Photo by albastrica mititica
San Francisco in the twenty-first century is the town that STEM built. A city increasingly synonymous with startup culture and tech-centric innovation, its rapidly growing economy speaks to the value of studying science and mathematics.
Which is why it came as a surprise when the San Francisco Unified School District (SFUSD)—the central office of which occupies the same rarified square mile as the corporate HQs of Twitter, Uber, and Square—announced in 2014 that it would no longer offer Algebra I to eighth graders. Instead, under the district's new mathematical course sequence, students would not be introduced to the joys of polynomials until high school.
Scale back math education in San Francisco? Why not cut Bible study at the Vatican while we're at it?
Such was the tenor of the response from irate parents who took to local radio and social media to voice their disapproval. Under the city's previous standards, precociously numerate middle schoolers had been allowed to skip ahead to Algebra or Geometry.
While SFUSD insists that its new approach does not compromise the rigor of its education, but ensures that all students enter high school with the same mathematical foundation, many parents see the district’s new standards as a dumbing down of the curriculum. As one angry commenter asked on an online petition website: “All the talk about American kids being behind in math and science, and now SFUSD makes a move to keep the most advanced math students from making progress?”
The battle over eighth grade algebra playing out in San Francisco is neither isolated nor new. Education experts have long considered Algebra a "gatekeeper" course that divides the more advanced mathematics of the college-bound set from the no-frills, computational arithmetic of general math.
The question of whether students should be ushered through that gate in the eighth or the ninth grade may seem like a small one, but it touches on a fundamental question in education policy: should schools push over-achievers ahead if that means leaving some students behind?
Algebra: "The New Civil Right"
It is telling that one of the first people to push for universal enrollment in algebra was a longtime civil rights activist.
Robert P. Moses founded the Algebra Project in 1982 as an extension of his long-standing commitment to racial equality. Two decades earlier, Moses had spearheaded voter registration efforts in Jim Crow Mississippi for the Student Nonviolent Coordinating Committee in the lead up to and during the Freedom Summer of 1964. As Moses wrote decades later, unequal access to high quality education is a comparable injustice to unequal access to the ballot box and is "the clearest manifestation of the nation's caste system."
This, he wrote, was particularly true of math. A more tech-intensive economy and society demanded that high-level numeracy join literacy as a basic expectation of our educational system. Algebra, the point at which abstract math forks off from the purely utilitarian math skills that all adults need to pay bills and balance a checkbook, seemed particularly ripe for democratization.
"If you go back 15 or 20 years, a good many students weren't even allowed to take algebra," explains Jim Ryan, STEM executive director at the San Francisco Unified School District. "They got to high school, and they took courses like basic math, general math, and consumer math, and that was enough to graduate."
This was the consequence of an early age tracking system that placed students on separate course sequences based on their exhibited mathematical abilities in elementary and middle school. Not surprisingly, these good many students routed onto the lower track were disproportionately African American, Latino, and members of other disadvantaged groups.
Photo by King of Hearts
But by the 1990s, globalization and the economic ascendency of Asia made "falling behind" in education an increasingly potent political concern. "Around the world, middle [school] students are learning algebra and geometry," bemoaned Bill Clinton in speech in 1998. "Here at home, just a quarter of all students take algebra before high school."
Over the course of the '90s and into the next century, the push for higher algebra enrollment took hold in high schools and middle schools across the country. In 1990, fewer than one-in-five eighth graders took an algebra course. Twenty years later, enrollment was up to nearly one-half.
When made explicitly, the case for early algebra enrollment comes in two basic flavors. First, there is the cold, hard reality of course sequencing. Pedagogically justified or not, high school students typically progress through advanced math in a fairly predictable series of steps. If a student can't take Algebra I in the eighth grade, it's often argued, they won't be able to take the Algebra II, geometry, and trigonometry courses required to take calculus in their senior year. And without calculus under their belts, high school graduates will be disadvantaged going into college, irreversibly stunted in their STEM careers, and destined to live a life of financial and scholarly impoverishment. These are the thoughts that keep parents up at night.
