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LC1bT01

LC1bT01 Protocol 1

Included Text Pages(14)

RAL protocol 01.1

RAL protocol 01.2

RAL protocol 01.3

RAL protocol 01.4

RAL protocol 01.5

RAL protocol 01.6

RAL protocol 01.7

RAL protocol 1.8

RAL protocol 1.9

RAL protocol 1.10

RAL protocol 1.11

RAL protocol 1.12

RAL protocol 1.13

RAL protocol 1.14

Included Materials(8)

Addendum 1
RAL protocol 01-A1

Addendum 2, BGB, BigBuilding
RAL protocol 01-A2

Terminal Log Pages (6)
RAL protocol 01-A3

RAL protocol 01-A4

RAL protocol 01-A5

RAL protocol 01-A6

RAL protocol 01-A7

RAL protocol 01-A8

LC1bT02

LC1bT02 Protocol 2

Included Text Pages (2)

Discussion
RAL Discussion before Protocol 2

Protocol 2.1
RAL Protocol 2.1

Included Materials (3)

RAL 2-A1 Terminal Log

RAL 2-A2 Terminal Log with Notes

RAL 2-A3 Terminal Log

LC1bT03

LC1bT03 Protocol 3

Included Text Pages

RAL protocol 3.1

RAL protocol 3.2

RAL protocol 3.3

RAL protocol 3.4

Included Materials

RAL protocol 3-A1

RAL protocol 3-A2

LC1bT04

LC1bT04 Protocol 4

Included Text Pages (2)

RAL protocol 4.1

RAL protocol 4.2

Included Materials (3)

RAL protocol 4.1 Add1

RAL protocol 4.1 Add2

RAL protocol 4.1 Add3

LC1bT05

LC1bT05 Protocol 5

Drawing a Fox (cf. discussion in Development of Objectives)
n.b. hand-written date at top of first page in error by 2 years.

Included Text Pages

Included Materials

LC1bT08

LC1bT08 Protocol 8

Included Text Pages

RAL protocol 8.1

RAL protocol 8.2

RAL protocol 8.3

RAL protocol 8.4

Included Materials

RAL protocol 8-A1

RAL protocol 8-A2

RAL protocol 8-A3

LC1bT09

LC1bT09 Protocol 9

Included Text Pages (2)

RAL protocol 9.1

RAL protocol 9.2

Included Materials
(5)

RAL protocol 9-A1

RAL protocol 9-A2

RAL protocol 9-A3

RAL protocol 9-A4

RAL protocol 9-A5

LC1bT10

LC1bT10 Protocol 10

Included Text Pages

RAL protocol 10

Included Materials

None

LC1bT11

LC1bT11 Protocol 11

Included Text Pages (2)

RAL protocoll 11.1

RAL protocoll 11.2

Included Materials

None

LC1bT12

LC1bT12 Protocol 12

Included Text Pages

RAL protocol 12.1

RAL protocol 12.2

RAL protocol 12.3

RAL protocol 12.4

RAL protocol 12.5

Included Materials

None

LC1bT13

LC1bT13 Protocol 13

Included Text Pages (7)

RAL protocol 13.1

RAL protocol 13.2

RAL protocol 13.3

RAL protocol 13.4

RAL protocol 13.5

RAL protocol 13.6

RAL protocol 13.7

Included Materials (6)

Figure 1
RAL protocol 13 Figure 1

Addendum 1
RAL protocol 13-A1

Addendum 2
RAL protocol 13-A2

Addendum 3
RAL protocol 13-A3

Addendum 4
RAL protocol 13-A4

Addendum 5
RAL protocol 13-A5

LC1bT19

LC1bT19 Protocol 19

Included Text Pages (7)

RAL protocol 19.1

RAL protocol 19.2

RAL protocol 19.3

RAL protocol 19.4
RAL protocol 19.5

RAL protocol 19.6

RAL protocol 19.7

Included Materials (2)

Addendum 19-A1
RAL protocol 19-A1

Addendum 19-A2
RAL protocol 19-A2

LC1bT20

LC1bT20 Protocol 20

Included Text Pages

RAL protocol 20

Included Materials

None

Vn00201

Vn002.01

Productive Cheating

5/9/77

Today was a difficult day. Snow in mid-May for a beginning. Before that problem appeared, Miriam came early with me in to Logo in our joint expectation of going to the Coop to buy a hula hoop. With that option closed by inclement weather, Miriam pushed me early in the afternoon to proceed with the day’s experiment. We proceeded as described in Logo Session 4.

Gretchen and Robby reached the lab later and Robby chose not to engage himself in my work with Miriam, preferring to play with SHOOT by himself in the central portion of the Children’s Learning Lab. Sam Lewis, another child frequently at Logo and a year older than Robby, played with him in the lab at that time. When Miriam declared a break from our work in writing a story, I discussed (with Gretchen) the children’s use of SHOOT and how I was awaiting their discovery of how to cheat. Instead of using the SHOOT : DISTANCE program to project the turtle into the target (which evaluates his location after movement and immediately judges the movement a ‘hit’ or a ‘miss’), one may locate the turtle within the target with a series of forward and turning commands; then, guaranteed of a bull’s-eye, execute SHOOT 0 to register one’s score. Such was my explanation. I noted that the most efficient cheat would be to execute a ‘HOME’ command (which puts the turtle in the target with a single command), then SHOOT 0.

Because of the snow and Miriam’s disinclination to proceed with writing a second story, I suggested Gretchen take the children home while I proceeded with some work they could not be involved in. Robby was most eager to stay and play with SHOOT. After a slow start in the first 3 Logo sessions, Robby was developing skill quickly. He had already, as he noted, scored 5 points that afternoon, and wanted to go on while doing well. I reluctantly agreed. I agreed because I believe the children should be allowed to follow active interests. My agreements was reluctant because I did not want Robby to make further significant advances without my observation. This is precisely what happened. As we discussed the day at supper, Robby noted that he had a good afternoon. His second use of SHOOT garnered him 9 points, giving him a total of 16 (? ). . . this may include in his calculation points from the 3 earlier sessions). Robby then added he had figured out how to score every time. “How?” Robby explained that after drawing the target, the turtle goes ‘Home’ before going somewhere [a setting of his heading and location to random values] and that if one were to key ‘H’ or ‘Home’, then SHOOT 0, he would score every time. To be certain Robby was saying what I thought I posed these questions.

Bob Suppose you key ‘H’, carriage return?
Robby The turtle goes to the center of the target.
Bob Like this?
Robby Yes. Then you say SHOOT 0. illustration:
Bob And what does the turtle say? target and turtle
Robby Ouch. Your score is 1.

I asked Robby if Sam had showed him that and received a negative answer and the claim that he had figured it out himself. I recall informing Robby, before his second terminal session of the day, that because of his squabble with Miriam in Logo Session 3, I changed the SHOOT program so that if the turtle were within the target after execution of GO-SOMEWHERE, he would be made to GO-SOMEWHERE-ELSE, i.e. land at a different location.

Miriam then confided to Robby in her most conspiratorial stage whisper: “Robby, you shouldn’t have told me; I’m going to do that every time.”

I pursued this question, asking Robby whether he had used this new idea to score all his points during the afternoon. Robby denied it, saying the trick didn’t work. I was surprised (it should work perfectly) and asked why not. Robby said the computer would respond ‘You didn’t tell me how to H or Home.’ I asked if he knew it wouldn’t work and how. The answer was that he hadn’t tried it, thus he couldn’t say why he knew it didn’t work.

Interpreting this incident depends on how open Robby is with me, generally, and on the extent to which his final comments were an attempt to delude Miriam by convincing her that his discovery isn’t worth attempting. Robby is usually quite open with me. Nonetheless, given the intellectual rivalry between the children, I would not be surprised at Robby’s attempting to throw Miriam off the track of a discovery he made which his revealing to her had made useless to him. An alternative explanation for Robby’s not trying the “Home SHOOT 0” cheat (and perhaps the impetus for it’s coming to his mind) is my explaining that I had modified SHOOT to forbid those lucky landings of the turtle within the target. He may have believed any time the turtle were found in the the circle at the beginning of executing the SHOOT procedure he would GO-SOMEWHERE-ELSE before being shot at the target. [Indeed, such is possible and is the way one would prohibit the ‘forward and turn commands/SHOOT 0’ cheat if one were so inclined.]

This incident promises further interest in that part of my intention is to guide Miriam’s concerns from getting a correct answer to attending to the process and operations by which one can achieve an answer. Her obvious engagement with the desire to succeed immediately will lead her to pursue Robby’s discovery. I expect and intend to have her succeed thus. My following countermove (which will be to relocate the target off center screen) may show how too simple “an answer” is inadequate and must give way to deeper comprehension of process by which “an answer” is developed. When, later, both children realize they can still succeed by deferring execution of SHOOT until the turtle has been relocated within the target circle through forward and turn commands, they will have extracted all the value they can get from the use of this introductory game.

Vn00401

Vn004.01

The Clever Hack (2)

5/12/77

At dinner this evening we talked over some of the incidents of the day. It had been one of novelty for Robby. His friend John (the son of a former naval officer with whom Robby shares an interest in naval battles and model building) came to Logo with Robby as a stopping point on a visit to the Hart Nautical Museum (a museum of models) in MIT building 5. Miriam stayed at Logo with me (the events are recorded in Logo session 7) while Gretchen took the boys to the museum. By the time the boys had returned, Miriam and I had finished our work for the day. While we played otherwheres with a hula hoop and some tennis balls, Gretchen and the boys went into the music room where Robby introduced John to SHOOT. When Miriam heard of this at dinner, she said, “I should have shown John the clever hack.”

The immediate surfacing of this suggestion to Miriam’s mind made me curious about what role, if any, it had played in Robby’s introducing John to SHOOT. These selections, from the transcription made by the chance of the tape recorder’s having been left running, are extracted from Logo session 7.

