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A Willing Subject


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.



A Willing Subject


As the children left for school this morning, I asked Miriam if she wanted to come to Logo today. She said she would not come. When I asked why not, Miriam replied, “I just need a day off.” After the previous day’s tensions, it seemed a most reasonable request.

I planned at Miriam’s return from school a small shopping trip, with perhaps a detour to a favorite playground. Miriam came bounding in from the school bus. “Hey, Dad, let’s go to Logo.” I objected that I had nothing planned to do for the day because I thought she didn’t want to go. “That doesn’t matter,” she said. “Let’s go anyway; I’ll play with SHOOT or something.” When I asked why she changed her mind, Miriam said, “I don’t know. I just did.”



Hula Hoop Analogies

One of the most active foci of developmental incidents so far has been Miriam’s use of the hula hoop. Four separate incidents come together as activities centered on this toy.

How we came to buy a hula hoop
Our family was having dinner at the house of a Cambridge friend. My children had been playing with Jenner (my friend’s 5 year old daughter) during the late afternoon. When I arrived from the lab, I found the three children, two bikes, and a red-white-and-blue striped hula hoop on the sidewalk. Since it fell my lot to put the toys away, I noted it well.

Because Miriam suffered some confusion about right and left turns in using SHOOT (see, for example, Logo Sessions 1 and 3), I decided to undertake “playing turtle” with the game (i.e. playing SHOOT with the floor taking the place of the display screen and Miriam and me taking turns being the turtle and being the turtle commander) Which we did in Logo Session 3. With this intention, I manufactured a hoop from some polyethylene tube lying in a pile of oddments in the music room. The hoop was adequate for playing turtle, but not as a hula hoop (Miriam attempted to so use it). Miriam suggested that we buy one at the Coop. (We had walked there the day before to buy the puzzles for Logo Session 2). Miriam had not seen any hula hoops at the Coop. When I asked her if she knew whether or not they were sold there, she said, “Maybe.” Other lab members had seen them on sale there, so we agreed to get one from the Coop before our next session.

The following Monday snow kept us from walking to the Coop. I asked Miriam if she would mind my buying the hula hoop the next day before she came to MIT. Miriam agreed to that on condition that I buy one with red-white-and-blue stripes. I argued the Coop might not have such a kind. In that case, Miriam responded, she would have to pick one out. Luckily, Jenner’s hoop had been purchased at the Coop also.



The Bicycle Analogy


During a break from Logo Session 7, Miriam discovered that the hula hoop will stay upright if rolled. For the past several days, maybe the past two weeks, Miriam has attempted to ride her bicycle without training wheels. She received one hint, one good piece of advice from Jim, our neighbor: if you try to go fast on the bike, it will stay up. Miriam has succeeded through doing that.

When I asked her now why the hula hoop stays up instead of falling over, she said, “Well, because I make it go fast.” When I asked if there were anything else she knew like that, Miriam replied, “Yeah, sure. The bike.”



Ping Pong Balls


Miriam continued playing with the hula hoop at Logo throughout this week. Since she is willing to watch other people and listen, adults incline to show her the things they enjoy and can do. This has caused me a problem. I will elaborate.

At the beginning of the project, Miriam underwent a number of experiments to permit the probing of her skills and understanding. One of these experiments involved showing her how to make a ping pong ball slide away and then return as an initially imparted backspin overcomes the impetus of its forward projection. (This experiment is described in The Grasp of Consciousness, Piaget (1974 French, 1976 English)). Since the time of that experiment, Miriam has been, whenever she has a ping pong ball at hand, making it slide away and spin back to her. She has shown this game to friends in the play group. The back spinning phenomenon is clearly one that engaged her interest.

A secondary intention of mine in buying the hula hoop was to conduct with Miriam a follow-up experiment to explore how easily she could generalize her ping pong ball knowledge to the similar back spin phenomenon with a hula hoop.

As I passed through the foyer a few days ago I heard Donna say, “Miriam, did you ever see this?” as she set the hula hoop on the floor with its circumference vertical. I asked Donna not to show Miriam the back spinning. Today, before our session began, Miriam was doing the hula in the foyer. She and Glen were apparently too noisy for the good order of the office, so while Miriam joined me in the music room, Glen went into the Learning Lab to play with the hula hoop. When Miriam and I came out for a break, Sam (an 8 year old) said, “Hey, Miriam, did you ever see this?” Glen had just been demonstrating back spinning to Sam. I stopped Sam’s explanation, explaining to him and Sam that Miriam and I were going to do an experiment about that and I did not want them to explain it to her now. Miriam and I left for sodas.

A while later as we re-entered the Learning Lab, Miriam, whom I was carrying at the time, glanced through the opening door, then excitedly turned to me and said, “Daddy, did you see what Glen just did?” I put Miriam down in the music room and asked what Glen had done. Miriam explained clearly enough to show that she had seen his back spinning the hula hoop. I turned on the tape recorder beginning again the transcription of Logo Session 10.

BobWait a minute. No, I don’t understand. You said he rolled something and made it come back?
Miriam A hula hoop.
Bob He did. How did that happen?
Miriam I don’t know. I think it went (a gesture in the air–unclear) like this.
Bob It did what?
Miriam I think it went like that (gesture again), then it rolled and came back.
Bob . . .well, wait a minute. Let’s see if I can get the hula hoop and you can explain what happened. (Bob brings in the hula hoop) Now, what happened?
Miriam It went like that (here Miriam gestures with the ping pong ball back spinning gesture on the edge of the hula hoop). Like that (repeating the gesture). I don’t know how he did it. (This gesture represents the only procedure Miriam knows creating a comparable effect; Miriam assumes Glen used some such procedure but is uncertain).
Bob Why?. . . I saw you pushing on it, the back of the hula hoop.
Miriam Yeah. (Miriam repeats the gesture several times).
Bob I get it. Have you ever done anything else like that?
Miriam Yeah.
Bob What?
Miriam The ping pong ball.
Bob That’s absolutely right, Miriam. I find that very striking. Did you ever see anybody else do that with a hula hoop?
Miriam Unh-uh
Bob Glen, would you come here for a while please? Miriam saw you doing this (spinning the hoop) for the first time she has ever seen anybody doing it. She figured out how it worked and why. So it doesn’t matter if Miriam sees it happening all over, now. (spins the hula hoop). Did you see it go out the door and come back?
Miriam Yeah. (Miriam tries once and is interrupted by talk). Hold it. I know. I’m going to do it. (Miriam tries backspin and succeeds, laughing). It rolled backwards that time.
Bob That’s a direct, analogous extension of our work with the ping pong ball.


