Updated: This story has been updated to include a statement from the San Francisco district.
A much-debated change to math course sequencing in the San Francisco schools designed to reduce racial inequities has increased Black students’ access to some higher-level courses.
But racial inequities at the most advanced levels of high school math remain largely unchanged, according to a new analysis released March 20.
The mixed findings, from a team at Stanford University, are almost certain to be seized on by both proponents and opponents of the reform, which has been hugely influential: A draft rewrite of the state’s math framework, for instance, would encourage other districts to use a similar course sequencing.
The study is descriptive, not evaluative. It doesn’t offer a value judgment of whether the reform was beneficial or not. Ultimately, the researchers said, district will need to continue to examine and address the root causes of these persistent inequities, which could lie in differences in course availability and guidance from educators, said Sarah Novicoff, a PhD student in educational policy at Stanford’s Graduate School of Education, and an author on the paper.
“I’m sure some people who read this study will call for a return to 8th grade algebra,” she said.
But that’s not the only option the district has going forward, she said. “Eighth grade algebra has its own tradeoffs. Gaps before this policy were very large.”
A history of San Francisco’s math reforms
The district, which shifted to the new course sequence in 2014, was responding to high Algebra 1 failure rates and big racial gaps in the percentages of students progressing to higher-level math—AP Calculus and AP Statistics in particular.
Its solution: Have all students take Algebra 1—the foundational course of high school math—in 9th grade.
System leaders had two main goals with the plan: First, to give all students a more solid foundation in 8th grade math, with the aim of better preparing them to succeed in Algebra 1 and beyond. And second, to avoid the early sorting of students into high and low math tracks, a practice that disproportionately disadvantaged Black and Latino students and made it harder for them to access advanced courses down the line.
In early data reports, the district claimed that the program was succeeding, improving access for all kids—including Black and Latino students—to advanced courses. Critics of the district’s policy change claimed that it was selectively presenting data.
“It was really the sense that outside commentators and the district weren’t fundamentally agreeing about what actually happened that motivated [this study],” said Thomas Dee, a professor at Stanford University’s Graduate School of Education and one of the paper’s authors.
Dee and his colleagues found that, after the policy went into effect, more students in the district took precalculus, typically offered in 11th grade. The largest gains came from Black students. There was also a districtwide increase in the number of students taking both AP Statistics and the district’s probability and statistics course.
But large racial gaps in the percentages of students taking Advanced Placement math courses remained. The percentage of Black students taking any AP math course didn’t increase significantly, and the percentage of Latino students taking any AP math course increased by just one percentage point.
“Closing those racial and ethnic gaps in advanced math coursetaking was a central stated goal of this reform. And it seems pretty clear that in that regard, it failed on its own terms,” Dee said.
In a statement, the district said that the research shows the math policy is “making some progress,” but also highlights areas that need improvement. The statement noted plans to conduct an audit of the math program and “examine the feasibility” of increasing acceleration opportunities.
“We are in the process of collecting evidence to inform needed improvements in mathematics programming,” Superintendent Matt Wayne said.
More students take precalculus, but AP gaps remain
Algebra 1 is considered a high school math course, but many students across the country take it in 8th grade. This timeline is tied to calculus: Students usually need to complete four prerequisites—Algebra 1, geometry, Algebra 2, and precalculus—to take the class, and have to start the progression in 8th grade.
The San Francisco reform shifted this timeline. All students would take Algebra 1 in 9th grade and geometry in 10th. From there, students who wanted to take calculus in 12th grade could take a special “compression” course, which combined Algebra 2 and precalculus in 11th grade.
To see how students’ coursetaking changed, the Stanford University team examined district data from six cohorts of high school students in San Francisco—three that entered 9th grade before the math policy change, and three that began 9th grade after the new policy was put into place.
Before the change, Black and Latino students were much less likely to have taken and passed advanced math courses like precalculus or AP classes than their white and Asian peers, and a slight majority of 9th graders were enrolled in geometry.
