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LC0aR6

LC0aR6: A Paper Inspired by Seymour Papert
for the Online Journal, Learning Landscapes
The paper was published on July 15, 2013.

Lawler, Robert. (2013). Getting Intelligence into the Minds of People
LEARNing Landscapes. Advance online publication.

LC1b Text

LC1b Text

Comments:

Source materials

This material consists of 21 protocols, primarily transcripts from audio recordings, some of which have been absorbed directly into the chapter “Sketches of Natural Learning,” and others used in “The Development of Objectives.” Some are in character more like the Vignettes of The Intimate Study, which derived from them. All are presented here, scanned from original typescripts, with addenda from Rob’s work and computer printouts, to the extent preserved. For pointers to source material about Rob in The Intimate Study, see LC1c-Text Rob in TIS Vignettes

Protocols 1-21, with supporting materials; Robby Lawler at 7-8 years

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Date

Theme

Link

pp.

Add#

Publications Reference xref.
1

10/8/76

Detailed audio transcript: Introducing Rob to TG prograns; relating that to using Zoom; confusions

LC1bT01

14

7

None.
2

~10/15/76

start using ZOOM; attempt to go from there to Logo TG
teaching bugs and problems
Miriam: adding (minimal)

LC1bT02

2

3

None.
3

Other approaches to programming intro; another teaching failure.

LC1bT03

4

2

None.
4

11/13/76

Triangle; Starting House

LC1bT04

2

3

LC1bA5: Retrospective: a house that failed
5

11/14/76

Drawing a Fox; using TG to assemble shapes.

LC1bT05

5

3

LC1bA5: Retrospective: a house that failed
6

11/13/76

Number represetations; Adding

LC1bT06

2

2

LC1bA3: Complex Minds and Homely Circumstances
7

Adding right to left

LC1bT07

2

2

LC1bA2: Third Encounter with Number
LC1bA3: Flexible Knowledge
8

11/18/76
(transcript year error)

Approaching programming by changing existing programs

LC1bT08

4

3

None.
9

Thanksgiving 1976

Instruction as Invention
“Supercraps”

LC1bT09

2

5

LC1bA3: Instruction as Invention, Memorization and Engaging Games
10

Inventing Negative Numbers:
Proving that many exist.

LC1bT10

1

LC1bA3: Complex Minds and Homely Circumstances
11

Christmas 1976

Place Value and Scale Conversions

LC1bT11

2

LC1bA3: Natural Confusions
12

a few days later

Using Multiple Representations

LC1bT12

5

LC1bA3: Mentioned but not quoted extensively.
13

Multiplication: the TIMES program

LC1bT13

7

6

LC1bA3: Guiding Constructive Analogy
and The Obvious is Unknown
14

No sense of commutativity
Estimating in Multiplication

LC1bT14

2

LC1bA3: The Obvious is Unknown
15

Feb. 1977

Showing a Solution

LC1bT15

1

LC1bA3: The Urge to Instruct
16

Transfering Dimensions

LC1bT16

2

2

LC1bA3: Concrete Action in a Non-square World
17

a month after protocol 14

Commutativity; the relation of money to concrete calculations

LC1bT17

4

1

LC1bA3: Multiplying (by Analogy with) and Money
18

A Companion Inspires some musical interest

LC1bT18

1

2

Not published.
19

Numbers and Letter codes
Beyond his grasp

LC1bT19

7

2

Not published.
20

April 1977

Emphasizing a Problem

LC1bT20

1

LC1bA3: The Urge to Instruct
21

The Multi-add Algorithm

LC1bT21

8

3

LC1bA3: The Natural Confusions

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

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

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

LC1bT20

LC1bT20 Protocol 20

Included Text Pages

RAL protocol 20

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None

LC3cA35

LC3cA35

The Genesis of Symbolic Thought

Learning, in General


Let us begin by going beyond a “stimulus-response” couple to a stimulus-response arc. That “arc,” represented as a link between input and output (more generally stimulus — which may be entirely interior — and response — which may be entirely interior) is the site for attachment of interventions. In a simple case (e.g. Meltzoff’s experiment), the output of the SR arc mimics the input.

