Or, How to Avoid Thinking in Math Class, Part 5
(See Also Parts 1, 2, 3, and 4)
Sometimes I fantasize about making scarecrows of myself.
They’d wear jackets, ties, and expressions of thoughtful patience. I’d scatter them around my classroom—maybe even one every desk (if scarecrow manufacturers happen to give bulk discounts). And they’d work wonders for my students, because a lot of the time, the students don’t actually need me.
They just think they do.
This idea goes back to my first year teaching, when one student would come to me after school, homework in hand. “I need help,” he’d say.
“Sure. What question?”
“All of them.”
It sounded grim. But when pressed, he could explain perfectly how to tackle every problem. His understanding was solid. “So what’s the issue?” I’d ask.
He’d shake his head solemnly. “I lack confidence.”
That autumn, we developed a peculiar routine. While I worked at my big wooden desk, he’d perch on the edge, quietly and independently doing his homework. He refused to sit at an adjacent desk of his own. He wanted to be extra close, with his paper in my field of vision—never mind that I wasn’t providing a shred of assistance, or even watching him work. It reassured him simply to have an expert close at hand.
He just needed a scarecrow.
The fact is, uncertainty is hard. It scares us. I myself run from it, without meaning to, or even realizing what drives my behavior. Faced with a hard task, I procrastinate: fleeing to Facebook, turning to Twitter, or suddenly “remembering” that I need to re-shuffle my computer files from 2007.
Sometimes, it seems I’ll do anything to avoid wallowing in my own uncertainty.
As for students, it can be frightening to start a math problem. You don’t know quite where it will lead. Will my approach be fruitful? Will it falter? Where do I even begin?
But unlike my desk-perching student, most kids don’t recognize that one rope holding them back is fear of the unknown. They just hesitate: too afraid to leap without a net, but never bothering to go in search of a net for themselves.
Sometimes they write nothing, paralyzed by not knowing. They won’t commit pencil to paper until they’re 100% sure.
Or, if they do write something, they immediately check answers in the back of the book, before inspecting or reflecting. Craving quick approval, they cut short their own learning.
Often, they just push the task aside, idly waiting for a resolution, too shy or un-self-aware even to ask for help.
Other times, they ask. And ask. And ask. They’re hoping I’ll slice the task into bite-sized pieces for them, sparing them the trouble of actually grappling with the unknown.
In all these cases, students are refusing to engage with their uncertainty. But if you’re uncomfortable with doubt, you’ll never break through to the other side. You’ll never have a “Eureka!” moment or an intellectual “Aha!” You’ll never… well… learn. After all, if you can’t bear to face the unknown, how will you ever come to know it?
I find that my desk-percher has it right. At times like these, the mere presence of an expert can supply the confidence you’re lacking.
“Just write down what you know.”
“Hey, give it a shot.”
“Well, how do you think we can solve this problem?”
Platitudes like these—despite being as vague and vacuous as any pop lyric—actually succeed in urging students forward in their problem-solving. I find myself saying such things constantly. In those moments, the kids don’t really need me. They just need a nudge. A pull-string teacher, with a few pre-programmed slogans, would suffice.
To be fair—and in defense of my employability—that’s not always the case. Many days, kids are legitimately stuck. And what seems on the surface like a generic suggestion (“Try a simpler case, like when there’s only one person”) or a pro forma question (“How do we actually define a circle?”) can actually point towards the key idea. A mannequin-me couldn’t give that kind of targeted feedback and encouragement.
Still, I’m surprised how often a scarecrow is all it takes.
If you can teach in a way that students learn to brave the deep waters of their own uncertainty, rather than fiddling around on the beaches of procrastination, that will benefit them their whole lives.
They’ll feel like it was a step they made, so you won’t get much credit for it, but the alternative is just so awful.
I also find that my students use their calculator as a scarecrow … they know perfectly well what 3 x 5 is, or how to add 72 and 49. But the calculator gives them reassurance. It takes a lot of work to build up that confidence in their own abilities, apart from the electronic security blanket. (And P.S. – these are 17-year-olds in 11th grade).
Students have a natural tendency to see a maths problem as something that is presented to them as Moses presented the 10 commandments, chiseled in stone. If they can come to accept the problem as their own then they will feel more able to “muck it around”, simplify it, change the numbers and so on.
Where is the encouragement to develop this attitude?
Even with simple “word” problems putting in whole numbers in the place of fractions, for example, can expose the meat of the problem.
I really enjoyed this post, because all of these lessons apply to how we go about learning and what our avoidance techniques can cost us in knowledge and of course, time.
When my son was in seventh grade, he was quick to ask me for help on his math homework. I asked his teacher for advice, and she said, “Tell him to try by himself for 10 minutes. He’ll figure it out 90% of the time.” She was right; pretty soon he stopped asking, mostly.
Your students are lucky to have such an understanding math teacher…
Reblogged this on a teacher's life.
I think this is a general problem about learning and experimenting. Students are discouraged from experimenting and testing their ideas in general (and they don’t know how to “test” their ideas in math), and that’s why they don’t want to write anything down. I disagree with some other commenters that it’s just a problem with math. Because the same problem shows up in basic computer programming, which I teach, where students are afraid to start typing on a blank document. Even though they’re not necessarily being asked to do any heavy thinking, and they’re just learning syntax and semantics of loops and such. I also get the question “so what do I type?” And this is in a setting where deleting an incorrectly typed thing is trivial! They don’t even have to scrub with an eraser.
Some of your questions sound like those in Polya’s “How to Solve It.” Questions like “do you know of a related problem?” or “can you draw a picture?” are not obtrusive, but still cut through the feeling of a blank slate.
I am really enjoying reading your blog. This article in particular cuts to the heart of learning, because there has to be some sort of struggle, some cognitive dissonance before real live learning can take place. That’s why confidence is so important.
Fearing the unknown applies to pretty much every aspect of life. My fear is of phone calls to and from unknown persons.
Reblogged this on tglennb and commented:
“we have nothing to fear, but fear itself…” apologies to Mr. Churchill. I try my very best to make failure survivable in my classroom. It’s OK to fail. It’s OK to be wrong. It’s not OK to not try.
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