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Binet Test


Miriam has known for over a week that our next trip into Boston would be for taking a test. I had introduced her to the idea with the explanation that nearly everyone takes such a test some time and that she was simply taking this test earlier than most other children. So, after kindergarten and a rousing 2 hours with her playgroup (see Home Session 3), Miriam put on a dress and we took the Green Line into the center of Boston.

Miriam had earlier expressed concern that she didn’t know how to get ready for this test. (The only other test formally so defined to her was having her ears checked. She apparently does not think of our experiments at Logo as being tests.) This concern surfaced again as we waited for the trolley car. “Daddy, what kind of questions did they ask you?” I could recall only one question from an earlier intelligence test (25 years ago). “They asked me who was the president before Franklin Roosevelt.” “Who was it?” Thinking she now had the inside track, Miriam asked who was the president before Carter, and before him, and before that one. We stopped at Eisenhower when the trolley came.

It was a beautiful day as we strolled through the Common, stopped at an ice cream store, and continued to the testing center. Miriam was clearly content and relaxed when she went with the tester. She was also relaxed and pleased with herself when she had finished.

Although we need wait another week or so for a formal evaluation, the tester offered these general comments: since Miriam had just turned 6, she began with the age 6 series; Miriam had to be confronted with questions from the eleven year old series before she failed to get at least some of them correct; they have never had to go through so many series with such a young child in their laboratory. I believe the comments need be put in this perspective: the laboratory (Tufts-New England Medical Center Neuropsychology Section) typically is called upon to diagnose problems. Thus, they do not see as a matter of course so young a child as Miriam who has no immediately caused requirement for such a test.

In the evening before going to bed, I asked Miriam if the questions were difficult or easy and if she tried hard to answer them. She responded that she tried as hard as she could, but that some of the questions were just too difficult for her to answer. She was pleased with her performance — having overheard the comment about never having to go through so many tests with a child her age; she was proud that she “did better than anybody else.” Her only gripe was that they didn’t ask her a single question about the presidents.



Arithmetic Ripples


After the session in which I introduced Miriam to adding large numbers (see Home Session 4, 5/28), passing Miriam’s room I noticed in her open loose-leaf book a page of computation. Miriam later gave it to me and I include it as Addendum 17 – 1.

Note that the written form of the equations mimics the horizontal form used in our introduction (see addendum 1 in Home Session 4). Additionally, Miriam attempted here a subtraction with large numbers (i.e. 80 – 7 = 73), her suggestion which I turned down during Home Session 4. Place value, as a topic of interest to Miriam, appears not only in her large numbers, but also in the directly contrasting sums: 11 + 1 = 12 and 1 + 1 = 2.

When she gave me the page, Miriam explained her attempt to subtract 7 from 1; how 1 minus 1 was zero and 1 minus 7 was zero. I expect she will conceive of the negative integers soon.


These incidents document the ways computation crops up in Miriam’s world.

Addendum 17-1


Comments Off on Vn01701


Vn032.01 The Word Box 6/20/77

As her term end in kindergarten approaches, Miriam brings home
more of materials from school. Today came the Word Box — a small
plastic case for holding 3×5 cards. As a reading-readiness activity,
the children are, occasionally, asked to select some word whose spelling
they would like to learn. The teacher prints it on a card; the child
then copies the word onto other cards and places the words in his box.
If one must teach spelling to children (and one must, eventually), this
is an eminently sensible approach.

Telling us about her word box over the noon meal, Miriam
explained a problem and her little joke in solution. Miriam was asked
to pick some words she wanted to spell; she didn’t particularly want
to learn to spell any words she didn’t already know. Noting her box
had nothing at all in it, deciding ’empty’ was a good beginning amused
her. ‘Word box’ followed. The other words — in no significant order
I can tell — are:

wonder wonder April
wonder post office Indian

Post office, as a member of her word list, may derive from the near
term end walk she took with her student teacher Sue to buy supplies for a
farewell party. Miriam also noted she had asked Mrs. Badger, her
kindergarten teacher, how to spell ‘floccinaucinihilipilification’ . . . .
And thereby hangs a tale.

