one exercise, students each wrote down their reasoning and revised it several times. “It’s great because any kid can start and improve,” Dye said.
To allow time for problem-solving and discussion, teachers streamlined the curriculum to emphasize key concepts. That meant cutting some algebra topics. Teachers made their own decisions about how to incorporate the review of middle school concepts students needed for algebra. Mr Dye explained that the review would be done on a short-term, “just-in-time” basis, rather than a complete unit reteaching.
Today, the district’s main high school has eliminated remedial math, and almost all students, except for students with severe disabilities, are enrolled in ninth-grade algebra or higher-level advanced classes. Abolishing supplementary lessons will not solve everything. Many struggling students still fail this subject and need additional support. And the wide disparities in math achievement within school buildings are not narrowing. But this could help the majority of children who are furthest behind, and is especially important after the pandemic, when even more teens are falling badly behind in math.