The numbers shifted after the policy went into effect. In its first year, the vast majority of 9th graders—about 93 percent—took Algebra 1. Most of these students then went on to take geometry in 10th grade.
After the reforms were put in place, significantly more Black students took and passed precalculus at some point during their high school careers. Twenty percent of Black students in the class of 2019 had taken either the compression or standalone precalculus class before graduation, while only 13 percent of the Black students of the class of 2018 had taken precalculus.
Still, the class of 2019 took fewer AP math courses than students who had come before them. White, Asian, Black, and Latino students all saw declines, with an especially sharp decrease for Asian students.
This finding, the researchers write, “is consistent with the hypothesis that delaying Algebra I until ninth grade made it difficult for some students to complete the sequence of course prerequisites that would position them to take AP Calculus before graduating.”
This concern was at the heart of opposition to the district’s policy. Parents argued that students interested in pursuing more challenging math courses, or preparing to major in STEM fields in college, wouldn’t be able to access higher-level courses in the new sequence.
But in the two cohorts that followed—the classes of 2020 and 2021—AP math enrollment in the district started to rebound, eventually returning to the same level it was at before the policy change.
Starting with the class of 2020, the district offered students more options for math acceleration within high school, including the ability to take geometry over the summer between 9th and 10th grades. More students started enrolling in standalone precalculus in 11th grade, rather than the compression course.
Still, even as AP enrollment crept back up, racial gaps remained.
The researchers found no significant difference in AP math enrollment or credit attainment for Black students in the cohorts after the policy was put in place. Hispanic students enrolled in and passed AP Statistics at slightly higher rates after the policy change, but there was no difference for AP Calculus.
What counts as ‘advanced’ math?
The Stanford analysis adds further nuance to what has been a contentious debate about whether detracking has actually led to better outcomes for students. It’s an argument that hinges in part on what counts as “advanced” math.
The San Francisco district has said that more high schoolers—including more Black and Hispanic students—are taking advanced courses, defined as any course beyond Algebra 2. Stanford’s analysis shows that more Black students are taking advanced courses, but only precalculus—not AP Calculus or Statistics. Hispanic students are more likely to take AP Statistics, but not other courses.
Some critics of the district’s policy, including STEM professors from several California universities, have claimed that the district’s precalculus compression course doesn’t provide students the same preparation for higher-level classes that a traditional precalculus course would offer. (The University of California system categorizes the compression course as an Algebra 2 course, and it doesn’t exempt students from precalculus prerequisites in state colleges.)
Stanford’s findings also show increases in students taking AP Statistics and decreases in AP Calculus.
“There is a legitimate debate about, do we overemphasize AP Calculus as a capstone for college-bound students?” Dee said. The paper doesn’t weigh in on the topic, in part because it comes down to a value judgment, Dee said, but it does differentiate between the courses.
National surveys have shown that parents and high school counselors are more likely to say calculus is necessary for college admission than admissions counselors actually say it is. And the UC system in particular has made policy changes in recent years that expand the data science and statistics courses that students can use to satisfy admissions requirements.
Course unavailability, guidance may deepen inequities
The study doesn’t identify the reasons why some racial gaps still persist in advanced course-taking. But Novicoff said there are two big factors that play a role in what classes students end up taking: What courses schools offer, and how students decide what to take.
One stark difference in course-taking patterns, for example, is in statistics. More students took statistics after the policy change. But Black students were more likely to enroll in the district’s general probability and statistics course, while Asian students were more likely to enroll in AP Statistics.
The researchers hypothesize that this could be a reflection of course offerings.
Despite the district’s equity goals, most of the high schools with the highest percentages of Black students don’t offer AP Statistics, the researchers reported. The students at these schools don’t have the option to take the course.
Then, there’s course selection. In the district, students and families make the final decision about what math courses high schoolers will take after they complete Algebra 1 and geometry. Still, Novicoff said, factors, including counselors’ recommendations, could influence students to take a less challenging course even though they are ready for harder ones.
There are ways to address both of these issues, Novicoff said, such as ensuring that at least one AP math course is offered at each school.