Skip to content
Archive with last of tag-string FT

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

LC1bT06

LC1bT06 Protocol 6

Included Text Pages (2)

RAL protocol 6.1

RAL protocol 6.2

Included Materials (2)

RAL protocol 6-A1

RAL protocol 6-A2

LC1bT07

LC1bT07 Protocol 7

Included Text Pages (2)

RAL protocol 7.1

RAL protocol 7.2

Included Materials (2)

RAL protocol 7-A1

RAL protocol 7-A2

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

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

LC1bT14

LC1bT14 Protocol 14

Included Text Pages (2)

RAL protocol 14.1

RAL protocol 14.2

Included Materials

None.

LC1bT15

LC1bT15 Protocol 15

Included Text Pages

RAL protocol 15

Included Materials

None

LC1bT16

LC1bT16 Protocol 16

Included Text Pages

RAL protocol 16.1

RAL protocol 16.2

Included Materials

RAL protocol 16-A1

RAL protocol 16-A2

LC1bT17

LC1bT17 Protocol 17

Included Text Pages

RAL protocol 17.1

RAL protocol 17.2

RAL protocol 17.3

RAL protocol 17.4

Included Materials

RAL protocol 17-A1

LC1bT18

LC1bT18 Protocol 18

Included Text Pages

RAL protocol 18

Included Materials 2 pages

RAL protocol Add-1

RAL protocol 18 Add 2

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

LC1bT21

LC1bT21 Protocol 21

Included Text Pages (8)

RAL protocol 21.1

RAL protocol 21.2

RAL protocol 21.3

RAL protocol 21.4

RAL protocol 21.5

RAL protocol 21.6

RAL protocol 21.7

RAL protocol 21.8

Included Materials (3)

RAL protocol 21-A1

RAL protocol 21-A2

RAL protocol 21-A3

Vn00101

Vn 001.01

Everyday Calculation

5/7/77

Miriam suffered a queasy stomach today, so she didn’t join us at our evening meal. She lay on the loveseat near our dining area. The speakers for our radio are directly behind the loveseat, thus more enforcing Miriam’s attention than ours.

During a radio commercial we others chose to ignore, Miriam burst out in disbelief, “That would be 60 dollars.” When I asked what her reference was, she explained that if the four of us attended a certain fixed-price dinner (one we had no interest in) the total cost would be 60 dollars. “How did you figure that out?” I asked. “Did you learn how to multiply already?”

Miriam coupled a disclaimer of any knowledge about multiplication with one of her ‘dumb-Daddy’ looks and explained that each meal cost 15 dollars and she knew that 15 plus 15 were 30 (which, as she added in parentheses, accounted for 2) and another 15 and 15 make another 30. The two 30’s making 60 dollars gave her a conclusion and accounted for the four meals she knew we would want.

Vn00102

Vn001.02

Commutativity

5/8/77

As I sat transcribing the dialogue from recent logo sessions, I heard Robby inquire of Gretchen, at work in the kitchen, how many were 5 twelves. Gretchen simplified the computation by elaborating the problem: 5 twelves is half of 10 twelves. How much is 10 twelves? As Robby worked away on that problem, Miriam, playing at a puzzle within earshot of that conversation, piped up: “the answer is 60.”

Poor Robby! How frustrating when working on a different problem to be prevented by some one else’s interjecting the ‘correct’ answer. And yet, Miriam did have it right. I was quite worried that she had computed the answer by summing twelves (which Robby could have done, albeit with some difficulty and uncertainty) while he wrestled with the transformed problem,

Gretchen had been watching Miriam. She saw Miriam compute 5 twelves by finger-counting thus: 5, 10, 15, 20, 25, / 30, 35, 40, 45, 50, / . . . 60. Thus Miriam’s procedure is more primitive than Robby’s but it is also more sophisticated. She makes use of the commutativity of basic arithmetic operations at every turn. Several weks ago, Miriam gave direct evidence of her use of commutativity in adding. Mimi Sinclair asked her: “How many is 17 plus 6?” ’23’ Miriam responded counting up from 17 on 6 fingers. When the query turned to 6 plus 17, Miriam responded with no hesitation, ’23, because it’s the same problem.

I speculate that she uses commutativity because it permits her to proceed to an answer which costs her little if wrong; Robby, more concerned with the correctness of his results than the unimpeded progress of the computation, is more inclined to ask for advice than to trust to a property, commutativity, which can give him an answer but one about whose correctness he is uncertain. This speculation may demean the actual extent of Miriam’s understanding.

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.

Vn00302

Vn003.02

Journals

5/11/77

When collecting the data reported in ‘Pre-Readers’ Concept of the English Word,’ I was shown by one of the children, Tina, a 3×5 notebook her mother gave her for writing down any words she wanted to learn to read. I bought Miriam such a notebook (a green one) some weeks ago for such a purpose. She asked me how to spell ‘floccinaucinihilipilification’ and proceeded to print that in her notebook (today she refused to give me that datum because she still wants to learn to spell that word). Her uses of the notebook are more various than my plan. I find: a list of models she would like to have; an upper and lower case alphabet page (the first set done by Robby as a set of patterns, the second Miriam’s copy); the address and telephone number of her friend Maria. The most frequent use of that notebook has been to make greeting cards for her friends: typically Miriam draws a picture, then prints “For ___” and “Love Miriam”. (It also has many blank pages.) Clearly, Miriam’s use of this notebook has been richer than my conception

I recently purchased another such small notebook (a blue one) for jotting down notes about what Miriam does during the day. Miriam saw that notebook and asked if she could have it for making cards. A conjunction of things occurred. Miriam wanted the notebook; the time she spends in school is one wherein I can’t observe what she is doing; an observation several years ago by Sarene Boocock at an AAAS seminar that children themselves had access to data most researchers could not get at and that one should consider enlisting them as agents of data collection. I told Miriam she could have the blue notebook if she would write in it the things she did in kindergarten. Miriam refused, saying she wanted the notebook for drawing pictures. When I said she could not have the notebook for drawing pictures, Miriam responded, “If you don’t give me the notebook, I won’t even tell you what I do.