GretchenWhy don’t you play SHOOT?
Robby That’s a good idea. (To John) Let’s play SHOOT.
John What is this SHOOT?
Robby [Robby logs into Logo, reads the file “SHOOT from secondary storage] You’ll want to see SETUP. Are you looking at the screen?
John Yeah.
Robby [executes the procedure SETUP. The procedure clears the terminal display, then puts a message on the logging portion of the display and creates a ‘screen’ (a movement domain for the turtle); the procedure increases the screen size in steps until it reaches the standard size, thereby pretending to simulate the distant first appearance of something coming into view. While the screen size increases, messaged are printed on the logging portion of the display. Robby reads them.]
Robby Look in the sky!
It’s a bird — it’s a plane.
No, it’s super turtle.
(The SETUP procedure then draws a bull’s eye on the screen and sets the turtle at random location and heading.)
Gretchen I never saw that before. Why don’t you explain to John what you are doing? (When Robby fails to respond, Gretchen continues), The object. . . this is the turtle, and the line in the middle shows which way he is pointing. The object is to get the turtle pointing towards the target. And then say SHOOT-
Robby Something.
Gretchen A certain distance. . . and see if he stops, if that gets him to the target.
Robby [keying]
GretchenRobby has just made a turn of 90 degrees. You try to get it lined up. Now he has to figure out how far to tell it to go.
Robby Yes! (meaning his shot hit the target)
Gretchen Just made it. If it’s a hit, the turtle says ‘ouch’. [exits]
John(laughs) . . . Can I try?
RobbyNo. I want to show you something. [keying] H . . . (then realizing he has omitted the carriage return) Oh . . . Now SHOOT O. It worked! Isn’t that a great trick?
JohnYeah.
RobbyIt’s sort of easy.
JohnHow do you do it? Show me how to do it. I want a turn.
Robby(after shooting successfully at the target, but in no way describing what he did). Here, John. You do everything now.
John Well, you have to help me.
Robby O.K. Right or left?
John Right. I want to do right . . . What do I do?
Robby I want to go home.
John What button do I push? This one? To aim it at this?
Robby Oh, . . . just do Home, SHOOT O.
John No, I don’t want to.
Robby [keying in Home, carriage return, despite John’s preferences] Just say SHOOT O. He’s already at Home . . . I want to go to my house, do you?
John What would we do there, Robby?
Robby Play soccer . . . play in the tree fort.
John SHOOT O. Oh, come on. (shortly after this point, the tape ran out)

Out of three cycles of SHOOT (from setting the target through hitting it), the clever hack was used for two, the basic turtle commands being used for the first cycle. In the second cycle, Robby clearly paraded for John a solution to a problem John could not appreciate. The second use of the clever hack was to short-circut John’s interest in finding out “how to do it”; by appealing to John’s interest in achieving the objective, Robby attempted to circumvent the more time consuming process of showing how to play the game. The mark of the clever hack in both uses is its salience; whenever little time is given to the problem solving process, either through motives of setting a dramatic effect or simply to reach a quick solution, the clever hack comes into its own.

Vn00803

Vn008.03

Doing the Hula

5/12/77


Despite Miriam’s success with the foot centered hula twist, she was unable to keep the hoop from falling down. She holds the hoop with both hands in front and a part of it against her back. She throws it in one direction or the other, moving her trunk in no clear way (it’s very hard to see any pattern because the hoop falls so quickly).

Over the following days, several people showed their skill in the Logo foyer. (Playing with the hoop was a favorite pastime on Miriam’s breaks from our sessions). Sherry Turkle claimed having once been champion of Brooklyn and gave a demonstration. So did Donna and many of those who wandered through. Miriam improved rapidly. Her later description of how to keep the hoop from falling: “It’s easy. Just keep pushing your belly in and out,” I believe puts at the surface what she saw as significant in her observations of others’ practice.

Vn00804

Vn008.04

The Bicycle Analogy

5/12/77


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.”

Vn00805

Vn008.05

Ping Pong Balls

5/19/77


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.

Relevance

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.

Vn00901

Vn009.01

Tic Tac Toe (2)

5/22/77


Miriam asked Robby to play with her this afternoon, offering “Sorry,” “Raggedy Ann” and “Chinese Checkers.” All were refused. Robby finally agreed to playing TIC TAC TOE. I asked the children to come sit in the reading alcove. They did so while I got out my tape recorder.

Two games were played before I could get a cassette in the recorder. In game 1, Robby went first [let the letters be his moves, the numbers for Miriam], and quickly won with his computer beating gambit:

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

Miriam should go first after being defeated, but she asked Robby to go first. He told her she must go first. I asked why she did not want to go first. Miriam: “I’m afraid he will take the place I want to go. I won’t get two ways to win.” This game was played when Miriam went first:

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

Robby again having the initiative. This game was played and the following dialogue was offered in explanation when I asked an unhappy Miriam how she lost:

 B |   | 2
----------
   | C |
----------
 1 |   | A

Miriam I put my X over there (move 2)
Robby She thought she could stop me from getting two ways to win, but I did that (move C in center square) because I already had one way to win.
Miriam ‘Cause I even saw that.
Bob Oh. You were trying to stop him from getting two ways to win.
Robby Yeah. But I did something else. O.K. Your turn to go first.
Miriam Are you going to block me? (i.e. put a counter in the diagonally opposite corner)
Robby No.
Miriam (puts an X in one corner)
Robby (puts his the the diagonal corner)
Miriam (shifting her piece to the common row corner)
Robby You took your hand off it! (outrage)
Miriam Liar, liar, your pants are on fire, your nose is as big as a telephone wire.
Robby Quiet! (Robby moves to the other diagonal corner)
Bob Miriam, please cut that out. What is all this switching and changing?
Robby You can’t do that.
Miriam He promised he wouldn’t go there.
Robby I didn’t promise.
Miriam You did!
Bob I think if you can’t play nicely together, you shouldn’t play together, you shouldn’t play together.
Miriam (moves her piece again)
Robby Miriam! (a shriek)
Bob Robby, leave the room. Miriam, put the toys away.

Relevamce

I believe this vignette confirms the data of number 5 (while Miriam is with another player) by showing the same concreteness and vulnerability to conflicting objectives. What is most striking is that while Miriam tries to negotiate a victory using an effective but vulnerable gambit, she utterly fails to adopt Robby’s counter-measure for her own defense against the same attack.

The conclusion of this squabble is that when Miriam wants to play TIC TAC TOE she will play with me instead of Robby.

Vn01101

Vn011.01

Taking Hints

5/22/77


One of Miriam’s proudest achievements since her 6th birthday had been learning to successfully ride her bike without training wheels. Because it had been her custom to make a considerable fuss on the occasion of a small scrape (from tripping over the dog, for example), I was disinclined to help Miriam. She borrowed Robby’s crescent wrench and removed the wheels herself. For several days thereafter her procedure was as follows: Sit on the seat and push off; try to get both feet on the pedals before the bike falls over; at the first indication of instability, turn the wheel in the direction of fall and stick both feet out to catch oneself.

The procedure is not bad; it’s nearly perfect in fact. The only flaw was that the bike would fall over after going about 3 feet. Luckily for Miriam, at this point she received some good advice from our neighbor Jim: “If you start off fast you won’t fall over.” When Miriam recounted that advice to me, I reinforced its authority, noting that Jim’s advice was absolutely correct and that for problems that look hard or mysterious, if you get one good hint you find they are not hard at all. Miriam conjoined Jim’s advice and a lot of practice. The advice provided the breakthrough she needed and with practice, she has refined her skills so that she now rides ably.

This evening when she encountered Jim in the courtyard, Miriam exhibited her skill with the hula hoop at both waist and foot. (confer Vignette 10) After being praised for her considerable skill, Miriam went on to tell Jim he should see her ride her bike, she was really good, and his “one good hint” had taught her how to do it.

Relevance

I consider these observations important because they reveal a central incident in Miriam’s developing view of learning. Two roles are defined: that of a person who is having trouble doing something he wants to do; and that of an advisor who gives advice with these qualities — the advice is directly applicable to the problem; the advice is abstract and non-directive, therefore leaving the person latitude to develop a personally satisfying particular solution to the problem to be solved. In general terms, the two outstanding features of this view are: the desire and execution are her responsibility and privilege; ideas (hints, good tricks) are effective and thus worth knowing. If Miriam can maintain this view, which I infer from her comment to Jim, the terms in which we talk, and from her behavior, her education promises to be a profoundly satisfying experience.

Vn03401

Vn034.01 Candle Fire Crackers 6/23/77

We usually dine by candlelight. We enjoy making candles and
using them, and the ill distribution of light in our dining area makes
this practice a useful enjoyment. Having agreed that he will not play
with fire, Robby has the responsible job of candle man: he brings the
candles to the table, lights them, and when the penny candles in old
bottles burn down, he replaces them. Having made a 1 stick candelabrum
in school (a ring of cardboard with pasted-on, brightly painted maca-
roni shells), Miriam after giving it to the family as a present reserves
its use to herself and the responsibilities pertaining thereto (lighting
it and blowing it out).

For some reason during the dinner Robby blew out a candle (per-
haps to replace one burned dowm). Miriam took this as her cue to blow
out hers. To minimize the air pollution Gretchen wet her fingers and
doused the smoke producing embers in the wick. Shortly thereafter, when
she attempted to re-light her candle, Miriam heard the sputtering
crackle made by the flame on the wet wick. “That sounds like a fire
cracker!” Questions immediately arose: what makes the candle sputter?
why doesn’t it light? It does now? Oh. Why didn’t it light before?
Because Mommy spit on it, the water. Miriam, Seymour, and I had just
been discussing the Piagetian experiments done earlier in the project.
I allowed that I thought Miriam most enjoyed the conservation of con-
tinuous quantity experiment because of the water play in pouring the
liquids from one container to another. (Miriam corrected my misappre-
hension: she most enjoyed the experiment of constructing tracks [cf.
Miriam at 6]). Thus it was a natural continuation that we indulge in
a little water play, even at supper. Seymour asked Miriam if she
thought she could make it happen again. I got her a small glass with
water in it. Miriam took her candle and inverted it inside the glass
slightly above the water. It went out. When she brought it to the
flame, the candle lit immediately without sputtering.

Miriam Hey! Why didn’t it work?
Seymour Did it go in the water?
Miriam It went out.
Seymour Try it again, just to be sure the end goes in the water.

Miriam dunked her candle in the water and upon the attempt to relight
it sputtered and crackled before catching fire. Miriam tried the
dunking again and it still worked. She remained curious as to why
the candle went out at first. Robby suggested that with the candle
inverted, the flame wanted to go up, but had no place to go, so it
went out. I suggested we make sure it wasn’t the water by holding the
candle about 2″ above the surface. Miriam did so, watching carefully.
“It’s the wax that does it!” Seymour asked, “Does it need to be in the
glass at all?” Miriam proved that it did not by inverting her re-lit
candle over a napkin.

Relevance
This vignette highlights the role of engaging phenomena, e.g.
the surprising crackling sound from a candle, and the supportive
milieu in leading a child into those discoveries that constitute his
knowledge. The rich environment is less one rich in objects than it
is one rich in surprise, in the stepwise exploration of which the
child confronts alternative plausible explanations of those phenomena.
Obviously, since this surprise derives from the child’s ignorance,
what engages one child need not engage another.

Vn04001

Vn40.1 Logo After Hours 7/4/77

During the bicentennial year Miriam was too young to enjoy the
fireworks. She was frightened by the noise of amateurs’ exploding
firecrackers and so sleepy by 9 o’clock that we abandoned a half-
hearted attempt to watch the display from the vantage of Corey Hill
in Brookline. Radio forecasts promised this year a smaller crowd
and a more impressive exhibition than last year. Uncertain that we
would be near Boston in the future, I decided the children should
seize this opportunity to see the biggest fireworks display on the
east coast.

