I find that lots of students are really good at how.
Like, how do you factorize a quadratic? How to you differentiate a cubic? How do you solve a system of simultaneous linear equations? How do you poach an egg?
(Apparently you need a gentle whirlpool to get the egg moving. Whirlpools: the unsung hero of the breakfast table.)
Why are they so skilled at how? It’s because students like procedures. They like certainty, clarity, the feeling that you know exactly what to do at every moment.
But they struggle with why. And – even more basically – they struggle with what.
I find that questions like this elicit one of two responses from students. Either this:
These aren’t questions students are accustomed to answering in math class. In history, perhaps, where they have to write IDs of historical figures and events; or even in science, where they have to understand each component’s role in a theory.
But not in math. We math teachers tend to ask lots of how questions, and not so many what questions.
If you ask me, that’s sort of sad. They’re experts in how, and they can’t even tell you what the how is for.
And in this case, it turns out, there’s a pretty satisfying answer. Continue reading
Okay, here’s a life regret: No one has ever stopped me on the street, grabbed me by the collar, and demanded that I explain to them the essence of mathematics.
I’ve envisioned it many times, though.
What math teacher hasn’t?
Me: So, you want to get math?
Assailant: Obviously! Why else would one human being violently accost another, if not for the acquisition of knowledge?
Me: Easy, then! All you need to do is listen to Sgt. Pepper’s Lonely Hearts Club Band.
Assailant: [arches eyebrow] You can’t be serious. The Beatles album?
Me: [easing out of their grip, brushing my collar] Naturally! The whole album is trippy and spectacular, of course. But I’m talking about the final moments of the final track, a song that Rolling Stone has hailed as the Beatles’ greatest: “A Day in the Life.”
Assailant: [listening on an iPhone] This better be good, or I’m going to pound you into a fine math teacher carpaccio.
Me: Patience, assailant, patience! Wait until three minutes and fifty seconds in. That’s when a cacophonous noise begins. It’s the sound of a 40-piece orchestra playing absolute gibberish.
What would you do, if you were designing high school math from scratch?
Well… probably not what we do now.
What in Noether’s name is going on here?
Why do we teach so many obscure technicalities, and so few practical facts?
Who the heck designed this monstrosity?
Nobody Designed Mathematics Education
I’ve come to believe that even this simple question—“who designed this?”—rests on a flawed assumption. The broad thing we call “the math curriculum” isn’t really “designed.” Rather, like all educational institutions and systems, it is shaped by a hailstorm of competing forces:
Over time, each of these parties tugs and prods at the curriculum, reshaping it to suit their needs. No single author writes the curriculum. Nor, even, do multiple authors reach a clear and coherent compromise. Instead, the curriculum is perpetually being nudged and tweaked, eroded and built up, by various actors who share no unified vision.
Math education isn’t like a skyscraper, designed by a single architecture firm.
It’s more like a mountain, shaped by many competing geological forces.