The Case for Accelerated Math
And why the folks making the decisions don't go for it
There’s been a lot of discussion of K-12 schools making cutbacks to advanced math classes and justifying them with social-justice rhetoric, which in turn are met with references to the Vonnegut classic “Harrison Bergeron.” Noah Smith posted a pretty good example of the form yesterday, which led to me posting a Twitter thread in response that I’ll expand on here a bit. As I said in the first of those tweets, though, I think the root problem is that the people pushing these changes don’t really understand the importance of offering advanced math in public schools, and won’t bear the consequences of not offering it.
The DEIB gloss on eliminating advanced programs is new, but the core phenomenon of schools looking to scale back programs for advanced students is nothing new. This went on back in the 80’s when I was in K-12. My parents fought really hard to get some gifted programs together in the district, and for a time my dad was in charge of coordinating what I think was a pretty good set of offerings across the district. (This was after I went through, though my sister was in the cohort that got to take full advantage.) They went away after not all that many years, though, because of budget pressures. The gifted programs were viewed as expendable, for reasons echoed in a lot of the defenses of the changes that have people worked up now: The students who would benefit are going to be just fine regardless, so the resources used for acceleration and enrichment of the top students should instead be redirected to students who really need them.
That’s true to a point, but it’s much less true of math and science than literature and social science. It’s relatively easy to provide enrichment activities for kids who excel in English or Social Studies in the context of regular classes— you can cover the same core material but ask them to go into greater depth in their assignments. (Honestly, you probably don’t even need to ask— they’ll just do it more or less on their own.) Worse come to worst, you can just turn a blind eye while they read beyond the level of the rest of the class on their own—I certainly sat through a few classes that were made tolerable by this approach.
Advanced math and science, though, pretty much have to be separate classes, because of the nature of the subjects. While it can be done, they’re much less amenable to autodidacticism, because at the end of the day there are concrete right and wrong answers and learning them well is really difficult without the guidance of someone who knows what those answers are and how to arrive at them. Anybody with a library card can readily explore the great literature of the world, or read a vast wealth of history on their own, but math and science have a greater need for an experienced teacher to gently steer students out of paths that lead to blind alleys or misconceptions.
That argument more or less works to explain why math and science are the first place to do separate accelerated tracks if you’re going to do accelerated tracks at all, but the obvious counter is “Why do them at all?” And that’s the failure point that leads to this whole silly mess, because the reason to do them is as a foundation for stuff that comes later, and thus isn’t directly within the purview of the K-12 schools where this is happening. That is, accelerated math is important to the students who benefit from it because it puts them in a better position to study math and science in college and beyond. But people making decisions about K-12 education mostly don’t care about that.
To be clear, and as I said in that Twitter thread, I think the “Harrison Bergeron” comparisons get a little overheated— advanced math in K-12 puts students in a better position, but not having that option doesn’t completely preclude being a math or science major. My day job is teaching college-level physics, and we can perfectly well handle students who never had calculus in high school. Honestly, it wouldn’t be the worst thing in the world if fewer of our entering students were rushed through a superficial version of calculus, provided they arrived with a better grounding in the basics of algebra.
But that introduces a massive coordination problem that doesn’t seem to be appreciated by people pitching less math as a social justice measure. If everybody agreed that the right and proper thing to do was to lower the top level of high school math, we could adjust our curriculum in a way that would compensate for that, and after a few years everything would be fine, except for the grousing of the older tenured faculty about how everything used to be better. (But you’re going to have that regardless…)
The problem is that this is being done in a stupid and patchwork fashion, without sufficient consultation with the people whose programs build on the courses that are being cut back. We’re tooled up to expect the students who enroll in first-year physics at our elite private college to have a certain level of math preparation, and can deal with a handful of exceptions to either side of the median— skipping a few students ahead, bringing a few more along slowly. If you suddenly start changing that in a handful of places but not in others, you’re throwing barriers in the way of students from the places that have changed.
(We’re struggling with this a bit in the wake of Covid, which dealt a serious blow to the math preparation of a lot of students. That’s at least closer to a universal change, though, and one that will hopefully sort itself out in a few years…)
And as Noah Smith and innumerable other people have noted, those barriers are going to loom largest for precisely the people these steps are supposedly going to help. That is, the students who have the resources in the form of educated parents, spare time, and cash will be able to get up to the “right” level regardless of what the public schools do. They can pay for external tutoring or move to private schools, and they’ll be just fine. The ones who will suffer are the students who might have the talent and inclination to excel in math or science, but don’t have the family resources to make up for a lack of opportunity at the public schools.
This is, admittedly, a smallish subset of the school-age population, but as one of the people who’s going to teach this subset science at the college level, they’re the ones that matter the most to me. They’re of much less interest to the activists and administrators who push these changes, though, mostly because the benefits to those people are extremely indirect. The students in question will do just fine in the classes those administrators are directly responsible for regardless of the level of the curriculum, and any inadequacies in their preparation for courses taught elsewhere are somebody else’s very abstract problem.
Which is how we end up with people very earnestly pressing forward measures that, from where I sit, are manifestly counter-productive to the ostensible long-term goal. It’s a combination of short-sightedness and a failure to understand that math and science really are hierarchical in a way that extends back into the K-12 years to a far greater degree than for other subjects.
(The right solution, as Smith notes, is to put additional resources into tutoring students who are struggling so as to bring everyone up to a higher level. But that “additional resources” is a killer…)
I made a concerted effort to not be polemical in the above, which will probably limit the engagement this will get; buy me a beer sometime, and I can give you a snarkier version. You can also try contributing to my beer fund by clicking this button and electing one of the paid options:
but I make no promises about whether that will get me to post snark. Should you feel so moved, the comments will at least start off as open:
Though I should note that this is a topic that sometimes veers off into bad places, so I reserve all my rights as owner of this virtual space to shut things down if that starts to happen.
In my experience, when my kids were in a public school in New York, I argued that it was the middle quintiles that we should worry about: there were Gifted and Talented programs, and there was Special Ed, and those ends got all the attention, but the mainstream kids got football. So I’m in the group that thinks it’s unconscionable to remove math.
With all the discussion about increasing inequality in the country, some social scientists from Stanford found that if you removed three counties, San Mateo and Santa Clara in Silicon Valley and King County in Seattle, there was no increase in inequality in the rest of the country (of course New York City is very unequal but it always was). And if you survey the tech companies in those counties you’ll likely find everybody took algebra. Correlation is not causality, but it’s evocative.
Check out Kevin Drums posts on covid school closures. Interesting.