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Archive with last of tag-string Jdg


3V0442.01 Verbal imitation of a “word to remember”: <[Stool]> (4/9/79)

Peggy’s verbal imitation is quite well developed. An everyday example.
I sat in my chair with a cup of coffee on a high stool beside it. Peggy
came along and started to shake the stool. “No, no, Peggy, don’t touch
the stool!” “Stool,” Peggy said to herself and toddled off.


3V0587.01 /cul’/du/vae/vae’/: CENTRAL INCIDENT;
major insight ascribed on basis of incident. 9/1/79

Over the past several weeks, our house has suffered a greater than
usual density and flux of Tintin cartoon books. As do the older kids,
Peggy enjoys them. She brings a magazine, says /aen//aen/ and
convinces one to hold her in his lap while she turns the pages and
points to various figures with little squeals of delight. Her favorite
character is “Snowy”, the little white dog and Tintin’s persistent
companion. When she points to the dog, we tell her it’s “Snowy”, but
Peggy has settled on her own term /cuhlduh/ (variously /cai/duh/ and
/cai/dae/ as her name for Snowy.

Now Peggy has in the past referred to our Scotty as [Scurry] (more or
less) and most recently used /vae/vae/ to refer to Scurry or some
distant barking dog. The point is that /vae/vae/ seems more related to
barking than to “dogginess” as such. One might think of her use
nominally as equivalent to “barker.” Therefore /cul/duh/ seemed
merely a new and different name for Snowy… but we were fooled, for
Peggy began to call Scurry /cul/duh/ and now does so regularly.

This evening, Peggy sat in my lap for a while. Scurry was waiting to be
taken out for her evening walk and Gretchen took the dog on her lap to
groom her a little. This is unusual and Peggy pointed at her /cul/duh/
(she said). Peggy got down, wandered off and behind my chair. The
dog began to growl on hearing a distant bark. Peg pointed at her
excitedly /vae/vae/, /vae/vae/. I responded in her tongue:
/cul/duh/vae/vae/, at which Peggy’s face lit up with a broad beaming
smile (so Gretchen notes and described it; I was looking the other way.)

Relevance: We both recognize this as an exciting moment of insight
into verbal communication for Peggy. She wanted to very much to
express her meaning “the dog barks”: but could not except by pointing
and saying /vae/vae/ simultaneously. My expression exemplified how
serial order expresses the subject-predicate relation in her vocabulary
and context. I judged then, and still hold (9/9/79), that this incident
marks the beginning of Peggy’s knowledge of generative syntax. That
is, here, Peggy learned how to assemble subject and predicate to
express a thought already formed, as distinct from expressing
idiomatically a thought “associable” with the idiom. I take this to be
one of the most important observations in this record.


3V0594.01 /wae/thaet/: issues: discussion of what a word is. 9/8/79

Peggy has enjoyed playing with my belt as a baby but has not done so
for quite a while. Today, she sat in my lap and, pointing at my belt
buckle, said, “/wae/thaet/?” I told her it was a belt buckle, which
answer seemed to satisfy her.

Relevance: This pair of incidents highlights the difficulty of ascribing
competence from performance — but they also show the extent to
which context of utterance, the pragmatics of speech, makes it
possible. Thus:
1. it is clear that Peggy uses /wae/thaet/ to mean “what’s that?”
2. she may also use it to mean “wash that”, but such would be a more
restricted meaning and would become, if not be essentially, secondary.
These observations are important because they come down on the issue
of what a word is. That is, is /wae/thaet/ an idiom or two words of
distinguishable meaning ? I believe the former is the case.


3V0603.01 [cup…mama]: word catenation used to express an instantaneous relation that later becomes syntactically expressed. 9/17/79

Peggy sat in my lap while I sipped at my morning coffee. She has lately
been naming the containers from which I drink things, e.g. /kaen/ for a
beer can and /kuhp/ for such a one as she pointed out this morning.
After Peggy had just named my cup, Gretchen walked by carrying her
cup. Peggy commented [cup mama]. Thus, the sequence of words was
[cup (referring to mine)…(pause)… cup mama].

Importance: this is another example of word catenation used to express
an instantaneous relation that later becomes syntactically expressed.
The pragmatics clearly shows Peggy commenting on Gretchen’s
possession of the cup. That is, her intention and knowledge of
relations was clearly more specific and much further developed,
refined, than her means of expression.