Having heard of how impossible is parking near the Charles, I
brought my family to Logo early in the evening. We all casually enter-
tained ourselves while waiting for nightfall. Gretchen and Robby occu-
pied themselves with reading, Miriam with drawing (Robby did that too)
and making letters. I reviewed material in various workspaces on the
Logo system, to refresh my memory with possibilities for future work
with the childlren. I showed Robby (but not Miriam) Danny Hillis’
“STRING” design procedure and an elaboration I had made thereon for
developing Lissajous figures. He was impressed, but drawn away by
witnessing the Cambridge police respond to an apparent mugging on the
corner of Main and Vassar. Miriam wanted to use the Slot Machine but
it did not work (as we had discovered earlier in the day: cf. Logo
Session 34A). We all watched the traffic build to an impenetrable
mass as dark approached.

We walked to Memorial Drive near the foot of Longfellow Bridge and
beheld that crowd of evening picnickers who had come prepared with
incredible paraphernalia and seized all the choice locations early on.
The air was acrid and pulsating from the frequent but irregular ex-
plosions by amateur incendiaries. The children’s chronic impatience
was only relieved by the distraction of fudge popsicles and the dis-
tressingly late beginning of the fireworks. Very few seemed to care
that hearing the 1812 Overture was impossible until the cannon fire
declared the beginning of the long-awaited fireworks. The display was
worth the waiting. Even though they were quite tired, both children
were excited and delighted.

At the end of the show, we repaired to Logo to await there the
subsidence of the traffic. We were all glad to find the lab occupied
by friends. Miriam perched herself on Margaret Minsky’s lap and
announced that we’re going to have a baby. Upon hearing that Danny
Hillis was back from Texas on a visit, we all trooped up to Marvin’s
office and interjected ourselves into their conversation. Miriam seized
Danny’s lap as her own property, and I shanghaied him to repair the
Slot Machine so that the two-terminal experiment could be executed the
next day (this was essential because of rearranging the lab for the
summer high school program). After Danny did a little magic to make
the Slot Machine work, we sat talking til midnight with Margaret, Bruce
Edwards, and Ellen Hildreth.

Relevance
These notes record the casual use of Logo as a place to pass the
time and meet friends.

Vn04201

Vn42.1 7/6/77

Because the High School Studies Program begins next week and the
lab will be filled with teenagers all day every day, we moved into my
office the equipment not to be used by the high school students: the
slot machine, the floor turtle, and the music box.
Since moving things around brings change and sometimes adventure,
I asked the children to come to Logo though no computer sessions was
planned. In a day full of disorganization, pushing, pulling, and helping
out, the greatest excitement for the children was in re-routing
data lines from the terminals to the computer. This involved lifting
up floor panels. The floor panel lifter goes in place with a loud
bang as it’s slammed down. The panels are heavy — a challenge Robby
can barely meet and Miriam feigns attempting. They greeted the under-
floor space, a dark maze of tangled wires, as a new, mysterious world
and began prospecting in the openings for souvenirs. As Hal Abelson
and I traced wires, the children invented impromptu games — being
stranded on islands or trapped by moats with escape possible only by
the fine balance that permitted them to walk on the floor panel holding
frame.

Margaret Minsky agreed to move to make room for the equipment in
our office. The children decided this was now their office, which
required getting nameplates for the door. They further dubbed the room
‘The Little Learning Lab’ since they were little (to distinguish it
from the Children’s Learning Lab which the high schoolers would be
taking over). Pope’s couplet

A little learning is a dang’rous thing:
Drink deep or taste not the Pierian spring.

and the obvious joke that this was a lab where little learning takes
place caused me pause but no inhibition so severe as to halt their
momentum.

Each child was allotted one of my 3 bookshelves, which they
provisioned as best they could. We walked to the Coop to buy each child
a large notebook for keeping the pictures they made with the Logo
printer. As we three trekked across the campus, the children fell
into ‘Follow the Leader’ and an immediate argument over who should be
leader. My turn-taking suggestion (one to the Coop, the other on the
way back) was no solution: it left the problem of who should be leader
first. Robby went first despite objections. Miriam undercut him by
giving Robby turtle commands to follow the obvious path whenever that
path was clear. To the Coop and back this game gradually was elaborated
as Robby raised syntactic quibbles to avoid doing what Miriam
commanded. For example, “You haven’t told me how to forward 30” (by
which he indicated that Miriam had not verbally specified that a space
separated the word ‘forward’ from the word ’30’). The most puzzling
impediment Robby introduced occurred while we were returning, skirting
the side of building 26. Miriam tried to make Robby walk into the wall
by commanding left 90 (to be followed by a forward). He stopped and
said nothing. After several commands and repetitions, Robby burst out
laughing. “You haven’t done a carriage return!” Miriam said, “New
line!” and Robby obliged her by walking into the wall.

Relevance
This vignette recounts the excitement of a moving day at Logo and
an example of how Playing Turtle arose as a game outside the lab.

Post script

This game of ‘Follow the Turtle’ has become a common game the
children engage in whenever we three walk together where there is no
crowd.

Vn04301

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.

Relevance
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.

Vn04401

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.

Relevance
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

Vn04601

Vn46.1 Rotten Hints 7/19/77

Two years ago, Miriam took swimming lessons. She was in the class
of ‘Blueberries.’ Their course of instruction amounted to splashing at
the edge of the lake. Their most advanced achievement was to say their
names with faces held in the water. Last year, in our move from
Connecticut to Massachusetts, Miriam and Robby missed out on swimming
lessons. With both children wanting to learn to swim, it seemed good
fortune that the summer swimming lessons at our lake were offered
during our 2 week vacation.

Robby, declaring the swimming lessons would interfere with his
visiting Raymond, decided not to enroll. Even though I was not willing
to spend much time at it, he figured I could teach him to swim. Miriam
was anxious to take the lessons. At registration, she was judged by
the teacher to be ready for ‘Kiddy 2,’ the class preceding beginners.
She seemed pleased enough.

Tuesday morning her class began with ‘Ring around the rosy.’ The
group of 8 joined hands, bounced around in waist-deep water, and on the
chant’s conclusion ‘we all fall down’ the children were supposed to sit
in the water, getting their heads completely wet while holding hands.
The next element of the lesson was the ‘dead man’s float’: one takes a
deep breath and floats face down in the water. Miriam refused. At the
end of the session they had another round of ‘Ring around the rosy.’
Miriam did not sit down as expected of her. One of the instructor’s
assistants approached me after the class and suggested that “we” might
try getting “our” face wet in the wash basin between swimming classes.

Miriam doesn’t like getting her face wet. Neither do I. My
version of the crawl (which I rarely employ) keeps my face out of the
water, as do the other strokes I prefer. Despite the ultimate limit
this may place on my speed or furthest reach, as a youth I achieved
swimming and lifesaving merit badges in the Scouts. I see no reason
why ‘face wetting’ should dominate early swimming instruction. This
strikes as even more forcefully true for a child whose allergies render
breathing difficult.

As we left the beach, I asked Miriam how she enjoyed her swimming
lesson. Her response was very direct. “That was terrible. She wants
you to get your face wet all the time. I’ll never learn to swim from
her. She can’t give me any good hints. All she knows is get your face
wet. What rotten hints.” I agreed she should not continue instruction
unless she wanted to. Miriam asked to go to the beach on the third day,
but once there refused to join the swimming class.

Relevance
This vignette describes an instruction situation which Miriam
judged to be especially bad. Her formulation of the badness was that
the teacher could only give ‘rotten hints’ for learning.

Vn05101

Vn51.1 Paper Ships 7/25/77

This has been a rainy, midsummer day with both children at home in
an acoustically live house. Having slept ill last night, under pressure
of the noise and our common confinement, I went to bed early. When the
children failed to fall silent instantly, I “yelled” at them, i.e. I
told them quite specifically that I had suffered too much of their noise
and commotion, that I needed sleep and they must be quiet.

Because of the rainy day bedlam, I had failed during most of the
day to make headway in my thinking about Miriam’s computations and my
understanding thereof. As I drifted into sleep, some imperfectly
remembered lyric from my early school days entered my mind:

. . . put down 6 and carry two —
Oh oh oh. Oh oh oh.
Gee, but this is hard to do
Oh oh oh. Oh oh oh. . . .

No greater fragment remains of that song, but I imagined that situation
and the woman conducting that song, and then another:

Some folks like to cry,
Some folks do, some folks do.
Some folks like to sigh,
But that’s not me nor you.
Long live the merry, merry heart
That laughs by night or day.
I’m the queen of mirth —
No matter what some folks say.

This ditty carried me along to a better feeling, one wherein I was
capable of feeling ashamed of my ill behavior to the children and happy
that our relationship was one where I could apologize to them and they
be capable of accepting that apology.

I called Robby. He entered my bedroom quietly and was obviously
relieved when I told him I was feeling better and was sorry I had been
so crabby. He asked if I would help him with a problem. When I agreed,
Miriam entered and pounced on me. (This was easy since my ‘bed’ was a
sleeping bag on the floor.) Robby returned with the book Curious George
Rides a Bike
. Both children had been attempting to make paper boats
following the instructions on pp. 17-18 (Cf. Addendum 51 – 1, 2). Robby
was stalled at step 5 and Miriam at step 3 of this 10-step procedure.

Both children were working with small (tablet size) pieces of paper.
I was sleepy and unfamiliar with the procedure, so instead of looking
at their problems, I first made a boat myself. A nearby newspaper pro-
vided paper of size large enough to escape folding-small-pieces-of-paper
bugs. When I reached step 3, Miriam noted that as the locus of her
impediment. When I asked, “Oh, you’ve got a bug there, sweety?” she
responded, “Yes. An I-don’t-know-what-to-do-next bug.” I slipped my
thumbs inside the paper and pulling at the side centers, brought the
ends together. Miriam said, “Oh, I get it now,” and continued with her
folding. (She had not been able to identify that transformation, failing
most likely to interpret the arrows and -ING STAR, that portion of the
newspaper masthead still visible after the folding as a clue.)

When Miriam some time later attempted step 7 (bringing the ends together
a second time), her construct disassembled. After I suggested she
hadn’t tucked in the corners carefully, Miriam described it as a ‘no-
tuck-in bug.’

In the transformation from step 9 to 10, because the central crease
must suffer a perpendicular crease in the opposite sense, one usually
has trouble pulling down the ends without the assembly’s failing. When
both children had made several boats, I asked Miriam what bugs she had
uncovered. She cited the original two and a third, the ‘last-pull-apart
bug.’

The construction expanded. The newspaper pieces made battleships
(and stopping half-way, hats). Miriam made life boats and Robby, by
unfolding a newsprint page before beginning the folding procedure, made
a large, flimsy craft he dubbed an aircraft carrier. It was a small
step to carrier war in the Pacific (my bed as Pearl Harbor) and the
pillow fight which ended this war.