At the current round of negotiations, Miriam agreed to use the notebook as I wanted when I agreed to buy a replacement for her green notebook after she uses up all the pages. Her intentions are suspect though because of the final inquiry she made: “If I do a rotten job can I keep the notebook and not write down what I do?

Contrast now the relative openness of the two children, Robby and Miriam. For reference, consider the protocols and 21 (on adding units of English length and on multiplication, respectively) from the series of Robby’s arithmetic development. These protocols are exemplary of a child’s uninhibited exposition of his thought processes; at 7, Robby is a ‘loud thinker’. Contrariwise, Miriam’s characteristic behavior shows her inclination to display a perfect result, a reluctance to exhibit pre-competence confusion

One may laud such a stance as reflecting essential good taste (for who wants to overwhelm the possibility of communication with the mess inside every mind). However, for an ignorant child (is anyone at six years anything else) such a performance criterion is unrealistic and counterproductive. One of my objectives is to render Miriam less sensitive to revealing her imperfect comprehensions in the expectation tha her doing so will provide guidance to those who are willing to help her learn.

Vn00501

Vn005.01

Tic Tac Toe

5/13/77

Years ago I bought a tic-tac-toe game for playing with Robby. The board is 12 x 12; the X’s and O’s are large yellow pieces. At that time I taught Robby a single strategy for playing the game: look for two ways to win. Robby quickly became quite good at the game. Miriam, at age four, learned that one took turns and that winning was getting your three pieces in a row. She did not take the strategy instruction so readily. The children played with the game with different competences: Robby winning with his strategy; Miriam winning frequently enough when he made errors to be satisfied. As Robby came to make fewer errors, Miriam played less, the pieces falling to other uses: the dog chewed one of the X’s, the play group used an O as a hockey puck.

Tic-tac-toe came forward again as a game at a recent visit to the Children’s Museum. Miriam lost to the computer when it, moving first, chose the center square. When she moved first in the center square she never did better than a draw. Robby beat the computer with a first move corner choice (let Robby’s sequence be 1, 2, 3, 4, and the computer’s A, B, C, D):

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

By move 3, Robby had forked the computer, had “two ways to win.” Since neither Miriam nor his friend John had done better than a draw, he gladly showed them the gambit on his next turn.

Tonight, after dinner, Miriam asked me to play tic-tac-toe with her. She was quite familiar with the terminology of two ways to win and implicit victory whenever she achieved a forking pattern. She understood and accepted the terminology of a forced move.

Whenever Miriam had the first move and chose the center square, and I chose a non-corner, she consistently won. This was true regardless of orientation of the board. Let these two games represent the rest as well (Miriam’s moves are the digits, mine the letters):

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

In both, her “two ways to win” victories were not noted as being ‘tricks’ of any sort.

I gradually altered my responses to her first move center choice until I chose a corner square in responsse to every center square first move. Making no mistakes, we come inevitably to a draw, thus:

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

Miriam began then a new gambit, the first move corner choice. When I responded with a center square choice (as did the computer at the Children’s Muuseum), Miriam had her two ways to win by the third move. Miriam described this new gambit as her ‘dirty trick.’ I was quick to tell her I thought it was not a ‘dirty trick’ but a ‘good trick,’ and we both later referred to it that way.

After being beaten several times by her new gambit, I blocked its effectiveness by refusing to make the center square response to her opening move. When I responded thus

  1 |      |
 -------------- 
    |      |
 -------------- 
    |      |  A   

Miriam complained vociferously. It was clear she did not know what to do. She eventually proceeded by placing her piece anywhere. In another variation, she was quite surprised at my victory:

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

She was so intent on her ‘good trick’ she failed to see the simple victory she might have achieved on her third move. This was the only ‘mistake’ I recall Miriam making.

I conclude from these observations that Miriam’s strategies are very specific in nature. When consolidated, they may be orientation insensitive, but not even orientation insensitivity is immediate. Further, Miriam made her ‘mistake’ because she had not yet integrated her ‘good trick’ with the primary rule of tic-tac-toe: make all forced moves. One might better conceive of her “two ways to win” less as a strategy than as a more complex and various, more immediate objective, more immediate than the victory criterion of three pieces in a row.

Vn00601

Vn006.01

Magic Words

5/14/77

While she was in the kitchen and returning to the dinner table, I asked Miriam to bring me something. She asked, “What’s the magic word?” My grandmother avers that the ‘magic word’ is ‘please,’ which can make so many things easy that would be impossible without it. We have never played such a game in our house; we try to use courtesy but do not require it.

I told Miriam I did not know the magic word and asked for a hint. “It begins with a ‘p’ and ends with an ‘e’.” This is the sort of hint Miriam has given in playing the game “I am thinking of a word” (described in ‘Pre-Readers’ Concepts of the English Word’). So I guessed: prime, purple, people, pupae, pleistocene, prune — all to no avail. “It’s ‘please,” Miriam chortled as she went to get what I wanted.