Interventions are, at first, interruptions of process, because of some sort of disruption (types might be failure, confusion, discordance, etc.); in this case, the links become sites for attachment of problem descriptions. When discriminations occur, these interrupted-links become the loci of extensions to the SR arc; how do the discriminations occur ? They follow Sussman’s formulation: problem descriptions are converted into prescriptions for change by local structure modification agents. (Minsky’s B-brains are intended to be capable of this functionality.) After a discrimination, the interruption has been repaired and is now an intervention in the preceding structure. Every link can be interrupted and the development of interventions occurs everywhere. As intervention-extended networks grow out of SR-arcs, they become slower in processing, more confusing for B-brains to manage, and ultimately, too complex for B-brains to change (this means they cease being capable of learning).

As these networks (societies of agents) grow, they compete with each other. Note well, the simplest processes (SR-arcs) still compete with them, and this can lead to the later replacement of a well established complex society of agents by a later developing but better fitting simple society.

Language-Specific Learning Theory


Following Peirce, we schematically represent three kinds of ways in which signs are involved with things signified: Iconic signs recall things signified, indexical signs indicate or “point to” things signified, and symbolic signs name things signified. (“Names” here implies conventional assignment of reference, variable by society and language groups.) The main issue to be explored is relations of the three kinds of signs, among themselves, and the way their interactions can be seen to explain important linguistic and psychological phenomena.

Iconic Signs as Fundamental Beginnings
In the simplest case, iconic signs are pristine SR arcs; they remind individuals of the things signified in that their intepretant recognizes No Significant Difference (NSD) between the icon and the thing signified. The interpretant for such an iconic sign is no more than a K-line which responds to the stimulus. The internal representations of the external sign or e-sign (which has in this case been taken as an iconic sign) becomes associated with the K-line; this association creates a change to the K-line where the counterpart “e-sign related modification to the K-line” serves as a personal-sign, or p-sign. This associated p-sign is used expressively to produce a vocalization intended to indicate the thing signified, e.g.:

  • the e-sign /”Scurry”/ used by family to refer to the dog [Scurry] is interpreted by Peggy to be associated with the dog [Scurry].
  • Peggy’s K-lines involving [Scurry] become associated with her p-sign for [Scurry] which, in her vocal expression, is manifest as /cul/di/.
  • when Peggy uses her p-sign { /cul/di/} to signify [Scurry], she is using the term as an indexical sign. This expressed p-sign functions as an indexical sign if and only if others recognize what it indicates.

How P-signs Become Indexical Signs
Knowing that Peggy expresses her p-sign for [Scurry] as /cul/di/, some people use the sounds /cul/di/ to refer to [Scurry] in the attempt to communicate with Peggy. It works. In this special case, the infant’s p-sign functions as the personal part of an indexical shared sign (s-sign) because the local Society accommodates to the infant. Consequently, association of the p-sign with the [Scurry] k-line is strengthened. The use by another person of /cul/di/ is not a p-sign itself (for them), but a transient, symbolic e-sign referring to the same entity [Scurry].

When the infant modifies the expression of her p-sign to accommodate to the Society, the p-sign becomes an indexical sign through a different process, as follows. Other people use the e-sign, e.g. /”Scurry”/ to refer to [Scurry]. Interpretants need to be developed to relate Peggy’s perception of /”Scurry”/ (already associated with her k-line for [Scurry]) through her p-sign { cul/di/} to a modified vocal expression similar enough to the conventional or common e-sign /”Scurry”/ to be recognized by others. In this general case, the infant’s p-sign functions as part of an indexical common sign (c-sign) because she accommodates her vocal expression to the conventional e-sign for the entity signified. In sum, every individual has p-signs as parts of k-lines associated with entities. When indexical signs are used in communication, it is because individuals negotiate the vocal expression of their signs to permit communication. In the special case above , we refer to these signs as s-signs; in the common case, we refer to these signs as c-signs. Both s-signs and c-signs are kinds of e-signs. The difference is that indexical s-signs are part of the infant’s idiolang. Indexical c-signs are part of the society’s public language. The need to associate infants’ idiolang-effective p-signs with others’ c-signs is a primary interior motor of the symbolic transition, as explained in the following.