Relevance
These observations show Miriam using the word ‘bug’ to describe
the difficulties she encounters in executing a complex procedure, both
with some direction and more nearly spontaneously.

Addendum 51-1

Vn 51-1 Curious George paper folding

Addendum 51-2

Vn 51-2 Curious George Paper Ship procedure

Vn05601

Vn56.1 TicTacToe 7/19/77

These games of tic-tac-toe followed immediately the arithmetic of Home Session 13. The focus of the session is on the bipolar (i. e. competitive) quality of tic-tac-toe. This focus is maintained by contrasting the game with playing SHOOT around the issue of clever tactics. (My moves are numbers; Miriam’s are letters.)
Game 1: Miriam first

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

After Miriam’s move C:

B Do you know any clever tactics for tic-tac-toe? . . . Do you think it’s easier to win at SHOOT or tic-tac-toe?
M [points to tic-tac-toe frame]
B It’s easy to win at tic-tac-toe?
B Do you notice anything special about the way your markers are?
M Two ways to win.
B Did you just see that after I told you?
M No.
B You knew it all along?
M I had a forced move, and I wanted to move there.
B They came together, your wanting and the forced move?
M Miriam Yeah.

Game 2: Bob first

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

When Miriam responds to a center opening with a mid-row move (as I had done in game 1), I introduce the theme of turning the tables on your opponent.

B I know what I’ll do. I’ll play the game you played. I’ll use your own clever trick to beat you.
M Yeah? [I don’t believe you can]
B Just like that [move 2], ’cause you have a forced move now.
M [moves B]
B I’m going to use your clever trick to beat you.
M [moves C]
B I’ll win anyway. I turned the tables on you.
M I know.

Game 3: Miriam first

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

The game was to provide contrast with normal competitive play by my taking Miriam’s direction about where to move. It harks back to her earlier proclivity for negotiation in the game (cf. vignette 5) and induces a resurgence of that style. We act out the fairy tale motif of the child (Miriam) defeating the ogre (me) by making a promise, then escaping from it by a quibble (not, in fact, necessary in the move configuration).

B Where should I go?
M Not there [center square]. Don’t. Don’t.
B You tell me where to go. I’ll go where you tell me.
M Here [upper left corner].
B Over here in the corner?
M No. No. There.
B [moves 1]
M B [moves].
B Now I have a forced move [center square].
M I don’t want you to go there.
B I’m going to go in the center.
M No no. No no. I’m not going to move there. I promise. A million dollars.
B Where should I move?
M There.
B You want me to go up here? [moves 2]
M [moves C] Two ways to win [laughing].
B Yeah. But what about this? [center square] You could have won right away by going there.
M Yes. But I promised you I wouldn’t a million dollars.
B Oh boy.
M That’s why.
B It looks like you’ve got 3 ways to win, but if you go that way [center square], you lose a million dollars, so I’ll put my 3 down here.
M [moves D] I mean just for that once [laughing].
B Oh, you stinker! . . . Do you think it’s easier to win if I do what you tell me?
M Yeah.
B What is it about my moving where I want that makes it harder for you to win?
M [no response]

Game 4: Bob first

	    |     |  A
        ---------------
	 3  |  2  |  C
        ---------------
	 1  |     |  B 

After Miriam moves A:

B You have frustrated my tactic.

M [laughs]

B I had a plan all set up, but you frustrated it.

M I always like to frustrate your plans.

B You do! Well. . . that’s what tic-tac-toe is all about. Stop the other guy from winning. . . . I’ll go here [moves 2 in center square].

M [moves B]

B You frustrated my — I was planning on going there. I was going to get two ways to win. Oh well, I’ll go over on this side [moves 3]. I’ve got you now. 2 ways to win.

M No. You made a mistake [laughing]. [moves C]

B Oh no. . . . It looks as though I didn’t have a good plan for getting 2 ways to win. I had one way to lose.

Game 5: Miriam first

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

The previous game exemplified losing by focusing on a winning tactic instead of attending to the opponent’s moves. Here, we try to exemplify how knowing a clever trick in an opponent’s repertoire permits frustrating it. After Miriam’s opening, she requests that I not move in the lower left corner.

B I’ll put a 1 right here in the center.

M [moves B]

B What’s going on here? . . . I remember now, you have a clever tactic in mind. ‘Cause if I go there [the other currently unoccupied corner], then you will have 2 ways to win, and I’ll have a way to lose.

M Yeah.

B I will frustrate your tactic.

M How?

B I will put my 2 here.

M Oh. [disappointed, she makes forced move C]

Game 6: Bob first

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

B I’m kind of tired of going in the center, so I’ll go someplace I hardly ever go.

M [moves A]

B There’s only one problem with your going in the center.

M What?

B It’s kind of hard for me to get 2 ways to win. I can go over here [move 2].

M [moves B]

B You’ve just blocked me by doing a forced move. Hmmm. Now I have a forced move too [move 3].

M [moves C; makes noises of discontent when I gesture to the square where D is later]

B You tell me where to move.

M Here.

B Shouldn’t I make a forced move?

M Unh-uh.

B How come? You want me to lose by making a stupid move?

M Yeah.

B O. K. [moves 4]

M [moves D]

B You won, ’cause I did what you told me.

Relevance
This vignette focuses on the contrast between SHOOT and tic-tac-toe as a 2 person game. “Turning the tables” is articulated as a clever trick. Frustrating tactics is exemplified 2 ways.

Vn05801

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.

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

Vn06001

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.

Relevance
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.

Vn06101

Vn61.1 Tic Tac Toe (5) 8/10/77

This material shows Miriam accepting instruction at corner opening play through a process of “turning the tables” on me after my exemplary victory. (The data were transcribed as Home Session 15.) A corner opening in tic-tac-toe is the strategy of choice, since its use nearly guarantees victory for the player moving first. Nonetheless, because it is possible to lose through failing to recognize opportunities or through one tie-forcing response by the second player, the power of the corner opening is not excessively obvious.

At the beginning of our play I introduced to Miriam as an extension of “ways to win” the notion of “chances to win.” You have a “chance to win” when you have only a single marker in a particular line and there is no blocking marker. The first game, wherein Miriam moved first, was a tie of the center-opening/corner-response sort. It was during the execution of this game that the “chances to win” terminology was introduced. At the beginning of game 2, I proposed teaching Miriam a good trick. Since the gambit begins with a corner opening, Miriam believed and asserted that she already knew it. She is aware of at least three corner-opening games:

A.      1 |  C  |  3         1 |  B  | 2         1 |  3  | C    

B.        |  A  | 4            |  3  | D         D |  A  | 5   

C.      B |     |  2         C |  4  | A         4 |  B  | 2 

The A game represents Miriam’s good trick, and B and C represent ways of blocking A which she can’t circumvent. In the games that follow where my move is first, Miriam attempted 3 different responses to my corner opening. In the other games, she “turns the tables” on me by using my play as a model to defeat me in turn.

Game 2: Bob moves first (numbers)

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

Miriam makes move A at my direction and after my move 3, recognizes not only that I have 2 ways to win but also that A has no chances and B 2 chances to win.

Game 3: Miriam moves first (letters)

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

Miriam here follows my advice to “turn the tables” on me by employing the same good trick (move 2 after response A to opening 1). During her role switch in applying this strategy, Miriam also switched from using X symbols as markers (which she had done in game 2) to literally copying the numbers I had used in that game (cf. games 2 and 3 in Addendum 61 – 1).

Game 4: Miriam moves first (letters)

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

Miriam moves first (out of turn) at my request to confront the challenge of turning the tables despite my choosing the corner response opposite to that of game 3. I asked her opinion:

Bob Is moving here [upper right corner] the same or different from moving there [lower left corner]?
Miriam Different.
Bob Can you play the same game even though I’ve moved in the opposite corner.
Miriam I think I can.

As we continue, Miriam comments, “I’m playing the same trick on you.” Miriam again uses numbers for her markers but disguises the copying by using numbers (9, 6, 5, 10) different from those I had used in game 2. After commenting that move 2 was a forced move as is move C, I emphasize that what is most important to see is that the single move C converts 2 chances to win into 2 ways to win.

Game 5: Bob moves first (numbers)

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

I warn Miriam after move 1 that I will probably beat her. She believes she can frustrate my plan by making move A (notice in the typical and familiar game B the outcome was a tie).

Bob In game 5 I am probably going to beat you —
Miriam Yeah.
Bob If you move where I tell you the first time, and after that —
Miriam I might not move where you tell me [laughing, she moves A; I had wanted her to move to the middle of the right column].
Bob Do you think I can beat you after that move?
Miriam Yeah [Miriam has not seen this game before, to my knowledge].
Bob I can. I will show you how.

After Miriam made her forced move B, I described my deciding where to move in terms of where I had chances to win and looking for a move where 2 chances to win come together. This game is one where selecting a usually valuable move (the center square) is not the optimal strategy.

Bob I can’t win this way [the 1 – 2 line is blocked by B]. I have a chance to win this way [in the row from number 1]. Do I have another chance anywhere? . . . Yes, I have a chance from 2 up through the center. And I have a chance along the top. So if I put my number 3 where the two chances come together, what do I get?
Miriam Two ways to win?
Bob That’s right, sweety.

Game 6: Miriam moves first (letters)

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

Miriam turns the tables on me successfully. The symbols she used in the actual game show her slipping over into direct copying of my previous game.

Game 7: Bob moves first (numbers)

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

Although I wanted her to go first (for another variation on game 6), Miriam insisted that I go first because it was my turn. After Miriam’s response A to the corner opening I proceeded, describing my reasoning at each step.

Bob I put my 2 here. Now watch. You have a forced move, don’t you [between 1 and 2].
Miriam Uh-huh [moves B].
Bob What chances to win do I have? I have one from the 1 along the top. I have one from the 2 along the bottom.
Miriam Two.
Bob I have one from the 2 through the center. . . but. . . I also have a forced move in the center. Right? . . . So I have to go in the center. But when I go in the center, how many ways to win will I have?
Miriam One?
Bob Watch. I have a way to win from the 2 and a way to win from the 1.

At this point Miriam confided to me that she would try to get Robby to move where she had placed her A, then she would make another move and try this trick on him.

I attempted to review with Miriam all the possible responses to corner openings, but she was tired and inattentive, and the session ended.

Relevance
This vignette describes my introducing to Miriam the idea of “chances to win,” seeing the forking move as placing a marker where chances to win intersect. The method was that of her “turning the tables” on me, i. e. using a tactic I showed as effective against me.