Vn00602

Vn006.02

Magic Words

5/15/77

Miriam tried again her ‘magic word’ game, “It begins with ‘p’ and ends with ‘e’.” The choice of time was unfortunate; I was in a hurry to some other purpose, so I snapped back “please.” “That’s not it,” Miriam claimed, for who can tolerate any conundrum’s immediate solution? Sensing my impatience, she laughed and said, “It’s a pickle.”

Later in the evening, when we were both unhurried and glad of the other’s company, Miriam asked for a bedtime story. Since she’s learned to read, Miriam’s bedtime stories have changed. We read many stories to her before, so now she reads to us. This evening she climbed into my lap and read two library books by Sid Hoff: Who Will be my Friends and Thunderhoof (a book she much enjoyed my reading to her last year). Miriam read both books perfectly; then, as I told her it was bed time and she should go for her bath, she inquired as to what was the magic word. ‘Please’ was rejected outright. “No. It begins with a ‘t’.” When I complained that such was too weak a hint, that there were ever so many words beginning with ‘t’, Miriam added that it ended with an ‘e’. I tried, with little hope: tie, and twine, tweedledee and terpsichore. “No.” Another hint, please? Miriam replied, “It has to do with hands.” Three, perhaps? “And it makes people laugh.” So I tickled her until she fell off my lap and left, supposedly to her bath.

To interpret this series of events, one need know that Miriam’s
current favorite of rhymes is this doggerel couplet:

Tickle, tickle, rhymes with pickle.
If you laugh, give me a nickel.

Miriam enjoys being tickled and I oblige her.

So, please goes to pickle and pickle to tickle: obvious connections after the fact with sufficient data available. But who would dare predict the next magic word ?

Vn00702

Vn007.02

A Willing Subject

5/19/77

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

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

Vn00802

Vn008.02

The Lemon Twist

5/12/77


I had purchased the hula hoop in the morning and was setting up the music room for our later use when one of the boys in an on-going class from CAPS (the Cambridge Alternative School Program) asked if he could use the hula hoop. After doing a hula, he let the hoop fall to the floor, slipped a foot under the hoop, and rotated it about one leg, raising the other foot so that the rotating hoop would not strike him in the ankle. I was impressed; I had never seen anyone do that with a hula hoop. But I had seen Miriam do a similar thing with one of her toys, the Lemon Twist.

The Lemon Twist has been one of Miriam’s favorite active toys for some time. Having seen it advertised on a TV commercial, she bought one with her own money. (This was the first such purchase she ever made). The toy has a hard plastic lemon at one end, connected to a small loop at the other by a piece of tubing about 18″ long. A child slips one foot through the loop, then kicks in such a way as to cause the attached lemon to swing around that leg. I remember the day last spring when Miriam bought the toy, her first trials, her showing it to older friends, her watching them, and her slowly developing skill.

This afternoon Miriam was delighted to find her new hula hoop.
It was perfect, even having the marble inside as did Jenner’s. I mentioned to her the boy from CAPS, how he made it go around on his leg. Miriam put her foot under the hoop and kicked it a few times. “Like that?” Obviously not. “I don’t know how he did it, Miriam, but he made it work just like your lemon twist.” With two or three tries, Miriam was able to make the hoop circle her leg several times at each execution

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.

Vn01201

Vn012

Miriam Collecting Data

5/23/77


While the children were awaiting the school bus this morning, I noticed the little blue notebook in which Miriam was to record her kindergarten activities. I took it out and offered it to her. She said she didn’t want it when I reminded her what it was for and then confided, “I can’t spell all the words of the things I do, but I’ll remember them.”

In a short conference with her teacher, I inquired about Miriam’s role in the skit she mentioned in Vignette 3. I was informed that the skit was an impromptu performance, no adults had been working with the children’s group at the time, and that the other children selected Miriam to be the narrator and tell them what to do.

Miriam and I drove home from school (we stayed a little longer to play in the playground). While Gretchen was making lunch for us, Miriam came to sit beside me, saw the blue notebook, and asked if I would help her write down what she did. Four main events:
– housekeeping corner
– going to the Star Market (a four block walk) with Sue to buy provisions for Wednesday’s farewell party
– making peanut butter
– recess

Relevance

Although this single collection of data is insignificant, such notes for the remaining 6 weeks of school will indicate Miriam’s foci while there. Because I go to the school freely, such data will help me select what parts of her school setting are most relevant to her development and worth detailing.

Vn01301

Vn013

Phonemics

5/23/77


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

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

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

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

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

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

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

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

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

Then:

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

And then:

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

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

Relevance

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

Vn01401

Vn014.1

Housekeeping Corner

5/24 & 27/77


Since Miriam started recounting where she spends her time in kindergarten (see Vignette 12), it has become clear that she spends most of her time in the ‘housekeeping corner.’ When I’ve been in the kindergarten class, I’ve usually found myself playing with blocks, or making designs and elaborate towers from Cuisenaire rods. Miriam has frequently played otherwheres. I have seen her there, curled up in the baby carriage, but I’ve had no good idea of what games she and her friends invented for that location.

