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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.

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