3V0718.01 Who’s there ? (Original notes on homely binding and lonely discovery) (1/10/80)

Peggy’s use of the knock-knock joke script has been monolithic — ie.
she would not respond in the victim’s role, nor would she continue in
any way no matter what response her victim made. This morning,
when I brought some coffee to Gretchen, I heard Peggy talking to
herself in the crib (Miriam was asleep). Peggy said, “Knock-knock.”
waited a while and then said, “Who’s there?” That is, she was clearly
rehearsing the entire joke script of her knowledge. The standard use of
rehearsing implies her objective of later performance. I mean no such
thing, but instead that Peggy was reciting both sides of a dialogue —
because she was alone, had no one to interact with.

Why is this significant ? Later that day, I said to Peggy, “Knock-knock,”
and she responded “Who’s there?” Subsequently, Miriam also noticed
that for the first time in her hearing that Peggy performed the victim’s
role. This seems a very early example of what I now see as a
fundamental process of learning which relates the elements of cultural
knowledge and indicates construction (see workbook, mid-January
1980). This process is the same as Miriam’s playing both sides of a
game in tic tac toe. Through homely processes of social binding scripts
are “memorized” from one role’s perspective. Through a later process
of lonely discovery, the multiple roles of a script are articulated. This
is a theory of enculturation and construction at a level of generality
comparable to Darwinian evolution as opposed to more nearly
computational theories of population genetics – but still it is a
beginning in an area currently too vague and unspecific.


Vn38.01 Robby’s Place in the Project 6/28/77

Robby raised a very difficult question today — how much of the
work he does at Logo will be a part of my doctoral thesis. The answer
Robby required, and it is a superficial answer, that the thesis will be
about Miriam’s development, was bound to disappoint him. My answer to
his question attempted to provide him with a perspective from which he
could see the value of his contribution to the project, could imagine
that contribution being adequately recognized in the future, and view-
point from which he could judge my preferring to study Miriam’s devel-
opment as a back-handed compliment.

The facts from which we began he knew well: that he was doing
precisely ‘the same experiments’ as Miriam; that the sessions with him
were being recorded as faithfully as were those with Miriam; that some-
times he did work that was beyond Miriam’s grasp (e.g. his understanding
of GUNSIGHT, an absolute coordinate variant of the SHOOT program).
The other outstanding fact was his seeing how hard I work: I sleep
little and spend the rest of my time transcribing the data and planning
future sessions. He sees every day that I have no free time. I ex-
plained to Robby that, for now, I was forced to choose; in effect I had
chosen to work with Miriam’s data first. Since I have also recorded
his work and can transcribe it later, that work is not lost although
little of it will appear in the thesis.

Here I suggested beyond the thesis lies the idea of a book, one in
which his work would appear as central as Miriam’s and even more so.
For Robby has worked at Logo longer than Miriam, and his sessions of
past years were for us the pioneering precursors of the more sharply
focussed study that this thesis work represents. I sketched for him
the theme of this book as our family’s involvement with computers and
the impact of that involvement. He could appreciate that our experience
now is unique, that his is a central role in that story, from its begin-
ning till whenever it ends, and that Miriam’s contributions follow his.

As for choosing to focus this study on Miriam, I explained my
intention was not to see how much she could learn (for Robby now appears
capable of learning more and more rapidly), but to understand the way
she learned things in detail. Further, I could not hope to understand
well how Robby learned new material because he already knew too much.
Robby recognizes that he knows far more about World War II than I do.
Referring to this as an example, I asked how I could hope to under-
stand his learning when he knew some things better than I knew them.

This issue touches a critical nerve of the project, for it is a family engagement
as well as being a focussed study of Miriam’s development.


Vn59.1 Air Conditioning 8/6-11/77

8/6 Logo came into our conversations twice this day at lunch. When
asked if she knew what a palindrome was (cf. Logo Session 39, 7/15/77),
Miriam offered two examples: ‘mom’ and ‘I’ (I checked that she did not
mean the word ‘eye.’) Miriam later said she would like to sleep at
Logo. I recall having told her that I once slept at Logo (when last
winter the city suffered 22″ of snow and I lived atop Corey Hill).
Miriam’s request was justified by her hope to sleep better there than
at home. She explained that she had slept well in Connecticut and had
slept very ill since returning to Massachusetts. During the heat wave
of mid-July, we had run the air-conditioner regularly. Miriam believed
she would sleep better in the air-conditioned computer room.

