### Vn105.1 **Hotel Magee; Two Microworlds; Decadal Computation** 10/20 & 27/77

10/20 With Robby’s introduction of WUMPUS to Miriam yesterday, the

mechanically recorded sessions at Logo cease. Vignettes continue to

round out and close off at natural stops various themes of the project.

The sense of closing off the mechanical recording is that the project

has REALLY ended. Thus our trip to witness my cousin’s wedding in

western Pennsylvania is both a vacation, an obligation, and a celebration.

After 7 and more hours of driving, nightfall found us in Bloomsburg,

on the east fork of the Susquehanna. We passed motel after motel with

NO VACANCY signs. After dark, we came to the Hotel Magee. (Their bill

board advertisements along the road declared ‘children stay free’; I

thought staying in a hotel (their first time) would offer them an interesting

contrast with the motel room we knew awaited us the next night at

our journey’s end.) We piled into the hotel, and while Gretchen and the

children freshened up after a day on the road, I sought a table at the

restaurant.

A grandmotherly hostess first informed me there was no room now and

no empty tables were expected till 8 in the evening. When I asked for

recommendations to other dining places about town — for my two hungry

children would not peacefully wait another hour for service — the woman

scratched a reservation from her list, making room for us.

Soon we were at table; the food was good and the variety quite

surprising. So even though Miriam was tired and refused to eat, the

meal had a festive sense for all of us for our various reasons. During

the evening we talked about the children’s sense of the project and some

of the amazing things they had done. I told Miriam how her addition of

96 plus 96 impressed me (cf. Vignette 100) and contrasted that with her

attempt to sum 89 plus 41 by counting hash marks 5 months earlier (cf.

Miriam at 6: Arithmetic). When I recalled that detail, Robby convulsed

with laughter. How could anyone attempt so absurd a procedure? I

asked Robby to think back, reminding him of the night he showed the same

response when I asked him to add 75 and 26 (Robby recalled having a late

pizza at the European Restaurant with our friend Howard Austin — Cf.

ADDVISOR, Logo W.P. #4). This reflection sobered him some. Miriam

piped up: “That’s a hundred and one.” “And how did you get that result?”

Miriam replied (to my surprise), “It’s like 70 [sic] and 20 is 95 and then you

add 6. 75 and 20 is 95 plus 6.” I was surprised because with those

particular numbers I thought Miriam might compute the result using a

money analogy. After assuring her of the correctness of her result, I

posed a different problem. “Miriam, suppose you had 75 cents and I gave

you 26 cents — say a quarter and a penny — how many cents would you

have?” When she responded “A dollar ten,” I asked where the extra 9

cents came from. Miriam computed for me in explanatory mode: “75 cents

is like 3 quarters and another quarter is a dollar. That’s a hundred

cents and one more is a hundred and one.” She denied her first answer

was a hundred and ten cents.

Note first that Miriam did not carry the result from one computation

to the second. Note further that although she applied directly her

decadal then unary algorithm for the numbers (75 plus 26), the same

numbers applied to money engage with a most minor variation the

well-known result that 4 quarters make a dollar. I can not confidently

explain the penny-dime confounding. I speculate that when not central,

they are not well distinguished. A dime won’t buy a 5-pack of bubble

gum and you can’t use pennies for anything but paying food taxes (cf.

Vignettes 54 and 55).

10/27 While waiting for the school bus this morning, I asked Robby if he

were doing anything interesting. He was enthusiastic about certain games

and said he liked especially the play time when the first graders come to

play with his class (3rd grade). I asked if they ever did any academic

stuff — TIMES problems and so forth.

Miriam informed us both she knew how to do TIMES. She argued her

point concretely: “Four twenties are eighty.” I laughed and reminded

her that I was driving the car yesterday while she and Robby discussed

that sum in the back seat. She protested, “I can do it.” “You can do

4 times 20. Can you do 4 times 90?” I challenged her. Robby knew and

said the answer. Miriam complained to him and walked down the driveway

kicking leaves. She returned. “The answer’s 3 hundred and 60.” Robby

claimed credit: “I told you first.” I argued that having the first

result was not so important, that what matters most is having an answer

you can understand yourself. Miriam said, “Can I tell you how I figured

it out?” and proceeded to do so: “I had a hundred eighty and a hundred

eighty. I took the two hundreds and one of the eighties. That’s 2 hundred

eighty. Then I took away 20 from the other 80 and I had 300

with 60 left over. 3 hundred 60.” I congratulated Miriam on good execution

of a very complicated computation and wished both children a good

day as the school bus came to rest where we waited.

**Relevance**

These notes close off my informal observations on Miriam’s computational

development. Miriam shows herself clearly in command of com-

plicated procedures for mental arithmetic, as witness her computation

of 4 times 90 with her decadal additive procedures and their integration

with unary adding. The contrast of computation performed on numbers and

money document the interaction of computation and microworld well-known

results.