The problem I mentioned at the beginning of the last incident receives its fourth illustration; after the end of Logo session 7, while I gathered my paraphernalia for our trip home, Miriam played with the hula hoop outside the music room. Marvin saw Miriam playing and said, “Miriam, have you seen this good trick yet?”

Thus, over the course of a few days, while the materials were at hand and Miriam was sensitized to the phenomenon, in four separate cases she encountered situations of potential informal instruction (if you count Sam’s attempt and Glen’s demonstration as separate). Can one control such exposure? I believe such attempts would fail, as this attempt of mine failed, because a lively intelligence, sensitized to an engaging phenomenon, will notice its manifestation with only the slightest exposure. Since controlling exposure is not possible, especially in a rich environment and an active culture, the problem becomes methodological. How to be in the right place (for me, with Miriam) at the right turn (when an insight occurs); how to recognize a significant development and document its occurrence in detail sufficient to support subsequent analysis and interpretation. I believe the design of this project, as an intensive, protracted, naturalistic study of a bright child in a supportive environment during a recognized stage of rapid development, focusses on a rich domain of developmental data. The breadth of this study with respect to child’s life in the home, at play with friends, and under tutelage (at Logo), being both intrusive (thereby perturbing the structure of her mind) and extensive (opening to observation situations not usually attended to), offers a better hope of following the fine structure of developing ideas than does any method limited to sampling ideas in separate minds. The recognition of significant developments is circumscribed by my sensitivity: whether that is adequate remains to be seen. The coupling of selective observation with mechanical recording and immediate transcription is my best answer to the documentation aspect of the problem.

Beyond the issue of methodology highlighted by these incidents, raised to theoretical prominence are the issues of analogy (how what is learned as a concrete action is extended to situations where the same action control structure effects a comparable result), the importance of sensitivity to phenomena (that periphery of effects, as Piaget has it, from which cognition proceeds to the center of explanation through the hypothesis of a known action), and the contrast of learning through analogy with learning through the progressive elaboration of not-yet- adequately-structured descriptions. These issues are raised but not to be addressed here.





In discussions some weeks ago with a distinguished Genevan psycholinguist, the question of instructing children in phonetics came up. My earlier work on children’s conception of wordhood (‘Pre-Readers’ Concept of the English Word’) and pig-latin (not available) had convinced me that children should learn how to read before delving into phonetics. (Such a point of view is contrary to much current practice in late kindergarten and early first year instruction). My colleague considered it an aberration in American education to emphasize phonetics as an introduction to reading.

Miriam now reads well, at what is generally considered the second grade level (see ‘Miriam at 6: Reading’ for more detailed infor-mation). I speculate confidently that her reading vocabulary is several thousand words. She now knows enough to appreciate the value of knowledge about the correspondence (and lack thereof) between English phonemic and lexical structure. The following observations record the upsurgence of Miriam’s interest in phonemic variation:

In the spring and summer of last year, one of Miriam’s favorite games was bouncing on my knees. We would sing the familiar chant:

Ride a horse to Boston,
Ride a horse to Lynn.
Careful when you get there,
Don’t fall in!

The child rides facing the bouncer, whose knees are the horse. On the last line, the adult separates his knees, and the child tries not to “fall in.” Boston was a place I went to. Lynn was the neighbor who lived across the street from our Connecticut home. (Miriam has yet to discover the existence of Lynn, Massachusetts). The other common variant chant is:

Trot, trot to Boston
To buy a loaf of bread.
Trot, trot home again,
The old horse is dead.

I introduce this history to enforce the idea of how well known are these rhymes to Miriam.

Today at lunch, having finished earlier than Gretchen and me who sat talking and unattentive, Miriam picked up a large rag doll, put it on her lap, and chanted (quietly, to herself):

side a sorse to soston,
side a sorse to synn.
sareful sen sou set sere,
son’t sall sin.


ide a orse to oston,
ide a orse to ynn.
areful en ou et ere,
on’t all in.

And then:

fide a forse fo foston,
fide a forse fo fynn.
fareful fen fou fet fere,
fon’t fall fin.

It is clear that phonemic separation is an issue that engages Miriam now.


Although she knows that letter represent sounds, it is not clear that Miriam understands the way in which phonetic knowledge will help her with reading. She may. Do note, however, that Miriam was introduced to phoneme separation two weeks ago (confer Logo session 5) through using my pig-latin system to drive the voice box. Five days ago, Miriam selected that activity as one she wanted to engage in (confer Logo session 10) even though I attempted to dissuade her from it by arguing that the programs I had available were limited and the output boring. Today I asked Miriam what I should plan for tomorrow: story writing, drawing, voice box. . . we didn’t always have to play SHOOT or READY, AIM, FIRE. “Voice box,” she exclaimd. “That’s what I want for tomorrow.”





Last night Miriam asked me to come to kindergarten this morning to help out with a rehearsal of ‘Goldilocks.’ (see Logo Session 17, 5/1). When Miriam began showing an interest in plays (cf. Vignette 3), I mentioned to her that those years I spent at Yale were in the Drama School, that I had also done the kind of thing she was describing to me. I can not justify it by having impressed Miriam. She told me she believed I could be of help to her because I had a good book about plays for little people [A Dozen Little Plays, Parents’ Magazine Press 1965]. (She has read that book and finds its costuming of major interest; she asked if I would make for her Fox and Duck costumes. That book is a piece of flotsam remaining from a Master’s thesis project on ‘role rotation’ I once proposed and dropped.)