That question received a major clarification today while Miriam was stringing beads for necklaces. I had given her a Bic pen cap to poke the string through the beads. After she learned the cap was from an exhausted pen, Miriam began this conversation:

Miriam Can I keep the cap?
Bob Sure.
Miriam Thank you. Tomorrow I’m going to take it to school.
Bob The cap?
Miriam Yeah.
Bob What for?
Miriam Because we usually play Doctor, there in the housekeeping corner.
Bob Un-huh.
Miriam And we give each other pretend shots.
Bob Oh my goodness. You’r not really going to poke anybody with that, are you?
Miriam No (you silly Daddy).
Bob But that will be your needle?
Miriam Yes. Sometimes we use pencils.
Bob I hope nobody ever gets hurt.
Miriam We don’t.
Bob Good. . . I think that’s kind of funny. That you have a house-keeping corner and you play Doctor. Is that because everybody likes giving shots?
Miriam Yeah.
Bob Does anybody like getting shots?
Miriam No. We always run away from the Doctors.
Bob Well, who’s the Doctors. . .or does it change?
Miriam It changes. We run away ’cause we don’t want our shots.
Bob Yeah.
Miriam We always have it in the summer. We run away because we don’t want it and the door’s always open in the summer.
Bob You mean the door to the kindergarten? Or the housekeeping
corner, a pretend door?
Miriam A pretend door to the housekeeping corner. It’s always open so we run right out.

One fact, of possible relevance in initially suggesting the game to the children, though not at all accounting for its continued interest, is that Dara’s mother is a nurse. Dara and Maria are the two girls Miriam most plays with in kindergarten.

After we focussed a while on the beads, I resumed the theme of the housekeeping corner by attacking the game of ‘Doctor.’

Bob I still think it’s kind of silly that you play Doctor in the housekeeping corner. Do Doctors come to houses or something?
Miriam Sometimes they do.
Bob Don’t you ever play anything else? Or is it always shot giving?
Miriam We like the Doctor but sometimes we play House of the Wicked Witch.
Bob Wicked Witch? How’s that go? I never heard of that. Is that
like something from the Wizard of Oz? Or a different wicked
witch?
Miriam From the Wizard of Oz.
Bob Does anybody know the song or what?
Miriam I and Dara know the song.
Bob You and Dara?
Miriam And Maria
Bob How’s it go? “La la the wicked, la la the wicked witch, la la the wicked witch is dead”? No? That’s not the song?
Miriam No. It’s about the Wizard.
Bob Oh. We’re off to see the Wizard?
Miriam Yeah.
Bob The wonderful Wizard of Oz?
Miriam Yeah.

It’s clear that my wicked witch was she of the west upon whom did fall Dorothy’s house. In retrospect, I’m sure the children think more of the Witch of the East, she commander of flying apes and profoundly allergic to water. No dancing Munchkins for them.

6/27 Miriam arranged for Dara to come play at our house today. Because Miriam expected to come to Logo, I asked her if she intended to bring Dara with her and wondered whether Dara would want to come. Miriam responded that she could get Dara to come to Logo by telling her it was a good place to play Wicked Witch. I had no idea why this was so.

Dara and Miriam at lunch told me a little more of Wicked Witch, not clearly perhaps but enough to reveal what sorts of sides and tensions exist. They mentioned that the boys build spaceships in the kindergarten and should they be left unattended, the girls play Wicked Witch, swoop down on the spaceships, and keep the boys away. This, I saw too late, was relevant to Logo’s being a good place to play Wicked Witch. Robby and Sam have been playing war games in the Learning Lab, building barricades or trenches from unoccupied chairs. When Miriam and Dara seized the momentarily unoccupied trenches, I realized from the commotion how Wicked Witch was being applied at Logo.

Gretchen informs me that while the children played at home, most of their time was spent playing Doctor in the tree fort.

Relevance

Both Doctor and Wicked Witch are highly mobile fantasies which appear to be role centered with improvised skits focused on dramatic actions: giving and getting needles; seizing somebody else’s place. From outside the kindergarten, the setting dependence of the games I speculate to be primarily in the nature of a space allocation. The girls play in the housekeeping corner. They use it as their home base for whatever fantasies they can construct with a sufficiency of roles for themselves.

Vn01501

Vn015

Tic tac toe

5/24/77


Miriam emerged from her bath not at all ready for bed but looking for someone to play with her. I agreed she could stay up and that we could play together while Robby was getting ready for bed. The game was my choice. My objective was to induce Miriam’s copying my successful gambits and her re-applying them against me (cf. vignette 9).

Miriam began with her currently favorite opening to produce this game, recorded in the following dialog (her moves are letters, mine are numbers):

1.   B |  3  | C
    -------------
       |  1  |
    -------------
       |  2  | A
Miriam Me first, please.
Bob O. K. You first.
Miriam Will you go in front of me?
Bob What do you mean?
Miriam Like here, if I go here [at opposite diagonal].
Bob Well, let’s try it and see. . . . Suppose I go over there? [at opposite diagonal]
Miriam No. Don’t.
Bob Suppose I go there?
Miriam O. K.
Bob That’ll be number 1. . . . Now I’ll put 2 right there.
Miriam [placing her third X] Two ways to win!
Bob Um. Do you have any ways to lose?
Miriam Yeah [in a small voice]
Bob You’re going to lose.
Miriam I’ll put —
Bob TIC TAC TOE.
Miriam [complaint — wah wah wah!] You stupid.
Bob I’m not stupid.
Miriam Yes you are.
Bob No. I’m pretty good at tic-tac-toe. How did I beat you?
Miriam You went to, to, to [noises match her gestures to the places I moved].

