The Great Acceleration Debate
Why eliminating advanced math is a bad strategy for achieving equity.
Last month, I wrote a post in defense of advanced math classes in high school. I was responding less to a specific event and more to a general undercurrent that I had noticed in the discourse around secondary education. At the time, I worried that I was arguing against a straw man, espousing an “unpopular” opinion that was, in fact, pretty much universally accepted. That does not seem to be the case.
Two weeks ago, Fox News published an article claiming that Virginia’s new Mathematics Pathway Initiative would eliminate accelerated math classes in the name of equity. It now seems likely that this article was at least partly manufactured outrage; the mathematics initiative is more suggestion than law, and administrators have clarified that schools will still be allowed to hold advanced classes. Nevertheless, it's clear that the once-fringe anti-accelerated math movement is gaining influence. From a Washington Post column about the Virginia math program:
The VMPI website has been revised recently to say that accelerated math is still possible under the plan. But it also cites as experts in this field two organizations: the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics. The first group says middle and high schools should stop tracking teachers and students in math. The second group is more vehement. “As a practice,” it says, “tracking too often leads to segregation, dead-end pathways, and low quality experiences, and disproportionately has a negative impact on minority and low-socioeconomic students. Additionally, placement into tracks too often lacks transparency and accountability.”
Similar ideas appear in the recently published 2021 revision of the California mathematics framework, which says:
In previous versions of this framework, students who have shown higher achievement than their peers have been given fixed labels of “giftedness” and taught differently. Such labelling has often led to fragility among students, who fear times of struggle in case they lose the label (see, for example: https://www.youcubed.org/rethinking-giftedness-film/), as well as significant racial divisions. In California in the years 2004–2014, 32 percent of Asian American students were in gifted programs compared with 8 percent of White students, 4 percent of Black students, and 3 percent of Latinx students (https://nces.ed.gov/programs/digest/d17/tables/dt17_204.80.asp).
[…]
The largest association of mathematics teachers in the nation, NCTM has made clear that districts and schools must confront the structural inequities of tracking and ability grouping, and to strengthen their efforts to support all students in learning along a common pathway.
Eliminating accelerated math classes strikes me as a bad strategy for achieving equity.
This topic has been coded as a battle in the culture war, so I want to make clear that I am a strong advocate for equal access to social mobility. I think it’s a real tragedy for everybody that lots of very talented and hardworking people are held back by poverty and/or racial/gender bias and never end up making our lives better by working at NASA or Google. We should do everything we can to ensure that all students have an opportunity to achieve great things. From what I can tell, the anti-accelerated math crowd agrees with me about this. Our disagreement is about how to get there.
I want to genuinely engage with the anti-tracking movement, so I am going to try my best to “steel man” three popular arguments against accelerated math. I’ve sorted them in ascending order of how compelling I find them.
Accelerated math gives privileged students a competitive advantage
It seems pretty clear that one function served by the current American secondary education system is to produce an academic ranking of students—why else do nearly all schools give grades beyond just “pass” and “fail”? (Note: I am not trying to make normative judgement about this). This ranking later helps determine the life outcomes of students, most directly through the college admissions process. Accelerated math classes give the students in them a major competitive advantage. This is often in the form of a weighted GPA, but taking lots of advanced math can in and of itself make students more attractive to colleges or employers.
The problem with advanced math classes, according to the competitive anti-acceleration argument, is that the advantages they confer are overwhelmingly enjoyed by privileged students. This makes a lot of intuitive sense to me. Sorting into accelerated tracks usually occurs when students are very young and likely to be highly impacted by their home environment. It often requires parental input, penalizing students from less-involved families and opening the door for influential parents to shoehorn their children into advanced programs. There is also the specter of direct bias on the part of teachers (although this national study found no racial differences in advanced program participation among students with similar academic achievement, so this particular factor seems less important than one might suspect).
Therefore, the argument goes, we should eliminate acceleration programs. Privileged students won’t get an early, rapidly compounding lead, and everyone will be on more equal footing when it comes time to compete for college acceptance let/ters and/or jobs. In a world where public schools are the only game in town, I think this argument has quite a bit of internal logic to it. Consider the following demonstration:
Suppose we model secondary education as a process which ends in a competition for limited spots (at top schools, for high-paying jobs, etc.). There are twenty such spots. Any student who has accelerated automatically wins a spot. If there are spots left over, they are awarded randomly to the remaining students.
