13. The Intelligence Behind the Mistake
Good Wrong Answers and the Pedagogy of the Imagination
Maybe when you tried the 9-dot puzzle, you found yourself stumped. Don’t worry, it stumps most people. The bigger problem would be if someone who tried an outside-the-dots answer might be too embarrassed to show anyone, fearing that it might be thought of as stupid. This may be because you’ve been taught that wrong answers are embarrassing. Let’s try something else and look closely at the kind of thinking that sometimes turns incorrect answers into correct ones.
We’ve discussed dots and spots already in this series, but here’s yet another story about dots, this time on an MCAS question. MCAS is an exam Massachusetts students need (needed?, long story) to pass to graduate high school. This is the story of a student whose wrong answer turned out to be right.
Dinner Party Math
Here’s a way-more-than-nine-dots problem. In the following sequence, a filled-in circle or switch means "off," and an empty circle means "on." The on or off sequences determine the number values seen at the right.
The test question asked which of the following represents the number 11:
The answer is C. The four switches represent 8, 4, 2, and 1 from left to right. If a switch is on, it is added to the other on switches. Under this system, C is the only answer that equals 11. A 10th-grade student found a completely different way to look at it, but her answer was deemed incorrect. However, after explaining what she saw to MCAS officials, they gave her and many other students credit for answering the question correctly.
The student found a pattern of white dots, as she said, “having dinner together.”
(Boston Globe 12/05/2000 Graphic: Christopher Melchiondo.)*
For her, the answer was B. So how smart was our Dinner Party Math student? Let’s take a look.
Really Mean IQ
Historically, intelligence and ability have been considered done deals. They were innate and relatively fixed. Your IQ was your IQ was your IQ. Consequently, a lot of education focused on determining who belonged where. Whether you call it IQ or genes, the message was the same: You’re out of luck, kid. It’s all in the cards, and the cards don’t lie. The Bell Curve authors claim that what matters most in intelligence is what they call “cognitive ability.”
How do you acquire cognitive ability?
Well, you see, it’s a gift!
How do you know who has the most cognitive ability?
Test scores, of course! *shakes head*
In What It Means to Be 98% Chimpanzee, Jonathan Marks criticizes the Bell Curve mentality as being sorta dumb. He says more is going on than meets the test-maker’s eye. About those gifted, high achievers among us Marks says, “No scientific statements can be responsibly made about such ‘gifts’ in the absence of the life history of the person to whom they belong.” Adding to this, Steven Johnson in Mind Wide Open says you are not “wed . . . inexorably to the fate of your genes, since life experience and learning also alter your neurochemistry.”
What does this mean? Well, maybe the cards do lie. It’s possible to study intensely yet still fail. In Lives on the Boundary, Mike Rose says some students fare poorly on tests because they are taught to focus on the wrong things. Focusing exclusively on the test’s stated content area before the exam is partially beside the point. (Go figure.) People unfamiliar with academic conventions need to learn more than the subject—they need to learn the tricks of the testing trade. Once they understand the ins and outs of how exams work, their performance improves. Rose and Marks insist that an emphasis on IQ, gifts, genes, or test scores alone is, well, stupid. Test results don’t tell the whole story.
The Pedagogy of Severity or Don’t Be So Mean
How we think about intelligence determines how we teach and how we learn. In schools, we need to create environments that cultivate and nurture intelligence and nourish potential rather than merely measuring them. Too often, schools employ what Kevin J. Porter calls a “pedagogy of severity” where “discussion [is] mainly centered around faults and problems.” (Writing instruction has had a sorry history in this regard.) Porter says,
I believe most of the miscommunications or failures to continue communication that occur in classrooms and consequently discourage learning result from failures to observe the principle of charity—failures that are in part inculcated by traditional classroom practices that form a pedagogy of severity.
Instead of just marking a student’s answer as incorrect, a pedagogy of charity approach would have you focus on the how, not the what. Your job is to investigate the student’s thinking behind her answer.
People who would like to write or would at least like to be better at it when the need arises may struggle because of the pedagogy of severity messages that may have been drilled into them during their schooling. Such messages don’t consider how what you perceive as a subpar performance may not have been as far off the mark as you think, or maybe not off the mark at all as we saw with our Dinner Party Math student.
Here’s the problem, though. If you are anything like me, you believe only the bad reviews. I suck at this, you think. You believe you’re not cut out for math, writing, physics, or athletics. You’re convinced you can’t dance or sing or play the saxophone.
Well, you can’t if you don’t, but it’s likely that if you do, you can—at least to some degree and probably to a greater degree than you believe.
If you had a teacher who made you feel as though you lacked ability, who left you hanging, join the club. You didn’t fail. That teacher failed. That approach robbed you of the chance to make cognitive leaps. When this happens, what we need is deprogramming. Nothing short of exorcism will do to rid us of Young-ha Kim’s “artistic devils” and Lynda Barry’s “Two Questions.” By helping us to see things like intelligence through a different lens, Rose, Marks, Lang, and others help to free us from the grips of all those bad reviews.