8/7 Miriam woke me at 4 am (a fairly regular occurrence) with her
coughing. Despite having had her standard dosage of medicine she was
wheezing. Because I believe it is important she not conclude that her
malady is hopeless, beyond remedy, I asked if she would like to go to
Logo. We left home at 5 with her pillow and medicine, and tape recor-
dings from my transcription backlog. We drove through a deserted city
to sign in at 5:30. Both wide awake, we walked through the lab. Tom
Knight was using the terminal at the mainframe, so we assumed Logo was
unavailable and found other entertainment. Miriam first set up her
pillow in a chair (the king size pillow barely left room for her) and
showed me a peculiar book she had found in the Children’s Learning Lab
(Ça Ne Va Pas, Charlie Brown). Miriam asked me to read it. I read her
a few frames from the first cartoon. A better resting place was needed.
We brought a bean bag chair to my office (Miriam preferred that option
to sleeping on Seymour’s or Hal’s couch). She curled up with her pillow
and the cartoons in the corner. Her last words before dropping off to
sleep: “Daddy! I can read ‘The Doctor is in’.” Miriam slept from 6
until 11. Her nap of 5 hours was the longest uninterrupted sleep she
has had since our return to Boston.

8/9 Miriam told me this morning she had had a good night’s sleep, her
first in a week. When I mentioned this to Gretchen in her hearing,
Miriam qualified the statement by “besides sleep at Logo.”
After her bath this evening Miriam stood at the balcony over the
court yard and said, “Hey, I see the first star:

Star light, star bright,
First star I see tonight,
I wish I may, I wish I might,
Have the wish I wish tonight. . . .

I wish I had ten more wishes.” Thus well provided with wishes and still
talking to herself, she made her first real wish: “I wish I had no
allergies at all.” Then her friend Scurry should get a new collar and leash.
I told Miriam those 2 wishes could happen, but the first could not, that
she would continue to suffer from her allergies into her teens, at the
end of which they might become less severe.

8/10-11/77 After calling those who advertised air conditioners in Tech Talk
and waiting to find out none would fit in the windows of Miriam’s room,
we purchased and installed an air conditioner in Miriam’s room. It is
not at all clear that air conditioning Miriam’s room will help her in
any physical way. It is most important, however, that she not feel
alone in confronting her problems and that we will attempt whatever
reasonable means are available to ameliorate her discomfort.

These notes may indicate how profoundly burdensome to Miriam are
her allergies to dust, trees, and mold. August and early September are
the worst times.


Vn68.1 Continuous Quantity 8/18/77

As is the case with many who have a few fine things, we hardly
ever use them. Our silver and china are in some dark corner, our
Venetian glassware sits empty, hardly touched. At dinner our common
wine goes into common wine glasses. Through accidents at table and
sink, the usable collection has become one made of odds and ends.

This evening a guest joined us at a picnic supper on the patio
behind the house. Unloading supplies from the basket, I found (beside
the dinner meats) one jug of wine and three glasses of roughly these

the figures are on Addendum 68-1, original text of the vignette.

I placed the empty glasses on the picnic table in the order shown and
posed a problem abstractly to the children: “How can I be sure nobody
gets gypped when I pour the wine?” No response was forthcoming.

As I poured wine into the first glass, Robby cried out: “I got it.
Pour the same amount at both ends. Empty one into the center glass,
then refill the one you just emptied.” It was clear he meant refilling
the glass would result in its matching the first. Miriam concurred in
this solution.

Because the middle glass had a non-standard shape, as I followed
Robby’s procedure I arrived at a wine distribution whose appearance was
deceptive. There appeared to be a greater volume in the center glass
because its top circumference was greater than that of the two matching
glasses and its height was greater than both (since its cross-section
was more nearly conical than cylindrical).

the figures are on Addendum 68-1, original text of the vignette.

When finished pouring, I exclaimed, “You’re wrong, Rob. Look. The
center one’s got more in it. I’ll take that one.” (My overacting was
supported by a few gleeful chortles). When I then disbursed the
matched glasses to Gretchen and our guest, Miriam censured me: “Daddy,
you’re just being silly.”

