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.
That’s why it’s so hard to find a clear sense of purpose in math education as a whole. Is it about pulling kids into STEM? Imparting broadly useful job skills? Cultivating critical thinking? Ensuring compliance and rule-following? Providing a neutral arena for students to compete for college admissions?
To varying degrees, the answer to all of these is “yes.” Math education doesn’t have one purpose. It has many—sometimes aligning, sometimes conflicting. Together, they form a knotted ball of twine that even the nimblest fingers struggle to tease apart.
Pleasing All the People, All the Time
Sounds like a teeming pile of contradictions, right?
Oh, I’m just getting started.
Take one actor from my list above. Put them under a microscope. You will not find a single goal-oriented organism, but instead a messy conglomerate, pursuing several contradictory goals of its own.
Start with universities. They seem to want:
Depending where you go on campus, you’ll find voices singing very different tunes about the nature of math education. There’s no way to make them harmonize. Instead, the math curriculum simply does its best to incorporate the whole scattered, dissonant bunch.
And that’s just universities! Think about a far more diverse and decentralized group, employers. Depending what business you’re in, you may want math education to cultivate in your employees any mix-and-match combination of the following traits:
When critics demand that math education provide more “real-world,” “professional,” or “practical” skills, they’re missing a crucial fact: the “real world” doesn’t agree what skills are valuable!
I haven’t even touched on the people actually delivering this education: teachers. They exert their own pressures, preferring to teach things that are:
The paradox? These are frequently opposites! “What I learned in school” is typically rote and spirit-crushing. “What I find fun and rewarding” is often far more creative and exploratory. Many teachers find themselves torn between what they know, and what they value.
Shelter from the Elements
So what should we do about this lumpy mass we call American mathematics education?
Well, let’s be frank. It’s hard to remake a mountain. Sure, you can rearrange the rocks, but the forces of geology will soon return it to its former state. You can’t fight the wind, the rain, and the grinding power of the tectonic plates.
Instead, the best you can do is to build a cozy little shelter.
When I read a piece like the recent hit The Wrong Way to Teach Math, I nod along to the criticisms. Andrew Hacker has a coherent and lovely vision for how to teach mathematics. But to treat his work as a blueprint for all of mathematics education is to make a category error.
A great class can no more become a national curriculum than a beautiful home can become a mountain.
Good education needs unity and clarity of purpose. My transcendent experiences in the classroom all came when an expert teacher built a gorgeous class, where every component—instruction, assessment, discussion—fit together in service of well-defined goals. A good class is a masterpiece of architectural design.
But “design” is precisely what the policy world—with its thousand competing forces and colliding actors—can never supply.
Teachers like Hacker provide their students with something beautiful and precious. They offer shelter from the punishing forces that shape educational institutions—the lack of resources, the need for sorting, the pressures of political orthodoxies. They give students a rare chance to engage in that most wonderful activity: learning.
But, to borrow a Silicon Valley verb, such visions cannot “scale.” It’s a mistake to think that educational progress means uniting behind a singular, coherent purpose, because our purposes are not singular, and will never cohere. One architect cannot remake the mountain.
Instead, what education needs are many architects, scattered across the mountainside, building shelters for the students under their care.
We cannot build a new mountain. But we can build our homes upon it.