When I retreated from the housekeeping corner (as described in Vignette 18), Miriam’s intention to stage a rehearsal came to the fore. She asked her teacher if the children could go rehearse in the gym but that was not possible so her cast gathered near the clothes closet. Miriam brought out the scripts of ‘Goldilocks’ we had created the previous day at Logo. The potential cast was 6 in number: Miriam, Maria, Michelle, Elizabeth, Meg, and me. Given the dramatis personae of the 3 bears and Goldilocks, though I was immediately type cast as Daddy Bear I declined and elected myself to the audience. Then the squabbling began. Counting remaining noses, I was quick to suggest that we needed an “announcer.” Miriam declared she would do that and assumed directorship: “Meg, you be Daddy Bear.” (Meg is the largest child in the class). “No. I was Daddy Bear last time. I want to be Baby Bear.” “Michelle, you be Mommy Bear.” “No. I was the Mommy already.” (confer Vignette 18). To Elizabeth: “Here.” (as she gave her a script). When I asked Elizabeth what she thought of the script, she said it was nice but gave it to me because she can’t read. Maria made a cone-shaped hat of hers: “I’ll be the witch.” (a probable reference to the “Wicked Witch” game). Miriam tried to cast Maria as Goldilocks — Maria quit. Elizabeth and Michelle also refused the role. We were at this impasse in casting:

Miriam Self-declared narrator and director
Meg grudgingly willing to be Daddy Bear (and practicing growls)
Elizabeth both bears but neither willing to be the Mommy Bear
Michelle both bears but neither willing to be the Mommy Bear
Goldilocks persona non grata

The problem was solved by ignoring it. “We need costumes,” said Meg. I suggested shopping bags with head and arm-hole cut-outs as making good ‘bear suits.’ “No. Masks is what we need.” Seizing on this suggestion of Meg’s, the children got paper plates to make masks. My contribution was to mark the position of their fingers when each held a plate to her face and located her nose, eyes, and mouth. The children had finished cutting out the necessary holes and made the faces those of bears with brown crayon. Miriam was told there was no time for putting on the play before gym, but they could do it after. So the children closed off their activities and got ready for gym.

After gym, it was clean up time. Put away the wooden lollipops and those fruits Michelle had dumped out in Vignette 18. The children did not go further with their rehearsal that day and I left.


This incident is important as an example of the cross fertilization of ideas from different domains of Miriam’s life: kindergarten and Logo. It also hints at some of the constraints: what good does it do a 6 year old to make a script if none of her friends can read it? This last question is obviously rhetorical — one may distinguish between a project’s being immediately effective in achieving a goal and its value in a person’s development.


Vignette 22.1

Emberley’s Faces


Miriam’s wheezing was so severe this evening she couldn’t sleep. About 10:30 she came from her room to ask if she could sit up with me because it was so lonely in bed and she didn’t want to read any more.

I brought from my briefcase Ed Emberley’s Drawing Book of Faces, a book we had used in Logo Session 9 (an unsuccessful attempt to engage Miriam in the use of an introductory drawing program). Miriam was delighted to draw with the aid of this book. The first face she drew was “Tired Tillie” from page 5. (How appropriate for a child 2 1/2 hours past her bed time). The second figure (at the top of page 4) has the face of “Happy Harriet.” (Notice the two eye circles were added late, when the hair bows were being colored in). The 6 and 7 fingered hands appear to be a free, somewhat controlled extension of the hair scribble motif. The body is merely indicated and the message is the common one appearing above Miriam’s name on all the notes she prepares and gives to friends. Miriam showed the page to me as she closed the book and returned my red pen: “Nice, Daddy?” I agreed. “Hey! I’ll do the Queen.” Then Miriam proceeded to copy the drawing from the back cover of the book (omitting the eyelashes and the collar at the neck).

I asked Miriam to write the date on this page in her notebook. She complained that she didn’t know how to spell ‘June.’ I suggested the number-slash-number representation and the date would be 6-slash-6. Miriam produced 6-back slash-6 for my examination. I said it was fine, but the more usual slant was the other way. Rather than abandon her work, with a simple elaboration much in the spirit of the earlier 3 faces and with the good humor of making a joke, Miriam created her own back slash face. Next, dating the work with the common form, 6/6, Miriam created the contrasting (and not so happy) front slash face, then elaborated the face with body and limbs.


This vignette documents the incorporation of ideas immediately available: both those in a structure of availability (i.e. the book) and those extremely accidental.

a Sample of Miriam’s Work



Writing Stories(2)


After dinner this evening, Miriam, who has been making late Mother’s Day presents for Gretchen, brought me “an early Father’s Day present.” The present, duplicated as Addendum 24 – 1, shows combined a typical drawing with another story in the WRITER model. Miriam could not spell the words, so she dictated it to Robby.


This material shows the expansion of the story form of WRITER into Miriam’s non-computer world. This conventional use of its story format shows its final liberation from the constraint of P, A, and Q stories. After writing the story about Scurry (see Logo Session 23), Miriam has apparently accepted the freedom of the form, and knowing she can get help with her spelling, will be now able to use simple text manipulators without the restraints of an excessive concreteness.

Addendum 24 – 1
Writing Stories: sample of Miriam’s work

Vn 24 story writer model


Vignette 25.1 TicTacToe (4) 6/3/77

Miriam wanted to play a few games of tic-tac-toe before going to bed this evening. After vignette 15’s instruction in the proper ordering of three rules,

    1. Look for a way to win (complete a row of three)
    2. Look for a way to lose (make all forced moves)
    3. Look for two ways to win (fork your opponent)

I wanted to document how well or ill Miriam could absorb those notions. Thus the game was recorded (on the tape of Home Session 6) but not transcribed in detail.

Miriam moves first (her moves are letters, mine are numbers) in this game where I make the sure-to-lose response of a non-corner move after she takes the center square:

	  C  |  1  |  2 
	  D  |  A  |    
	  B  |     |  3 

Miriam recognized my second move and her ‘C’ as forced moves and knew she had two ways to win before my third move.

After my defeat, I move first in this tied game:

	  B  |  4  |  5  
	  3  |  1  |  C  
	  A  |  D  |  2 

Miriam asked if I were going to try my ‘good old trick’ (a corner opening); instead I took the center. She replied “Not usually” to my question of whether she ever moved ‘in these side places’ (as I had just been defeated doing). When I asked “How come?”, she simply said, “I don’t know.” Then she revealed her plan of going on both sides of my center move, and also a third corner, thereby getting two ways to win. Such is a terribly unrealistic plan as it neither recognizes the importance of being one move ahead of the opponent nor makes allowance for the opponent’s possible moves to block such a plan. I made move 2, telling Miriam I would not let her complete such a plan. She said, “Then I won’t do it. I’m thinking of something else.” She made her forced moves.

We had been taking turns drawing the grids in which our games were played out. I introduced the word frame to Miriam as a label for the grid with our third game.

B I get to write the frame. I will call this the frame, O. K.?
M Alright.
B And that’s just the little tic-tac-toe thing but we will call it the frame.
M Me first.
B ‘Cause the frame tells us where to go and what to do.

Miriam begins with a corner move.

	  3  |  C  | B  
	  E  |  1  | 4   
	  A  |  2  | D  

After Miriam’s first two moves, I asked her advice. “Go anywhere.” She said then, “Oh, shucks, I’ve got a forced move,” and she followed all her forced moves appropriately. I requested her to draw the next from and she did so.