Now suppose we have a population split evenly between privileged and underprivileged students. There are fifteen privileged students eligible for acceleration. There are fifteen equally talented and hard working underprivileged students, but due to various inequities only five are identified for acceleration. In the old days, these twenty students would accelerate and get all the spots. Then privileged students make up 75% of the competition winners despite being only 50% of the population. Not great.
If we eliminate acceleration altogether, then nobody accelerates and the spots are awarded randomly. The winners will be 50% privileged and 50% underprivileged, perfectly representing the population.
We’ve arrived at my problem with this line of reasoning: public schools are not privileged students’ only option. Wealthy families can afford to pay to attend private schools, where students take classes like Advanced Linear Algebra and Advanced Multivariate Calculus. Even in the absence of private schools, privileged students can differentiate themselves with out-of-school math tutoring and math camps.
Let’s return to our earlier no-acceleration model, but allow wealthy students to transfer to private school. Now all fifteen eligible privileged students are accelerated, but none of the underprivileged students are. These fifteen students win the first fifteen spots. The remaining five are awarded randomly to the rest of the population. The expected proportion of privileged students among the winners is now 82.5%—worse than the number we started with.
If the actual process for determining the competition winners is accelerated > private school > public school (which seems closer to the truth), we end up with a set of winners who are 100% privileged!
This model is at best a very rough approximation of reality, but—as far as I can tell—it represents the logic of the competition-focused anti-acceleration argument. I think it’s fair to carry the game theory to its logical conclusion.
If you buy into this zero-sum worldview, it may actually make sense for public schools to provide more differentiated instruction. Allowing students to complete truly challenging coursework as part of their normal schooling is one way to make sure that underprivileged students can stand out when compared to their privately schooled peers.
All told, it seems very hard to justify eliminating the option for public school students to accelerate in a world where privileged students have that option and more.
Heterogeneous classrooms are better for student learning
Another argument against accelerated classes is that heterogeneous classrooms produce better learning outcomes. In an accelerated math class, students are more likely to have similar backgrounds and ways of thinking. Heterogeneous classrooms allow students to interact with peers with a diverse range of worldviews and abilities. Harvard buys into this idea, saying it “creates the conditions for dramatic and meaningful growth.” If our nation’s best universities do this, why shouldn’t our middle and high schools do the same? Moreover, heterogeneous classrooms allow the most vulnerable students to receive academic support from their more advanced peers.
I buy into some aspects of this argument. All things being equal, a culturally and neurologically diverse student body can be very valuable; I have certainly learned things from my peers at Yale that I would not have if everyone was an introverted, systematizing C.S. major from the Midwest. That being said, it’s worth pointing out that Harvard and Yale also select for academic excellence; these schools get the best of both worlds.
My own experience makes me dubious of the claim that heterogeneous classrooms work well for everybody. At the high school I attended, math was “tracked” and physics was not. Math was not perfect, but generally good. Physics was something like an order of magnitude slower. My (excellent) physics teacher tried his best to keep everybody engaged, but was forced to spend much of his instruction time back-filling basic algebraic concepts. As a result, I came to dread physics, a subject I had previously enjoyed reading about in my spare time. This has played no small role in the fact that I have taken lots of math and no hard science in college. Had none of my classes been accelerated, I’m not sure what I would be studying.
Luckily, we don’t have to rely on anecdotes. Does the research support this argument? The California math revision claims that it does:
Two longitudinal studies, one in the United Kingdom and one in the U.S., followed students over three and four years, respectively, from the ages of 11 to 18. The studies aimed to consider the impact of tracking, curriculum choices, and teaching. In both studies, students in schools using mixed achievement groups achieved at significantly higher levels than students in schools employing tracking. In both cases, the schools using heterogeneous grouping did so as part of equitable initiatives and in both cases the schools using heterogeneous grouping reduced inequities during the time students were in school. The schools achieved success with heterogeneous grouping by using low floor high ceiling tasks that all students could access and that students could take to very high levels (see Chapter 2) and by having high expectations for all students. This success held across different countries, cultures and schools (Boaler, 2011, 2015, 2016; Boaler & Staples, 2008).
This sounds convincing, but some digging reveals that authors of the California revision appear to be engaging in highly motivated reasoning. I think the U.S. longitudinal study they are referring to is this 2004 paper by Jo Boaler. As far as I can tell, the study compared three California high schools (about 700 total students). One of them had much better outcomes than the other two. That school also happened to have more heterogeneous classrooms. I’m sure there are some interesting things we can learn from a comparison like this, but anybody who knows the difference between correlation and causation can tell you that this is pretty far from knockdown evidence for the superiority of heterogeneous classes.