Consider this anecdote as an informal post-test of Miriam’s
conservation of quantity. I do. I intend to introduce such ‘experiments’
into our everyday life as this project draws to a close. My purpose
is to reduce the testing burden Miriam will face by performing informally
those post-tests whose conclusions should be beyond question, without
rendering the evaluation sequence subject to the criticism of

Addendum 68-1

Vn 68-1 Original Fair Text of Vignette 68


Vn91.1 Squirming and Thinking 9/14/77

Miriam had a very bad night last night; she had missed a dose of
medicine and played with kittens. Miriam and I were up much of the
night. Still wheezing badly this morning (she had reached the point
where she could not hold down any orally-administered medicine), she
went with Gretchen to the doctor for a shot of adrenalin.

Robby and I were left alone in a quiet house. While I was attempting
to write in the reading alcove, Robby assembled a puzzle on the
living room floor. He left off the puzzle and lay on the floor, bending
his body back and forth at the pelvis. When I told him that was most
distracting, that he should stop squirming, Robby sat up and said:


Daddy? You know all that stuff about 3 hundred and 60? [This is
a back reference to our discussions in Logo Sessions 61 and 62
of the effect of reducing an angle by 360 degrees]


I understand it now.

Wow! How did you figure it out?

Well, you know if you have an angle that’s 3 hundred and 61?


And you take away 360?

Uh huh.

It’s 1, and that’s like it’s starting all over again.

That’s really great, Rob. When did you figure that out?


Just now? When you were squirming around there on the floor?

Yeah. Squirming around helps me think.

Robby returned to his puzzle. Shortly thereafter, Miriam came bounding
into the loft, so full of energy that she pushed me into leaving early
for our Logo session today.

This particular incident, though it occurred with Robby and not
with Miriam, highlights what I see as the central methodological
problem in the study of learning: being able to observe the
manifestation of a centrally-determined mental process, being there
when it happens.


Vn92.1 Company for Dinner 9/14/77

This has been a week for company at our house. Fernando Curado and
José Valente first, then Bertrand Schwartz and Antoinette together with
Laurie Miller, and this evening Seymour and the Minskys. My intention
in asking Marvin and Gloria here at this time was to provide a sense of
setting for the variety of descriptions of our lives that Marvin, as a
member of my thesis committee, will encounter in my data; and further,
through a short exposure to one evening in my family’s life, to provide
a sense of the relations and qualities of interaction from which the
observations in these data arise.

Unfortunately for my purposes this evening’s guests arrived too late
to tour the grounds of our landlord’s mansion, those places where the
children have played this summer when not under my eye (and under foot);
yet they did have a chance to participate in a more or less typical
evening at home. If the evening was atypical, it was so in two respects
mainly: Robby was tired and went to bed directly after our late dinner;
Miriam (could she possibly have been still energized by the adrenalin
shot in the morning?) was lively and stayed up much later than usual.
Since Miriam was expected to go to school the next day, I told her
several times to go to bed. She took my instructions as reminders
merely, and chose to ignore them. Further, it was appropriate that
Marvin should see as much of her as she wished to show him.

We talked some of Miriam’s work (I showed Marvin one of Miriam’s
“Seahorses” [an INSPI with an angular increment of 13]; Marvin allowed
that he did recognize it — indeed, he noted he was the first person in
the world ever to see that particular design) and of some of the unusual
turns of mind that Miriam now exhibits (the data of Vignette 76, Where
Do Ideas Come From, were then much in my mind). Gloria gave us her
appreciation of the Brookline schools, from the perspective of her special
knowledge and from the experiences of Margaret, Henry, and Julie. When
Gretchen and Seymour brought dinner to the table, talk turned more
intellectual for a short while. Miriam redirected that tendency after
dinner by engaging Marvin’s help in her weaving of a potholder. Eventually
both Miriam and the evening wound down and our guests departed.

This evening, representing a for us natural mixture of social,
intellectual, and family concerns and activities, provided a more or
less typical experience of an evening in our family for two members
of my thesis committee.


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.)

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.


