Curriculum

A Bold Effort to End Algebra Tracking Shows Promise

By Stephen Sawchuk — June 12, 2018 9 min read
BRIC ARCHIVE

San Francisco

Four years ago, school district leaders did something counterintuitive in this tech-laden metropolis, where STEM isn’t just a buzzword but practically a way of life.

They got rid of accelerated middle-school math classes.

Part of an ambitious project to end the relentless assignment of underserved students into lower-level math, the city now requires all students to take math courses of equal rigor through geometry, in classrooms that are no longer segregated by ability.

That means no “honors” classes. No gifted track. No weighted GPAs until later in high school. No 8th grade Algebra 1.

In terms of curriculum, this is about as controversial as it gets. And that’s not just because of its math implications, but because of the parental pushback such a plan is guaranteed to generate.

In effect, by de-tracking math classes, San Francisco has done away with one of the key avenues that the well-connected use to give their children an academic advantage.

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Fallout was swift. Parents, concerned about rigor and whether their children would be able to take calculus by senior year, barraged everyone from the district superintendent’s office to City Hall with complaints and petitions.

But the district has held firm, and now, preliminary evidence suggests that San Francisco’s gamble may be paying dividends for black and Latino students, without hurting students who otherwise would have taken algebra earlier.

But the question still remains: Is that going to be enough to keep the policy in place for years to come?

Context for a Debate

The 56,000-student district’s theory of action is clear: Math is by far the most heavily tracked course in the American secondary education system, and the ramifications for students of color are life-altering.

Federal data show that white and Asian students disproportionately take Algebra 1—long seen as a critical gateway to advanced math—before high school, while African-American and Latino students are overrepresented among those taking it for the first time in grade 9. Many of them take it as late as their junior or senior year.

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Like so many other elements of K-12 education, those disparities partly reflect parents’ relative socioeconomic capital.

“Many of these parents are thinking, ‘How can I get my kids into the few spots in Stanford and Harvard?’” said James Ryan, who was until last month the science, technology, engineering, and mathematics executive director for the district. “They think the earlier students distinguish themselves from their peers, the better off they’ll be, rather than seeing math as a platform for equity.”

As if the politics of de-tracking math weren’t bad enough, a minority of mathematicians worry that it will hold back the most math-minded students—ultimately harming America’s supply of well-trained graduates. Calculus is virtually an entrance requirement at top-tier colleges, they point out, and that usually means taking Algebra 1 in 8th grade.

The tug of war over these competing beliefs has led California to experiment with just about every possible algebra permutation over a decade. In 2008, the state all but required every 8th grader to take algebra. It reversed course in 2010 after adopting the Common Core State Standards.

Research paints a far more nuanced picture than either side in such debates typically acknowledge. For the average student, researchers say, early exposure to a challenging class like algebra probably does pay off.

But in a 2015 study, the University of North Carolina’s Thurston Domina and colleagues tracked how California’s uneven 8th grade algebra-for-all rollout played out across districts. In a surprise finding, they discovered that higher enrollments in early algebra were linked to a decline in students’ scores on a state math test.

“I think the failure of 8th grade algebra was one of just not preparing teachers and school leaders to understand the policy and to implement it well,” said Domina, an associate professor of education policy and sociology. “The whole idea was to have heterogeneous, rigorous classes, and schools didn’t have the capacity to pull that off.”

A New Approach

With that history in mind, San Francisco’s commitment to de-tracking math tries to navigate between two rocky shoals: politics and implementation.

To address the first, the district permits students to accelerate after completing Algebra 1 in 9th grade—most notably through a compressed class combining Algebra 2 and precalculus. That way, students can still take advanced math as upperclassmen.

“All of the acceleration paths are family and student choices, not based on test scores or teacher preference,” Ryan said. “You make the choice when you’re 16, when you actually know a bit more about what kind of student you are.”

It can still be difficult to explain the theory of action behind the new course sequence to parents, especially when they carry a preconception of which students should be grouped together in a math class, said Hoss Koch, an assistant principal at the district’s Denman Middle School. In particular, Koch said, he tries to explain to parents that 8th grade math under the common core contains a significant amount of algebraic content, such as linear functions, that wasn’t in earlier 8th grade math iterations. Algebra isn’t so much gone from 8th grade as it is now taught much more deeply over two school years.

As for implementation, San Francisco administrators have shaped day-to-day teaching and curriculum to support the district’s focus on equity. Heavily based on work by Jo Boaler, a Stanford University professor of math education, the curriculum emphasizes having groups of students work through a series of ambitious math tasks.