In game four, as I went first, I attempted the three corner strategy to see if Miriam was able to block it yet.

	 3   |  C  |  2  
	 4   |  B  |      
	 1   |     |  A 

After my move at 2:

M Oh, no.
B What did I do?
M You’ve got some plan.
B Does this look like a familiar plan?
M Unh-uh.
B Two ways to win [making move 3].
M [move C]
B That was a nice gambit, Miriam. You really did good work there. That was a good idea: trying a different way to beat me.

This is interesting in showing an attempt to block the corner opening on the first move.

	  3  |  C  |  B 
	  E  |  2  |  4 
	  A  |  1  |  D

Noting her last attempt at a non-center response to a corner opening and its failure, I moved 1. Her attempt to continue the three corner strategy failed with her forced move 'C' and its sequels. Miriam drew the next frame.

In game 6, I refer back to Miriam's earlier statement that she had a plan to get on both sides of a middle move. The center opening again:

	  5  |  C  |  2 
	  4  |  1  |  D 
	  A  |  3  |  B 

Since I have no forced move at 4, I discuss with Miriam whether I should put it in the corner (which can never win) or at the side (where I get 1 way to win). Miriam is happy to block it.

Miriam begins game seven with a center move.

	 2   |  4  |  E  
	 C   |  A  |  3  
	 1   |  D  |  B	 

I note how every time I go on the side, I end up losing, so I move 1. When Miriam remarks she has no forced move D, I note it was like the game we just played. I ask Miriam where she can go to win and not win; can she tell the difference. She moves D.

I note how every time I go on the side, I end up losing, so I move 1. When Miriam remarks she has no forced move D, I note it was like the game we just played. I ask Miriam where she can go to win and not win; can she tell the difference. She moves D.

	 C   |  B  |  4   
	 D   |  1  |     
	 A   |  2  |  3  

Move 3 forces Miriam's C. I remark on having a forced move at 4. Miriam responds to a 'forced' move between 3 and 4. We both discover together that she has overlooked the A - C win. Miriam changes her move to D.

B Oh well. You had two ways to win and didn't even know it. How did that happen?
M I went here [I had a forced move 'B'] so I have a move here ['C'] also. Then I couldn't see that because I was trying to keep my eye on if you were going to win.
B Hum. O. K.

In game 9, I request that we play the last game again because it was so tricky. Instead Miriam starts with a corner move.

	 D  |     |  1 
	    |  B  |  2   
	 A  |  3  |  C   

I play out this game in such a way as to duplicate the lesson, though not the form, of the last game. By move 2, Miriam is forced to move 'C' which also gives her two ways to win.

We stopped playing as it was near bedtime, and Miriam wanted to show Gretchen the videotape of the plays she and Meg had made at Logo today (Logo Session 19).

One clear conclusion is that Miriam now subordinates her strategy of finding two ways to win to that of making all forced moves. Game 8 shows an instance of her failing to make a winning move while responding to a forced move. I value game 4 for showing specifically how far advanced from its initial rigidity (cf. vignette 5) is her response to the three corner strategy employed by an opponent. Games 8 and 4 exhibit for Miriam how one can be forced into a series of moves that forks the opponent.

The word frame is introduced to Miriam to name the grid upon which the game is played. The idea is that it is a structure with implications for action.


Vignette 26.1 The Clever Hack (3) 6/13/77

After not using the SHOOT programs for nearly a month, today (in
Logo Session 24) Miriam returned to playing with that game. She started
using the Clever Hack to run up her score (keying ‘H’ followed by
‘SHOOT 0’; the former locates the turtle inside the origin-centered
target, the latter guarantees a hit). I showed her then that in the
interim I had added a new feature to SHOOT, the option (under control
of a switch) of having the target relocate as well as the turtle after
every hit.

This fact came up in our conversations after dinner. Robby was
quite pleased with the letter he had written (using the LETTER program,
Logo Session 24) to a friend in Connecticut. Miriam interjected, “You
know what Daddy did today. He made SHOOT so tricky the clever hack
doesn’t work any more.” What struck me was Miriam’s tone — she was
imparting to Robby some shocking news.

My intention is to lead Miriam to the discovery that she can get
the turtle inside the target area using forward and turn commands
(deferring execution of the SHOOT procedure until certain of a hit).
I will describe such an action as a clever tactic. My objective is to
introduce to her a set of distinctions which focus on the particularity
of a problem’s solution: the ‘hack’ (like the gambit) being the most
context dependent; the ‘tactic’ being a set of specific actions which
may be catenated to solve any member of a class of well-understood
problems; and the ‘strategy,’ a set of actions one employs where the
goal is clear but the appropriate operations and intermediate states
are not obviously limited.


Vn44.1 A Boring Session 7/12/77

Riding home after this morning’s session (Logo Session 38) Miriam
said she thought the work was boring today. When I asked why, she said,
“Oh, I don’t know.” I have to look otherwheres for an explanation.

Today I tried to exhibit for Miriam the relation between closed
polygons and in-going spirals sufficiently regular to be judged ‘mazes’
rather than ‘pretty pictures.’ (Cf. Addenda 1 and 2). Yesterday Miriam
suggested for today that she would like to try to get more good numbers
for making mazes. I believe she had in mind a result like that of Logo
Session 27 (where we made a list of the members found with the ANGLE
procedure for making ‘pretty pictures.’) I made such a result our ob-
jective, but Miriam showed little interest in the work.

Note that Miriam was feeling sick this morning before we came to
MIT and also during the session. She ws disinclined to come in today
but agreed when I pointed out that we would be away from the lab for
the next 2 weeks. It may be that this was just a ‘bad day’ for her,
but I incline to believe I’ve been pushing her too hard in one direction .
(Turtle Geometry variable separation).

After we finished trying to find good mazes, Miriam began drawing
at my desk. She asked, “Hey, Daddy, how much is 14 and 14?” “Let’s
ask Logo,” I replied and keyed the expression. This captured her
interest. “I want to do some numbers.” Miriam keyed addends of about
20 digits each. Logo produced an answer in floating point format.
Miriam said, “That’s funny. It’s got a dot in it. That can’t be right.
I guess Logo doesn’t add very good.”

After Miriam complained about the session on the way home, I asked
the children what we could do to make the sessions better. Robby said
the day would have been OK if the printer worked, if we had been able
to make pictures out of designs. Miriam said she would just rather do
some adding instead.

This vignette discusses the circumstances surrounding a Logo
Session Miriam found boring. I suspect I’ve been pushing her too
hard. Though the conclusion is uncertain, I feel it’s appropriate
to go easy for a while.