Last summer, while we were moving from Connecticut to our
quarters in Massachusetts, the whole family made the trip several times
(we did some renovating of those quarters and performed the thorough
cleaning Miriam’s dust allergy required). To amuse the children we
often played the game ‘I am thinking of a word.’ In this game, the
selector informs the others of the initial and final letters of some
word as hints for their guessing. It fell my lot to select a word once
under difficult driving conditions. I said: “I am thinking of a word.
It begins with ‘F’ and ends with ‘N’ and it’s one you’ll never guess.”
This permitted me to deny without thinking FAN, FIN, FLOWN, FAUN, FUN,
FON (the ruler of an African kingdom; Gretchen was with us. Cf. Gerald
Durrell’s book The Bafut Beagles). Traffic improved; I was ready for
the outrage then when I announced ‘floccinaucinihilipilification’ (which
is the habit of making small of things. [The word does not appear in
Webster’s Third International but may be found in the Oxford English
Dictionary.]) A few days later Miriam and I drove back to Massachusetts
in my MG (a 1953 TD). Above the roar of the engine, Miriam began, “I
am thinking of a word. It begins with ‘F’ and ends with ‘N’.” In my
turn I guessed the obvious monosyllables. When they were rejected I
tried those with long vowels marked in spelling by the terminal ‘e’.
(Miriam was just beginning to read at that time). When I finally gave
up, I listened quite attentively as Miriam burst out laughing and said,
“Floccinockihilification.” (She mispronounced one vowel, a diphthong,
and omitted 3 of the 12 syllables). Since that time of her great
surprise, Miriam has wanted to learn to spell the word.

It is my intention that Miriam should continue using the word
box during the course of this project for words she encounters at Logo
(both Logo-words and others — for example, those she needs help with
in writing letters). The incidents here illuminate some of the non-
pragmatic use of words that elevate their interest for Miriam.


Vn43.1 Binary Counting 7/7/77

At dinner this evening, the topic of counting on fingers arose.
After performing some finger sum, Miriam turned to Robby with 2 fingers
of her left hand raised and all the fingers of her right and asked:

Miriam Robby, how much is this?
Robby 7.
Miriam No. It’s 25.

Tricked by this representation shift, Robby gave her an equally challenging
problem. Holding up both hands with 5 fingers extended on each:

Robby How much is this?
Miriam (Uncertain and not consistent) 10?
Robby No. 25. It’s 5 times 5. Get it?

With these fluid finger counting representations in the air, Gretchen
asked me to explain hexadecimal finger counting (I use such a procedure
to keep track of telephone ring counts so I can think of other things
while waiting for people to answer the telephone). Since Miriam had
just invented a second finger counting representation and Robby a third,
it seemed appropriate to show the children binary (Richard Feynmann
introduced this procedure to me in an informal chat when I was an under-
graduate). I held up three fingers of my right hand — pinky, fourth,
and index. “How much is this?” Knowing 3 was not my answer, Miriam
guessed that number. I believe Robby guessed 21. I said, “11. I have
a funny way of counting. Let me show you how.” I proceeded to count
from 1 to 31 on the five fingers of my right hand. When Miriam opined
that it sure was a funny way of counting, I told her there was some-
thing she used a lot that counted that funny way; could she guess what
it was? Miriam could not guess that computers count in binary. It
made no sense to her that they could add such a funny way and not take
forever to get a result.

Miriam, in order to trick Robby, invents (with one example only)
a 2 place finger counting representation. Robby counters with multi-
plication of the finger count of both hands. I show both a one hand,
five place binary counting representation.


Vn67.1 Think and Do 8/17/77

I asked Miriam today if she had read all the stories in the book
Friends, Old and New (the book used in initially assessing Miriam’s
reading ability in Miriam at 6). She thumbed through the book, said
she hadn’t read them all, but found the stories just too easy.

What does one believe? I asked Miriam if she had done all the
exercises in the Think and Do book (a set of companion exercises to
accompany the text). She had not, but picked up the book, announcing
that she would do some then, while I continued with my work. I asked
Miriam to write the date (8/17) on those exercises she elected to do.
Miriam did write the date on page 3 (in red pen) and did some of the
exercises there as well as those on pages 2, 3, 4, 6, and 13 (these are
integrated here as Addenda 67 – 1, 2, 3, 4 and 5).