The “U.K. study” appears to refer to a 1997 paper, also by Jo Boaler. This one compared two schools, one of which was fairly traditional, with tracked math classes. The other was extremely progressive, allowing students to work in many different settings (including alone and in mixed groups). In the end, the progressive school achieved better results. Given that one school employed an entirely different education paradigm than the other (and presumably attracted a different type of student) I find this even less convincing than the U.S. study.
These case studies aren’t devoid of value, but it strikes me as extremely disingenuous to present them as authoritatively showing that heterogeneous classes boost student performance. I’m sure I could find many pairs of schools where the better-performing school uses tracked classes and the worse-performing school doesn’t.
This misleading use of research is even more puzzling given that there are plenty of high-quality studies on heterogeneous classrooms. The research literature is nuanced (I encourage curious readers to check out this Slate Star Codex post, which provides a readable overview), but one fact that seems fairly well established is that heterogeneous classes do not produce better academic results for students, struggling or otherwise. Bob Slavin, an opponent of accelerated math, found this result to hold in large studies of middle and high schools. Unlike the papers cited by the California revision, Slavin’s studies are large-scale meta-analyses which include randomized experiments.
The question of whether or not accelerated classes do any better than heterogeneous classes is more disputed, but many studies have shown a positive effect for gifted students (so long as the curriculum is accelerated to match). A long-term longitudinal study of thousands of mathematically gifted students found that (controlling for mathematical ability) students who were allowed to accelerate were more likely to pursue advanced degrees in STEM and author peer-reviewed publications in STEM, accomplished both of these things earlier, and accrued more total citations and highly cited publications by age 50.
Overall, I am left with the impression that heterogeneous classes have no provable academic benefit for students, struggling or otherwise. Accelerated classes, on the other hand, show some signs of better serving high achieving students. This is particularly true when considering long-term outcomes in STEM. Tom Loveless of the Brooking Institute comes to a similar conclusion in his comprehensive review of the acceleration literature:
The evidence does not support the charge that tracking is inherently harmful, and there is no clear evidence that abandoning tracking for heterogeneously grouped classes would provide a better education for any student. This being said, tracking’s ardent defenders cannot call on a wealth of research to support their position either. The evidence does not support the claim that tracking benefits most students or that heterogeneous grouping depresses achievement. High achieving students are the exception. For them, tracked classes with an accelerated or enriched curriculum are superior to heterogeneously grouped classes.
Against this evidence, it’s hard to buy into a purely academic case for ending accelerated math.
Accelerated classes can reinforce stereotypes
A third possible motivation for eliminating acceleration is that it can create de facto segregation by race or income. The IB program at my high school was certainly wealthier and more white/asian than the school as a whole. This trend seems to be true nationwide. Exposing students to this image day in and day out can cause them to internalize negative stereotypes. These stereotypes can go on to lower the self-confidence and passion for learning of students from disadvantaged backgrounds, reinforcing the trends which caused achievement differences in the first place. Eliminating accelerated classes is a step towards breaking this vicious cycle.
I find this argument much more compelling than the first two. All things being equal, visible gender, racial, and wealth imbalances are bad—it is very intuitively plausible that this sort of thing might lower the academic confidence of disadvantaged students. The APA review of research on “stereotype threat” concludes that being reminded about negative stereotypes can lead members of stereotyped groups to score worse on standardized tests. If there’s some risk that accelerated classes are causing this reaction down the line, that’s not great.
I don’t have an easy rebuttal to this line of reasoning. It’s possible that eliminating accelerated classes really would lead to some improvements along this axis, although it’s worth pointing out that these effects weren’t significant enough to show up in the studies of tracked and untracked schools described above.
Conclusion
All told, it seems very hard to support the elimination of accelerated classes on the grounds that heterogeneous classes improve disadvantaged students’ competitive odds or boost academic performance. On the other hand, there is intuitive logic to the idea that accelerated classes might reinforce negative stereotypes. Because the potential costs of eliminating accelerated math classes—both in diminished outcomes for high-achievers and in the introduction of another competitive disadvantage for public school students—are so high, I would advocate for attacking the causes of inequity rather than its symptoms. Instead of removing tracked classes, we should invest in disadvantaged communities and make sure every child has the resources to succeed. At the elementary, middle, and high school level, administrators can make it harder for wealthy families to game the system in favor of their children and ensure that talented and hard-working students are not overlooked due to bias.