Post Script

Miriam decided to take off the next 2 days, so we did not go into
the lab again until the 15th of July.

Addendum 44-1

My files no longer contain this figure, if they ever did.
I suppose it was intended to show the collection of the
regular polygons (triangle, square, pentagon, etc.) to be
followed by Addendum 44-2 below, as an example of a “maze.”

Addendum 44-2

Hexagonal Maze

Vn 44-2 Hexagonal Maze


Vn45.1 Going Home 7/15/77

When today’s Logo Session (#39) and errands were finished, we
hurried home to pack up provisions for a 2 week vacation in Connecticut.
The house is empty between tenants, and since we are renting it
unfurnished, it IS empty. What did the children expect of this vacation?
What did they look forward to? And how did they first react to going

Both have looked forward to the trip. The outstanding feature of
our home is lakes and two beaches a few hundred feet away. Learning
how to swim was an activity both talked of with anticipation. Miriam
asked me to commit myself to spending time with her several places:

the playground at the Guilford Lakes School — Miriam said
specifically that she wanted to use the rings where she had learned to
skin-the-cat last year, noting she would be able to do it much better now.
the playground at Jacob’s Beach — this town beach at the Guilford
Harbor on Long Island Sound has swings for babies, tots, and adults,
and small and large sliding boards; from the top of the larger you can
look over the harbor and town dock and watch sailboats and water-skiers
out on the Sound. Miriam remembered as a primary description of the
playground another piece of equipment, a large metal cross with a sit-
upon animal at each end (Elephant [her favorite], Pelican, Turtle, and
Hippo). These four seats are centrally supported by springs which permit
motion vertically with small excursions of rotating and twisting.
Great Hill — this names a specific section of the road from
Miriam’s nursery school behind a hundred foot bluff and down to Lake
Quonnipaug. The road drops and twists quite rapidly and was thrilling to
follow in my old MG.

Notice that Miriam’s focus was on places, whereas Robby’s primary
interest was to play again with his friend Raymond. Miriam has friends
in Guilford (Scott, Toddy, and Sarah are three from nursery school;
Karen and Lisa are girls she liked and played with while at the baby-
sitters’) but her interest did not focus on them. This focus on
places where she had done things may be an artifact of her leaving
Guilford soon after turning 5, before developing the close sort of
attachment Robby shows to his friends.

Upon arrival we unloaded our portable goods into our empty home.
We found in the basement objects of ours and experienced a delight of
repossession. Miriam was obviously as happy to find the mattress from
her crib (which she slept on for 2 weeks) as I was to restore above the
hearth the motto I burned in wood upon first occupying the house —

	I built this house with my own hands 
	And needed helps of friends
	Memento be -- a friendship house --
	Past days when friendships ends.

These notes document some of Miriam’s expectations for
the 2 weeks’ vacation at our house in Guilford.


Vn58.1 Owning an Angle 8/4/77

As far back as the end of June (in Logo Session 32) making hexagonal
mazes has been a part of both children’s Logo work. Before our Connecticut
vacation both children worked together generating pictures of mazes
(7/8/77: Logo Session 36). During that session, Miriam “discovered” the
60 degree angle input creates a hexagonal spiral. During today’s session
Robby generated a “family of mazes,” including the hexagonal form with
the other regular spirals of integer angles (120, 90, 72, 60, 45, 30).
Both Robby and I were quite pleased with his work of the day and hung
on the wall the pictures made by the spiral procedure with those inputs.

While we were preparing to leave, Miriam entered my office (now
dubbed the ‘little learning lab’). Robby, naturally enough, showed her
his pictures — at which she complained vigorously that he had used
“her” angle of 60 degrees. One could dismiss the complaint as a
manifestation of sibling rivalry or a more general jealousy that I praised
his work. Nonetheless, it is clear that Miriam saw “her” hexagonal
maze as a unique object in a collection of other objects.

Miriam’s complaint has been repeated frequently in the weeks
following its surfacing.


Vn60.1 Surprise Party 8/8/77

Spoiled by living in the air-conditioned comfort of our Connecticut
home during the mid-July heat wave, when the next spell of hot weather
found us in the hot air heated loft of our Boston carriage house little
persuading was needed to induce Gretchen to join Miriam and me at Logo
yesterday. With the hot weather continuing and both children expecting
to do an experiment this morning, it was a natural consequence that
Gretchen should join us at her later convenience, bringing lunch if she
so chose, and plan to spend the afternoon at the lab.

We three gave Gretchen birthday presents, wished her happy birth-
day, and sped off to our morning’s work at Logo. As we drove across
town in the MG, I broached the idea of a surprise party with the chil-
dren. They were as enthusiastic as I was and far more certain that it
would work out.

We completed our morning’s experiment, enjoyed together the lunch
Gretchen brought a little later, and settled down each to his afternoon’s
occupation: the children browbeat Margaret Minsky to carry them around
and played at frisbee with the students of the HSSP; I worked at data
transcription; and Gretchen read a book newly selected from the library.
I had alerted a few friends and hoped others would drop by the lab in
the afternoon. Since the children and I planned to get an ice-cream
birthday cake, we had to concoct some plausible excuse for the three of
us to ride off leaving Gretchen behind at Logo. My script’s argument
called for moving the MG from a block away to the Tech Square lot to
render easier carrying down to the car the remains of lunch, my recor-
ding equipment, and so forth. The children were to set up a cry in
their normal fashion that they wanted to go for a ride with me.

Our little ruse worked a little bit, for Gretchen surely knew it
was her birthday and the children kept approaching me to whisper, “Is
it time to go get the cake?” The circumstance that gave away the secret
was unforseeable. We moved the MG at 3 o’clock, thereby escaping the
earlier ban on cars without the appropriate parking stickers. Gretchen
said her car was parked on the street right in front of mine and she
should walk along to move hers also. I tendered some completely inade-
quate reason for not doing so, and Gretchen was sufficiently insightful
not to push the argument.

We picked out a cake at Baskin-Robbins. Robby held the cake on
the way back (the privileged function) and Miriam rode in the boot (the
seat of choice). We gathered a collection of dishes, forks, and friends
and sprung our surprise on Gretchen. She was pleased.

As is the case with most Logo parties, as many people were absent
as present; the place seems sometimes a crossroads in the paths of
over-committed people, but Andy, Donna, Margaret, Marvin, José, and the
children and I met the challenge of consuming Gretchen’s birthday cake.

