I’ve so often wondered why so many students haaaate writing down their math steps, insisting instead on trying to do the work in their heads or on their calculators. Perhaps they feel as if writing is slowing them down, or maybe they dislike the scratchy feel of pencil on paper. (Whenever I’ve asked, kids invariably say “I don’t know).
Meanwhile, kids who don’t write out their math steps, skip copying down formulas and refuse to draw and label diagrams, make a lot more mistakes and also tend to be way more confused. They’ll stare at a problem and then give up, without ever making a mark on paper.
One of the first things I do as a tutor and a test-prep coach is to get students to pick up and use those 100-pound pencils, and persuading them is not easy!
Writing forces you to organize and clarify your thoughts. But organizing and clarifying thoughts is hard work, not to mention scary work.
I know that when I’m writing a newsletter entry or a blog post, I routinely hit mental snags where I realize I don’t, in fact, know what I’m trying to say, and that sensation is unpleasant, even somehow threatening, like suddenly staring into a chasm of uncertainty.
Or, I discover a gap in my logic, or I notice some area in which I realize I need to go and do some tedious rereading or further research…and I just don’t wanna!
I’m certain that this happens to my students, too, when they write essays and also when they do complex math problems.
And I’m not alone in noticing this tendency towards, well, laziness. Psychologists say that human beings are built to avoid expending extra energy, be it physical or mental.
Tom Stafford writes:
An influential theory among psychologists is that we’re cognitive misers. This is the idea that we are reluctant to do mental work unless we have to, we try to avoid thinking things through fully when a short cut is available. If you’ve ever voted for the political candidate with the most honest smile, or chosen a restaurant based on how many people are already sitting in there, then you’ve been a cognitive miser. The theory explains why we’d much rather type a zipcode into a sat-nav device or Google Maps than memorise and recall the location of a venue – it’s so much easier to do so.
For that matter, it’s way easier to grab a calculator and punch in some numbers than to pick up a pencil…there’s some version of magical thinking that hopes the calculator will spit out the right answer, just like the GPS effortlessly guides us to the movie theater.
In Thinking Fast and Slow, Daniel Kahneman gives us a taste of cognitive miserliness in action. Just try the following!
Step One: Multiply 17 x 24.
Step Two: I’ll bet you either skipped Step One, or at least you felt a dragging reluctance before you then began calculating mentally or reached for pencil and paper…both are illustrations of cognitive miserliness in action!
Kahneman’s blow-by-blow description of the feelings of then actually working the problem seem spot-on to me:
You experienced slow thinking as you proceeded through a sequence of steps. You first retrieved from memory the cognitive program for multiplication that you learned in school, then you implemented it. Carrying out the computation was a strain….The process was mental work: deliberate, effortful, and orderly…
And this effort wasn’t “just in your head”…your body was also involved. Your muscles tensed up, your blood pressure rose, and your heart rate increased. Someone looking closely at your eyes would have seen your pupils dilate. Your pupils contracted back to normal size as soon as you ended your work – when you found the answer (which is 408, by the way) or when you gave up.
-from Thinking Fast and Slow
Academic work is REAL work, and it is hard work!
I’ve been explaining this to my students, who seem interested and also relieved to know that, despite the hype they’ve been raised within, all about how learning is supposed to be easy and fun…?
In fact, nope, learning is a lot more like weight-lifting: rewarding, yes, eventually, but every step of the way entails combating that natural desire to take the easy way out, and instead choosing to pick up that 100-pound pencil.
[photo of the EMP Museum in Seattle]
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Last reviewed: 8 Mar 2014