Just as you get songs stuck in your head, sometimes I get graphs stuck in mine. Like this one:
Now, like any catchy song, this graph runs its risks. The astute and thoughtful Tracy Zager objects to the entire premise of this graph, making three key points:
- Teachers of young, fresh-faced kids need deep content knowledge, too! Try explaining what it means to divide or multiply fractions. It’s shockingly hard! Most high school teachers can’t do it. And yet deep understanding of core concepts like is crucial for elementary teachers.
- Teachers of old, decrepit kids need pedagogical skills, too! It doesn’t matter how expert you are if you only know how to deliver dry-as-chalk-dust lectures and pass out worksheets. You’ve got to meaningfully and creatively engage with your students, whatever their age.
- This zero-sum approach is probably not healthy for teachers!
(For what it’s worth: I totally agree. Check back for a follow-up post soon.)
Still, I hear this graph echoing my experience. It’s not a photorealistic portrait, but it’s a recognizable caricature. The basic ingredients of teaching don’t change, but the recipe does.
The question is: Does this graph show us the world as it should be, or merely the disappointing reality we’ve got now?
What mud-crusted nonsense is this, Daniel? Does this look like Belgium to you? Get that metric profanity out of here, and let Sierra draw her lines in peace.
Uh, correct me if I’m wrong, but cake isn’t a number. Cake is a moist brick of carbohydrates that you light on fire to honor the Birth Person.
And what is that green vegetable doing there? I don’t need the government policing my diet. I have apps for that.
“I’m frightened and I cannot sleep,”
the little child said.
“I fear there might be triangles
underneath my bed.”
“There might be ghosts,” the mother mused.
“I cannot speak to those.
There may be ghouls and goblins
who will nibble on your toes.
There could be long-toothed monsters
with their eyes a gleaming red.
But there’s no such thing as triangles!
They’re only in your head.”
Teaching math is a weird job. I’m paid to tell children about imaginary things. To be sure, no one mistakes me for J.K. Rowling or J.R.R. Tolkien; there are no slow-talking trees, giant spiders, or unionized cleaning elves in my line of work.
I traffic in things much stranger than that, and much less beloved.
It’s happened again: a math question made students cry.
This time it was in Scotland—very discouraging, as I’ve always assumed the Scottish raise a tougher, more stoic, northerly breed of mathematician. Alas; it seems they’re as skittish and frightened as the rest of us.
Here’s the offending question:
(My two cents? This question is more than just fair; it’s really good!)
But students panicked. Then they tweeted their panic. The BBC quoted a former examiner denouncing this question as “unfit for purpose.” And commentators leered at the spectacle—by this point routine—of students freaking out about a hard math question.
This sort of ordeal threatens to confirm our darkest and most cynical suspicions about students. They’re incurious. They’re mercenaries. They’re on a witch hunt for anything that pushes them out of their comfort zone. They worship at the Church of the Right Answer.
So who do we blame? The students? Their parents? Their teachers? Educational bureaucrats, who are always a fun punching bag?
I believe that this flawed state of affairs emerges not through someone’s sinister design, but by well-intentioned increments. The problem isn’t that we want too little from our tests.
It’s that we want too much from them.
I’ve always felt conflicted about repetitive practice.
On the one hand, I see how vital practice is. Musicians repeat the same piece again and again. Soccer players run drills. Chefs hone their chopping motion. Shouldn’t math students do the same: rehearse the skills that matter?
But sometimes, I backtrack. “This is just going to bore them,” I fret, scanning a textbook exercise. “I’m emphasizing the rote aspects of math at the expense of the creative ones. They’re going to forget this skill anyway, and be left only with the insidious impression that math is a jackhammer subject of tooth-grinding repetition.”
(Then I assign the exercise anyway, because class starts in five minutes and— despite my repeated petitions—the administration has denied me access to a time turner.)
These two trains of thought suffer daily collisions in my mind: repetition is dull, but repetition is necessary. This inner conflict takes for granted the idea that repetitive practice is a separate endeavor, a distinct stage of the learning process. First, you learn the concept. Second, you practice it. In this view, practice is like cleaning up after a picnic: absolutely essential, but not much fun.
But this summer, a very wise teacher showed me a path forward, a way to reconciliation.
I’m referring, of course, to a two-year-old named Leo.
Last year, I conducted alumni interviews for Yale applicants. It’s an easy gig. You take a smart, ambitious 17-year-old out for hot chocolate, ask them about their life, and then report back to the university, “Yup, this is another great kid.”
I recently got an email asking me to re-enlist. Was I ready for another admissions season?
I checked “No,” mostly because “Aw, hell no” wasn’t an option.
Why my reluctance? No grudge, no beef, no axe to grind. It’s just that the whole admissions process is so spectacularly crazy that participating in it— even in the peripheral role of “alumni interviewer”—feels like having spiders crawling out of my eyeballs.
In the last 15 to 20 years, Yale’s applicant pool has gone from “hypercompetitive” to “a Darwinian dystopia so cutthroat you’d feel guilty even simulating it on a computer, just in case the simulations had emotions.”
I don’t fault the admissions office. For every bed in the freshman dorms, twenty kids are lining up, at least five of whom are flawless high-school rock stars. From that murderer’s row, they face the impossible task of picking just one to admit. There’s no right answer.
But two things freak me out about this process.