Miriam’s description of my winning play was not illuminating to me. I hoped replaying game one in reversed roles would help decenter her focus. In game two Miriam refuses to replay game one, preferring to block my third corner move (contrast games two and one). Her putative blocking attempt fails because of the symmetry of the gambit. Game three replays game one with the original roles maintained. When I call attention to the place of forced moves in my play, Miriam follows that lead in modifying her failing three corner strategy.

2.    2  |     |  B        3.    B  |  C  |  3    
     ---------------            ---------------
      C  | A   |                 4  |  2  |  E     
     ---------------            ---------------
      3  |  4  |  1              D  |  1  |  A 
Bob You watch. I’ll play the same game you played. I’ll put my 1 there. Where are you going to put your piece? [center square X move] Oh. You don’t want to play my game, huh. How ’bout I put my 2 up here? [Miriam then puts 2nd X in opposite corner] Are you watching now? what have I got?
Miriam Two ways to win.
Bob How did I do that to you?
Miriam You went to, to, so you can have a way to win.
Bob Could you do that to me?
Miriam Yeah.
Bob Let’s try it again.
Miriam Me this time first.
Bob You want to go first?
Miriam Are you going to go in front of me?
Bob I don’t think I’ll let you beat me. . . . You’re afraid I’ll go over in this diagonal corner here? Right there? Well, I won’t do that. I’ll go some other place. But remember: in this game [1] I did not go in the diagonal corner and still had you, didn’t I? Yeah. I’ll go right here.
Miriam Oh. You’re trying to play your dirty trick.
Bob I don’t play and dirty tricks. I play good tricks. . . . Now. You have one way to win there. I am forced to move here.
Miriam [tooting noises — continuing intermittently]
Bob Do I have one way to win? Yes. You are forced to move down there. You have one way to win there. I am forced to move there.
Miriam X.
Bob So that’s a tie.

Game four proceeds as my attempt to show Miriam what is expected of a player whose initial plan is frustrated, i. e. one should not gripe nor negotiate turn takings at victory but should adopt the best expedient one can.

4.    A  | 4  |  C 
     --------------
      D  |  3 |  B  
     -------------
      2  |  B |  1 
Bob Let’s play game #4. I’ll go first now. I’m going to go right there. Are you going to go across from me? Are you going to block my move? Go ahead. Can you block me so I don’t do that? Oh phooey. Now I’ve got to figure out some other way, because I know I can’t use that good trick that you know, so I have to figure out some other trick. I will go here [2]. Now I have one way to win.
Miriam [blocking row] None way.
Bob O. K. You blocked me. Ha. I will go here [3]. Now I have one way to win. . . . Hum. Right here, I see you have a way to win. I will go there [4].

In game five, I attempt to exhibit the purposes behind each of my moves, specifically showing that I think of her responses to my moves as well as my own objectives. Instead of attempting to negotiate a victory, I assume she will move to block my plan and adopt a different gambit on that basis.

5.   A  |  C  | 3 
    --------------
     4  |  1  |
    --------------
     D  |  2  | B  
Miriam Me first. Will you block me?
Bob Maybe. But even if I don’t block you, it still seems I do pretty good, don’t I?
Miriam Yep.
Bob Did I block you here? [in gane 1] No. But I beat you. . . . If I go here [at perpendicular diagonal corner on 2nd move] you can block me and get two ways to win. Right?
Miriam Right.
Bob If I go here and you block me, do you get two ways to win? No, you can’t. I am going to go here [move 2] and I have one way to win. You made a forced move [C]. You have one way to win, so I am forced to move [3] [Miriam blocks 3 – 1] and you have one way to win again. So I have another forced move and it’s a draw.

In games six and seven, after defeating Miriam, I again attempt getting her to re-apply an opponent’s successful strategy against him. (My opening in game six, Miriam’s in game seven; dialog describes game 7):

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

7. 3 | A | C -------------- B | | 4 -------------- 2 | | D

Bob You move first. Let’s see if you can beat me the same way I just beat you. O. K. You’re starting with an X. I’m going to go right where you went. Let’s see if you can beat me just the same way I beat you.
Miriam Wish.
Bob Is that the same way?
Miriam Did you go here?
Bob Yes. O. K. So you’re going in the corner now. Now this [2] is a forced move, because you have one way to win, so I have to go here.
Miriam Two ways to win.
Bob Yes, you do. And you went over here [3]. So I will too, and you beat me. . . . O. K.
Miriam [cheering herself] Yaaaa. I won for the first time. Hooray.

The interest in game eight is that it shows Miriam more intent on blocking the opponent’s next move than winning directly. Her failing to notice a winning move leads into my codifying the order in which she should apply her decision principles.