This vignette shows the children in preparing a surprise birthday
party. This informal party was more or less typical of those at Logo
in that the summer dispersion and other commitments kept the size
small and made the guest list a nearly random selection of people from
the lab.


Vn64.1 Jumping Rope 8/13/77

Miriam began jumping rope after we moved to Massachusetts. Earlier
she had played a game ‘Angels/Devils’, a group rope jumping game in
which a child in the center of a ring turns, saying alternately ‘angels
devils angels devils. . .’ until one of the children in the peripheral ring
fails to jump up as the rope comes to his place. If that child is hit
by the rope while ‘devils’ is being said, he takes over in the center
of the ring; otherwise the child in the center starts the rope spinning

At kindergarten, the children apparently jumped with a long rope
(with a person to turn at each end). Miriam asked to have such a rope.
I bought some rope and we played with it in the court yard and at Logo.
Jumping with this rope was one of Miriam’s favorite activities on the
‘breaks’ she took in the course of Logo sessions. Inasmuch as I was
maladept at turning a rope with the proper rhythm and clearance,
Margaret Minsky and Ellen Hildreth were frequently attached for this
service. Margaret got caught up enough in Miriam’s enthusiasm to buy her
a book on jumping rope (Jump Rope, Peter Skolnik, Workman Publishing
Company). During this period of jumping rope at Logo, Miriam gradually
increased her skill to the point where her counting becomes confused
before her jumping fails.

Yesterday at Robby’s party Miriam attempted for the first time to
jump with the rope traveling backwards. Today she has been achieving
3 or more jumps per attempt. When I asked her why she was doing it
backwards and had she ever seen anyone else do that, Miriam replied,
“Just because I want to,” and “Lisa Larson.” Lisa, a former playmate
in Connecticut, was that daughter of Miriam’s baby sitter and her
senior by two years. After the rope jumping of today, this evening
Miriam was reading her jump rope book. I saw her with her arms crossed
on her leap and a puzzled look on her face as she apparently tried
figuring out from pictures how to jump “crossie.”

Rope jumping was an activity which much engaged Miriam at the
beginning of our project, which was put aside for about two months,
and is now coming back as Miriam considers attempting procedures more
complex than those she mastered before.


Vn75.1 Logo Seahorses 8/29/77

At the end of the day’s work (Logo Session 56), when the recording
equipment was packed away for the trip home, I was preparing material
for tomorrow’s session. Robby had been using procedures where DELTA
named a variable increment applied to a linear distance and today was
introduced to a use of DELTA as an angle increment. I had written a
POLYSPI analogue procedure (call it “A”; examine its listing on Addendum
75 – 1) and was showing it to Gretchen. (An execution of “A” creates
1 of the s-shaped curves in the picture of the addendum.)

Miriam entered my office and asked, “What’s that, Daddy?” I told
her it was a SEAHORSE and tried to distract her attention. This is work
I intend to pursue with Miriam in the near future, and did not want to
expose it to her early. Miriam was most insistent; she wanted to do
SEAHORSE. I would not tell her how to spell it. She spelled ‘SEA’
then got Robby’s help in spelling ‘HORSE.’ When Logo complained that
no one had told it how to SEAHORSE, Miriam complained to me. I relented
and wrote this procedure:

        1  A  10  60  2

Miriam cleared the screen and was delighted when SEAHORSE executed
to create the figure she expected. She called Robby, executed it a
second time. He remarked, “It looks like you’re making something.”
“I am,” declared Miriam. “A flower.” She proceeded through another 7
executions and happily printed her flower in triplicate — with copies
for Robby and me.

This vignette documents Miriam’s engagement in a small project
(which won’t appear in the Logo Session recordings), her attraction by
something not-quite-familiar, her elaboration of the artifact of the
procedure through repetition, and her fitting in the developing design
to a class of objects she is accustomed to. (To Miriam, the ‘flowers’
of drawing or design include any shape of manifest circular symmetry).

Post Script:

Miriam was sufficiently pleased with her SEAHORSE/FLOWER to send
copies to her great-grandmother (G.G.) and to her friend Maria (who has
moved to Spain). To the latter’s copy she appended a hand-written note:
‘I made this on the computer’.

Addendum 75-1


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.


Vn94.1 Miscellany 9/dd/17

At lunch today a variety of topics came up for discussion. Miriam
said she would like to bring her friends over to visit Logo. I thought
of previous visits. “You mean something like the earlier visits of Meg
and Dara?” Miriam added, “I want Michelle and Laurie Ann and Elizabeth.”
I asked if she wanted all her friends to visit at once. She replied,
“No. The whole class.” I am happy that Miriam wants her friends to
visit our lab and get some sense of what she has been doing. After the
final phase of the project ends might be best, since such a visit
would take a lot of preparation.

I discussed with the children our moving into the project’s final
phase. Because there had been some complaints about how specific
experiments were ‘bad,’ e.g. bending rods, I asked if the children had
any good ideas for improving our experiments. Miriam’s response I find
a little bizarre, but worth noting: “We should do more things with clay.
The best thing of all would be if we made things on the computer, the
computer would give you them in clay, like PERSON.” (PERSON is the name
of a procedure Miriam made in Logo Sessions 59 and 60; Miriam uses the
printed images of the procedure’s output for cut-outs and coloring. For
an example see Addendum 94 – 1.)

Later on, a few knock-knock jokes passed across the table. Miriam
noted of them the thing that makes them knock-knock jokes is you have
to say “Who’s there?” We all agreed; then Miriam began what seemed a
divagation. She said to Robby:


Knock knock.

Who’s there?

Will you remember me in 5 years?

I don’t get it. . . . I thought this was a joke.

Will you remember me in 5 years?


Will you remember me in 10 years?

. . . Oh, I guess so.

The conversation generally started drifting another way.


Knock knock (interrupting).

(a little exasperated) Who’s there?

(Looking right at Robby) Don’t you remember me?

I found this a very unusual example of the genre, and asked Miriam if
she had read this in the collection of knock-knock jokes she took out
of the library. Miriam claims to have made it up herself. I find this
an interesting variant because it makes very direct use of the rigid
knock-knock script without having its humor depend on a pun. That is,
the equivocation is at a discourse level, not at a verbal level.

This collection of incidents touches on 3 points: Miriam’s interest
in showing Logo to her class; her imagining computers with a more
physical and less representative output; finally, her articulate knowledge of
the structure of knock-knock jokes.

Addendum 94-1

Using Logo printed images

Vn 94-1 Using Logo printed images


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.


