Meanwhile, ordinary students seem unharmed. Those who were randomly assigned to the new mixed-grade class had test scores in the 11th grade that were no worse than those who had taken Algebra 1 separately.
Some conservative advocates argue that everyone benefits from mixed-ability classes, but there has been no increase in test scores for students who are high achievers on these tests. Most students in mixed ability classes would have been given Algebra 1 anyway and relatively few were low achievers. There may be a time when the concentration of low-scoring students becomes so high that it has a negative impact on peers, the researchers said.
Among the low and average Algebra 1 students, there was a middle group of students who scored just below the cutoff for placement in Algebra 1 and were traditionally assigned a double dose of algebra in ninth grade. The results were ambiguous for these students, whose instructional time was cut in half by giving them only one dose of algebra in a mixed-grade class. They are less likely to pass geometry in 10th grade, but they don’t seem too bad over time in 11th grade. “One interpretation is that this was a successful experiment for many students, but if you pair it with more instructional time, it could be more effective,” Huffaker said. It will be more expensive too, he said.
The Sequoia High School District, where this experiment took place, educates a variety of students. It includes affluent neighborhoods in Redwood City, Menlo Park and East Palo Alto, as well as low-income neighborhoods. About one-third of students in the district are poor enough to qualify for the state-sponsored lunch program, and 15 percent are classified as English learners. About half of the students are Hispanic, 11 percent are Asian, and a third are white.
This test did not include more advanced students who had taken algebra in the eighth grade or earlier. More than one-third of the 2,000 ninth-graders went on to be taught in separate geometry or Algebra 2 classes. A few of the fastest-growing freshmen were in precalculus.
That allowed this reduced standardized test to avoid the social unrest that plagued San Francisco, where advanced students were barred from taking algebra in the eighth grade and everyone else was put in the same ninth-grade math class.
Tom Dee, a Stanford education professor who conducted the math study and his former student Huffaker, said the study shows that there is little that schools can do between the two extremes of forcing all students to take advanced courses or preventing any student from advanced courses in the name of equity. “If we speed everyone up,” said Dee, “it can be dangerous for children who are not fully prepared for that speeding up.” And if we limit everyone, it can be very detrimental to the success of kids who do well and limit the kinds of things they can do.”
“But it’s not the only arrow in our quiver,” said Dee.
Dee emphasized that this is just one group of students in one school district and the results will need to be replicated in other areas before he recommends eliminating high school remedial math as a national policy.
Inside the classroom
It is difficult to say what might be the key to success in this experiment. It’s possible that half of the remedial students never really needed remediation and were misplaced because of their middle school math. At the same time, the district changed the way we teach in these mixed ability classes and those changes may have made the difference. Better teachers may volunteer to teach them. These teachers had more training, and were given more non-teaching time each day.
The school caters to a variety of abilities in an unusual way. Instead of differentiating instruction by giving different practice problems to different students, which is common practice in US classrooms, teachers are trained to give the same problems to all students. Victoria Dye, Sequoia Union’s director of professional development and curriculum, told me that the district chose open-ended word problems that would challenge even a low-ability student, but that provided a challenge for stronger students. (An analogy would be a game with simple rules, like Othello, which still offers a challenge to expert players.) Dye said these “low-floor, high-ceiling” problems were chosen to complement the district’s curriculum, which emphasizes procedural fluidity. and statistics.
Class math discussions were moderated for students to discuss their analysis. In another exercise, each student wrote down their thinking and reviewed it several times. “It’s very good because any child can start that and improve,” said Dye.
To allow time for problem solving and discussion, teachers organize the curriculum to emphasize key concepts. That meant cutting some algebra topics. Teachers made their own decisions to weave in the revision of middle school concepts that students needed in algebra. Dye described this review as occurring briefly “just in time”, not a complete re-teaching of the unit.
Today, remedial math has been removed from the district’s core high schools and nearly all students are in ninth-grade algebra or more advanced classes, except for students with severe disabilities. Completion of maintenance calculations does not fix everything. Many struggling students are still failing the course and need additional help. Nor does it reduce the large differences in math achievement within school structures. But it can help a large proportion of children who are further behind, and that is especially important in the wake of this epidemic when many young people are woefully behind in mathematics.
