### Vn123.1 **Computation Finale** 2/12 & 14/78

2/12 Since completing Vignette 121 (Double Perspectives) I have tried

to engage Miriam in executing a difficult addition. My purpose was to

introduce the idea of a simultaneous, double perspective as what one

needs to appreciate carries by challenging her with a puzzle — “What

number is 10 when you take it away but 1 when you add it in?” Thus,

days ago, I wrote on my chalk board the problem: 22857 plus 47345.

(N.B.: this is the sum of Vignette 122 with addends inverted). Miriam

has refused to look at the problem because, as she explained at lunch

today, I had told her before that she had done so much arithmetic for

me she wouldn’t have to do any more.

She is quite correct, and I tried to make it clear she should feel

no pressure to do any more experiments with me. We continued talking

about how great her skill in computation has become. I speculated that

playing SHOOT at Logo was most important in her learning how to add.

Miriam disagreed and averred finger counting was most important; she

specifically identified her counting up procedure as the most useful.

I objected. Such a procedure was fine for small numbers but not for

big ones, such as 20 plus 30, because one does not have so many fingers.

Miriam demonstrated base-10 finger counting. . . and then generalized her

procedure for my confounding: 20, 40, 60, 80; 40, 80, 120, 160, 200.

I asked if she could count by 12’s. Miriam did so easily up to 60, then

continued on her second hand: “72, 84, 98 — no, 96. . . (a fairly long

pause), 1 hundred 8. She stopped at 9 twelves but answered “120” when

I asked her what the next number would be.

We discussed multiplication in passing. Miriam volunteered her

knowledge of 4 times 90 and when asked, said 2 times 90 was 180. She

was at first non-plussed when I inquired how many were 3 times 90. She

produced her result through counting up in decades from 180.

2/14 What an afternoon! The children and I returned late from shopping

(this was our first auto trip since the Blizzard of ’78 left us snow-

bound). We had gone out for staples, but on this Valentine’s Day

Miriam would have been heart-broken did I not stop to buy her some

heart-shaped candies (she was very explicit). During the course of

lunch, I promised the children we could play with the Logo Cuisenaire

rods afterwards. They ate quickly and began pestering, but I demanded

the right to finish at a relaxed pace the bottle of ale I enjoyed with

my lunch.

While I talked with Robby in the reading alcove, Miriam entered

that area and executed “the next experiment” before I was ready (as she

put it later, “on purpose, to trick you.”)

10000 1000 100 10 | 2 | 2 | 8 | 5 | 7 | + | 4 | 7 | 3 | 4 | 5 | _______________________________ | 7 | 0 | 2 | 0 | 2 |

Miriam executed the sum perfectly, writing in the carries as I have

copied them above. When I asked how she could do this sum perfectly but

had manifested bugs on a similar sum days before, she replied, “I remem-

bered how to do the carries.” When Miriam had completed the sum and was

confident that it was correct, I recalled for her her jokes about “what letter

do you drink?” (cf. Vignette 121) and asked if she would like to try a

puzzle of mine. She agreed but was utterly unable to guess “what number

is 10 when you take it away and 1 when you add it back?” Miriam did

understand when I told her the answer was “a carry.”

Days later, Miriam told me she had enjoyed surprising me, doing

“the next experiment” before I was ready, because she likes to trick me.

But more, she said she would not have done it except for one thing: the

day was Valentine’s Day and her effort was a kind of present for me.

On this day, Valentine’s Day, the children and I spent the

afternoon playing with Cuisenaire rods, building the Logo-style right

rectangular polygonal spiral as described in Home Session 24.

**Relevance**

Miriam exhibits fairly clearly her grasp of carrying and distributed

addition is sufficiently strong that she will remember it. She may

produce occasional errors and may even suffer minor confusions, but

I believe she now understands distributed addition. By this I mean her

understanding of the parts and wholes of numbers in vertical form

addition will permit her to reconstruct the addition procedures she

needs however many times she forgets them.