US Math Wars: What I Know and What I Don’t
So many people have asked me about the US “math wars” during my recent visit, that I thought I’d comment in a blog, rather than repeat myself over and over again.
Briefing for those not in the US: there is open warfare between “reformers” and “non-reformers” of math education. The latest round is ostensibly over whether “data science” should be accepted as an alternative to traditional subjects like “algebra II” for admission to top colleges. Many countries have mounting concern over math education—mostly how to reform it, not whether it needs reform. But the US is notable for how enmeshed math has become with completely different political issues—and therefore polarised and puritanical.
I’m not a US resident or citizen, with no agenda except around math itself—an outsider. But for math, I’m the ultimate insider—I’m more in the centre of the revolution that’s enveloped the real world in the last few decades than almost anyone. I represent real users of math or computation with a far broader perspective than many of those fighting in the math war trenches: as employer, user, maker of the most extensive math platform that’s in all continents—and often space!
Which is no doubt why I’m being asked to comment and will probably offend everyone to some extent. Here goes:
Fundamental change essential. The curriculum of school (and early college) math education is hugely out of line with an optimised, modernised core computational subject that’s needed. That misalignment is chiefly because computers mechanised calculating beyond previous imagination, and in turn this has massively broadened, deepened and made math or computational thinking more critical to everything in life over the last few decades. No technology innovation and subject has been more successful in transforming the real world, perhaps ever in history. But with that fundamental change comes fundamental transformation needed for the educational subject. What we’re preparing people for is completely different—as well as more, harder, broader—than it was a few decades ago. But our curriculum has only evolved a bit. By late high school, the content is something like 80% off what’s really needed.
What we need is more conceptual, not less. A modern, computer-based core computational curriculum will be more conceptual, not less. Some would say “harder”—intellectually challenging beyond today’s subject, as well as more practical. The two are in fact increasingly aligned as computers and AI take away procedural tasks. A common mistake is to conflate rigour of learning hand-calculating procedures on simplistic problems in traditional math courses with conceptual understanding and application of a far wider range of higher-level math concepts (amenable with computers) on hard, real-life, messy problems. The latter is today’s requirement and pushes many a human harder.
Everyone benefits. Fixing the subject will benefit almost everyone by some measure, and society collectively a lot, just like mass literacy benefitted almost everyone, their employers, and particularly jurisdictions who adopted it first. Even those doing great in today’s math ed often can’t use it effectively; they could go much further and faster doing real, messy, hard problems, and with the right techniques given computers, like machine learning. Many more potentially good computational thinkers are put off from trying. Others are struggling through something they’ll never use and really need the very different computer-based subject instead.
The right subject regardless of who wins most. Whether one section or slice of society benefits most, or doesn’t gain as much, must not control subject matter. Matching real-world requirements is supreme. Once we have the subject straight, we should of course optimise delivery to each group, but whoever benefits most, however this ends up playing out, we need the right subject first.
AI tutoring on today’s subject will upset the applecart anyway. For those worried about realignment of the social order (in particular who gets to top colleges), AI tutoring availability, applied to the traditional subject, will upset that applecart. That’s because top grades can be (ideally shouldn’t be, but are) obtained today largely with enough good teaching, attention to the student, and rote learning. Money makes a big difference to that. But soon AI tutors will offer a great substitute, and cheaply. Much more is up in the air for a changed curriculum. Don’t fight fundamental math reform because you think keeping traditional math standards will go on helping your children get into top colleges (or for that matter, because math was scary to you and and change multiplies the scariness for your children!).
A curriculum set for and by users of mathematics, not for mathematicians. Mathematicians and those who have spent their life in education are, say, 95% unrepresentative for setting the core curriculum’s content (the subject matter, not the pedagogical approach). Why? Because their work isn’t up-to-date in the fast-moving “real world” of math that that core curriculum is supposed to be preparing students for. There are two dimensions to the issue.
(a) Firstly, most users of (even higher-level) math are not mathematicians, but scientists, engineers, in finance, CEOs and many more besides. (Last time we checked, fewer than 5% of Mathematica users classified themselves as mathematicians—which gives you some gauge.) This is such a difference because modern math or computation and the thinking behind it has become so widely used. Most are users, not specialists in building the subject itself, and the gap between these roles has expanded hugely since computers. Think of the difference between setting a curriculum for learning to drive (even advanced NASCAR driving) and for being an automotive engineer.
(b) Secondly, those whose full-time jobs are delivering education aren’t those using the subject at the cutting edge. This is not an attack on teachers, just a statement that it’s not their job, specialty or where they spend their time. For subjects that don’t change fast, this difference might be more academic; for example, if you’re a Latin teacher, you can still be up-to-date for curriculum setting, as the subject hasn’t changed much from when you learnt it. Because math and computation is the fastest moving field in history, it’s essential practitioners’ actual conceptualisation and uses today are what feeds the curriculum.
Top CEO? Techy? Influencer? You’d think highly intelligent, techy CEOs and other senior people in the real world would immediately get this. Some do. Some just complain about too few people with the right skills. But most haven’t thought about it deeply. They think “it (math) is important” but haven’t questioned the “it” like they should have done before they comment. I have from a pretty good vantage point, for years, intensively; and have gone further, by building what a high-concept curriculum "assuming computers exist" could look like. I’m happy to discuss why it’s important that others get the perspective I’ve achieved, too. Almost always, they get it when starkly presented—sometimes more starkly than me(!); it’s a great conversation, in fact.
US leadership valuable. Just like it has done for entrepreneurship, the energy, technology, scale, and zeal of the US could lead change: a new era of computational literacy for all and a computational thinking elite that make better decisions. Or that same zeal could suppress the inevitable for a bit longer; others will lead the world more slowly.
One thing I would say in all of this: don’t let your visceral reaction overwhelm reasoned, logical thought (like math hopes to achieve!). It’s taken me some 15 years to dig deep into what’s needed. Remember, I’m a math person—a keen math believer. I spent a lot of time learning the traditional subject; I don’t want that devalued; I was told how important it was; but more—I’ve been involved for years in pushing the envelope of math, and our first product was even called Mathematica!
Viscerally, I reacted like most people’s initial "of course we need to learn the math we always have". But when confronted with the cold, hard look, I realised (as do most people I talk to about this on round two or three) we needed to think differently... and in fact far more differently than I’d originally thought.
That's the short of it. The longer take is in my book The Math(s) Fix—from spelling out the problem, to proposing the fix, to change!