8     B  |  1  |
     --------------   
      C  |  A  | D2
     --------------   
      3  |  D1 | 2  
Bob Would you like to first again, Miriam?
Miriam O. K. Yeah.
Bob That one’s yours. Let’s see if you can beat me a different way. I will go there again. But see if you can beat me some different way. Oh. O. K. I have a forced move. I have to go here [2].
Miriam [gets two ways to win]
Bob I have a forced move here. So I must go here [3].
Miriam [starts to block 2 – 3 row]
Bob No, no.
Miriam I blocked you.
Bob But look. Is it better to block me or better to win?
Miriam Win, win.
Bob But one of the things you have to figure, Miriam, every time, you have to ask yourself: does the other guy have a way to win? Can I beat him, first? ‘Cause if you can beat him, first, you don’t have to stop him from winning, ’cause you won already.
Miriam Right.
Bob So let’s see. The number 1 thing you look for [writing list], you say: can I win?
Miriam Can we stop for a while?
Bob Yeah. The second thing is: forced moves. And the third thing is what? Two ways to win! O. K.?
Miriam O. K. What’s the seventeenth thing?
Bob No, they’re the only three things you have to look for, Miriam. . . . Can you tell me what the three things are you look for?
Miriam Yeah
Bob The first thing is what?
Miriam Can I win.
Bob What’s the second?
Miriam Forced moves.
Bob And the third?
Miriam Two ways to win.
Bob Which one do you look for first?
Miriam Can I win.
Bob Second?
Miriam Forced moves.
Bob Third?
Miriam Two ways to win.
Bob You got it. That’s all there is to tic-tac-toe. If you always use those three rules, in that order, you’re going to be a winner. O. K.?
Miriam Yeah.
Bob Or else maybe you’ll come to a draw. I think you’d better wash your face and go to bed.
Miriam Good night.
Bob Good night, sweety.

Relevance

I expect tic-tac-toe to serve Miriam as a simple model of a bi-polar activity, i. e. one wherein at each step of your activity you must attend to your previous actions and a response to that action. (By a model, I mean a framework in terms of which one may conceive of other activities, such as putting questions to nature.) The features of tic-tac-toe which I see as useful are: its interactivity; the opening gambit may be yours or your antagonist’s; there are a set of good tricks one can learn; there are pitfalls to avoid; when one does not see a sequence of forced moves to game end, there is an ordered set of heuristics to follow.

If Miriam can reflect on her own procedures in playing tic-tac-toe and uses tic-tac-toe as a model for exploring phenomena, reflexive abstraction will be a natural consequence .

Vn01701

Vn017A

Arithmetic Ripples

5/28/77


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

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

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

Relevance

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

Addendum 17-1

ADDENDUM 17-1

Comments Off on Vn01701

Vn01702

Vn017B

Arithmetic Ripples

5/30/77


As Robby and Miriam came in from play for a little refreshing juice, I heard from the kitchen the squabbling one expects of near-aged siblings:

Miriam I can add big numbers.
Rob Oh brother!
Miriam I can. I can do one thousand and thirty five plus two thousand.
Rob Easy.
Miriam No. Three thousand and thirty five.

When I asked Miriam later where she got those numbers for adding, she replied, “From the adding you and I did the other day.”

Relevance

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

Vn01703

Vn01703

Arithmetic Ripples

6/1/77


Miriam was playing in the kitchen with Scurry this morning. Gretchen and I were discussing some topic, and I mentioned a division problem. Miriam piped up, “I can divide, Daddy. . . . 8 divided by 8 is 1.”

I congratulated her on her prowess. For Miriam the formula she recited constitutes division. The division problem is the one I executed in playing Dr. World’s computer game (in Home Session 5, 5/30). Despite her ability to divide sets concretely (see Miriam at 6: Arithmetic), Miriam does not appear to associate dividing with “division,” a process for which she has, I believe, this one example.

Relevance

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

Vn01704

Vn01704

Arithmetic Ripples

6/1/77


When she came home from school, Miriam asked to stay home today. I suggested we do her second adding session. Miriam then countered that we should do math at Logo and use the computer. I agreed.

At the lab, while I was logging in, Miriam began playing with a pile of bricks and set them in a row to mark off a “stage.” Instead of doing math, we did “Goldilicks,” her version of the 3 bears story.

Relevance

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

Vn01901

Vn019

Rehearsal

6/2/77


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

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

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

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

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

Relevance

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

Vn02001

Vn020A

In the Gymnasium

6/2/77


Twenty four children filing into the gym, a space about 20 by 40 with a wall-wide, wooden climbing rack at one end. During the half hour, when any children did not want to play some game or other he might climb around on that climbing rack, come sit on the sawhorse where I was standing, or sit against the opposite wall. It was common for several children not to join each game.

During the period, I recall 5 games being played:
ICICLES — a few children are ‘it’ in the center of the gym; the others at command run lengthwise to the gym’s other end; anyone tagged should ‘freeze.’

COWBOYS AND INDIANS — a chase game with two teams; one team hides its eyes against the wall; as the second team sneaks up on the first, the teacher intones, “Oh, you sleepy cowboys, you’d better wake up. Here come the INDIANS!!!”; with this cry the cowboys chase the indians across the gym.

BATTLESTATIONS — a general exercise game in which the children leap to stereotyped postures (e.g. at attention, saluting for “here comes the captain”) or actions (e.g. swimming gestures for “here comes a shark”) when the teacher gives commands. These were usually given in pairs, the exercise value in going from one state to the other — port/starboard here comes the captain/all hands on deck naptime/chowtime

FIRE CHIEF — one child is the chief, getting to select which of three teams responds to the teacher’s alarm: “Fire, fire, fire: alarm at station. . .” When the chief yells his number, the selected team members race to the climbing rack, climb far enough to tag the top, then race to the opposite end of the gym. The winner of the race gets to be the new chief.

ANIMAL FARM — this final game of the period is the decrescendo of the hectic excitement of gym. The children sit in a circle. The teacher, in the center, covers the eyes of one child who must guess the identity of another, selected from the several who volunteer to make animal sounds.

After gym, the children spilled back into kindergarten, where
they began, relatively slowly, to pick up the variety of materials they
had so liberally scattered before gym.