Addendum 61-1

from Home Session 15

Vn 61-1 Addendum from Home Session 15

Vn06301

Vn63.1 Another Birthday Party 8/12/77

This was a party for Robby’s Boston friends, boys he has met while
at school here. With respect to planning, this party was pretty much a
rerun of the party in Guilford (cf. Vignette 53). The party favors were
the same: Hershey bars, bubble gum, and balloons. Match box racers were
still Robby’s ‘prizes’ of choice and the game to decide priority of
choosing the racers was again to be ‘Pin the tail on the donkey.’ A new
wrinkle was added by Robby’s attending the party last week of his friend
John. Then, the children played ‘Pin the ear on the Snoopy.’ The idea
was adopted here. The children waited impatiently while Robby opened
the presents. He was delighted to get several ship models and a game.
The boys were astounded that Miriam had made Robby 9 birthday cards.

Most of Robby’s friends were out of town on vacation. The three
boys who did attend were brought by their parents and picked up by them.
The suburban distances and the parents’ schedules provided a more rigid
time frame than that of the party in Guilford. One child had to leave
early; thus the cake eating ceremony was moved forward in time. This
circumstance helped fill the gap created by having no other games planned
for inside play on this sporadically rainy day. When Reese left early,
Robby showed the other 2 boys his collection of models, and they decided
to play outside even though the sky was overcast and the court yard
flooded. So the game of the day was kickball, with a huge puddle for
first base.

Miriam sulked inside. I believe she was jealous of the attention
Robby received (2 birthday parties is excessive!) and she was mad at me.
Her attempt to pin an ear on Snoopy was a dismal failure; the ear not
just missed Snoopy, but was pinned on the perpendicular wall. Since I
had been the spinner of children, the fault was mine. After Miriam’s
persistent complaints, this evening, Robby advised her that there was
a good trick she had not yet learned: when you play ‘pin the tail on the
donkey,’ you don’t start walking right after the spinning; you wait until
you’re no longer dizzy, then walk straight forward.

Relevance
These two vignettes on birthday parties indicate the balance of
plan/script driven behavior and a general coping with whatever comes up.
Miriam found herself very much on the periphery of this party as of the
other. Robby’s advice indicates that he and Miriam both find it possible
to communicate in the language of ‘good tricks’ for coping with trouble-
some situations.

Vn06401

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
again.

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.”

Relevance
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.

Vn06901

Vn69.1 Chatterbox 8/19/77

In Vignette 3, I noted one of my objectives was to render Miriam
more willing to reveal her thoughts than was formerly the case. Such
a change has gradually but very definitely taken place. Gretchen now
complains that Miriam is never quiet, that she talks about every least
action she undertakes; for example, “I’m taking my dishes over to the
sink.” A more typical example is what Miriam said just now. (She is
making a “card” for a friend; Gretchen and I are sitting in the same
room, 10′ and 20′ away.

Miriam

I am coloring the flower red. . . and blue. . . and now yellow. . . .
I am coloring the cloud white, Daddy, isn’t that a good idea?
Bob

Yes.
Miriam

Do you know why I am making the cloud cry?
Bob

No.
Miriam

Because the sun is very hot and it can’t rain.

This is a description of ongoing action, mixed with request for approval
and her explanation for the meaning of her drawing.

First ask is it a good thing for Miriam to be so open at this
point in her life? I believe it is good now and that she will eventually
learn when to bite her tongue. What is one to make of the very
pervasiveness of Miriam’s chatter? Is this a regression of sorts to
ego-centric speech? I choose to think of it differently, in a way
recently suggested to me by Laurie Miller. In this view, Miriam is
giving evidence that she has discovered self-description as an inter-
esting thing to do. . . and is overdoing it. (Recall G. B. Shaw’s asking,
in a paraphrase from the book of Proverbs, “How can you know what
enough is, unless you’ve had too much?”) Such self-description may
result from the reflection and explanation I have asked of her in the
Piagetian tasks of April’s experiments as well as from the rudimentary
debugging we have undertaken in our Logo sessions.

In the little snippet of dialogue above, Miriam was not using the
description of her actions for any purpose which is reflected back into
the action. However, to the extent that she articulates her actions,
it is clear that she can reflect upon them when that engages her interest.

Relevance
This vignette notices the change Miriam shows in the public
description of her actions. This indicates she has available descriptions of
her action upon which she can reflect if she finds such an activity
interesting.

Vn07001

Vn70.1 8/22/77

Over the past few weeks, Robby has shown an interest in playing
frisbee. Miriam has tried to play with us but has been so inept that
the game always became a squabble. Robby usually argued that since the
frisbee was his, he should choose the players for the game.

It was an obvious conclusion, then, that Miriam should have the
frisbee I received at the IJCAI registration. We three played in the
court yard in a 20′ triangle. Miriam was supposed to throw to Robby,
but even when she did her best she came nowhere near him:

Vn 70-1 Frisbee Bugs drawing

Robby tried to evict Miriam from the game for ineptitude, but could not
because the frisbee was hers. I asked if maybe we could fix the bug?
Miriam agreed. I described the bug as a ‘holding-on’ bug. We slowly
executed her throwing motion, and I noted the point in her swing (a
cross-body arm sweep with a wrist flick) at which she should let go of
the frisbee. On her second throw, and thereafter, Miriam was able to
aim the frisbee in Robby’s direction.

The second bug frequently manifest after fixing the ‘hold-on’ bug
was one Robby described as a ‘too-low’ bug. Miriam developed her own
fix.

Relevance
This incident shows Miriam’s application of debugging to her own
actions. This way of talking is endemic in the Logo culture. It is
clearly accessible to this child and productive in actions she values.

Vn07101

Vn71.1 Tic Tac Toe (7) 8/25/77

This material provides Miriam with an opportunity to exhibit what she retained of instruction in the previous tic-tac-toe session (cf. vignette 61, 8/10/77). Where Miriam fails to elect a winning strategy (game 3), I subsequently demonstrate how she should have played, then provide the opportunity for her to turn the tables on me. (These data were recorded in Home Session 17.)

Game 1: Miriam moves first (letters)

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

After my first move, I ask Miriam:

Bob

Can you beat me if I move here?
Miriam

I think so [moves B].
Bob

Oh ho. I’ve got a forced move. I bet you’ve got me already [moves 2]. Do you?
Miriam

[shaking head ‘yes’, smiles and moves C]
Bob

You do. You’ve got two ways to win already.
Miriam

[laughing] I did the forced move and two ways to win.
Bob

That’s absolutely perfect, Miriam. You got it.

Game 2: Bob moves first (numbers)

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

This dull game is of interest only in Miriam’s avoiding the middle of the row response to a center opening.

Games 3, 4, and 5 —

Game 3: Miriam first (letters) Game 4: Bob first (numbers)

	  
	 A | 4  | D 
	 1 |    | 4    
	 C | 2  | 1 

	 B | 3  | A    
	 3 | 5  | B	
         2 |    | C   

Upon my response (1) to Miriam’s corner opening, she had the opportunity to beat me directly and failed to do so. When she made her second move (B), I informed her of her oversight. She was angry and had to be cajoled to play game 4 with roles reversed. When she moved A in game 4, I review her move of game 3 (B) comparable to the one I then made (2).

Bob

You went down here, where the B is, next to the 1.
If you had gone over here, where my 2 is now —
Miriam

Yeah?
Bob

You could have beat me. You know why?
Miriam

Why?
Bob

‘Cause you’ve got a forced move between the 1 and 2.
Miriam

Oh [she move B].
Bob

Now, what chances to win do I have? From the 2 across
the bottom; from the 1 across the top; from the 1, down through the middle;
from the 2 up through the middle. And I have to go in the middle because
you have one way to win. Now look at this —
Miriam

I get it.
Bob

I take my forced move —
Miriam

I get it.
Bob

Two ways to win. . . .

Miriam became very angry upon suffering this defeat. She cried a little, wanted to quit, and generally made me feel like a bad guy. When she was convinced to turn the tables on me, she played game 5 and beat me directly. With her compensatory victory achieved, she no longer wanted to quit.

Game 6: Bob moves first (numbers)

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

My opening gambit (1) I characterize for Miriam as “probably a pretty dumb move. I’ve never seen anyone go first here before.”

Game 7: Miriam moves first (letters)

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

I check at first to make sure we have not played this corner opening response in this session; then upon moving (1), ask Miriam:

Bob

Do you remember how to beat me?
Miriam

Unh-huh [then she laughs and moves B].
Bob

Oh, you’ve got me now.
Miriam

[gestures toward moving next in the center]
Bob

[stopping her] Show me your chances to win.
Miriam

[gestures along the top and from B up through the center square]
Bob

If you want two ways to win, you have to move where the chances to win come together.
Miriam

[gestures to move in the center square]
Bob

That’s wrong.
Miriam

It is?
Bob

Where do the two chances come together?
Miriam

Here [along the top], here [up through the middle]. Here [the intersection corner].
If I go here, you can block here [the center square], but I’ll go here.
Bob

O. K.

Miriam makes move C, getting her two ways to win.

Relevance
This vignette continues the documentation of Miriam’s tic-tac-toe experiences. Her preferences suggest that she has begun to think of appropriate strategies selected by response to the opening move, and show she can think in terms of intersecting chances to win even though her first inclination is to move in an empty center square. (I myself played so before analyzing the game in the course of this work with Miriam.)

Vn07201

Vn72.1 Tic Tac Toe with Robby 8/25/77

Having seen Miriam play tic-tac-toe with me and feeling a little left out, Robby asked to play with me after Miriam went to bed.

Game 1: Robby moves first (numbers)

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

Robby originally made move 3 in the middle of the top row, belatedly recognizing his error, and asked to move instead in the middle of the bottom row. Such oversights appear to be characteristic. When I mentioned, before placing C, that I had a forced move, Robby noted, “This is probably going to turn out to be a draw.”

Game 2: Bob moves first (letters)

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

After Robby’s first move (1), I asked:

Bob

Do you believe I can beat you?
Robby

No.
Bob

You don’t believe that? I’ll prove you wrong.
Robby

All right.
Bob

Watch. I put a B in that corner. Do you have a forced move?
Robby

Arggh.
Bob

How many chances to win do I have?
Robby

[gesturing across the top and up through the center from B]
This way and this way.
Bob

Two chances to win, right?
Robby

Yeah.
Bob

Do they come together?
Robby

Yeah. In that corner.
Bob

So I put my letter C up there and what do I have?
Robby

Two ways.

I had not in the past described play in such a manner with Robby. His finding it immediately natural is a sign he thinks of the game in such terms himself.

Game 3: Robby moves first (letters)

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

After Robby’s corner opening, I brag that I’m not so easy to beat as the computers at the Children’s Museum. He responds:

Robby

I also have a different technique if you do that [unclear referent;
perhaps: respond with center move to his corner opening as the computer did].
Bob

You think I’ll do that? Well, suppose I go over here. You think you can beat me
if I go there? . . . Son of a gun, you got me. Do you believe you have me?
Robby

[a less than absolutely confident smile]
Bob

You’re right. You know why?
Robby

Yeah. You’re forced to go there (2) and I can go there (C), then I have two ways to win.