The Theoretical Context of Modeling

We will model language development in the theoretical context of Minsky’s Society Theory of Mind and its suggested forms of representation. The central ideas used in setting the context of this model are that the general processing structure of the mind is represented by Minsky’s “ring closing” structures (p.205), with K-lines as the basic structural elements of memory (p.82 ff.). It is presumed that SR arcs grow into elaborate K-lines through the processes described below and may also grow into societies of agents, depending on the circumstances of learning. A first assumption is that one can think of the interior perceptions of “iconic” signs as Not-Significantly-Different from associated memories. A second is that incremental learning with respect to any SR arc proceeds in the Sussman paradigm, with B-brain structures modifying interrupted arcs, which leads to the recognition of e-signs for distinguished external things.

Indexical Signs and Learning Processes
The meaning of an iconic sign is determined entirely in the mind of the infant. The beginning of the indexical sign learning process is in the infant’s attempt to communicate something. Grant that the infant has associated some producible sounds, such as /cul/di/, with the entity [Scurry], through a listener agency mimicking what the infant perceives of the e-sign /”Scurry”/. {/Cul/di/} is then a p-sign which serves the infant’s expressive intentions. The e-sign/p-sign couple does not function as an indexical sign until there is negotiated a shared meaning between the infant’s talker agency and that of some other person who understands what the infant intends to communicate.

This can happen either through the infant improving her production of sounds to match better the conventional e-sign or by the other person changing his language to better communicate with the infant. In Peggy’s case, Bob started referring to [Scurry] by /cul/di/ when in her company. /Cul/di/ functioned as an indexical sign between Bob and Peggy because both used the same sounds to refer to the same thing signified by a convention, explicit here in Bob’s decision to adopt Peggy’s term for [Scurry]. This is a shared sign, or s-sign. Such signs are the main elements of the individual infant’s idiolang. Subsequently, Peggy modified the vocalization of her p-sign { /cul/di/} to conform to the sound /”Scurry”/ used by her mother and siblings when calling the dog or referring to her. This exemplifies the second process of negotiation of meaning between the infant and her local society, through which her idiolang p-signs are brought into correlation with the c-signs of the public language in her Society. Negotiating meaning is the common ground of these two different processes, even though the first is so transitory and the second is so dominant.

Negotiating meaning has been described as the primary means for learning to communicate with sounds. I argue that the portion of the process in the interior world — one linking modifiable responses to external signs (e-signs) in recognition processes with modifiable personal signs in expression processes — is the prototype for the symbolic use of words. Can we more precisely articulate this process to clarify the transition from using indexical signs to using symbols as a natural consequence of processes of communicating?

If the infant’s listener agency does not discriminate initially between what she perceives on hearing /”Scurry”/ and what her talker agency expresses as /cul/di/, there may be either improved discrimination with respect to /”Scurry”/ or better correlated expression by modifying /cul/di/ to become more like /skuh/ri/, or both. The first case is a modified discrimination on the recognition side of the SR arc. The second is one of modified production on the expression side of the SR arc.