Relevance

The observations focus on an important part of the world of Miriam’s peers, and her standing apart from that. I infer that, because of her limitations and specific experiences, she has a different framework for thinking about gym activities from her peers.

Vn02201

Vignette 22.1

Emberley’s Faces

6/6/77


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

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

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

Relevance

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

a Sample of Miriam’s Work

Vn02301

Vignette 23.1

Arithmetic Ripples

6/5 & 11/77


Miriam does not yet recognize the existence of negative numbers. The typical problem this causes her was shown as we rode home from buying a Sunday paper (the children go with me to buy chewing gum). Miriam was discussing making change with Robby. She knew that paying for a 15¢ pack of gum with a quarter involved a ‘take-away’ problem. She asked Robby (getting the formulation backwards):

Miriam How much is 15 take away 25?
Robby 10.
Miriam That’s not right. I made a mistake. I said 15 take away 25.
Robby Minus 10, like 10 below (cf. Protocol from the series on Robby’s arithmetic development).
Bob Does that make any sense to you, Miriam?
Miriam No. You can’t do that. That’s like 1000 take away 7000. You can’t do it.
Robby 6000 below.
Bob Does that make any sense to you?
Miriam No.

6/11 Today was one of those terrible days. Gretchen and I had bad headaches. The weather was foul, rain for two days running when the forecast had been for a bright weekend. The children played inside all day; they played chase with the dog. And finally, Miriam is mad at me.

Late in the afternoon, she came to me: “Daddy, I’m mad at you for two reasons. You didn’t do any arithmetic with me today, and you told me it was going to be sunny.” I promised to do some adding (she said then both adding and subtracting) on the morrow and disclaimed all responsibility for the weather.

A little later, Miriam found Robby willing to talk about arithmetic. The two entered our reading alcove with this conversation:

Miriam 10 times 10 is 35.
Robby No, Miriam (counting on his fingers), ten 10’s are a hundred. Isn’t that right, Mommy? (Gretchen confirmed his result).
Miriam It can’t be. 5 times 5 is 25, so 10 times 10 is 35.

As Robby went on to other affairs, Miriam asked me, isn’t that a big number? I can add three thousand and thirty five (cf. Vignette 17, 5/30). Upon my responding that the number was something like that, she suggested we look in my notebook. We found there the number 3132 as an addend (cf. Home Session 4). I promised that she could learn to add some more big numbers.

Relevance

These three incidents point to three separate themes that will be developed in future arithmetic sessions with Miriam. I intend to confront her, gradually, with situations which will require her inventing the negative integers. I intend to introduce her to ‘times’ as counting in non-unary increments. I intend to reveal to her that what she has learned of adding already (in Home Sessions 4 and 6) permits her to add all big numbers.

Vn02501

Vignette 25.1 TicTacToe (4) 6/3/77

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

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

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

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

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

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

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

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

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

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

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

Miriam begins with a corner move.

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

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

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

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

After my move at 2:

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

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

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

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

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

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

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

Miriam begins game seven with a center move.

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

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

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

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

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

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

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

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

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

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

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

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

Vn02701

Vignette 27.1 Emberley’s Faces (2) 6/17/77

A large portion of Miriam’s drawings during the past year have
taken the form of presents she makes to others. She has spoken of them
as presents many times. One formal element of these notes reflects
that character. Each typically bears a tag of the form: “TO _______/
LOVE, MIRIAM” (see Addendum 1 for an example). Her initial tags were
of the form: “TO ________/FROM MIRIAM,” reflecting, I believe, the
format of tags she read on presents received at Christmas and so forth.
Their great-grandmother sends both children postcards whenever she goes
on trips with a valediction “Love, G.G.”

The note presented in Addenda 1 and 2 is to a fellow of Miriam’s
play group. Brian is a boy whose entire family is committed to foot-
ball, so it’s most appropriate that Emberley’s ‘Football Fred’ face
(page 11) should be a present for him. The face inside is ‘Sleeping
Simone’ (page 7). Because the note lay on her desk for several days,
I had the opportunity to ask Miriam how she came to draw such a nice
picture. She replied that she copied Football Fred’s face but made
the body up herself. The shoulders of that body come from Football
Fred’s face. The ‘bar’ arms, ‘stick’ legs, and circular body are
typical of her earlier drawing. The striped shirt is the costume of
a rugby player ( a very popular shirt style now, which is also found
in Emberley’s book on page 28).

Relevance
The note/present Miriam made for her friend Brian shows in
high contrast the appearance of sophistication which she is
developing from copying faces in conjunction with the quite
primitive body-drawing she invented herself.

Addendum 27-1

Football Fred

Vn 27-1 Emberley's Football Fred

Addendum 27-2

Sleeping Simone

Vn 27-2 Sleeping Simone

Vn02901

Vn029.01 Making Puzzles 6/18/77


Vn29-1

Vn29-2 Addendum1

Vn29-3 Addendum2

Vn03001

Vignette 30.1

temporary upload

Original Fair Copy, Scanned page 1

Vn 30-1 Original Fair copy; temporary upload

Original Fair Copy, Scanned page 2

Vn 30-2 Original Fair copy, temporary upload

Vn03101

Vn031.01 Collecting Tolls 6/19/77

Robby and Miriam each receive a nominal ‘allowance’ weekly,
regardless of whether they’ve been ‘good’ or ‘bad’ or done what we
parents have wanted them to. They know it is computed by multiplica-
tion: for each child the ‘allowance’ is 5¢/year times the child’s age.
Thus Miriam recently began receiving 30¢/week. Robby receives 35¢ and
will soon receive 40¢. Such is a small amount of money, enough to buy
one stick of chewing gum a day with only a little left over.

