Stats vs. Calculus and the Lesson of "Common Core" Math

Changing curricular capstones is complicated

Some of The Pip’s recent math work, involving basic algebra

SteelyKid started school in 2013, which was close to the peak of the freakout over “Common Core Math.” The inscrutability of the new standards for elementary school math was an endlessly recurring topic in late-night talk show monologues and frustrated Facebook rants from high-school classmates whose kids are a bit older than mine. Nobody seemed able to understand what was now deemed to be third-grade math, and everybody was pissed about it.

As is often the case with issues touching on STEM in schools, I found this a little puzzling. As SteelyKid started to get into the math curriculum, I thought it was great— not just the endless algorithmic chugging I dimly remembered from my own childhood, but something much closer to actual math. Students were being asked to get answers by multiple methods, check them against each other, and explain how they knew their final answers were right. These are all things I struggle to get college frosh to do in intro physics, and here it was built right into the elementary school math curriculum.

So, on reflection, I guess it’s pretty obvious why everybody else hated it…

I was thinking about this because I’ve seen a recent flurry of calls coming through my social media feeds for replacing calculus with statistics as the capstone of the high school math curriculum. This is an idea that’s been around for years, with slight shifts in the justification offered: ten years ago, it was all about relevance (“Hardly anybody uses calculus, but learning stats would help people process complex information”), now it’s more often cast as a way toward greater equity. (The idea being that poorer school districts struggle to find the resources to teach calculus, but would find it easier to do statistics instead. I think; I don’t entirely understand the pitch, here…)

I’m actually kind of agnostic on the question of what the capstone high school math course ought to be, which might seem an odd stance for someone who teaches a lot of intro physics (which in many ways is just applied calculus). The standard intro physics curriculum is calculus-based on more of a conceptual level than a practical one, though— we use the idea of rates of change from differential calc, and the idea of summing up small changes from integral calc, but spend very little time actually doing derivatives and integrals in class or on homework. There are variants of the curriculum, like the Matter and Interactions course, that do even less formal calculus, and that I personally like better than the standard version.

And there’s a case to be made that having students know more statistics and probability would be just as useful to intro physics as the level of calculus knowledge they come in with now. One of the perennial struggles of doing lab courses is the need to deal with errors and uncertainties, which mostly involves teaching a loose and operational version of stats on the fly. If the high school curriculum was aimed at stats rather than calculus, some of that effort could be shifted out of the labs and into shoring up calculus concepts, and I suspect we’re probably better at doing that than we are at conveying anything about statistics through lab exercises.

The thing that gives me pause about this, though, is the lesson of “Common Core math,” and specifically the freakout over changes to elementary math instruction. I’m not sure that a lot of the people casually advocating replacing calculus as a capstone course with statistics really understand the scale of the undertaking they’re proposing. If you were to do this correctly, it would require not only changing the content of courses at the college level, but also reaching back into the curriculum to give concepts of probability and statistics a more central role much earlier.

One of the features I really liked about the math classes that my kids have gone through is that they started doing a kind of proto-algebra in elementary school. They didn’t call it that, but that’s what it was— when they were learning addition and subtraction in first and second grade, they didn’t just do endless reams of problems like “26+47=??” but also a bunch of “26+??=47” type problems. These lay the groundwork for thinking about equations down the road. And, indeed, The Pip’s recent math test included explicitly asking them to write equations with variables, in sixth grade (he’s in fifth, but in the accelerated math class), which is a grade or so earlier than we got to that back when I was walking uphill to school through the settling dust from the Chicxulub impact.

They’re able to get to algebra early because the much-reviled “Common Core” curriculum was a comprehensive and well-thought-out project to do exactly that. It’s not just endless drill on basic arithmetic, but a systematic approach to lay the foundations for thinking more deeply about math, so that students would arrive in high school and college with a better understanding of what math is really about. (Fun fact: It was also largely the work of a guy I overlapped with at Williams, though I doubt I ever had a meaningful conversation with him.)

So, if you want to replace calculus at the peak of the K-12 math pyramid in the service of some broader public interest, that’s a thing you could probably do. But doing it right will reach back toward the K just as much as it reaches forward into the college curriculum. I’m not sure exactly what that would look like— I’m not a math education expert— but I suspect that to really set it up would require bringing in probability concepts much earlier, and making them more central to the classwork. That’s going to change what math homework looks like, and the main political lesson you can draw from “Common Core math” is that people really f*&king hate it when their kids’ math homework doesn’t look like the math homework they remember hating when they were that age.

Again, I’m very much agnostic on this in terms of its effects on my personal interests (teaching physics to college students); I’m skeptical of claims that it would make a big difference in any of the societal issues it’s supposed to address, but doubt it would ruin the preparation of the students I see. I’d be happy to leave it to actual mathematicians and math educators to sort out, and the STE fields can adjust once the M’s have figured out what works best for them.

But I do think that before proposing this kind of sweeping change, people should have a clearer idea of what it would involve, and I’m really not convinced that a lot of the folks tweeting about this have any real idea what they’re asking.

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