We have already postulated that the infant’s p-sign generates a vocalization, but we have not previously noted that corresponding to the expressive aspect of the p-sign represented by the vocalization, there is a perceptual aspect which also needs to be represented. Let’s say that on hearing /”Scurry”/, the [Scurry] k-line perceives /skuh/ri/ but does not discriminate it as different from /cul/di/ through which it expresses p-sign {/cul/di/} . When subsequently a discrimination is made that perceived /skuh/ri/ is different from the normally produced /cul/di/ the infant’s listener and talker agencies have to negotiate an integration of the two aspects of the internal sign. It is this process that is the prototype of word definition by symbolic use of known words. Consider the following example:
We know that Scurry is a dog, and that /”dog”/ or /”doggie”/ are appropriate words to use in referring to [Scurry]. How could such a word enter the repertoire of indexical signs in Peggy’s idiolang ? We might say “Scurry is a kind of dog.” Peggy surely heard the word /”dog”/ before she had any well formed concept of [dog] as a category of kinds of entities. For her, when she understood that the term /”dog”/ was meant to indicate [Scurry], the sense she would have made through interpreting /”dog”/ would be that “dog” is another name for [Scurry]. /”dog”/ is thus a synonym for aspects of the p-sign represented either as { /skuh/ri/} or { /cul/di/} , depending on the time that the association was made.

Synonyms are common in an infant’s world. Mom and Dad have personal names. The infant herself may be Peg, Peggy, sweetie, or have any of a myriad of affectionate appellations. It is an open question as to the point in time at which anyone learns that what one assumes is a synonym for a well known entity’s name refers to some other entity. Recall, for example, that Peggy’s first two word sentence was /cul/di/va/va/! The context made it clear that she was referring to the barking of a remote dog. Did Peggy intend to communicate that ? Did she even know there were other dogs in the world besides Scurry ? No — this is a case of her marking no significant difference between her notion of [Scurry] and any other similar creature.
This reflection can help us understand one simple way that Peggy’s listener and talker agencies could integrate the perceived vocalization /skuh/ri/ of e-sign /”Scurry”/ with the expressive vocalization /cul/di/ of p-sign { /cul/di/} . Let it be the usual case to have multiple names for entities. Then /cul/di/ could be Peggy’s personal name for [Scurry] whom others may choose to refer to as either [/cul/di/] or /”Scurry”/. Some people might even refer to [Scurry] as /”dog”/ or /”chien”/. Development from the infant’s idiolang of indexical signs to a broadly flexibly public language then proceeds through elaboration of names for well known entities, where the relation of synonymity is the first wave of definition of new words (symbolic signs) in terms of preceding linguistic structures (indexical signs). It is in this specific sense that the integration of perceived and expressive vocalizations related to a specific k-line is the precursor and prototype of the development of symbolic thought, the key aspect of which is that words have meanings specifiable in terms of the network of meaning of other words.

.

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.

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.

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.

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 ?

Vn00701

Vn007.01

A Willing Subject

5/18/77

Today was the most difficult experiment of the initial series, separating the variables implicated in the flexibility of bending rods (Cf. The Growth of Logical Thinking from Childhood to Adolescence, Inhelder and Piaget). Of the many experiments through which one may distinguish concrete from formal thinking, this one shows best the distinction between conceiving of things as objects with properties which may occasionally be of interest and conceiving of objects as instantiations of intersecting ranges of properties of which some may be relevant to its use in a specific context.

How could Miriam possibly be interested in distinguishing the contribution of different properties to rigidity? How many adults could, or would care to, distinguish between the relative importance of a rod’s thickness parallel to a force and its cross-sectional shape? How to quantify, or even balance, such factors is not obvious to the untrained intuition at any age. And Miriam is 6, not 16. Need one not subject a child to exorbitant pressure to have her work at such an experiment? If any experiment in this initial series is vulnerable to such a criticism (either through its very nature or through my execution) it is this experiment.