Upon our moving to Boston, Robby took over the chore of mopping
the floors, the frequent necessity of which derives from Miriam’s dust
allergy. Because I consider it my responsibility, and not one I can
manage easily and directly, I pay Robby to do this work for me. He
saves his money andy buys models of boats when his hoard is large enough.
Because Miriam cannot perform any similar work, this difference has
become another element of sibling competition and has intensified the
children’s general interest in money as an instrument of power.

After an early spring trip to Connecticut (which included
travel on the toll-collecting Connecticut Turnpike), I found Robby had
set up a toll booth at the entrance to the secretaries’ office at Logo.
(At one point he claimed Greg owed him $18.) I objected to that game
and told Robby to play it no more at the lab.

This Friday Gretchen brought home a stack of cut yellow paper,
the pieces being about 3×8″. When he first saw them, Robby referred
to the papers as ‘tickets.’ In fact, they are about the same size and
shape as the parking tickets I have collected with distressing regu-
larity at MIT. With this minimal suggestion of tickets (and paying
fines), Robby conceived and both children executed a plan to establish
toll booths in our carriage house, Miriam at the entrance to our general
living area and Robby at the entrance to our bathroom.

This seemingly harmless game was a good answer to the recurrent
question of what to do on a rainy day. The game was one of the chil-
dren’s invention, a simultaneous practicing at being grown up and an
expression of their concerns and ideas. It had the ultimate value, the
sine qua non, of absorbing their time and energies in a direction-free
project. The children made signs for the toll booth, tally sheets of
accrued obligations, and collections (typed) of commutation tickets
(examples may be seen in Addendum 31-1).

This toll-collection project finally spanned several days.
Aside from increasing the general clutter, the only flaw – and this a
fatal one – was that the children confounded the toll collection ‘debt’
with what we considered real obligations, i.e. the providing of their
weekly allowances and the daily snack allotment (50¢) the children
receive when they come to work with me at Logo. Robby began computa-
tions such as this: if I save 2 fifty centses, mop Miriam’s bedroom
and the hall, and you pay your tolls, with what’s in my bank I’ll have
enough to get a model of the King George V.

Direct confrontation was the only way to disabuse Robby of the
notion that we would really pay his tolls. I began by charging him a
quarter for a glass of soda (the commercial rate at MIT). His strenuous
objections were exacerbated when he found the evening meal would cost
him 3 dollars. When he countered that the price was too high, so he
and Miriam would ‘make their own,’ I announced the 1 dollar refriger-
ator opening fee and my 50 cent kitchen entry toll. Robby accepted,
albeit with little grace, the collapse of his scheme. Miriam persisted
for days thereafter making tickets charging me 99 cents for opening
the refrigerator (if you can charge me a dollar, I can charge you
99 cents).

Relevance
These notes document the spontaneous generation and working
out of a small project at home with no grown up intervention.

Addendum 31-1

Toll Collection Records

Vn31 Toll Collection Records

Vn03801

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

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

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

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

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

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

Vn03901

Vn39.01 Good News 7/1/77

At lunch today we told the children that Gretchen is pregnant.
When the children and I finished our morning’s experiment (Logo Session
33), we joined Gretchen at home, picked up a stack of their favorite
books, and all went to the doctor’s office.

We all suffered a delay (the doctor was late in returning from a
delivery). Each child read his own books, then the other’s, and finally
whatever children’s books they could find in the office. They seemed
to take no special notice of most women being about 7 months pregnant.

After our interview with the doctor ( and our listening to the
fetal heart beat!) Gretchen remained for some laboratory tests while
I took the children outside. They were rambunctious from their hour’s
wait and argued with me that we should have left them home. When I
raised the surface objection that we couldn’t find a baby sitter, they
claimed to be big enough to stay home by themselves and that a compro-
mise solution would be for them to work in the garden with Steve (our
landlord’s handyman).

When we sat down to lunch at home, I asked both children if they
had noticed anything unusual about the patients in the doctor’s office.
Robby said several of the women had big bellies. When I asked why,
Miriam said that meant they had babies inside. Neither guessed why
we had gone to that doctor’s office. “Kids, we have some good news.
Your Mommy has a baby in her belly!” The children were thrilled. To
their first question, “How do you know?” we could say we had heard its
heart beat. “Is it a boy or a girl?” Both children were looking for
an ally. Robby: “I hope it’s a boy.” Miriam: “I hope it’s a girl.
What do you hope, Dad?” I replied that I hope the baby is healthy,
and was content to wait, as I must do, until the baby is born to find
out if it’s a boy or girl. They started to plan:

Robby If it’s a boy, he can sleep in my room and I’ll give him the crib.
Miriam It’s my crib.
Robby No. I just loaned it to you.
Miriam Well, I’ll give the baby my little blanket. What toys should we get for it?

Gretchen cautioned the children that the wait would be a long one. I
added that the baby would be a late Christmas present for everybody.

Robby asked to be excused from the table so he could tell our
neighbors. I warned both children I wanted no racing or fighting
about the good news. They could tell whomever they wanted but they
had to do it together. Miriam left her lunch and both went across the
court. We could hear their cries: “Steve, Carol, Annette, Jim — we’re
going to have a baby!”

Relevance
This vignette witnesses the children’s excitement over an event
which will complicate and enrich our common life.