By the way, once the DPM student showed test makers what Rose calls the “intelligence behind the mistake,” they decided the student's answer was correct. After the test makers gave credit for her newly correct answer, 500 people in Massachusetts who thought they had failed MCAS, who thought they might not graduate, actually passed. Miss Dinner Party proved to have an innovative solution to the problem and a kind of intelligence that the test could not measure. She had a different frame of reference. The test makers were blind to alternative solutions to their own test questions. The student had to teach the test makers how to think her way. Once they learned, they saw the question anew. This illustrates Marks’s claim that “A good performance indicates good ability; but a poor performance need not indicate poor ability.” The Dinner Party girl may not be a star student in the traditional sense, yet she outsmarted the exam board when she argued her case against them and won.
Even after receiving credit for her answer, even though she helped hundreds of others pass, the DPM student failed. She exhibited a kind of thinking, however, that while not valued in testing, would surely be highly valued in many environments. She came up with a novel way of seeing the problem. Asimov might say coming up with novel solutions is extra smart. The DPM student was “unconventional in [her] habits” which Asimov says is essential for coming up with new ideas. This is a skill set we need. Also, classmates would benefit from having their eyes opened to a new perspective in this way. Imagine a classroom where thinking from a non-star student is also valued.
If intelligence is not just a gift, then how should teachers teach? More tests? How much room is there in the current system for play and for "make a change; see the result" or for DPM? And if there is no room for that, what does it cost us?
In writing, there is (or should be) room for DPM-style thinking. Writing that stands out is often the kind that breaks free from all those ho-hum, template-centered compositions. The key is revision. When you are writing and revising, things that were not part of the plan pop up, and often they make that old plan seem dull and beside the point.
Pedagogy of the Imagination
Italo Calvino talks about how writing seems to have a mind of its own.
as soon as I begin to put black on white, the written word begins to take over . . . until little by little it rules the whole field. Then it is the writing that must guide the story toward its most felicitous verbal expression, and all that’s left for the visual imagination is to keep up.
He calls this a “pedagogy of the imagination” which he claims has “ad hoc methods and unpredictable results.” Our DPM student engaged in this style of thinking when she came up with her answer.
In writing, the pedagogy of the imagination opens up space for you to let the writing take over. You can stop bossing it around, give up control, and listen. With practice, you’ll learn how to be comfortable with this for long stretches, even if it’s not what they taught you in school.
School has trained you to keep inside those dots, and in a pedagogy of severity world, the boundaries you face, though often artificial, are real. It’s too dangerous in those environments to dare draw outside the dots, even if the most interesting and productive solutions depend on that.
Writing, by nature, tends to take you beyond where you planned to go or are allowed to go. This is a feature, not a bug. When writing leads students this way, however, they often pull back for fear of harming their grade. Later, when you don’t have to worry about grades anymore, the habit of not straying from the original plan may have become so ingrained that just the thought of doing so makes you sweat.
For writers, unlike exam-takers who don’t get do-overs, the solution comes when you develop the practice of revising. As George Saunders** says, “The first draft doesn’t have to be good, it just has to be—so you can revise it.” Lynda Barry calls this “putting things together again, again.” She says this is part of the process of “making something into something else” which sits at the core of creative work, whether you are revising, drawing, working with origami, or painting a picture.
This helps with writer’s block as well. Saunders says, “In writing, the most powerful antidote we have for worry is revision” and “You’re not going to resolve [the problem] by thinking about it. You’re going to resolve it by revising.” Once you begin to trust in the power of revision, there is more opportunity for outside-the-dots/DPM-style thinking as you discover, like Saunders, that “the revising part of me is smarter than the everyday thinking part.”
Miss Dinner Party wasn’t writing when she came up with her unconventional answer, but she exhibited a writer’s mindset. She turned the question into a story where she could reimagine and revise the problem. She was like the “successful artists” Flower and Hayes cited who “rearrange and play with alternatives.” It’s a beautiful example of Calvino’s pedagogy of the imagination.
Smart kid.
Notes
Section 14 on Writing/Teaching issues will be published in several parts that will build upon what we’ve covered so far, but not exactly in the style I’ve used previously. I’ll take a bit of a leap into the Dinner Party Math zone to say some things that are not so easy to say in a typical essay format. It will begin with a story about a boy, his father, and a thunderstorm followed by a story about can opener designers. I mean, who doesn’t like a good can opener designer story? This Calvino-like “ad hoc method” will likely have “unpredictable results,” which, though a little scary, are my favorite kind.
*The original link to this article no longer works, and I haven’t been able to find it through searches yet.
**The Saunders quotes are from his Substack, which, unfortunately, is mostly behind his subscriber paywall.