Page 2 apparently tests the extent to which a child can inflect
verbal forms and recognize the significant lexical morphemic correlates.
Miriam did the exercise without error.

The exercises of page 3 ask the child to identify the initial or
final consonant sounds of items pictured. Miriam responds generally
with the initial and final letters in the spelling of the word, e.g.
‘w’ for wheel and ‘h’ for the th of mouth. Two other anomalies appear.
Miriam does not attempt (perhaps can not recognize) the peach and
appears to spell chain with a terminal e (‘chane’).

Page 4 tests reading comprehension (and possibly, recall). Miriam’s
conclusions are error-free.

Page 6 examines a child’s ability to select appropriate modifiers
in a context. Miriam made no errors.

The questions of page 13 make an interesting contrast because
Miriam got them all wrong. The question posed is, in which [picture
word] do you hear the vowel of it? Miriam apparently identifies the
sound of the ‘vowel of it’ as the sound of the letter name i rather
than the phoneme /I/, thus choosing ‘lion’ in preference to ‘pig’ and
‘fire’ in preference to ‘bridge’.

That speculation is not confirmed by the final 4 questions wherein
Miriam does not select ‘mice,’ ‘pie,’ ‘slide,’ or ‘knife.’ Her decisions
may be both spelling-based and based on imperfect spelling.

These data sample the language skills expected in school of some
one who can read at Miriam’s level. They show, not surprisingly, that
Miriam is largely ignorant of phonetics as it is taught in school.

Addendum 67-1

Vn 67-1 Think and Do pg.2

Addendum 67-2

Vn 67-2 Think and Do pg 3

Addendum 67-3

Vn 67-3 Think and Do pg 4

Addendum 67-4

Vn 67-4 Think and Do pg 6

Addendum 67-5

Vn 67-5 Think and Do pg13


Vn73.1 Not Being Ready; Logo vs. School 8/26/77

For the past week Miriam has been mentioning that she doesn’t ‘feel
ready for school.’ I’ve tried to find out what Miriam means by her
feeling ‘not-ready.’ In one case, she explained to me that she didn’t
know what they do there. In another incident, at the dinner table,
when Miriam mentioned not being ready for school, I pointed out to her
that she was surely ‘ready’ for Logo and asked both children if they
thought of Logo and school as being the same or different. Robby
answered first, that Logo and school are different.


How are they different?

You don’t learn anything at Logo.

Oh? And you do at school?


What do you learn? I know you have art, but you knew how to draw before you went to school.

You learn. . . ah. . . mathetating.


Mathetating; what you do with numbers.

Don’t you ever do adding at Logo?

Yeah, but all you learn at Logo is how to use computers.

I learned how to write.

A third incident showed a different perspective.


(To Robby) I wonder what school will be like? Was it very fun in second grade?

Pretty much fun if you have a teacher like Mrs. Johnson and Mrs. – – – [a student teacher]

Miriam, are you more concerned with school’s being fun or your being ready?

Fun. . . but I’m not sure I’m ready.

In what way?

They may be different people. I hope not. I want the same people again.

This last comment recalls the difficulty Miriam had in making friends
at the beginning of the last year. That September was the first major
upsurge of her hayfever allergy (previously only dust and mold had
been diagnosed); her reaction was so severe that she was physically
depressed for the first 8 weeks of school. I surmise she remembers
that time as a very bad time and has vague fears associated with the
returning to school.

These three notes touch on Miriam’s sense of being ‘not ready’ for
first grade and some contrast of what they do at school and at Logo.


Vn80.1 Planning for School 9/2/77

Miriam, showing her unprompted concern, began the following
dialogue. I transcribed it from memory (not tape) about 2 hours after the
fact. The content is accurate, though the sequence of points may be a
bit muddled.


What do you think the teacher will say when she finds out I can add?

What do you think?

I think she’ll be mad at me.

Are you worried about that?


Don’t worry, sweety. I’m going to have a meeting with your teacher next week. She knows you’ve been working with me at Logo and wants to know what she should try to teach you.

What do you think?

I don’t know. What do you want me to tell her?

I guess I should just do the regular stuff.

You mean like 2 plus 3 is 5?


For a whole year? When you already learned to add big numbers at Logo?