I was hurried into the bending rods experiment by Miriam’s declaration that she would not come to Logo today unless she could do it. Despite feeling imperfectly prepared, I acquiesced in her demand since the obvious problem was that she felt ‘left out’; I had done the experiment earlier with Robby for practice. During the preliminaries wherein I hoped to establish with certainty a common terminology for the experiment (for a description of this work see Miriam at 6: Bending Rods) Miriam was rambunctious. When not interested much in my questions, Miriam began to create chaos by throwing around dice and balls, which were the experimental materials. I stopped the experiment and we had an argument of this general form:

Bob I won’t tolerate your throwing things and causing this confusion; it will ruin the experiment.
Miriam Then I won’t do it. You’re asking me dumb questions. I’ll play SHOOT instead.
Bob That’s not fair. You demanded we do this experiment today and now we have to finish it.
Miriam I never promised I would do all your experiments. I only said I might do them.
Bob That’s not true.
Miriam I wish I was a baby again so I wouldn’t have to do these experiments.
Bob But you’re six now and doing something important.

Miriam reluctantly agreed to continue; she agreed because of the pressure I put on her, because, in effect, I made her do it.

Despite this grim start to the main experiment, Miriam quickly became engaged in working with the materials and finding “which one is the champion” for bendings. She exhibited no interest at all in separating the variables; consequently, the latter part of the experiment bored her silly.

Riding home from Logo, I told Miriam I felt bad because I thought I was pushing her too hard in the experiment. She said she didn’t want to do any more like that, and I replied that we would do no more of that sort for several months. I expanded that we should think of doing other kinds of things. That this thesis project could be not just going to Logo, but going to other places too. Part could be my coming to kindergarten with her; another part could be visiting friends and family and telling them about our project; another part could be trips to places around Boston. I noted that she had been to the Harvard Peabody Museum and I never had; she could take me there. Miriam said we should do that soon.

Vn00801

Vn008.01

Hula Hoop Analogies

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

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

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

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

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

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.

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.

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.

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

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.

Vn02401

Vn024.01

Writing Stories


Robby called me from Miriam’s bedroom: “Dad, come see the puppet show.” They have played with, even made, hand puppets for a while and enjoy giving shows — whose typical script has been, “Hello, my name is Owl. Goodbye.” I was in high spirits after a very successful arithmetic session with Miriam (see Home Session 7). Sucker that I am, I came along. Walking through the door, I found the children were playing “Ambush” — both lying under covers on the top bunk and crying “BAM BAM” as I walked through the door. Riotous laughter.
Suffering only flesh wounds, I managed to return their fire, then said I thought it was a dirty trick for them to call me to see a puppet show, then shoot me. Miriam responded, “This was our puppet show —

Once upon a time,
There were two guns.
Bang. Bang.
The end.

Her joke was a spontaneous expression of the WRITER program’s story format. Her use of it in this explanatory way shows her recognition that it is a shared model of what a story structure is.

The puppet-show play continued; the children agreed to put on a real puppet show. I had to leave the bedroom, and when ready, they summoned the audience with toots on a toy horn.

Act I The fierce Owl (Robby) swooped down and pounced upon the dancing ballerina (Miriam’s doll).,
Act II The fierce Owl, joined by Eeyore, climbed a tree, and both pounced upon whom? The ballerina had become a teacher and had to be pounced upon because the owl and donkey didn’t want to go to school.
Act III The owl and donkey climbed a tree whence better to pounce upon the teacher, now riding upon two toy horses because of injuries received in act II. (Miriam plays such an action herself because she is so big and her favorite toy horses so small). Miriam argued that it was O.K. for Robby to pounce upon the teacher, but he shouldn’t bite “little horsey.”
Act IVThe horns again called me into the room. “BAM BAM BAM” — ambushed again.

When I had resettled in the reading alcove of my bedroom, the children rushed upon me with cried of “Act V.” We engaged in a general rough house and pillow fight.

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

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.

Vn04101

Vn41.1 7/5-7/77

Whenever we ride to Logo in the MG, Miriam has a standing request
that we follow Memorial Drive down past the underpass at Massachusetts
Avenue. The children like the magnification of their voices provided
when they shout in a closed place. Over the past several years, we have
agreed that they may do such shouting when I am driving them about in
the MG, but not otherwise.

