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November 22, 2002
The un-mis-informing of Ali

I promised the other day that by way of a change I would soon be mentioning (and I promised it rather sooner than now apologies) some actual teaching that I'd done. Well, the most recent teaching I did was when I was helping my friend Mariana run something called a Kumon Centre, which is a franchised after-school maths club, managed locally but in accordance with a centrally imposed set of guidelines first developed and still presided over in Japan. I wrote a piece for the Libertarian Alliance about this experience, but the events I am about to write about happened after that piece had been published.

Regular school maths usually seems to involve the children working through only a few rather hard problems. Kumon makes them do many more much easier ones. Instead of hoping that they get, say, about half to two thirds of their stuff right, Kumon says they must get nearly everything right. At the heart of the Kumon method is the difference between a child painfully working out that seven plus six equals, er, thirteen? (anxious glance at face of teacher), and knowing with real certainty that seven plus six equals thirteen, with no doubts or hesitations. The usual educational emphasis is on "understanding". The Kumon literature talks of "mastery".

Each child does a clutch of sums selected for him or her personally (there is no everyone-in-the-class-does-the-same-stuff rule) each day, which are supposed to take about twenty minutes to complete. In schools, teachers do the teaching. With Kumon, the system does the teaching. All we did was mark the work the children had done, and then Mariana would follow the rules of the system to set them their next lot of sums.

It worked. Almost all children made steady progress, and in some cases - and in more than just maths by the way progress was truly astonishing. Kumon sometimes seemed to administer nothing less than a psychological transformation.

But there was one boy for whom Kumon did not seem to be working its magic. Ali was the boy's name, and he seemed to be in such serious trouble that Kumon seemed beside the point. When he did sums they were all over the place. Answers were totally wrong, and figures written the wrong way round. He could hold a pencil and write, but what he wrote was crazy. We seriously doubted if there was anything we could do, and we were ready to give up right there. He would make repeated mistakes, both of calculation and in the way he wrote numbers, and we even started to believe that he might be "dyslexic", or even brain damaged. Also, Ali seemed to be an extremely arrogant little boy. He had a way of lowering his eyelids and raising his head that made him look as if he thought the world to be populated entirely by fools.

At which point I got very, very lucky. I said, let me have a try with him. I decided to do some teaching.

As I say, with Kumon, you're not supposed to teach. You simply shove the stuff in front of them and they do it with the minimum of guidance, and at the end you tell them how they've done, and they learn. The system teaches them, not us. But that wasn't going to work with Ali.

I sat Ali down in front of a clutch of Kumon sums and sat myself down right next to him. I got him to do each one exactly right, telling him exactly what to do and getting him to correct all errors immediately, as soon as he made them, and telling him exactly what to do whenever he didn't know.

I separated the task he faced into a succession of tiny steps and got him to do each step right before proceeding to the next. You start by writing your name there. No, there. What's your name? Ali. Good. Can you spell that? Good. Please write Ali there. Good. Now: what does this say? I point at a two. Two. Good. And what does that say? I point at a one. One. Good. What about that? I point at the plus in between the two and the one. No? That says plus. That means you are adding two to one. What does this say? Don't know? That says equals. That means what does two and one come to. What's it the same as? What is two plus one, two and one, two added to one? So. What's two and one? Don't know? It's three. Do you know how to write three? You do. Good. Please write three there, which is where the answer is supposed to go. Excellent.

And so on. I never made him guess more than once, and I was unfailingly polite. I always said please before asking him to do anything, and I never raised my voice. I never, that is to say, confused Ali being ignorant with Ali being stupid. I did nothing that would be unfamiliar to an averagely capable aerobics instructor working with a arthritic old-age pensioner, but for some reason this sort of thing, when needed by a child, is not always supplied, even in something as widely known as simple arithmetic.

Aside from not knowing the answers, Ali's biggest problem was writing the numbers the correct way around. He would routinely write mirror reflections of them instead. Not all the time, just rather a lot. (This was what had prompted the dyslexia diagnosis.)

When Ali did this - getting, say, the answer right but writing it mirrored - I would say well done, you got the answer right. The answer is five, and that's what you wrote. Well done. However, you wrote the five the wrong way round. Please rub out the five you did, and rewrite it the correct way round. Good.

