What Level of Teaching is Right for Me?

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:

  1. 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.
  2. 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.
  3. 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?

Continue reading

9 Questions That Show How Common Core Math is Ruining America


cc satire 8

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.


cc satire 7

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.

Continue reading

There’s No Such Thing as Triangles

“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.

Continue reading

The Differentiation: A Survivor’s Tale


The constant functions perished first.

Everyone began planning a vigil, a sort of funerary service in honor of their memory. I don’t mean spit on anybody’s grave, but let’s be honest about who the constants were: simpletons. They stagnated in time. Never grew, never shrank, never changed. I pity them not so much for their grisly demise as for the bland, purposeless life that had come before. Call me an elitist and an unfeeling snob, but to me, a constant’s existence is no existence at all.

Not that they deserved their fate. Nobody deserves that.

I came for the vigil, of course. (I’m an exponential, not a monster.) I held my tongue and let the lower-order polynomials drain their tears on eulogies. They told anecdotes of the constants’ reliability, their steadfastness. They told self-aggrandizing stories of intersection and tangency, moments when the constants had told, say, a quadratic, something about itself: where it was, where it was going. Simpleton wisdom. Charming stuff, I guess, but not my cup of tea.

Filing out of the vigil was when I first heard the word. It rode a wave of terrified whispers across the crowd, uttered like the name of a demon or a plague.

The Differentiation.

Rumors painted it as a waterless flood, an invisible Armageddon. It sized you up like the Hand of God: how you’d grown, how you’d receded, where you’d been and where you were destined to go. It knew the curvature of your past and the untold shape of your future. It swept through in an instant, like the mad justice of a tsunami or the silent pulse of a neutron bomb, pain outpacing sound. It had slain the constants, smothered them like infants, and no one knew when if or when it would come again.

Or who it would claim next.

We should have known. We should have put it together: the constants’ slaughter, plus the slight changes in everyone else—quintics going quartic, quartics going cubic. We should have seen what was coming.

But even if we had, what could we have done?

Continue reading

The Quixotic Search for a “Fair” Math Test

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.

Continue reading