I didn’t learn that at Logo. You taught me.

Oh. I don’t mean the really big ones. I mean numbers, say, that you use in
playing SHOOT. Like 90 plus 90 is a hundred 80.

I didn’t learn that [I didn’t figure it out]. You told me.

But I don’t have to tell you any more, do I?

No. . . . When do they usually do numbers like that in school?

At the end of second grade, maybe third grade.

You mean I can skip a grade?

You can read well and do computations. I guess you could skip a grade if you wanted.
Do you want to?

Do I have to?

No. You said before you wanted to stay with your friends. I think that’s a good idea
and you shouldn’t skip a grade. But how will you feel about school?

Art should be a lot of fun. And so should gym.

I bet they’ll let you read whatever books you want. That should be good.


About the arithmetic: maybe I should worry about that, make the work for you to do.
Maybe I could get some good advice from Dan Watt. How would that be?

Well, I don’t know. Maybe it would be O.K.

At this point, Miriam terminated our conversation, drifting out into the
court yard to watch people moving furniture.

In this dialogue, Miriam and I discuss what she should do when she
starts school. She expresses fear that her teacher will be mad at her
because she already knows how to add. I inform her of an impending
conference with her teacher and ask her advice.


Vn90.1 Meeting Miriam’s Teacher 9/11-12/77

9/11 This Sunday morning, Miriam inquired of me if I knew what kind of
a teacher she had. When I admitted I did not, she continued:


Nice. She says if the math problems are too easy, I won’t have to do them.

What will you do instead?

Play with other games, I guess.

Why did she talk to you about this? . . . Did you have math on Friday?

No. I went and asked her about it.

9/12 Early in April before this project began, I discussed with Bob
Gracia, guidance counselor for the Heath/Baldwin schools, the possible
impact on Miriam’s school life of her work on my thesis project. I
raised such questions as these: if Miriam’s level of knowledge and
capacity for rapid development placed her markedly ahead of her peers,
would this be a problem for her? The senses in which I imagined possible
problems were these: her teacher, coming under an additional burden to
provide separate guidance for Miriam, might come to dislike her; to find
continued intellectual challenge, might Miriam be forced to skip into a
higher grade with other children who would be more mature in other ways?
Bob assured me that neither of these possible problems would arise, that
where special needs were clearly shown, the school assumed the respon-
sibility to provide individualized curricula. He proposed a meeting with
Miriam’s first grade teacher at the beginning of the academic year.

Today Gretchen and I met with Bob Gracia and Sue Fieman, Miriam’s
new teacher. Our concerns were three — that Sue know of Miriam’s
allergic vulnerabilities; that she know that our project is still con-
tinuing, that during the next month after school Miriam will be coming
to work at Logo with me; finally, that she not get mad at Miriam. The
first two points are of information, and not too difficult to address.
Both Bob and Sue were interested in the work of our project as I des-
cribed it to them. Sue was excited at the opportunity to see first hand
how Miriam’s experiences at Logo would interact with her standard school
work; she mentioned in passing having done some preliminary assessments
of her students and how surprised she had been that in a class with a
number of ‘non-conservers’ she found Miriam solving class inclusion
problems without difficulty.

Given Sue’s reaction to my description of Miriam’s work on this
project, I believe Miriam has little to fear of teacher antipathy. Nonetheless,
I told Sue the little story of Miriam’s discussion with her from
yesterday to indicate Miriam’s hope to avoid boring work. I also
mentioned Miriam’s earlier fear that the teacher wouldn’t like her because
she knew too much already. On the contrary, Sue seems quite eager to
work with Miriam and wants to know what sort of instruction would be
best for Miriam — “where should she start her out?” I avoided answer-
ing that question in a school-oriented way. I did tell her not to worry
about special instruction: Miriam had previously expressed a wish to
do what everyone else did; and that, with the exception of adding, I had
not been working on school-like material. Miriam would have some special
knowledge, for example about geometry, but such special knowledge would
be outside the normal curriculum. The greatest differences between
Miriam and her peers I expect to be in her tendency to focus on mental
processes and her ability to discuss thinking articulately. I concluded
that the experiments from now on will best provide answers about her
question of where to start Miriam out. Sue remarked that was no problem,
that first grade never began any academic work until October so that each
child had a month to get used to the people and surroundings.

