“I’m planning a series of posts,” I told my dad the other day as he drove me home from the airport. “The title is How to Avoid Thinking in Math Class.”
Before I could get any further, he rubber-stamped the idea. “That sounds great! I always tell people, the point of school is to help you not to think.”
It’s a good thing he was the one behind the wheel, because if it were me, I’d have slammed the brakes and spat my latte all over the windshield.
“Really?” I sputtered. “I meant the exact opposite. I was going to catalogue all the silly ways that kids avoid doing real math. You know: blindly carrying out operations; hating word problems; worshipping right answers; focusing on procedures instead of ideas. I was going to take inventory of all those cognitive shortcuts and how they impede learning.”
“Well, sure,” he said. “But they can’t think all the time.”
“Well, isn’t thinking the whole point of math education?” I countered. “Math class is like a gymnasium for thought. You work out daily with a trainer who knows how to stretch your limits. You watch your mental muscles build. You see the payoff of intellectual risk. You learn that just as people can grow faster and more agile, they can grow smarter, too.”
“Yeah,” he mused, “that’s part of it. But that’s not the whole thing.”
“Because thinking is hard.”
I had to admit, I knew what he meant. Just a few hours before, on the plane, I’d been reading a book when I realized that my eyes were just gliding over the words in a mindless imitation of reading. Meanwhile, my attention roamed and drifted. I wondered which sandwiches can and cannot be improved by bacon.
“Sure, sometimes we focus deeply,” my dad continued as he absentmindedly accelerated to make a yellow light. “But our natural state is autopilot.
“It’s like he says in that book,” my dad added. This is my dad’s usual level of specificity; he once described his favorite television character as, and I quote: “Oh, you know. Him. The guy.” Luckily, this time I knew which book he meant.
“Thinking, Fast and Slow,” I said.
“Right. By Khina… Khena…”
“Daniel Kahneman,” I said. My dad nodded.
Kahneman (a psychologist and Nobel laureate) describes human thought as governed by two systems. The first is fast and automatic. It employs shortcuts, heuristics, and dogmas—quick-and-dirty rules that save our mental strength. The second system is slow and deliberate. It musters focus, frames scenarios, tests assumptions, and reconciles contradictions—all those cognitive activities that exhaust students and excite teachers.
“We can only do that deep thinking on special occasions,” my dad said. “It’s just too tiring to focus intensely all the time. It’d be like sprinting everywhere instead of walking.
“That’s why the goal of school has to be automaticity,” my dad concluded. The Sunday morning roads were empty, and we’d nearly made it home. “Take learning your times tables. You’ve got to know them cold so that you can go on to finding common denominators, or reasoning about algebraic functions, or whatever. You need each task to become automatic before you can move onto the next intellectual step.”
“I guess you’re right,” I said. “But how do you reach automaticity? Isn’t the only way to get there by thinking deeply? Don’t you need to wrestle with the ideas before you can make them automatic?”
He drove quietly for a moment. “Yeah.”
“So then,” I said, “you’re saying that the purpose of school is to make you think hard now, so you won’t have to think later.”
(All this, of course, to allow you to think even harder.)
“Yeah,” he said, signaling a turn and pulling into the garage. “That’s learning, pretty much.”
And that, in a nutshell, is what I hope to write about over the next month.
In teaching math, I’ve come across a whole taxonomy of insidious strategies for avoiding thinking. Albeit for understandable reasons, kids employ an arsenal of time-tested ways to short-circuit the learning process, to jump to right answers and good test scores without putting in the cognitive heavy lifting. I hope to classify and illustrate these academic maladies: their symptoms, their root causes, and (with any luck) their cures.
But, as my dad points out, it’s not always bad to avoid thinking. It’s often healthy, even necessary. So I also hope to highlight the good heuristics, the sensible shortcuts, and the wisdom of seeing math class as an effort to program your autopilot.
I hope to make posts on the following topics (subject to abrupt change, regional blackout, second thoughts, and personal whim):
- Number Smoothies. Throw the numbers in a blender, and press “puree.”
- Dish-Washing Robots. When thinking less means working more.
- Word Quarantine. Do math with no word problems! Then, paint with no pigments, and breathe with no air.
- Garden of Doubt. Watering the seeds of uncertainty.
- Sharpening the Axe. The wisdom of Abe Lincoln, math teacher.
- Little Waldens. As Thoreau advised: “Simplify, simplify, simplify!”
- Church of the Right Answer. Where do my students worship?