Math shouldn’t be seen as just a tool, or a compulsory subject. It is an enriching mental experience. Yet more and more young children are fleeing from it, right at the start.
DOCTOR #1: Who are you? Why aren't you masked? Who are these people?
DOCTOR #2: I don't know.
DOCTOR #1: What the hell is that? What are you doing?
McCOY: Tearing of the middle meningeal artery.
DOCTOR #1: What's your degree in, dentistry?
McCOY: How do you explain slowing pulse, low respiratory rate, and coma?
DOCTOR: Fundoscopic examination...
McCOY: Fundoscopic examination is unrevealing in these cases!
DOCTOR #1: A simple evacuation of the expanding epidural hematoma will relieve the pressure.
McCOY: My God, man, drilling holes in his head's not the answer. The artery must be repaired. Now put away your butcher knives and let me save this patient before it's too late!
I love this scene from Star Trek IV. Dr. McCoy is at his most irascible, shocked by what he sees as the “primitivism” of late 20th-century neurosurgery. Were he an educator, he’d be saying the exact same thing about how we respond to students that are struggling in some subject. Such as math!
We hear all the time how math is crucial for academic success, and for that matter, dealing with the demands of modern technological life. “Do well in math and you’ll do well in school: and in your job, if and when you get one!” But to ask a very obvious question: “Why?”
Is it because school, or at least, the STEM subjects, are biased towards math: keep testing the same sorts of things, albeit in ever more complicated ways? Are HR officers secretly testing you on math skills? Is there something special about “mathematical thinking,” whatever that might be, that transfers to life in general?
But is it really necessary to know how to calculate percentages when I can just load “Tip N Split” on my smartphone? I realize you could ask exactly the same question about learning a foreign language; but then, why shouldn’t we ask that question? The day when we have a “Universal Translator” no longer seems all that far away—not with the current AI explosion.
For me personally, the answer is that I love speaking a foreign language. Not because it’s useful when I travel, or even because of the pleasure I experience as I stumble along. It’s because I begin to think differently: to see the world through different eyes. And I value that experience in a way that could never be simulated by a “Universal Translator.”
It’s the same thing with math.
The real reason why I want my kids to learn math isn’t so they do well in school (although yes, I do want that); or so they can impress their friends at restaurants. It’s because it is so enriching.
I would love to see my kids pick up a book like Strogatz’ The Joy of X, not because they have to, but because it is so much more rewarding than, say, watching the latest episode of Good Mythical Morning (which, to be fair, is a lot of fun, but not all that enriching).
But maybe “rewarding” isn’t quite the right word. It’s a bit like saying that I want my kids to learn about classical music because it “pays” to listen to Vivaldi's Stabat Mater. For me, listening to Andreas Scholl sing this piece is deeply moving: I am transported, humbled, inspired. And that’s rather the way I think about math.
I have to laugh when I read about the debate raging today as to whether kids need to learn the “basics” before they can tackle the “interesting” problems. We tend to forget just what an enormous leap is involved in learning these “basics.” I’ll never forget the day when my daughter said to me “Daddy, can I have two pieces of toast” rather than pointing at one and then another. In cognitive terms, this event was momentous; just as it was for humanity when the concept of number was first developed.
It marks the moment that we start to think in abstract terms. Pretty soon my daughter was doing this in all sorts of ways. “Daddy’s chair” had become “Daddy’s chair,” which was different from mommy’s chair because it has arms and is at the end of the table, but similar because of what it’s used for. So much so that when I asked her to fetch a chair from the living room for her aunt to sit on she knew exactly what to get, although it looked nothing like our kitchen chairs.
But math is different, unique.
This is an abstract world—a language, if you like—that we create, purely by thinking. And what is most incredible about math is that this creation of the mind can be applied: used to do all sorts of things, like figure out a tip or how many pieces of toast to put on if there are four of us and each wants two. I can even prove something incredibly arcane—like, "the shortest distance between two points is a curve and not a straight line"—if I start out with a different set of axioms; and then, over a hundred years later, discover that this system is the perfect tool to use for navigating through outer space.
Of course, there are an awful lot of steps between learning multiplication and mastering the intricacies of non-Euclidean geometry; but it all starts with learning how to count. And what may look like a “small step” is actually a “giant leap” for a child. But it’s easy to lose sight of this fact if all you can think about is beating other kids in the competition to get good grades, or beating other nations in the race to get to Mars.
If a child learns how to speak this “language” because of the pleasure and personal fulfillment it affords, and not because it is forced down their throat, you open up whole new mental vistas for that child. But what we’re seeing instead is a version of what psychologists refer to as “hodophobia”: an intense and somewhat irrational fear of travel. (Actually, they call it “arithmophobia,” but you see my point.)
Why is this happening? That question will be the theme of next week’s blog in this three-part look at the worrying decline in math in early learners.