Vn103.1 Reprise 10/15/77

As we have attempted reducing Miriam’s cortisone dosage, she has
again begun wheezing severely. Her problem was especially unfortunate
today, for she had asked a friend to come visit. Lizzie is an energetic
red-haired colleen of 6. At lunch she disclosed to Miriam and Robby all
the problems they could expect with a younger sibling. (Her sister
Katie, at 14 months, not only keeps her awake but also tackles Lizzie
every time she strolls by). The weather was so bad no one could play
outside. Miriam, hoping for some relief in the better air of the Logo
lab, agreed to Robby’s suggestion that we all go over there to play.

Once at Logo, Miriam showed Lizzie around — through the Learning
Lab, the Music Room; the toilets out here and the coke machine across
the hall. Lizzie said she wanted a picture of a flower and then explained:
earlier in the year Miriam had made copies of the image made
by a FLOWER procedure and took one for each member of her kindergarten
class; the children colored them and some took them home. Miriam was
still feeling low, so I helped Lizzie get what she wanted. First, a
FLOWER picture. Next, looking at Miriam’s work hung on the walls of my
office, she declared she wanted a copy of PF (for PRETTYFLOWER). As we
waited for her picture to come from the printer, Lizzie saw a 6-fold
near triangular polyspiral which Robby had printed from a different
terminal. “Wow! I want one of those. Show me how to do it.”

I started the SHAPES (or MPOLY) procedure. Miriam showed some signs
of improvement and the two girls worked together creating designs which
they would color in later (cf. Addenda 103 – 1 and 103 – 2). Whenever
they got in trouble, I was available to help them get started again.
This play of making computer designs, then printing pictures of them for
later coloring, occupied both girls for about two hours. Both girls
made some very pretty novel designs. For example, the design of Addendum
103 – 2 was one I had never seen before and judge pretty (more so
with the drawing in light on the cathode ray tube). When Robby and I
tried to show SHOOT to Lizzie, she could not get interested in it and
returned to MPOLY.

As the day wore on, Miriam’s apparent improvement faded. We drove
home by way of a playground on St. Paul Street. (Miriam and I stayed
in the car while Robby and Lizzie ran around). As we continued on to
her home, Lizzie revealed that her daddy had a computer too where he
worked, but ours sure was different from his.

These notes record the children’s continuing engagement at Logo
though our project be over, and provide a glimpse of the reaction of
one of Miriam’s peers.

Addendum 103-1

Colored Polyspiral at 155 degreesVn103-1 Colored Polyspiral

Addendum 103-2

Six-fold MPOLY with a person in the middle

Vn 103-2 Six-fold MPOLY with person


Vn105.1 Hotel Magee; Two Microworlds; Decadal Computation 10/20 & 27/77

10/20 With Robby’s introduction of WUMPUS to Miriam yesterday, the
mechanically recorded sessions at Logo cease. Vignettes continue to
round out and close off at natural stops various themes of the project.
The sense of closing off the mechanical recording is that the project
has REALLY ended. Thus our trip to witness my cousin’s wedding in
western Pennsylvania is both a vacation, an obligation, and a celebration.

After 7 and more hours of driving, nightfall found us in Bloomsburg,
on the east fork of the Susquehanna. We passed motel after motel with
NO VACANCY signs. After dark, we came to the Hotel Magee. (Their bill
board advertisements along the road declared ‘children stay free’; I
thought staying in a hotel (their first time) would offer them an interesting
contrast with the motel room we knew awaited us the next night at
our journey’s end.) We piled into the hotel, and while Gretchen and the
children freshened up after a day on the road, I sought a table at the

A grandmotherly hostess first informed me there was no room now and
no empty tables were expected till 8 in the evening. When I asked for
recommendations to other dining places about town — for my two hungry
children would not peacefully wait another hour for service — the woman
scratched a reservation from her list, making room for us.

Soon we were at table; the food was good and the variety quite
surprising. So even though Miriam was tired and refused to eat, the
meal had a festive sense for all of us for our various reasons. During
the evening we talked about the children’s sense of the project and some
of the amazing things they had done. I told Miriam how her addition of
96 plus 96 impressed me (cf. Vignette 100) and contrasted that with her
attempt to sum 89 plus 41 by counting hash marks 5 months earlier (cf.
Miriam at 6: Arithmetic). When I recalled that detail, Robby convulsed
with laughter. How could anyone attempt so absurd a procedure? I
asked Robby to think back, reminding him of the night he showed the same
response when I asked him to add 75 and 26 (Robby recalled having a late
pizza at the European Restaurant with our friend Howard Austin — Cf.
ADDVISOR, Logo W.P. #4). This reflection sobered him some. Miriam
piped up: “That’s a hundred and one.” “And how did you get that result?”
Miriam replied (to my surprise), “It’s like 70 [sic] and 20 is 95 and then you
add 6. 75 and 20 is 95 plus 6.” I was surprised because with those
particular numbers I thought Miriam might compute the result using a
money analogy. After assuring her of the correctness of her result, I
posed a different problem. “Miriam, suppose you had 75 cents and I gave
you 26 cents — say a quarter and a penny — how many cents would you
have?” When she responded “A dollar ten,” I asked where the extra 9
cents came from. Miriam computed for me in explanatory mode: “75 cents
is like 3 quarters and another quarter is a dollar. That’s a hundred
cents and one more is a hundred and one.” She denied her first answer
was a hundred and ten cents.

Note first that Miriam did not carry the result from one computation
to the second. Note further that although she applied directly her
decadal then unary algorithm for the numbers (75 plus 26), the same
numbers applied to money engage with a most minor variation the
well-known result that 4 quarters make a dollar. I can not confidently
explain the penny-dime confounding. I speculate that when not central,
they are not well distinguished. A dime won’t buy a 5-pack of bubble
gum and you can’t use pennies for anything but paying food taxes (cf.
Vignettes 54 and 55).

10/27 While waiting for the school bus this morning, I asked Robby if he
were doing anything interesting. He was enthusiastic about certain games
and said he liked especially the play time when the first graders come to
play with his class (3rd grade). I asked if they ever did any academic
stuff — TIMES problems and so forth.