Traditional math teaching, the thinking goes, tends to reinforce rather than break down inequities.

“If you have a procedural textbook, not only is there nothing to collaborate about, the ‘smart kid’ in the group is always the one who gets the computation right,” said Lizzy Hull Barnes, the mathematics supervisor for the San Francisco district. But when students wrestle over problems together, they can use different methods, compare approaches, and figure out why some work and others don’t, making all of them active participants in the learning, she said.

The focus on instruction, rather than just courses, is laudable—and too often absent from discussions on de-tracking, said Patrick Callahan, a math consultant who has advised California school systems, including San Francisco’s, on their math programs. “I talk to districts about this, and they think it’s like switching textbooks. That’s really missing the point,” he said.

Teachers React

If you asked how San Francisco’s math-teaching philosophy might ideally look in practice, it would probably resemble geometry teacher David Russitano’s classroom. On a cloudy morning in May, his students at Burton High School are working on a probability and statistics task. They pull playing cards, one by one, out of a suit, using math to bet on whether a higher or lower card will appear next.

As the lesson progresses, the questions get tougher: How do the odds change if three cards are randomly taken out of the suit? Why would you want to bet in some situations and not others?

In groups, students approach the problem in different ways: One girl crosses out each card on a sheet of paper as it appears; others are more easily able to make the leap to a fraction notation.

Russitano breaks in from time to time to highlight some of the strategies—a technique math leaders here call “assigning competence"—and correct common errors, always while posing lots of questions for students. Productive chatter is an expectation, not a rare occurrence in his classroom.

“Don’t be this quiet! Talk about it,” Russitano tells his students, during a lull in the middle of the lesson. “Don’t be afraid.”

Most teachers praise the social-justice impetus behind the math plan. But they also say that heterogeneous classes pose unique problems.

Students bring vast achievement differences to class, a situation that’s not helped by ambitious parents who, now, shell out thousands of dollars for students to take non-district algebra classes over the summer in the hopes of getting their children into geometry early.

“We have kids who have seen some of the math before. Their knowledge may not be deep, it may be procedural, but they come in thinking, ‘I know this already.’ You have to authentically challenge them, too,” said Daniel Yamamoto, an algebra teacher and the math-department chairman at Burton High. “And there are other kids who say [in response], ‘I have nothing I can add to this discussion.’ ”

It’s something that occasionally throws a wrench into the group tasks, as visits to several classrooms demonstrate. Sometimes the groups fall into “tutorial mode,” with one student doing most of the cognitive work on her own and then conveying her answers to the others.

Getting the balance right between equity and responding to real variation in student ability makes the work quite difficult for teachers, math experts say.

“Tracking is an evil. But fear of tracking is a problem, because you do have to talk about differences in students’ backgrounds,” said Phil Daro, a common-core-math writer who helped San Francisco design the new course sequence.

Does It Work?

This year, San Francisco got something of an ace in its back pocket to show skeptics of the plan: Data shows better math outcomes for students who took the de-tracked courses compared with the cohort before them.

The number of students repeating algebra has fallen among all ethnic and racial groups, and fewer are receiving D’s and F’s in Algebra 1. About a third more students are ready for calculus, and that pool is more diverse than it’s ever been.

While it’s not proof-positive that the new course sequence has caused the better outcomes, leaders say, it’s a hopeful sign.

Nevertheless, the new math sequence remains high on parents’ radar. Most recently, “protecting algebra” appeared on the campaign platform of London Breed, a candidate in the city’s June 5 mayoral election. Breed said she’d create enrichment programs “so motivated students whose passion is not currently met by the curriculum sequencing can thrive.” (She was narrowly in second place at the time of this writing, with the outcome not yet certain.)

Daro, the education consultant, said he continues to worry that San Francisco leaders’ decision four years ago not to offer a limited amount of Algebra 1 in 8th grade might someday backfire. “I thought politically it was a mistake,” he said. “It may still turn out to be one.”

District leaders, for their part, are focused on more immediate concerns. Asked what challenges remain, Barnes points to the progress of black students as an area in which the city needs to double down. Those students have gained in math and science credits, alongside their peers, but those gains aren’t yet showing up on state test scores or in enrollments in AP Calculus.

Her colleague Angela Torres, a math-content specialist, cites the difficulty in ensuring that all teachers feel confident in the new curriculum and teaching methods.

“This work is hard, and the challenge is to continue to come at it,” she said. “You can’t just put kids in groups and hope for the best.”

A version of this article appeared in the June 13, 2018 edition of Education Week as In San Francisco, A Bold Effort to De-Track Algebra

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