I congratulate Robby on being “pretty good at this” and inquire how he learned to be so good at tic-tac-toe. Robby explained that the 3 times we were at the Children’s Museum he played tic-tac-toe with the computer “quite a bit.” He suggested as many as 26 games.

At this point in recording Home Session 17 the tape recorder malfunctioned and the remainder of the conversation was lost.

Game 4: Bob moves first (letters)

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

This game exhibits use of the block I developed to counter the strategy Robby first employed against the computer at the Children’s Museum (cf. Vignette 5).

The remaining three games we played this evening were all center openings by Robby. When I responded with corner moves twice, we tied. When I responded with a middle row move, he beat me.

At the end of the games, we discussed the game generally. Robby, in response to a question of how many ways one could start out, explained that there were possible only 3 opening moves (center, side, and corner). He also knew that when responding to a center opening, a move in the middle of a row invariably led to defeat, whereas a corner move would guarantee a tie unless you made a mistake.

Relevance
These data are collected for comparison and contrast with the more extensive collection of Miriam’s games. My general impression is that there are two main differences between the children’s grasp of the game. Robby appears to conceive of an entire game as a single entity, the sort of game it is being determined by the first 2 moves. I infer this from his being able to describe and discuss the games in a relatively abstract way: there are only three opening moves; there are only two responses to a center opening. This is a different way of thinking of the game’s symmetry from the way it is manifest in Miriam’s thought: she will recognize one game as equivalent to a second when both appear for judgment in that respect. Her response to such questions needs further probing.

Vn07301

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.

Bob

How are they different?
Robby

You don’t learn anything at Logo.
Bob

Oh? And you do at school?
Robby

Yes.
Bob

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

You learn. . . ah. . . mathetating.
Bob

Mathetating?
Robby

Mathetating; what you do with numbers.
Bob

Don’t you ever do adding at Logo?
Robby

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

I learned how to write.

A third incident showed a different perspective.

Miriam

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

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

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

Fun. . . but I’m not sure I’m ready.
Bob

In what way?
Miriam

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.

Relevance
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.

Vn07601

Vn76.1 Where Do Ideas Come From? 8/29/77

In this hot, humid weather, Gretchen and the children have been
spending all day at Logo with me. This morning I found Sylvia Weir had
taken a desk in the room where Robby had just laid claim to an empty
desk. She seemed intent on reading, and knowing how distracting the
children can be, I asked Robby to move to a free desk in the adjacent
room. Later, when I asked him had he done so, Robby told me he had been
locked out of the office.

When Sylvia returned from lunch, she was as surprised as everyone
else that the door had been locked — and that was for her a problem,
because she needed to pick up her materials before leaving shortly. Did
Donna have the key? No. Greg or Eva? Perhaps, but neither was about.
George or Gordon, could they help — neither could. An impasse.

Recalling one of the avocations of students at Caltech had been
lock picking, I thought maybe Danny or Brian might have become similarly
skillful here. Going back into the computer room, I looked toward the
locked room and noticed a roof panel was out of place. Aha! Should
the lock picking be difficult (I had never developed skill at that),
one could go over the partition through the roof. Both lock and door
were sturdy, the lock not accessible to a knife edge or spatula prying
gambit (the only one I know). I looked again at the ceiling and worried
that it would be too tight to snake over except for a child, and I
wouldn’t risk one of the children’s falling from ceiling height. I was
standing on the floor; it is raised for the computer cabling and also
could be dismantled. I walked to the Logo foyer and told Sylvia not to
worry. We couldn’t open the door, but we could open the floor.

Removing the floor panel in front of the door, I could see that one
would have to crawl under the floor for a distance of at least 2 feet,
then lift the panel beyond the next to rise up inside the room. There
might be a desk inside on that second panel; this possible impediment
would make it too difficult for Robby to tackle — if the simple plan
failed he might feel trapped and become frightened. Danny Hillis,
declaring he had done so before, volunteered to crawl under the floor
and open the door. Thus Sylvia’s afternoon was saved and we all had a
good time solving a practical problem.

At dinner this evening, Miriam asked: “Daddy, how did you ever
think of going under the floor? Was it because you remembered how good
a time we had before when the floor was up?” (Cf. Vignette 42) I told
Miriam her guess was pretty good, and I set out my “problem solving
process” in the previous paragraphs to show how good her guess was —
for these notes show how local were the changes, stepwise, to the problem
as I perceived it, by which I arrived at a solution others saw as an
imaginative transformation. What I find most striking, however, is that
Miriam asked me how I got a particularly good idea. This implies she
is capable of reflecting not only on her own thought processes, but also
on mine as well, and even more, has formed her own hypothesis to explain
my thought process in this instance.

Relevance
Miriam inquires how I generated a good idea and offers her
speculation on how I might have done that. This is as clear an example as
one could want of her sensitivity to and reflection upon the process of
thought.

Vn07701

Vn77.1 A Geometric Puzzle 8/29 & 31/77

8/29 Since Miriam’s completion of our work with picture puzzles (cf.
Logo Session 40, 8/1/77), it has been my intention to examine her
performance with geometric puzzles. In the past, she has played with a
puzzle, the Pythagorean puzzle, which I had made from wood.

The Pythagorean puzzle is of 5 pieces and fits together in two ways.
The first fitting provides a square whose sides are the hypotenuses of
4 congruent triangles. The second fitting may be seen as the contiguous
placement of two smaller squares whose sides are the same length as the
two sides of the four congruent triangles.

Vn 77-1 Pythagorean puzzle

Today I found Miriam and Robby playing on the floor of Glenn Iba’s
office with a small geometric puzzle. Robby played with a plastic
version and Miriam with a duplicate cut from cardboard. The pieces
below form squares in two ways:

Vn 77-2 Glenn's puzzle (1)

Pieces 1 through 4 fit together to form a square. Pieces 1 through 5
form a slightly larger square.
During their play in Glenn’s office, Robby accepted a proffered
hint (Glenn first showed him the outline of the square and the location
of one piece). Miriam first refused to look at the hint Glenn offered,
then got mad at him when later he refused to show it to her. I brought
the cardboard puzzle home and put it on my desk for later use.

8/31 I found Miriam working at the puzzle this morning. She succeeded
relatively rapidly at the 4-piece assembly. As Robby tried to show her
Glenn’s hint, the arrival of the mailman drew the children away from
that task. Gretchen picked up the pieces, assembled the four, and left
it on a chair near the reading alcove.

Later Miriam joined me and tackled the 5-piece assembly. She failed.
She went over to my book shelves and took out the Pythagorean puzzle as
she said, “I’m going to give myself a good hint.” Miriam successfully
assembled the Pythagorean puzzle in both forms, but did not find that
success useful with Glenn’s puzzle. She decided first to make a design,
then asked for my help.

I had seen Glenn’s hint. I recalled the orientation of piece 1
with respect to the square’s edge and showed it to her. I noted that
the edge with 5 pieces was bigger than the edge with 4 pieces and set
as a sub-task finding a combination with edge length equal to that of
piece 1 with piece 5 inset. Once we found the place of piece 2, thus,

Vn 77-3 Glenn's puzzle (2)

success was in reach. Miriam attempted piece 3 and failed repeatedly.
I recalled to her mind the picture puzzle hint: rotate the pieces.
Miriam then fit pieces 3 and 4 in place. Miriam is very happy and says,
“Robby thinks he’s the only one who can do this.” Miriam shows Gretchen
she can assemble the puzzle, then calls Robby to witness her success.

Before lunch, Miriam encountered the puzzle disassembled on the
dining room table. She talked to herself as she tried to assemble the
5-piece variation: “I’ve got a forgetting bug about this puzzle. . . . That
can’t be right. . . yep.” Miriam gives up and gets a snack.

In the afternoon, Miriam retries Glenn’s puzzle. She clearly
remembers the relation and placement of pieces 2 and 3. She also states
explicitly that piece 5 must be inset at the corner in piece 1, yet she
can not see how to fit the pieces together as she tries to place the 4th
piece adjacent to pieces 2 and 3. She is about to quit when I advise
her to rotate piece 4 once, then again, arriving at this arrangement:

Vn 77-4 Glenn's puzzle (3)

at which point she sees how to fit the 1 – 5 combination into the 2-3-4
sub-assembly.

Relevance
Miriam’s puzzle assembly skill does not seem to generalize easily
from picture to geometric puzzles, nor from one geometric puzzle to
another. She knows when she is frustrated that she needs a ‘good hint’
and can apply it when given specific advice (note, however, that she
had to be directed to rotate piece 4 two times; she interpreted the
hint as: turn piece 4 so the next edge is adjacent to the 2-3 assembly,
instead of turn piece 4 until the configuration can accommodate sub-
assembly 1-5).

Vn07901

Vn79.1 Sums Over a Hundred 8/29/77-9/1/77

8/29 While we sat at lunch today, Miriam introduced the topic of adding
with this claim: “Daddy, if you live for another hundred years, I know
how old you’ll be.” When I expressed surprise Miriam demonstrated:
“A hundred 37.” Two complications derailed this discussion. Robby
introduced my birth on February 29th with its implication of quadrennial
birthdays. Before we entered more complicated computations on this
basis, I noted that I would be dead before a hundred more years and
that one stops counting a person’s birthdays when he dies. Both children
looked at me blankly, and we proceeded to a discussion of what death is like.
(If curious, confer the note appended at the end of this vignette.)

9/1 This evening, I read aloud to Gretchen an excerpt from a draft-
section of Seymour Papert’s Logo book, a sardonic description of the
class structure of the mathematics education world:

Mathematicians create mathematical knowledge, math education
researchers package the material for children, teachers deliver
the packaged stuff, evaluators measure how badly the whole
process worked.

When Gretchen laughed, Miriam, out of sight in the adjacent area of the
loft, commented, “I don’t get it. I don’t think that’s funny.” Although
in one sense this is not at all funny, in another way it is, and so I
told Miriam. She replied, “What do you mean?”

Bob

How much is a hundred 70 plus 27? [original has a hundred 7]
Miriam

97. . . a hundred 97. Did I do it right?
Bob

Yes. Did you use your fingers?
Miriam

You want to know how I did it?
Bob

Sure.
Miriam

I said 70 plus 20. That’s 90, so I have the 97.
Bob

Where’d the hundred come from?
Miriam

It was a hundred 70. . . . Did I do it right?
Bob

You did it beautifully. . . and that’s more important than doing it right.
Miriam

I know that.
Bob

You also did it correctly.

Miriam went back to playing at what had occupied her before the dis-
traction of my reading aloud, so I did not explain why this problem she
solved, documenting as it does her ongoing progress in constructing her
own algorithms for addition, shows how ‘funny’ in another sense are the
best efforts, even the well-intentioned efforts, of the mathematics
education establishment.

Relevance
Since Miriam’s forgetting how to add multi-digit addends and her
subsequent reconstruction of adding procedures on a different basis,
I have let her curiosity guide our discussion of the algorithms she
employs for computation. This vignette records Miriam’s recrossing
of the hundred barrier with her own method of adding.

