Learning by the Skin of His Teeth
By Seymour Papert
This learning story was excerpted from The Connected Family: Bridging the Digital Generation Gap (Longstreet Press, 1996).
In The Children's Machine I told a learning story about how I helped a student in the "resource room"—which is where they send the kids who are supposed to have learning disabilities—of a public school in one of our big cities. I was able to guess why this kid was looking all around him with an unhappy expression on his face. He had been assigned a list of little "math problems" in the form of numbers to add together but knew that he was not allowed to use his fingers as he liked to do. I guessed that he was unsuccessfully looking for some external support he could use in the place of fingers. I thought for a moment about whether to intervene and how. I did not want to offend the teacher. I certainly did not want to get the kid into any trouble. On the other hand I was firmly convinced that allowing him to use external aids was the best way to encourage real learning and denying the use of fingers the best way to make sure that he hated doing these sums. So I thought for a while and then said in a loud enough voice for the teacher and the kid to hear: "What about your teeth?"
The result was exactly what I hoped. The teacher saw no connection with the assignment but I saw from his face that the kid did: first a puzzled expression, then a lighting up that expressed "aha, I get it" and then a little moving bulge in his cheek and lips. "Learning disability indeed" I thought to myself "this is one smart kid."
This incident happened ten years ago. Since then I have asked a lot of people about using teeth as a support system for mental work. Most people need some explanation to know what I am talking about: obviously they had never done it. But quite a few kids admitted to using teeth in such ways and quite a few adults —including one of the leading theorists of computer science—remembered doing so in the past. One adult explained how he still used his teeth as a support for remembering telephone numbers.
Now is this bad? (I have to admit that I have been scolded several times by people who read the original account in my book. Presumably the teacher who had ordered the kid not to use his fingers thought that physical supports were bad for learning. Some of my critics connected this opinion with their belief that using calculators and computers prevents children from "learning to do math." "It makes them dependent on machines." "It makes them mentally lazy."
The dependence argument doesn't worry me at all. So what? I am dependent on my eye-glasses and on my wristwatch. I wish I wasn't, but no big deal. On the other hand I would be very worried if I believed the mental laziness argument. But I don't.
What I have learned from conversations with tooth-using kids confirms my original impression that I actually stimulated that kid to do more, harder and better thinking about math than the repetitive exercises in the assignment he didn't want to do. Just try using your teeth. It needs some thinking to do it even for small numbers like 7 + 4. A first shot at doing it might go something like
Count seven teeth touching each with your tongue.
Count four more in the same way.
Now count all of those you touched.
And that's the answer.
But unless you have anticipated this, you may have trouble remembering which teeth you touched. So a good strategy should include always starting at the same place, counting seven and another four, then counting backwards to the start tooth. In my view working out something like that, and obviously my kid did it without adult help, is a better exercise than just adding the numbers.
But in reality he had to go further because he had numbers more like 67 + 24 than 7 + 4. To handle this he could split the problem into 60 + 20 and 7 + 4. Now working out methods like that is what I'd call real math at a level suitable for his age.
I wish the story could have ended with a discussion in class of the methods of tooth math led by the young discoverer. But of course he would never dare suggest that lest he be scolded for breaking rules.
One final twist to the story is needed to avoid leaving the impression that I am blaming teachers for the faults of school. In an informal poll of teachers more than half thought I did the right thing although more than half of those said they would not have done it out of fear of getting into some kind of trouble.