But beyond the practicalities of course sequencing, algebra demands a way of thinking that is fundamentally distinct from what is required of the reading, writing, and 'rithmetic of elementary and middle school.
"Algebra is the first time that a lot of kids are asked to do pure abstract thinking," says Thurston Domina, an associate professor at University of North Carolina's school of education. "There was this idea [that] if we want to be training good thinkers, we should be exposing [students] to algebra early."
In challenging each and every student by exposing them to algebra early, the logic goes, districts promote both equal access to education and academic excellence—as otherwise low performing students rise to the occasion. "This literature can kind of be summarized with a line like 'Nobody jumps high over a low bar,'" says Domina. “But that’s not at all what the data suggests.”
Tripping Over the Bar
In fact, the evidence on early algebra is decidedly mixed.
A bird's-eye-view of the available data isn't encouraging for early algebra advocates. A 2013 study carried out by the Brookings Institution looked at the relationship between eighth grade enrollment and National Assessment of Educational Progress math exam scores at the state level. In short, they didn't find one.
In a more recent study, UNC's Thurston Domina and three researchers examined California's experiment with algebra-for-all. In 2008, the state made a hard push for such a policy by requiring that assessment exams for eighth graders include an algebra section. But because the mandate never went into full effect, the implementation was inconsistent and varied in intensity across the state, allowing Domina and his colleagues to compare and contrast students across more and less algebra-boosting districts.
Surprisingly, they found that early exposure was actually associated with a net decrease in average student math score exams within a given district. The magnitude of the decrease wasn't negligible either: "By way of comparison," the authors wrote, "this estimated negative effect is approximately the same size as the average positive achievement effects associated with the federal No Child Left Behind Act." What the Bush-era educational plan did for middle school math scores, early algebra seemed to have reversed.
This doesn't mean that algebra somehow poisons young minds. In fact, says Domina, individual students generally benefit from early exposure.
"If you're asking me, 'Do I want to push my kid into eighth grade algebra?’, the answer is almost certainly 'Yes.' At the kid-level, any given kid is better off in a more challenging class," he says. What complicates matters is how a particular school will change its curriculum, restructure classes, and rearrange staffing patterns in order to meet an algebra-for-all mandate.
"Algebra seems to help [students], but it's not clear it's the curriculum. It's the peer environment. It's the teacher. It's just the pat on the back for being in an advanced class. All kinds of stuff is going on there, and we don't know which it is," says Domina. "Now, when you change that and put a lot of kids in algebra, you change the peer environment, you have teachers who have never taught algebra teaching algebra, and you've got this problem in the classroom where you've got to figure out whether you're going to teach algebra at all, because a bunch of the students don't know fractions."
Results vary, of course. There is no single education policy called "increase algebra enrollment." Getting eighth graders to learn how to manipulate variables is a goal that each district approaches with its own particular curricula, its own set of teachers, and its own ancillary supports for struggling students (or not). All of these factors affect educational quality independent of whether and when a student is enrolled in something called "Algebra I."
Still, on the whole, Domina calls his results "discouraging" from a policy perspective.
In some ways, the Common Core State Standards in California are a response to this realization. A set of academic standards for K-12 education adopted by 46 states with the endorsement of the Obama administration, the Common Core was officially introduced in the Golden State in 2010. Backing away from the early algebra-for-all orthodoxy that has dominated state educational policy up until 2012, the new standards recommend that districts focus on pre-algebra throughout middle school.
Though many districts across the state are moving towards the Common Core recommendations, Domina calls San Francisco "unusual relative to other California districts" in its decision to phase out eighth grade Algebra I entirely. While districts in surrounding suburbs have adopted CCSS-compliant standards, in response to outcry from parents, most now allow advanced middle schoolers to take accelerated math courses.
This is exactly the concession that Supervisor Katy Tang hoped to extract when she co-authored an open letter last spring with Supervisor Scott Weiner to SFUSD Superintendent Richard Carranza criticizing the district’s “one-size-fits-all math policy.”