* For the curious: when I elaborated somewhat further, I said,
“You don’t count birthdays ’cause you can’t think at all when you’re
dead. You don’t eat or breathe either, but that doesn’t matter because
you can’t feel anything at all.” Robby came back: “Oh, I get it now.
Being dead is like you blew a fuse.” I agreed: “And each of the major
organs in your body — your heart, your lungs, your liver — each of
those is like a fuse and when one of ’em goes, you die.” Robby has
spent time since building two models, the Invisible Man and Invisible
Woman, attempted over a year ago and judged too complicated then.

Vn08001

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.

Miriam

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

What do you think?
Miriam

I think she’ll be mad at me.
Bob

Are you worried about that?
Miriam

Yeah.
Bob

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.
Miriam

What do you think?
Bob

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

I guess I should just do the regular stuff.
Bob

You mean like 2 plus 3 is 5?
Miriam

Yeah.
Bob

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

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

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.
Miriam

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

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

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

At the end of second grade, maybe third grade.
Miriam

You mean I can skip a grade?
Bob

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

Do I have to?
Bob

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?
Miriam

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

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

Yeah.
Bob

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?
Miriam

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.

Relevance
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.

Vn08101

Vn81.1 Imitating Machines 9/3/77

Ever since their first encounter with the Votrax Voice Box back in
May (Logo Session 5, 5/22/77), both children have thought it funny to
imitate the peculiarly mechanical tone of that speech generator. I have
suspected some correlation between my asking them questions they consider
stupid and their adopting this mode of reply, but that speculation
has never been clearly tested. Today, in between the sessions for Robby
and Miriam, Robby entered the room I was in and said something in Votrax
mode. I have felt generally uneasy about this imitation and I complained:
“You are not a Votrax Voice Box.” Robby responded (in Votrax
mode): “I am too a Votrax Voice Box. But I can do other things besides
talk. I can walk. And think. And poke.” (Here Robby poked me in the
stomach). I grab him: “And get tickled.” “And run away,” he concluded
as he broke away from me.

At the end of our day’s work, Robby was lying on a desk whereon was
a pencil sharpener. Miriam entered, sharpened her first of six pencils,
and held it up for examination. Robby blew the wood and carbon dust off
the pointed end. Miriam told him to stop and he did. With the next
pencil, at the appropriate time, Miriam commands Robby to “blow”; he does.

Miriam

I’ll push your thumb. That will be your stop button. . . . Blow.
Robby

(Blows on pencil end and stops when Miriam presses his thumb.)
(Robby then gets up, stands beside Miriam, holding up two thumbs —
one for starting, apparently.)
Miriam

Hey. Instead, this button can be for sort of running in place.
Your nose will be the start button. (Miriam raises a pencil before him
and presses his nose.)
Robby

(Blows on pencil and runs in place.)
Miriam

(Presses his ‘stop’ thumb.)
Robby

(Stops)
Miriam

(Presses ‘start,’ ‘stop,’ and ‘run in place’ buttons all at the same time.)
Robby

Arrgh. How did I ever get mixed up in this?

Relevance
This game of imitating machines, like ‘Follow the Turtle’ of
Vignette 42, is a direct outgrowth of the children’s experiences art
Logo. Does Robby seriously think of himself as a machine? If he does,
he is also articulate about highly specific differentiae. . . and maybe
that’s not too wrong.

Vn08201

Vn82.1 Hanging Designs 9/3/77

After today’s session was complete, I asked Miriam why she had not
pinned on the wall — as she had said she intended — those designs made
in yesterday’s session (Logo 58, 9/2/77). She explained that she had
started to do so earlier but needed help.

I separated the designs from the interleaved blank pages in the
pile on her desk, then asked where to hang (“Up there.”) and how.
Miriam’s directions: “In alphabetical order, by the numbers.” When I
found this opaque, Miriam explained, “Like the way Robby did it.”

At Miriam’s direction, we set up a display of poly spirals varying
from the base of 60 degrees (we had originally called such a shape a
‘maze’) in order by the turtle’s angle of turning up to 67 degrees.
Miriam had created this complete set of designs with considerable direction
from me (cf. Session 58), and she used Robby’s arrangement of designs
as a model. Nonetheless, the creation of this family of shapes was her
idea.

We came to a last design. All the others had been made with an
increment (‘delta’ we call it) of 2 turtle steps. At the angle of 67
degrees, we made a design with delta = 1. (This was done because I had
been too directive earlier in the session, requiring Miriam to hold
delta constant.) I asked: “Where do we want to put this one? We have
a 67 degree design already, but this one’s got a different delta; should
we just put it under like the others?” Miriam instructed me (by placing
the design in this place) to tack the design on the wall at the side of
the other 67 degree design and “we may want to make another family later
like the other one.”

Relevance
In the directions Miriam provides for how her poly spiral designs
should be hung on the wall, one can see her beginning to organize them
into groups defined by the changing of one variable while the others
are held constant.

Vn08301

apparently, this file needs to be recreated, from earlier sources.
The tags attached to the source suggest it is important.

Vn08401

Vn84.1 Go Cart Demon; Knock-Knock Jokes 9/5/77

The third-floor tenant in our landlord’s mansion was moving out
today. Robby and Miriam went to help. One comment of Miriam’s came
floating up from the court yard. When she chanced upon a collection
of records brought down in a wooden case, Miriam said, “Hey, Robby,
let’s ask Bill if we can have that box. If we get our wheels, it’s
just what we need for our go cart.” (Cf. Vignette 50). From this
comment, with the availability of ‘found’ material now rendering less
than fantastic for Miriam the construction of a real go cart, I see
Miriam thinking more in the style of a bricoleur than does Robby on
this project. (Recall his engineer-like inclination to draw up a materials
list for purchases to be made at the lumber yard.)

On this day, the children also encountered a book about which we
have heard since — a book of knock-knock jokes. Robby introduced this:

Jokester

Knock knock.
Victim

Who’s there?
Jokester

Robin.
Victim

Robin who?
Jokester

Robbin’ you. Gimme your wallet.

Miriam recalled a second:

Jokester

Knock knock.
Victim

Who’s there?
Jokester

Ivanitch.
Victim

Ivanitch who?
Jokester

I’ve an itch I can’t scratch.

While this theme was before us, Miriam recalled a third joke:

Jokester

Knock knock.
Victim

Who’s there?
Jokester

Irish.
Victim

Irish who?
Jokester

I rish I never said “Knock knock.”

Relevance
The first incident contrasts Miriam’s idea of acquiring materials
for the go cart project with Robby’s. The second series of jokes —
the first 2 coming from a book I hadn’t seen and the third from a TV
commercial I did not watch indicate how rapidly Miriam’s perimeter of
experience is expanding beyond the reach of my knowledge. I believe
it is still possible to trace the sources of Miriam’s knowledge but
feel keenly how important it is that she has become accustomed to
discuss her ideas, her thought processes, and their sources.

Vn08501

Vn85.1 9/6/77

When we started playing tic-tac-toe, I asked Miriam how many different ways can you start when you move first. She claimed 9 ways, one for each block in the frame. I pushed the point further by inquiring whether these three frames were really different or the same:

          X |   |   	   |   |   	    |   |      
            |   |   	   |   |   	    |   |      
            |   |  	   |   | X	  X |   | 

              1	             2                3 

She judged the first two to be the same and the third different from them. My intention in today’s play was to work through the range of all game Miriam could see as different responses to the corner opening. We pursued this by my letting her move first in every game with the specific objective of finding those responses which would not lead to my immediate defeat.

Game 1: Miriam moves first (letters)

          A | D | C    
            | 2 | 3    
          2 |   | B 
Bob

If I go here [the middle of an outside row, not adjacent to A],
can you beat me?
Miriam

Yeah.
Bob

There, in that side place? Or if I go in the corner?
You don’t want me to go in the corner? [opposite diagonal to A]
Miriam

I want you to go some other place.
Bob

How about if I go here. Can you beat me? [the adjacent corner
where move 1 is made]
Miriam

No. Don’t go there. . . . O. K. You can.
Bob

How about if I go over here, in this other corner? [the alternate adjacent corner]
Miriam

It doesn’t matter [the moves are equivalent].
Bob

Oh. If I go there, the moves are the same?
Miriam

Yep.
Bob

I’ll go in one of these corners here that are the same. . . .
You think you can beat me?
Miriam

I don’t know [moves B].
Bob

You think you beat me already?
Miriam

Unh-uh.
Bob

No? Do I have a forced move?
Miriam

Yeah. . . . Actually, I have [beat you]. You have a forced move.
Bob

Then what?
Miriam

I’ll move there [the alternate adjacent corner] and get two ways to win.
Bob

So you’ve beat me already.
Miriam

I know.
Bob

Actually, so long as I made that move there (1), you beat me already.
And you told me you didn’t want me to move there. . . . Did you know you could beat me
when i moved there? . . . You did? Did you trick me?
Miriam

[smiles] Yeah.

Game 2: Miriam moves first (letters)

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

I recapitulate the last game, identify both adjacent corners as responses with which I can get beaten, and recall Miriam’s assertion she can beat me anytime. I respond with a non-adjacent, middle row move.

Bob

That means I should either move in this far corner [opposite to the opening]
or in the middle, or here or here [in the two adjacent, middle of row moves]. Let’s suppose
I move here [opposite corner]. Will you beat me?
Miriam

I don’t know.
Bob

I’ll try it [moves 1].
Miriam

[laughs] I’ll put my B here!
Bob

Oh. Oh-oh. Do you have me beat already?
Miriam

Yep. See. I go there [alternate adjacent corner] and I’ve got two ways to win
[gleeful laughter].
Bob

So, as soon as I put my 1 in there, you knew you could beat me,
because you didn’t have a forced move.
Miriam

Uh-huh.
Bob

Did you know that? Were you just trying to trick me?
Miriam

Unh-uh.
Bob

You probably didn’t know it really.
Miriam

Right.
Bob

Do you know it now?
Miriam

[smiles]
Bob

Yeah.

Game 3: Miriam moves first (letters)

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

This game begins with the moves Miriam originally sought for the execution of her ‘dirty trick.’

Bob

If I go here [center], can you beat me?
Miriam

I think so.
Bob

I’ll put my 1 right in the middle. How are you going to beat me now?
Miriam

[moves B] Whichever side you go [she gestures toward the corners],
I’ll go on the other side [the alternate corner] and get two ways to win.
Bob

Ah ha. That’s a good strategy.
Miriam

Right.
Bob

But it assumes I make a move in that corner or the opposite corner.
Miriam

I. . .I know what you’re going to do.
Bob

What am I going to do?
Miriam

You’ll go here [bottom row, middle].
Bob

[pointing to the others in turn] Or here or here or here. Does it matter
which of these four I go in?
Miriam

Unh-uh.
Bob

Will you beat me if I go here? [corner]
Miriam

Yeah.
Bob

I don’t like to lose all the time. I’ll go here [moves 2].