While we lived in Connecticut, the children introduced the ejaculation
“Daddy is a dum-dum” as their underpass chant. I don’t recall
the details but merely the impression that its use involved some sort
of trick (perhaps a promise, not to be kept, that if I let them shout
they would not broadcast what a dummy I am). The children believe this
annoys me, and they relish it as a way of teasing me.

When, two days ago, from the BU Bridge I preferred the Vassar Street
route to the Mass. Ave. underpass, Miriam claimed she was mad at me and
was going to quit my thesis project. I complained to her: “Do you think
I like to hear you shout that I’m a dum-dum? You always yell that.
Don’t you think that hurts my feelings?”

Today, as Robby, Miriam, and I drove home from Logo, we took the
scenic route — down Memorial Drive. Once again the cry was raised.
We continued down Mem. Drive and Miriam looked troubled. “Daddy, we
really don’t think you’re a dum-dum. But we like to shout under bridges
and don’t know anything else to say.”

Relevance
This anecdote exemplifies how peculiarly specific is Miriam’s use
of speech. The phrase “Daddy is a dum-dumb” is thought of as a chant-
for-passing-under-bridges, but one devoid of semantic content.

Post Script

Miriam’s sensitivity to my feelings led her over the past few days
to attempt the development of a new chant. She came up with:

Daddy is a smart-smart.
Daddy is a smart-dumb.
Daddy is a dumb-smart.

Having asked Robby for help she received this suggestion (his view is
different from hers):

Leader

Respondent
Is Daddy a dummy?

No!
Is Daddy a smarty?

No!
What is he?

An idiot!

This latter expression is clearly a relatively flexible variation on
some small script for a shouting-insult.

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.

Vn04801

Vn48.1 Tenable Explanations 7/23 & 25/77

7/23 We drove to town late in the afternoon. In the clear sky, Miriam
could see a bright half moon (I could not from my seat). “If you were
on the moon, Daddy, what would happen when it got skinnier and skinnier?
Would you get bumped off?” I couldn’t understand her question. Miriam
referred to the half moon in the sky, then restated her question: “Would
you get bumped off. . . or does part of the moon become invisible?” When
I returned the question to her, she decided that part of the moon becomes
invisible. I believe her use of the term is such that she conceives of
a part of the moon as becoming transparent in contrast with the (now)
standard view that it is not able to be seen because of our perspective.
When I asked her later, Miriam did not confirm this speculation. I
asked, “When part of the moon becomes invisible, can you see through
it?” She replied, “No.” When asked how it becomes invisible, Miriam
replied, “I don’t know.”

7/25 Miriam found a golf ball in the basement a day or two ago. I was
surprised to hear her complain of Scurry that she had put a lot of
“holes” in it by chomping on the ball. This suggests that she may not
yet divide all small white balls into two classes: ping pong (hollow,
of smooth surface) and golf (solid, with concave ‘bumps’ on the surface).

This ball entered play in a familiar way. I returned from other
engagements to find Miriam showing Gretchen how to make a ball go for-
ward and return. She said, “You do it like this,” and attempted to
backspin the ball. She was not able to control the ball effectively
(I speculate that she was unable to compensate for the differences of
weight and friction both). When I asked Miriam how backspinning had
worked with the ping pong ball, she offered to show me and cautioned:
“But, Daddy, don’t think about it.” I believe this showed no admission
on her part of my (false!) explanation of backspinning during the
experiment recorded in Miriam at 6, but had a more complicated purpose:
Miriam, confident of her ability to backspin and intending to disabuse
me of my incorrect notion, warned me not to “think about it” so I could
not offer that explanation of the phenomenon. Backspinning failed.
Miriam rolled the ball to Gretchen, who kicked it back to her. She
noted of the golf ball, “This doesn’t work too good,” then continued
the explanation with an excuse, “because the ball’s too heavy.” Miriam
tried again with a different ball, one she described as ‘lighter’: the
ball is solid rubber foam 2 1/2 ” in diameter; it is heavier than the golf
ball but smooth and compressible. When her attempt to backspin the
rubber ball failed, Miriam’s interest waned and she went off to some
other activity.

