### 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.