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Archive with last of tag-string Jdg

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.

Vn10201

Vn102.1 The Last Day 10/8/77

Both children and I had planned to spend another Saturday afternoon
at the movies. For the past three weeks, we have spent our Saturdays
watching Marx brothers movies (cf. Vignette 93). These last two weeks
we have seen A Night at the Opera and A Day at the Races; Animal Crackers,
Horse Feathers, and Duck Soup. Great movies, a pleasure to attend with
children when you too can enjoy them. Alas, those Saturdays the movie
was nearly deserted, and today we found the Marx brothers festival was
ended.

“Hey, Dad, let’s go to Logo and do an experiment!” Miriam suggested.
Whence this enthusiasm? The day before we had done the Bending Rods
experiment. (Miriam hated it; Robby found it tolerable). The children
knew the last experiment was to be ‘The Snoopy Train’ (cf. “Constructing
Tracks from Rails” in Piaget’s Grasp of Consciousness). Though I was a
little less prepared than I had intended to be, the children were both
enthusiastic. I considered this the more important feature of the situation.
I agreed — on condition that we finish off quickly two experiments I wanted
to duplicate from April (Inclusion and the Islands).

After a minor squabble about who should go first, the day went well.
Both children each did two experiments, we had lunch, and then each, in
turn, played with the Snoopy Train. As they expected, at the end of the
day they were able to take the train home, and they have played with it
persistently since then.

Thus this project has come to a relaxed and happy end. As I’ve
discussed it with them, the children remember some bad times and a lot
of good ones. They have had the rare privilege of involvement in a
project which they believe is meaningful and significant work. Miriam
will be 6 and a half tomorrow. Twenty six weeks have gone by all too
rapidly, even thought this last month has been quite wearing for me. (I
believe this has been due to my allergies, the antihistamines they
required, and so forth). The children will continue coming to Logo with
me any time they want. We will do a few more videotaped sessions. The
end of the project will be marked mainly by my ceasing to collect data
and reducing constraints on the children (e.g. they can play Tic Tac Toe
with Glenn whenever they want). The immediate future promises a
broadening of their interests. Both children will be studying French and
Woodworking in the Brookline after school program. Robby has decided to
take up the cello.

Relevance
Now remain my burdens: one, with which Gretchen has volunteered her
much-needed help, that of processing these data to a form more publicly
accessible; the other, of making good sense of the data.