This report of a meeting with Miriam’s new teacher leads me to
conclude that Miriam will have no difficulty with her. She is sympathetic,
open-minded, and considers it an opportunity that a child with Miriam’s
unique experience is in her class.


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


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


Vn122.1 Carrying Bugs 2/5/78

Invited to play at a friend’s house, Miriam waited for Gretchen to
drive her there. During this vacuum of activity, I asked her if she
remembered how to add with carries (cf. Home Session 23). Miriam
reacted impatiently, as though it were foregone that she did. She
agreed to solve a problem I posed on my chalk board and showed
sufficient interest that she tried to peer over my shoulder as I wrote
the sum in vertical form.

                1000   100   10
         |  4  |  7  |  3  |  4  |  5  |
       + |  2  |  2  |  8  |  5  |  7  |	
         |  7  |  0  |  1  |  9  |  2  |

After drawing the columnar division lines, Miriam first said, “5 plus 7
is 2 carry the 1.” “Carry the what?” I asked. “Ten,” she replied and
wrote her marks above the tens column (these marks of hers are hand-
written in the sum above [italics]). She then proceeded: “5 and 4 are 9 plus
10 is 19; put down the 9 and carry.” Miriam did carry a hundred but
failed to add it to her sum of 8 plus 3. Adding the carry from that
11 into the thousands column sum (7 plus 2), Miriam wrote the carry
from that 10 above the identical column with four zeroes (see above)
and added the carry of 1 into the ten thousands column sum (4 plus 2).
Satisfied with her result, Miriam asked me to indicate any columns she
should check.

When I drew an arrow under the tens column and asked whether the
4 was a 4 or a forty, Miriam crossed over the 9 with a zero. Upon my
pointing to her dropping the carry into the hundreds column, Miriam
(who knew the 3 and 8 were 3 and 8 hundreds and that a hundred had been
carried) quit and refused to do more arithmetic before going to her

Even though Miriam appears to have gained a sensible way of
thinking about carries and representing them for herself, her command
is still imperfect, as these two mis-steps of hers indicate. Can she
make such errors and still be judged as understanding carrying?
I believe so. One test would be to see whether on a similar sum
she exhibits these same errors or shows confusion.


Vn129.1 Robby Computes a Tax 4/5/78

Robby caught on fire again today. He approached me inquiring,
“How much is half of 423?” Miriam responded to his question from the
other room, “2 hundred and 11 and a half.” I told her to stop butting
in and asked Robby how much was half of 400, then half of 22, then half
of 1. He came to his own conclusion of 2 hundred and 11 and a half.

But why this concern with the specific question? $423. was
the price of a swing set in a catalog the children had been perusing.
They had agreed to go halves on buying this much-desired super-toy.
I opposed their doing so and raised as an objection along the way the
observation that they hadn’t included the amount of tax they would
have to pay.

“Is there a tax on toys?” was the incredulous question. “If
food is taxed,” I responded, “should you not expect toys to be taxed
also?” When he asked how much it was, I explained to Robby that he
could think of the tax as a nickel for every dollar of the purchase
price. Here we got into complicated computations.

Robby tried to figure out how much money is 4 hundred nickels.
His confusion was great, even including such faux pas as “there are 200
nickels in a dollar.” Correcting to 20 to the dollar, he went on to
observe that $100. of the purchase price converted to $5. of tax. Here
he was stymied but began to add $5. and another. I complicated his
computation by suggesting he use the multiplication results he had
learned at school. He looked blankly at me. “How much is 4 times 5?”
I asked, and received an answer: “20.” “How much is 4 times 5 dollars?”
No answer was forthcoming. He came to $20. eventually (I believe by
adding). Robby then computed the tax for 20 dollars more (of the
original $423.), and with Gretchen’s reminder, added another 15¢ for
the last 3 dollars.

This incident required a surprising amount of time, as much
as 5 minutes, to develop.

This was a very exciting incident for Robby — his first
computation of a sales tax. He brought the idea of “a tax” under
control as a comprehensible percentage, thus eliminating that
mysteriousness which has troubled his world of money since
at least last summer (cf. Vignette 54).