Last April 13th, I emailed a few friends to let them know I was starting a blog. “I’m a little afraid it will land with a dull thud against the hard pavement of the internet,” I wrote.
Two weeks later, I posted an essay called What It Feels Like to Be Bad at Math, about my struggles with topology. It was stubbornly hard to write. I spat out 500 words of excuses and hedges (which I later deleted) before I could bring my fingers to type the truth.
Then the post started getting passed around. Continue reading
I’ve always dreaded being asked for my “teaching philosophy.”
For years, I gave nonsense or scattershot answers. “Logic and critical thinking are paramount.” “I care more about conceptual understanding than computational skill.” “A balanced, student-centered approach is always best.” “We buzzword to buzzword, not for the buzzword, but for the buzzword.” At best, each of my disjointed half-theories captured only a piece of the puzzle.
Worse still, none of my replies explained why I devote so much class time to plain old practice. Continue reading
I don’t usually struggle to distinguish toys from tools. Gas stove? That’s a tool. Easy-Bake oven? That’s a toy. Bricks? Tools. LEGO bricks? Toys.
Mathematical tools are similarly distinctive. They harness industrial-strength power—think of Taylor series, or completing the square. Mathematical tools shine floodlights into dark corners. They unlock doors, solve problems, and make attentive students utter, “Whoa, deep.” They often come with complex instruction manuals, requiring weeks (or months (or years!)) of technical training to master.
Mathematical toys… not so much. They’re simple to grasp, fun to handle, and not much substantive good to anyone. Think of Sudoku puzzles, or differentiating cos(cos(cos(cos(x)))). We might get a kick out of poking and prodding such problems, but solving them won’t teach us anything fundamental about the workings of the universe or the necessities of logic. Toy problems aren’t floodlights; they’re more like flashlights dangling off of a keychain.
But just as the Incas mistook the wheel for a mere toy, sometimes mathematicians get it wrong. Sometimes what seems to be a toy is, in fact, a powerful tool.
Sometimes a toy is just a tool in waiting. Continue reading
A pessimist’s take
“Hooray, it’s tax season!” said nobody ever, except for the clinically ill and the clinically sarcastic. But I’m here, in this season of paperwork and low spirits, to offer a hymn of praise to the poor, misunderstood public servants that make income taxes work. No, not IRS agents, although goodness knows those sorry devils could use a defender or two.
I’m talking about tax brackets.
“I’m worried about Joe. He’s been hitting the Klein bottle pretty hard lately.”
“Well, that explains why he’s totally sober. It’s hard to get much liquid in those things.”
Like everyone else, I’m heir to the prejudices of my culture. So even though I know firsthand that teaching is a profession, on some level I see it as an act of self-sacrifice, as a hard path undertaken for the greater good.
This might not sound like a prejudice. Not a damaging one, anyway. It paints a generous portrait of teaching as noble and virtuous—a useful antidote to the too-common caricature of educators as lazy, union-fed bureaucrats. This ethic of “the greater good,” in fact, helped draw many of us into the profession. What we lack in salary and prestige, we make up for in civic-mindedness, in moral conviction, in feeling we’ve taken a high road through our professional life.
But all this high-mindedness has a dark underbelly. In painting the choice to teach as an act of self-sacrifice, I believe that we may harm our schools more than we help them. Continue reading