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Vn79.1 Sums Over a Hundred 8/29/77-9/1/77

8/29 While we sat at lunch today, Miriam introduced the topic of adding
with this claim: “Daddy, if you live for another hundred years, I know
how old you’ll be.” When I expressed surprise Miriam demonstrated:
“A hundred 37.” Two complications derailed this discussion. Robby
introduced my birth on February 29th with its implication of quadrennial
birthdays. Before we entered more complicated computations on this
basis, I noted that I would be dead before a hundred more years and
that one stops counting a person’s birthdays when he dies. Both children
looked at me blankly, and we proceeded to a discussion of what death is like.
(If curious, confer the note appended at the end of this vignette.)

9/1 This evening, I read aloud to Gretchen an excerpt from a draft-
section of Seymour Papert’s Logo book, a sardonic description of the
class structure of the mathematics education world:

Mathematicians create mathematical knowledge, math education
researchers package the material for children, teachers deliver
the packaged stuff, evaluators measure how badly the whole
process worked.

When Gretchen laughed, Miriam, out of sight in the adjacent area of the
loft, commented, “I don’t get it. I don’t think that’s funny.” Although
in one sense this is not at all funny, in another way it is, and so I
told Miriam. She replied, “What do you mean?”

Bob

How much is a hundred 70 plus 27? [original has a hundred 7]
Miriam

97. . . a hundred 97. Did I do it right?
Bob

Yes. Did you use your fingers?
Miriam

You want to know how I did it?
Bob

Sure.
Miriam

I said 70 plus 20. That’s 90, so I have the 97.
Bob

Where’d the hundred come from?
Miriam

It was a hundred 70. . . . Did I do it right?
Bob

You did it beautifully. . . and that’s more important than doing it right.
Miriam

I know that.
Bob

You also did it correctly.

Miriam went back to playing at what had occupied her before the dis-
traction of my reading aloud, so I did not explain why this problem she
solved, documenting as it does her ongoing progress in constructing her
own algorithms for addition, shows how ‘funny’ in another sense are the
best efforts, even the well-intentioned efforts, of the mathematics
education establishment.

Relevance
Since Miriam’s forgetting how to add multi-digit addends and her
subsequent reconstruction of adding procedures on a different basis,
I have let her curiosity guide our discussion of the algorithms she
employs for computation. This vignette records Miriam’s recrossing
of the hundred barrier with her own method of adding.

* For the curious: when I elaborated somewhat further, I said,
“You don’t count birthdays ’cause you can’t think at all when you’re
dead. You don’t eat or breathe either, but that doesn’t matter because
you can’t feel anything at all.” Robby came back: “Oh, I get it now.
Being dead is like you blew a fuse.” I agreed: “And each of the major
organs in your body — your heart, your lungs, your liver — each of
those is like a fuse and when one of ’em goes, you die.” Robby has
spent time since building two models, the Invisible Man and Invisible
Woman, attempted over a year ago and judged too complicated then.

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