Vn98.1 Miriam’s New Reader 9/24/77-10/3/77

9/24 Since I was uncertain how much Miriam’s reading skill had developed
over the summer (focused as much of it was on reading Peanuts and Pogo
cartoons), I could not easily judge what would best test Miriam’s capacity.
We discussed the problem. Miriam characterized the book used in
Miriam at 6, a reader for the first half of second grade, as being
“easy-bezy.” “Was it so back in April?” I inquired. Miriam answered
that the book was pretty hard for her to read earlier. We agreed the
solution to my problem was for her to select the book for her final
reading evaluation. When we went to Hammett’s supply store, Miriam
checked out the fifth and sixth grade readers, declaring them too hard;
examining the third and fourth grade readers, she selected More Roads
to Follow
(a third year spring semester book) as having a level of
difficulty comparable to the book we used in April. Back at Logo, our
experiment of the day was a reading evaluation. Her judgment was proved
correct: she was able to read the book but exhibited some difficulty.

9/25 Miriam has been praising her new “Dick and Jane” book to Robby.
She explained that not only have Dick and Jane been left out (a great
advance in Robby’s eyes), but that it also contained a chapter from the
Pooh stories with much prettier illustrations than their paper-back
versions. Miriam asked if she might take her book to school. I agreed
it was a good idea, since Ms. Fieman wanted to know where should she
start Miriam.

10/3 Miriam has been reading More Roads to Follow quite regularly.
This evening she recommended to my attention “The Gingham Dog and the
Calico Cat”, remarking on its absurd good humor of the fight ending
with each eating up the other.

Miriam’s continuing reading of her evaluation book confirms her
original judgment in selecting it and my conclusion that it represents the
right level of challenge to her skill. Without tutelage, her reading
level has advanced a year in the six months since the beginning of the


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.”

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.


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

“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.

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.


Vn104.1 Back to School 10/14/77

During the last days of our project experiments, I promised Miriam
to visit her first grade class as I had visited in kindergarten. I had
the mistaken impression that Miriam had arranged my visit with Ms.
Fieman. The oversight proved to be no problem, for despite my beard
and over-size frame I blended in well with the group of children.

It was “Read me this, read me that. Do you know my name?” David
B. said, “I remember you. Last year you came and we set up that thing
from the ceiling.” His reference was to a 3 string pulley I rigged in
the spring which enable the children to hoist heavy weights, their
desks (!) and each other (!!) a few feet off the floor. One of the
other boys (was it John?) asked if I still had that machine for making
electricity. Curtis brought over a soma cube and the children squabbled
over it. Miriam did not have a chance to work on the puzzle for any time
with 5 classmates each wanting a turn. Meg and Laurie Ann sat with me
and Miriam before the class split into two groups — one headed for the
library, the other for an introduction to the class’ activities for the

The librarian attempted to introduce to the children the distinction
between factual and fictional writing. It is possible my presence, my
sitting on the floor with the children, caused her some unusual confusion.
Nonetheless, it appeared that she neither had articulated for herself
any consistent set of criteria nor had any good language for communicating
her ideas to the children.

Once again in class, Miriam took up the writing activity. Curtis
and I joined her. The task was one of sentence completion: e.g. “With
my eyes I can see ________.” The children’s task is to write a description
and draw a picture of some appropriate object. Miriam chose to spell
and draw flowers. Her other senses led her to taste corn on the cob and
ice cream; to feel fuzzy things (here Scurry was the exemplar); and to
hear a song — which she represented by a person singing the complete
text of “Drive, drive, drive your car, gently down the street” as sung
by Don Music on Sesame Street.

After Miriam’s work was approved, we had a few minutes to play
before I left. She suggested checkers. Lately we have been playing
variations of the standard game. We tried a 4×4 board (played with 2
checkers on each side) and a 6×6 board (played with 6 checkers on each
side). The board fell to the floor while still folded but with squares
showing. I suggested we play ‘half a game’ of checkers. (The board
was thus 4×8 and played with 6 checkers on each side). We played 3
games. Miriam’s friends came crowding around and all wanted their turns.
But I did have to leave and suggested Miriam could play ‘half a game’
with them.

