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Vn00701

Vn007.01

A Willing Subject

5/18/77

Today was the most difficult experiment of the initial series, separating the variables implicated in the flexibility of bending rods (Cf. The Growth of Logical Thinking from Childhood to Adolescence, Inhelder and Piaget). Of the many experiments through which one may distinguish concrete from formal thinking, this one shows best the distinction between conceiving of things as objects with properties which may occasionally be of interest and conceiving of objects as instantiations of intersecting ranges of properties of which some may be relevant to its use in a specific context.

How could Miriam possibly be interested in distinguishing the contribution of different properties to rigidity? How many adults could, or would care to, distinguish between the relative importance of a rod’s thickness parallel to a force and its cross-sectional shape? How to quantify, or even balance, such factors is not obvious to the untrained intuition at any age. And Miriam is 6, not 16. Need one not subject a child to exorbitant pressure to have her work at such an experiment? If any experiment in this initial series is vulnerable to such a criticism (either through its very nature or through my execution) it is this experiment.

I was hurried into the bending rods experiment by Miriam’s declaration that she would not come to Logo today unless she could do it. Despite feeling imperfectly prepared, I acquiesced in her demand since the obvious problem was that she felt ‘left out’; I had done the experiment earlier with Robby for practice. During the preliminaries wherein I hoped to establish with certainty a common terminology for the experiment (for a description of this work see Miriam at 6: Bending Rods) Miriam was rambunctious. When not interested much in my questions, Miriam began to create chaos by throwing around dice and balls, which were the experimental materials. I stopped the experiment and we had an argument of this general form:

Bob I won’t tolerate your throwing things and causing this confusion; it will ruin the experiment.
Miriam Then I won’t do it. You’re asking me dumb questions. I’ll play SHOOT instead.
Bob That’s not fair. You demanded we do this experiment today and now we have to finish it.
Miriam I never promised I would do all your experiments. I only said I might do them.
Bob That’s not true.
Miriam I wish I was a baby again so I wouldn’t have to do these experiments.
Bob But you’re six now and doing something important.

Miriam reluctantly agreed to continue; she agreed because of the pressure I put on her, because, in effect, I made her do it.

Despite this grim start to the main experiment, Miriam quickly became engaged in working with the materials and finding “which one is the champion” for bendings. She exhibited no interest at all in separating the variables; consequently, the latter part of the experiment bored her silly.

Riding home from Logo, I told Miriam I felt bad because I thought I was pushing her too hard in the experiment. She said she didn’t want to do any more like that, and I replied that we would do no more of that sort for several months. I expanded that we should think of doing other kinds of things. That this thesis project could be not just going to Logo, but going to other places too. Part could be my coming to kindergarten with her; another part could be visiting friends and family and telling them about our project; another part could be trips to places around Boston. I noted that she had been to the Harvard Peabody Museum and I never had; she could take me there. Miriam said we should do that soon.

Vn09501

Vn95.1 Why the Project is Ending Now 9/18 & 27/77

9/18 Miriam has expressed her desire to do the same work as her class-
mates, her preference for doing the whatever ‘math’ they will do at
school to learning the kind of math we do together. I take this prefer-
ence as a strong commitment on her part to be one with her peers and
not as a rejection of the arithmetic we have done together. (My doing
so is justified by her initiating most of our math sessions and her
enjoying them.) Further, Miriam’s social needs begin to conflict with
our engagement at Logo. She likes to play with her friends; seeing
more of them now that school has begun, she will demand playing with
them more often. With her friends back from vacation and more readily
available for play, she will have less time available to play with me
at Logo.

For the time being at least, the focus of Miriam’s interests has
shifted out of the home toward the social world of her peers. I con-
sider this a natural change, my struggling against which could be bad
for Miriam and counterproductive for me. I believe Miriam will become
bored with school relatively quickly (perhaps by November or December)
and will rebound with a newer interest in our learning together at home
and Logo.

I discussed this situation tonight with the children. I further
explained my sense of exhaustion — that as much as Miriam has had
allergy problems since our return from vacation, I have also had them.
The antihistamines I have taken to suppress hay fever symptoms have
made me often drowsy and have undermined my ability to stay on top of
the data I have collected.

We three agreed that now is the time for the project to close. We
begin our final series of evaluations tomorrow.

9/27 When attempts to circumvent my allergy/medication based drowsiness
by changing medication failed, I arranged for skin tests to specify
precisely my allergies in the hope of controlling them some other way.
I respond, as Miriam does, to a broad range of substances: I am most
sensitive to house dust, mold, and cat dander; I am slightly less sensi-
tive to ragweed and various grass pollens; at a lower but still signifi-
cant level I am allergic to varieties of trees. This allergy profile
is the same as Miriam’s with minor variations (she is more sensitive to
oak, I to maple). It helps explain the common difficulties we have
experienced these last two months. (This has been an especially bad
year for ragweed.)

Relevance
These notes document the ways in which two factors — the children’s
return to school and allergic reactions — lead us into the final project
phase two weeks earlier than I had anticipated.

Vn10001

Vn100.1 Arithmetic Ripples 9/26/77-10/2&7/77

9/26 Miriam tells me today was her first day of doing math at school.
“But we did it differently there from what we [she and I] did here.”
She explained that school math was playing with cuisiniere rods. I
told her I thought that was great, and asked what she did with them.
Miriam said she used them for building. As this project comes to an
end, I will ask Miriam to build, out of cuisiniere rods, a POLYGONAL
SPIRAL. . . or perhaps ask her to describe my procedure for doing so in
the Logo language.

10/2 Robby and Miriam have lately been making home-made clay. They
mix flour, salt, and a little water, knead thoroughly, and thereby develop
a clay which they later fix by baking. Robby began counting the layers
of material he made by folding the material over and into itself. After
reaching a count of 96 (by what path I am not certain), Robby cut his
clay ply in two pieces, and superposing one on the other, declared he
had 96 plus 96 layers.
Miriam said, “That’s a hundred 92.” Robby asked me if she were
right. Miriam responded, “90 plus 90 is one eighty (looking at him for
concurrence); so it’s one eighty six, seven, eight, nine, one ninety,
one ninety one, one ninety two.” thus completing her proof.

10/7 To inquire whether Miriam’s 90 plus 90 sum might derive now from
the sum 9 plus 9, I asked this morning (after warning her I wanted her
first answer, not one thought about too much). “How much is 9 plus 9?”
After a shosrt pause, Miriam responded, “18.” “How did you get that
result?” Miriam answered, ” ‘Cause 8 plus 8 is 16; so it’s 16 plus 2.”

Relevance
These notes document Miriam’s beginning of math at school and
suggest one simple way to begin binding her experience at Logo to her
future school work. The second observation documents the ease with
which Miriam has incorporated well-known sums from turtle geometry’s
decadal arithmetic into her procedures for mental computation. This is
an indication of their permanence as members of her repertoire.