Now, over a year later, Tang, who represents one of the city's wealthier residential districts, says she still objects to the new standards and still hears from parents concerned about the quality of their children's education.
“A lot of the correspondence I got was just sharing their own personal frustration,” she says. “How they were glad that their child was soon leaving the school district system, or how they were trying to find ways to get out.”
Algebra I by Any Other Name
Jim Ryan from SFUSD acknowledges that the district took a "bold" step in its course sequence redesign. "As evidenced by the fact that I'm talking to you, there are people who it makes uncomfortable," he says.
Still, Ryan bristles at the suggestion that the eighth graders of San Francisco are no longer learning algebra. Under the Common Core State Standard, he explains, there is a much stronger emphasis on developing a more intuitive understanding of math from an early age. "There is [now] a ton of what you would consider algebra in grade school and all the way through middle school," he says. "So the question about Algebra I in middle school really just doesn't fit the current paradigm because the standards are so different than what has historically been taught."
How each state stands on the Common Core State Standards
Graphic by MediaKill13
As Ryan points out, the CCSS Math 8 course that eighth graders are now expected to take includes 60% of the material from the old Algebra I course. This includes linear equations, roots, exponents, and an introduction to functions. The new course also offers students a taste of geometry and statistics—hardly your typical middle school fare. According to Ryan, this helps students to understand the "why" and "what for" of pre-algebraic math.
Likewise, the course called "Algebra I" that students will now take in their first year of high school introduces a number of the concepts we all associate with introductory algebra (quadratic equations, say), but also delves deeper into modeling with functions and quantitative analysis. Call it what you want, in other words, but this is not your grandmother's Algebra I.
This may be cold comfort for anxious parents concerned about packing in Calculus before graduation. But Ryan insists that acceleration is still possible under the new system. The key difference is that numerically-inclined students aren't tracked ahead of their peers until high school. Last week, the district announced that it would allow freshmen to choose from an array of math courses ranging from Algebra to Geometry.
Still, advanced eighth graders, prevented from skipping ahead in the course sequence, will be encouraged instead to delve deeper into the material.
"If a student, for instance, has completed an assignment in a U.S. History course about the Revolutionary War and done the reading, the teacher doesn't say, 'Oh, you're done with that, we'll move you onto the War of 1812.' Instead, they give them additional reading and additional writing that will deepen their understanding of the Revolutionary War and that time period," says Ryan. "We can do the same thing in mathematics rather that simply moving them along at a faster clip."
Yet Ryan’s suggestion that teachers offer different material to different students with different skill levels within the same classroom could put a significant burden on teachers. And if star students complete an assignment before their peers, how likely are they to raise their hand to ask for more homework?
Supervisor Tang says she sees the value of encouraging students to deep dive into complex material, but only up to a certain point.
“We could spend forever on Algebra. We could spend forever on every single subject,” she says. “People want that movement—whether it’s the student or the parent—onto the next level once you’ve built your foundation.”
The argument that is playing out between proponents and opponents of SFUSD's relatively rigid form of the state Common Core reflects the warring priorities of academic excellence and equity that often rears its head in education policy debates.
Proponents of San Francisco’s current policy insist that delaying acceleration will have no effect on acceleration-ready students. Meanwhile, opponents insist that allowing wiz kids to branch off from their peers in middle school will have no implications for the racial or socioeconomic achievement gap.
The historical record suggests that both sides might be ignoring the downsides of either policy. In practice, it has proven difficult to create separate classes of gifted students without removing pedagogical resources from their non-accelerated peers and without creating classrooms that are disproportionately white and Asian and relatively affluent.
But as UNC's Domina points out, most schools have also found it very difficult to institute what Katy Tang calls a "one-size-fits-all" mathematical curriculum without boring the math nerds to tears.
"There's a trade-off. There's a tension there. I don’t want to say that it’s impossible to square that circle," says Domina. "But overall, on average, schools don’t know how to do that.”