Game 4: Miriam moves first (letters)

          A  | 2  | B   
          1  | C  |      
          D  |    | B1-> 3 

Beginning this game, I review the moves I made and where I’ve been defeated. I cite the adjacent middles of rows as the only locations I haven’t attempted and select them as the next trial.

Miriam

I’m gonna beat you I think [moves B1 ].
Bob

Why do you think you’re going to beat me?
Miriam

‘Cause. . . . Oh no, I can’t if you go there [in the center].
Bob

The move you made is not a winning move. I have a forced move in the center.
Miriam

I’ll go here [adjacent corner move].
Bob

Then I’ll win because you would miss your forced move there.
Miriam

Arrgh.
Bob

If you want to take that B out, cross it out and try some other move; maybe you should.
Miriam

Where else? . . . Here? [move B in adjacent corner] Is that O. K.?
Bob

Let’s see. The problem with the other corner [now crossed out]: if I went in the center
you have a forced move in the side. . . but now I must move here [move 2] and you have me beat.
Miriam

How?
Bob

Where are your chances to win?
Miriam

Here [from A through the center] and here [from B through the center].
Bob

If you move where they cross you get two ways to win.
Miriam

[laughs, moves C]
Bob

Oh brother.

At the end of this game, I summarize: “If you start off with a corner opening, you can beat the other guy no matter where he goes — almost — unless he plays in the middle and side as I did in game 3.” Miriam ran off to announce her victories to Gretchen.

Relevance
These data show Miriam and me working through all the responses (except one: see vignette 71, games 3, 4, and 5) to a corner opening. They provide a good sense of the range of Miriam’s strategic thinking.

Vn08601

Vn86.1 An Unexpected Test 9/8/77

Today, the children’s first day of school, was a tough one for me. The combination of a late arrival at Logo and logistics problems put our work under an unusual time pressure. Miriam was tired (and later said she wished she had taken a nap) and didn’t pursue with enthusiasm her exploration of good numbers for the SEAHORSE (an INSPI procedure). Thus, she yielded up the remainder of her time when I was reluctant to let her have a break. Robby, in his turn started off in what was a normal fashion for him, but soon we ran into a problem, the extent of his reactions to which I still can not fathom. The session with Robby was dreadful, the worst so far since our project began. He was confused, began crying, but refused to stop our session; his allergy caused stuffy nose made his crying dreadful. His reasons for sorrow increased when he began lamenting the time lost which he could have spent making designs,,,, Affairs finally reached such an impasse, we just gave up on the day.

After a few minutes alone, trying to regroup my scattered aims for the day, I carried the video camera into the storage room and saw Glenn (a graduate student) doing paper folding games with the children in the foyer of our lab. Because Glenn enjoys playing with the children and is good at it, seeing them together made me uneasy. Twice through chance, through the availability of materials, and through enjoying games to which I have heightened Miriam’s sensitivity, he has performed before me, in effect, experiments I was developing (confer Vignettes 8 and 77). When I saw peeping out from under a pile for other papers they were folding, the sheet I in Addendum 86-1, I realized my five month long, complete collection of data on Miriam’s development in Tic Tac Toe was in jeopardy.

I asked Glenn to try to reconstruct the move patterns of the games they had played. His notes are on the 3×5 card shown in Addendum 86-1.

Game 1: Miriam moves first (letters)

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

Glenn remarked on Miriam’s telling him, after her move B, that should he move in either of the other corners, she would win. He did not move there.

Game 2: Glenn moves first (numbers)

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

Miriam and I have not played this game to the best of my recall. Note that had Miriam moved in a space adjacent to A, this diagonal configuration would have permitted the opening to gain two ways to win, thus:

          A | B | 3
            | 1 |   
            |   | 2 

Game 3: Miriam moves first (letters)

          A | O | X
          X | X | O
          O | X | O

Glenn’s only dependable recollection of this game is that Miriam opened at the corner. The tie must have followed one of these patterns of a symmetric variation:

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

The data of Vignettes 71 and 85 argue that game A was most likely the one played (I believe Miriam would have beaten him had Glenn responded to her opening with B or C.

Game 4: Glenn moves first (numbers)

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

Glenn notes that Miriam requested he place his marl at the location of 1. Recall Miriam’s comment (at the time of game 7 in Vignette 61) that she would attempt to get Robby to make such a move so that she could play her newly learned tactic on him. When I asked Miriam, while discussing the game with Glenn, how he had beat her, she was a little apologetic, saying, “Well, gee, Daddy, you can’t win all the time. I guess I must have made a mistake.” She speculated further (at least agreed to my suggestion) that she missed a forced move. As game 5 shows, Miriam learned well how with a corner opening she could defeat an opponent responding with a far, mid-row move. This particular game suggests that she had not yet accommodated her configuration based view of the game to the relative advantage obtaining to the opening player. (Notice her foiling this same opening of Glenn’s in game 6 by abandoning the corner move.)

Game 5: Miriam moves first (letters)

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

Glenn seemed a little surprised at my suggestion that Miriam ‘knew what she was doing’ (i.e. executed a game-length strategy) as she beat him here. When asked her opinion of Glenn as a player, Miriam allowed that he was pretty good. Glenn acknowledged that Miriam did make all forced moves.. . and showed a surprising inclination to adopt the corner opening.

Game 6: Glenn moves first (numbers)

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

This game is notable in showing how quickly Miriam abandons the losing strategy of game 4. I believe this is the third game she has played with a mid-row (non-center) opening.

Relevance
This vignette raises two issues. First, how does Miriam apply in other situations what she has learned n the structured sessions of this project? Second, how complete can these data really be? It is clear from game 4 that when the knowledge is directly applicable (as in playing Tic Tac Toe with a new opponent), Miriam applies that knowledge directly in a minimally modified form. (She hopers to catch a “naive” opponent with her preceptor’s “dirty trick.”) Learning anew, at her cost, that a significant attribute was not marked in her formulation (its success depending on the corner opening move), Miriam when confronting the same opening a second time retreated to a seize-the-center play (this reduces maximally the opening player’s chances to win).

How complete can these data be? If it be the case that Miriam interacting with one person on the occasions described here and in Vignettes 8 and 77, engages in three significant ventures in learning, must it not also be true that other such incidents occurred which have escaped my notice? I think not. The extent of time I spend with the children and the sensitivity to precisely this sort of influence argue that not much has been missed.

Addendum 86-1

Games with Lab Student

Vn 86-1 Games with grad student

Vn08701

Vn87.1 Turtle Tactics 9/7/77

This night is the last of summer, so defined by the children’s
beginning school on the morrow. Over this summer they have gradually
become accustomed to going to bed late, and now, in order to rise early,
they should go to bed early. No one found this argument convincing.
We negotiated a compromise that the children get into pyjamas, return
for dessert (delayed by conversation with dinner guests, José and Fernando),
and then go off to bed. Robby lived up to the agreement. Miriam did not.

When given a direct order to go to bed, she went to my bed instead
of hers. I had mentioned during dinner the children’s inclination to
play turtle. Fernando tried to help. “Miriam, forward.” She did nothing.
I advised him that he had left out the carriage return. Upon his “carriage return”
Miriam complained, “You haven’t told me how far to go,”
chuckled, and popped back onto my bed. Gretchen attempted, “Forward 100,
carriage return.” With gripe “You haven’t told me how to FD100” still
in the air, I described the bug as the well-known space omission between
operation and input. Fernando was then precise: “Miriam — forward,
space, 100, carriage return.” Miriam played fair and proceeded stepwise
(and counting each step) down the length of the loft. At first we
expected 100 steps to be too few. Miriam counted 70 in the kitchen, and
at 88 gleefully announced, “Out of bounds!” as she walked into the wall
in the hallway. While so close to her bed room, she picked up her
‘security blanket’ (the air was a little chilly) and came skipping
back into the living room.

The game wore on (hide turtle under the blanket and so forth), after
a while becoming wearing, and I directed her to bed with the threat of
physical force. Miriam replied, as she has for some months now, with
the counter-threat of “I’m quitting your thesis, Daddy, I really am.”
Having thus preserved her dignity, she acquiesced to the demand that
she go to bed.

Relevance
This vignette describes the way Miriam employs her knowledge of
Logo as a delaying tactic to avoid going to bed early. The ease with
which she adopts the turtle’s role in a command/execution script (using
it, of course, for her ends) shows how directly that script can represent
the actual ‘authoritarian’ portion of relations in a family. Lest
this seem mechanization obtruding into a human relationship in an un-
healthy way, remind yourself that this was to her a useful game which
permitted her to survive for a while by her wits in a situation where
her other obvious options were to submit to authority, to rebel (make
a fuss), or to wheedle from me some relaxation of the order.

Vn08801

Vn88.1 9/8/77

Over the past few weeks, Miriam has spoken, in the context of
repressing her desire for things she can’t have, of having “an eraser
mind.” When asked to explain what she meant, Miriam conveyed the
image of ideas written on a tablet and subject to erasure.

As supper drew to a close this evening, Miriam cited the existence
of another mind (I believe, but am far from certain, that we were dis-
cussing future meals and Miriam noted her “liver-hating mind”). Remarking
my surprise at her thought of having an ‘eraser mind’ and another kind
as well, I inquired if she thought she had any further “minds.” The
topic lay unheeded for a short while. I made some coffee and sat down
away from the table.

The children picked up the theme as a game between themselves.
Miriam: “I know another mind I have, a “remembering mind”. . . and another,
a “stay-away-from-sharks mind”.” Robby asked if she had a “talking
mind.” Miriam responded that of course she did, it had a voice box in
it. These seemed to exhaust her invention for the moment, so Robby
proceeded: “You must also have a learning mind, or all your other minds
would be empty.” Miriam agreed, going further to claim that her “learn-
ing mind” was the biggest one of all. Robby continued further that he
had an “electric mind” whose function was the manufacture of electricity,
“for that’s what everything else runs on.” In response to Miriam’s
objection that she had no wires inside, Robby pointed to a wall socket
and explained that the electric energy was carried through the bones to
outlets, such as the one in the wall, where it was made available for
local distribution.

At my inquiry of where they had picked up such unusual notions,
Miriam said, “It’s all in your brain.” When pushed further with the
question of whether mind and brain were the same, she clarified thus:
“Actually, it’s all in your everything mind.”

Finally the joking grew stale. On my inquiring, pen in hand, what
was that second mind she had cited, Miriam remarked, “Daddy, if this
shows up in your thesis, I will be mad at you.”

Relevance
This vignette cites some jocular ways Robby and Miriam discuss
what goes on in their minds. Robby’s relative advancement can be seen
in his concern with a “learning mind” which develops the contents of
others. Though Miriam’s references are not ‘constructive’ they indicate
reflexivity.