As I say, you aren't supposed to do this in Kumon. If all the children were to get twenty minutes of solid attention, the way I was attending to Ali, the place would have stopped being the learning factory for everyboy and everygirl that it's supposed to be and would have reverted to being a few tutors helping a few rich kids. But I didn't care.

And the reason that I didn't care was that it worked. After about three sessions along these lines, Ali reached his personal plateau of arithmetical excellence (a few sums wrong but almost all of them right), just like any other Kumon kid.

There was nothing wrong with Ali's brain. Nothing whatsoever. He wasn't stupid, far from it. He had merely been misinformed.

Nor, in my opinion and in my brief experience, and despite my initial prejudice along exactly such lines, was he arrogant. My guess was there was something a bit wrong with his eyesight, and he did the lowered eyelids and raised head thing to correct it.

I don't know for sure how or why Ali had been misinformed and anyway, the cause of the problem wasn't important; what mattered was that the problem was being dealt with. My guess is that (a) his mother may not have been that sure about doing or writing out arithmetic and had consequently not been helping him with it, the way most mothers help most kids with easy sums. Confusions created at school were not cleared up at home. (The more I contemplate state education, the more important remedial home teaching seems to me to be.)

So how had Ali's school created these confusions? I surmise that at his school Ali had not had all his errors corrected, only some of them. Maybe, what with all the other kids to be worrying about, they just couldn't or didn't bother to find the time.

Maybe Ali's teachers had become gripped by the fallacy that ignorance is stupidity and that therefore to correct someone's mistakes - all of someone's mistakes, all of someone's numerous mistakes - is to launch an all-engulfing personal attack on them. (Better to boost the little kiddy's confidence and self-esteem by telling him he's doing better than he is.)

Maybe, what with Ali looking down his nose at everybody, they judged him to be difficult, and feared that if they told him the full story of how badly he was doing he'd make a scene. (That Ali and his family were Muslims might also have made them fear some kind of cross-cultural battle.)

Whatever the exact reasons, Ali had been getting wrong information. Here, two plus one was three, but here, where he'd put two plus one was two, no-one had objected. So presumably that was correct also. Numbers written both the right way round and the wrong way round were left unmolested, so presumably both answers were okay. Except that sometimes the wrong answers weren't okay.

Actually, I believe that Ali was very intelligent, and that had he been less intelligent he would have been less confused. He was getting a mass of bad information and, poor fellow, he was taking it all in, the way a less clever boy might not have.

As I say, Ali wasn't arrogant at all, but if he had thought arithmetic too silly and arbitrary and irrational to be worthy of his sustained attention, who could have blamed him?

I believe I did Ali some big favours, and in a very short time. With luck I convinced him that arithmetic could, if explained properly, make perfect sense and that he could make perfect sense of it. I told his parents that there was nothing nothing whatsoever - wrong with his brain, only the information that had previously been fed into it, and with any luck they believed me. If Ali's learning environment later reverted to confusion then presumably Ali went back to being confused, but with more luck, both Ali and his parents will then blame society rather than Ali, and seek out non-confusion.

I could go on at even greater length, and in an earlier draft containing this (for another Libertarian Alliance Educational Note) I did. There are plenty of "lessons" here, I think. But this is blogging, and I'll leave this story to speak for itself.

Posted by Brian Micklethwait at 12:51 PM
Category: Brian's brilliant teaching careerMaths

I like this post very much and like you I cannot think of anything particularly profound to say.

Comment by: Patrick Crozier on November 22, 2002 07:06 PM

In some schools, students are supposed to "construct" math for themselves. They aren't taught right answers, lest it shortcut their personal discovery process. But not every child discovers math without adult guidance.

Comment by: Joanne Jacobs on November 24, 2002 04:13 AM

Yes, 'new' maths appears to me to be the arithmetic equivalent of whole-language reading instruction ie. give some clues and then let them work the rest out for themselves.

Comment by: Susan Godsland on November 24, 2002 05:25 PM

Bravo, Brian! Well done!

Re Ms. Godsland's comment: Are you acquainted with the term "pedagogical poisoning"?

Comment by: Mark Odell on November 25, 2002 02:19 PM
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