These notes try to capture both the continuity and change of Miriam’s
kindergarten and first grade. There is more structure in that the children
cycle through a set of selected activities (of such a sort that they
could be interesting). The children can get some play time by finishing
their work quickly. Ms. Fieman is good with the children and flexible
enough to let a parent visit with insufficient notice. Miriam seems
comfortable in the situation and enjoys school to the extent that she
chooses to attend even if she feels unwell.


Vn112.1 How Her Teacher Sees Miriam 12/7/77

Miriam’s teacher, Sue, sees her as a special child in several ways.
Her surprise at Miriam’s easy solution of class inclusion problems (cf.
Vignette 90, Meeting Miriam’s Teacher) shows she had reason outside of
anything I told her in our first meeting. She learned of Miriam’s continuing
work at the Logo project and was favorably impressed by our links
with the now-respectable scientist Piaget. Thus Miriam appears special
by developmental progress for her age and by the experience of her ongoing
engagement in a serious study.

As The Intimate Study concluded, the children asked if they could
bring their classmates over to visit Logo. I agreed to help them work
that out if they wanted to, on condition that a few children came at one
time and that Robby and Miriam be the ones who ran the show. Both accepted
this scenario as the best one. Robby suggested that their teachers
be first to visit (I don’t know why). Miriam was not keen on the idea
but didn’t argue enough to undermine Robby’s support of the plan. About
the middle of November, the two teachers spent approximately 2 hours at
Logo. The children showed off their computer pictures and their desks,
then explained their work to the teachers. I stayed in the background
as much as possible. Both wanted to play Wumpus, but because this was
confusing to their teachers, they showed them SHOOT and its variations,
explaining the primitives and exhibiting the arithmetic tasks the game
involved them in. Otherwork included the use of POLYSPI and INSPI,
drawings, and a text manipulation work. I believe the teachers were
impressed by the work and the children’s command of it. Sue’s note (see
Addendum 112 – 1) witnesses her response.

Yesterday Gretchen met with Sue for an evaluation conference. (The
report is attached as Addendum 112 – 2, 3, and 4). I was unable to attend
the meeting, but Gretchen recalls these comments:

- Miriam gets a great deal of pleasure from seeing and playing with 
     her school friends.
- Miriam always did her work with a great deal of attention to detail, even
     if she was merely drawing to fill in time between organizeed activities.
- Miriam didn't copy from other people, either to get directions 
     for what she should be doing or to get an idea.
- Miriam cooperated and worked well with her classmates, but not 
     merely that. She tried to help them and was able to do so.
- Miriam seemed to enjoy solving problems. Her focus was not on getting 
     the answer; she seemed to enjoy the process of working out problems, 
     to take pleasure in the process more than in the result.

These notes record a view of Miriam independent from mine.

Addendum 112-1

Note from Miriam’s Teacher

Vn 112-1 Teacher note

Addendum 112-2

Conference Report, page 1

Vn 112-2 Conference report, pg 1

Addendum 112-3

Conference Report, page 2

Vn 112-3 Conference report, pg 2

Addendum 112-4

Conference Report, page 3

Vn 112-4 Conference report, pg 3


Vn114.1 The Game Goes Ever On 12/28 & 29/77


In the first incident, Miriam invents the idea of opening advantage for “Tic Tac Toe two in a row.” I believe this is connected to her introduction to Hexapawn (a pawn capture gain played on a 3×3 board) as a reduced form of chess, and my invention of “half a game” of checkers as a reduced form. This invention of Miriam’s is a significant advance whose development I will follow in its application to Tic Tac Toe Three in a Row (cf. Home Session 20, Tic Tac Toe Finale).

Miriam’s defeating the Children’s Museum computer brings her back as master to her point of engagement with the game.

Vignette 114, page 1, scanned from Original Fair Copy

(click on the image to englarge it; back arrow to return here.)
Vn 114-1 Scanned Original Fair Copy

Vignette 114, page 2, scanned from Original Fair Copy

Vn 114-2 Scanned Original Fair Copy


Vn128.1 Robby’s Topological Game 4/2/78

About a month ago, Robby was shown a paper-cutting game by a
classmate’s parent. The procedure to follow was this:

1. Cut two paper strips of equal length (8″ will do)
2. Draw a line down the middle of each (using lined paper makes
this unnecessary)
3. Bend each strip of paper into a circle and tape the juncture
4. Join the circles perpendicularly and tape the juncture
5. Cut around the mid-line of each circle.