Miriam informed us both she knew how to do TIMES. She argued her
point concretely: “Four twenties are eighty.” I laughed and reminded
her that I was driving the car yesterday while she and Robby discussed
that sum in the back seat. She protested, “I can do it.” “You can do
4 times 20. Can you do 4 times 90?” I challenged her. Robby knew and
said the answer. Miriam complained to him and walked down the driveway
kicking leaves. She returned. “The answer’s 3 hundred and 60.” Robby
claimed credit: “I told you first.” I argued that having the first
result was not so important, that what matters most is having an answer
you can understand yourself. Miriam said, “Can I tell you how I figured
it out?” and proceeded to do so: “I had a hundred eighty and a hundred
eighty. I took the two hundreds and one of the eighties. That’s 2 hundred
eighty. Then I took away 20 from the other 80 and I had 300
with 60 left over. 3 hundred 60.” I congratulated Miriam on good execution
of a very complicated computation and wished both children a good
day as the school bus came to rest where we waited.

These notes close off my informal observations on Miriam’s computational
development. Miriam shows herself clearly in command of com-
plicated procedures for mental arithmetic, as witness her computation
of 4 times 90 with her decadal additive procedures and their integration
with unary adding. The contrast of computation performed on numbers and
money document the interaction of computation and microworld well-known


Vn107.1 Self-Understanding 10/22/77

My cousin’s wedding has been a day of reconciliations, of growing
closer to family from whom I had been long and much estranged. After a
late breakfast, we attended the wedding. I felt proud of Robby later
when he told me the nicest part of the wedding was a piano-organ duet
(‘Jesu, Joy of Man’s Desiring’) even though my engagement was other.
As I later told my cousin, the groom, in a scene reminiscent of the end
of The Madwoman of Chaillot wherein I stuttered several times
then spoke clearly, I came to bear witness that marriage and paternity were
the two great blessings of my life.

At the reception, as we arrived early I took a table for 8 and then
asked my brother, his family, and my father to join us four. There, and
at a later party for the immediate family, we spoke much with Dave (my
brother) and his wife. As their daughter has gone through school they
have become appalled at the quality of the “education” to which she has
been subject and indignant at the pretense of knowledge ignorant
teachers make. (We spoke freely because I told them my difficulty in
foreseeing an academic future was that I could not endure the pretense
of knowledge with its implicit deceit and manipulation of other people
that the professorial stance systematically demands.) I explained to
them parts of our newly completed project: one of our goals was to render
a child more articulate, to give a child better control of his own
mental procedures and knowledges.

Miriam was playing chase outside with Robby and Peter (a second
cousin, her junior by nine months). When Peter last tagged her, he hit
her in the back of the neck and pulled her hair (thus her story goes).
I found Miriam outside, sobbing and very much out of breath. I would
have judged she needed a dose of her wheeze-suppression medicine at
that time. I loaned Miriam my handkerchief and speculated that his
unkindness had been an accident, or perhaps a thoughtless act, but
surely not a mean one directed at her as a person. Inside, my brother
sat down with Miriam, who was still wheezing heavily, in an out-of-the-
way place. As he subsequently related their conversation to me, Dave
told her of his severe childhood asthma, a difficulty he suffered when
the practice was less sophisticated and medications fewer than today’s:
he had found that through conscious effort, he could stop an impending
asthma attack, bring his breathing and his emotions under sufficient
control that his bronchi could recover from the particular assault they
suffered in a given incident. Miriam tells me they made friends. Dave
said if Miriam comes to visit him, she can play in the large playhouse
he made for his daughter (almost 7 years Miriam’s senior) and could
watch for the deer which visit at his four apple trees.

Later in the evening I accosted Miriam outside. She was again
breathing heavily, engaged once more in a game of chase with the two
boys. “Come walk around slowly with me.” When Miriam refused, I
pointed out how she was breathing so heavily and that I didn’t want her
to end up wheezing. She explained to me, “Daddy, I have a very good
trick, to stop it when I have trouble breathing.” “How’s that?” I asked.
“I just think about it [pointing to her head], and after 5 minutes, or
maybe even 15, I won’t be breathing so hard.” I left Miriam playing tag.

I reported Miriam’s reply to my brother, who said this was
substantially the advice he had given her and filled in the information
I noted previously. Dave remarked further that he didn’t really under-
stand my description of our project’s work at Logo but volunteered the
judgment that he had never met so young a child so well able to under-
stand the idea of controlling her own processes.

This incident reports one example of how Miriam’s work on this
project has developed a perspective on self-control which may be
profoundly valuable for her in an entirely separate area of her life —
controlling her allergic reactions.

Some more detailed notes. My brother is an engineer, not an
educator nor a psychologist, so his exposure to young children is limited
to his daughter and her friends. His daughter is in her school’s pro-
gram for ‘gifted’ children, which fact I cite as witness that he is used
to having a bright girl child around. Further, he is a design engineer
for microcomputer-based milling machine control systems; by this I imply
that he is used to thinking in terms of procedures and control.

I would not claim that Miriam understands herself in the profound
sense of placing herself coherently in her world. It is clear she can
talk with and comprehend the ideas of a mechanistically-oriented but
sophisticated 40-year-old engineer in his attempt to explain what he
views as a milestone of self-understanding. It is very likely that her
ideas of herself in this respect are influenced by our work at Logo (cf.
Vignettes 87, Turtle Tactics, and 88, One or Many Minds). It might be
more direct to say that Miriam can establish a theory of herself as an
object. (For a discussion of whether that is a good thing, see Vignette 81,
Imitating Machines.) If one criticizes a culture or subculture for
leading people to think mechanistically about themselves, one criticizes
an approximation to the actual human condition — and are not approximate,
wrong theories a first step toward the truth? Contrast a theory I might
impute to Miriam, wherein she sees herself partially as a coughing robot
who can be commanded to stop (by another agent’s insistent
will), with an alternative conception — that of a small creature wakened
in the dark of her bedroom at midnight by coughings which fall her way
through ill luck, whom nothing can help. The wrong, mechanical theory
may be the lesser evil.


Vn126.1 Turtle on the Bed 3/14/78

This Saturday morning I sat in the reading alcove working away, and
Miriam came to join me. Robby was downstairs and Gretchen out of the
house. Miriam offered to sit in my lap, but I protested to being busy
and turned her down.

Miriam moped a little, then crawled on my bed and into the center.
She began to move and spin in a most puzzling and distracting fashion.
“What are you doing? You’re driving me batty!” My gripe inspired
Miriam to explain. Requesting a pen and a 3×5 card, she drew the picture
below of what she was doing in her “crawling on the bed game.”

Vn 126-1 Turtle on the Bed

Miriam’s verbal description was that she was “making one of those maze
things.” (Cf. Home Session 23, 2/14/780

I value this incident as an example of Miriam’s exporting into her
play world the kinds of knowledge and activities The Intimate Study
involved her with at Logo.