When two strips of equal length are so connected and cut, the surprising
result is that, though having passed through a circular phase, the strip
halves end up taped together as a square.

Squaring two circles

Robby enjoyed this game when shown it. Yesterday, I removed
a paper form he had made in the past (an 8 x 11 sheet divided into 11
strips 8″ long) from my clipboard and gave it to him. When I inter-
rupted his reading to give him this sheet of paper, Robby recalled the
game and quietly took it up on his own. He was very happy when the
procedure produced a square and showed it to Gretchen and me. We neither
paid much attention.

Going on to three circles, Robby cut two of the three along
their mid-lines. He judged (in error) that he had finished by finding
a square with a bar (a double strip) across the center. It lay flat.
Still no one paid attention. Robby went on to four circles, and he
cut all the mid-lines. What he got was a confusion of floppy paper.
I advised him to try to get it lying flat. Robby again borrowed my
clipboard, clipping and taping the product to it. He was delighted
when he succeeded in flattening the strip-figure and subsequently
taped it to a large piece of cardboard. The resulting shape is this:

But why stop at 4? Robby went on to connect and cut 5 circles. Here
he met another surprise. When cut, the 5 circles separated into
identical, non-planar shapes. Robby likewise taped these to another
piece of cardboard. When he made a cutting of 6 circles, controlling
the floppy strip-figures became a big problem. Robby succeeded at
taping it to the box from which he had been cutting cardboard backing
pieces, but in doing so went over an edge. He decided the problem
was getting too complicated to be fun and quit.

This morning I told him I had been thinking about his paper
cutting game and asked Robby to find the figure made from three circles.
When he returned, I asked him if he had cut all three circles. Robby
thought so, but when I pointed out the middle bar in his square was
double thick, he agreed he had only cut two. Robby saw immediately
that his square would divide into two rectangles. He cut the center
strip. “The 5’s made 2 too. Hey! I’ve got a new theory: the odd-
numbered circles make 2 and the evens all stay together.” I agreed
that this was an interesting speculation and that I could believe it
might be true, but that I couldn’t see immediately why it should be.

I see this incident as one exceptionally valuable for
characterizing how significant learning occurs very naturally in a
mildly supportive milieu. First note that the initial exposure to the
“phenomenon” was quite memorable and puzzling. (How can you make a
square from two circles?) Robby clearly marked this phenomenon in his
mind as one which he would explore later. This pending explorarion was
invoked by the accident of his seeing a piece of paper approximately
meeting the material requirements for use in the game. The circum-
stance was one of no pressure. (He had been reading all of Gretchen’s
collection of Oz books and was probably a little bored.) He had no
outside direction or motivation at all. Once Robby succeeded at
making a square, he continued executing the procedure with stepwise
complications all focussed on one variable — the number of circles.
(He might have chosen to make the strips of different lengths — a
possibility he mentioned.) With the 3 circles, Robby stopped prema-
turely because he had produced a result (a square with a bar) only a
little different from the next simpler case (2 circles make a square).
With 4 circles, the outcomes of cutting were apparently sufficiently
confusing that completion could not be judged from the product but
depended on verifying that individual steps of the procedure were
completed. With the figure of 4 circles he was excited and delighted
to have succeeded in imposing some sort of order on the tangle — and
that the final product showed a family resemblance to the earlier
products. Finally, Robby was quick to jump to conclusions (his new
theory) in explaining why some figures were connected and others were

Post Script — 4/3/78

After writing the preceding, I spoke to Robby again of his
game and his theory, inquiring whether or not he could prove it correct.
His method of choice was to test the case of 7 circles (which, as he
later found, splits into two planar figures of overlapping near-squares).
I tried to introduce the idea of a proof in place of another case study,
suggesting he take all possible cuttings of 3 connected circles and
figure out which one cuts the strip-figure in half. He said he had cut
the center first one time and at another had cut from one end.

Robby then drew the two pictures below on my chalk board:

Vn128-2 intermediate state squaring circle

He argued that it is always the last cut that severs the strip-figure
in two, representing the situation as at the above left. By cutting
along the dotted line, one joins the two small circles (here he made
motions of pulling apart the strip pieces) into the one large one.
Note well that this argument is merely a restatement of how he
appreciates the deformation, but it contented him.