Relevance
The two incidents cite a class of explanations or descriptions
which most adults would think silly but which Miriam still accepts as
serious, albeit mistaken, explanations.

Vn05001

Vn50.1 The Go-Cart 7/25/77

Kept inside on a rainy day and with me working in the living room,
Robby and Miriam were constrained to play quietly (more or less) in the
kitchen-dining area of our Connecticut house. Since we vacationed in
an unfurnished house, they had few of their usual toys and a limited
selection of books.

During the afternoon, I discovered them playing with empty boxes,
and shortly after Robby entered with the drawing of Addendum 50 – 1
inquiring whether or not it was a good plan for a go-cart. The vehicle
is to be propelled by pedaling. (The long hair on the front figure
indicates Robby thinks of Miriam performing that function.) The
‘steering wheel’ is for holding on to, for steering is to be provided
by a tiller at the back of the cart which turns the ‘tail’ wheel. I
admitted it as a good start but cautioned that more detail would be
needed before it would be a plan for construction.

The project was a joint one. The children planned to construct
and use it together. Miriam’s sense of construction was different from
Robby’s. She took one box, opened to a single flap on the top, and
declared this the front of the go-cart. Another box, ripped apart,
provided the rest of the carriage. She jumped in and was “off,” driving
the cart around while Robby explained to me how the pedals would be
mounted (drawing therein the ancillary figures below the side view).
Miriam seized Scurry to take her for a ride, put her in another empty
box, and declared it a ‘rumble seat.’ Robby redrew his plan as a three
seater with a ‘rumble seat assembly.’

Robby took his play very seriously and eventually found a set of
wheels in the garage I had salvaged from a junked garden tractor. He
began to talk of going to the lumber yard and to wrestle with the design
of a brake. (The final drawing of Addendum 50 – 2 is my advice; his
original idea had the shoe forward of the pivot). To Robby, building
a real, usable go-cart is an achievable objective. To Miriam, the idea
of a go-cart is a focus for a fantasy. Its symbolic realization is as
adequate to her use of the idea as she requires. A real go-cart, some-
where else at some later time, would be much less satisfying to her than
the play construct of the moment.

Relevance
This vignette describes the joint efforts of Miriam and Robby in
a go-cart “project.” The children play together in the intersection of
fantasies that are worlds apart.

Addendum 50-1

Addendum 50-2

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

Vn05201

Vn52.1 Fort Griswold 7/26/77

From many places in Boston when you look to the north you can see
the obelisk on Bunker Hill rising above the buildings of Charlestown.
There is a similar but smaller monument in Connecticut, at the site of
the lone major battle of the Revolutionary War that took place in that
state. The dedication of that monument reads:

In memory of the Brave Patriots
who fell in the massacre at Fort Griswold near this spot on the
6th of September A.D. 1781
when the British under command of
THE TRAITOR, BENEDICT ARNOLD,
burnt the towns of New London and Groton and spread
desolation and woe throughout this region

This monument commemorates the cost of war and its butchery. The
British commander, Major Montgomery, was slain by bayonet in the final
charge over the ramparts. When the British controlled the fort, the
officer in charge asked, “Who commands this Fort?” The rebel commander,
Colonel Ledyard, tendered his sword and said, “I did, Sir, but you do
now.” He was slain on the spot with his own sword. This is a place
where one can not escape reflecting upon Thucydides’ epitaph for the
Athenians defeated at Syracuse:

Having done what men could, they suffered what men must.

To this historic place I brought 3 children: Robby and his friend
Raymond and Miriam. After climbing the 166 steps of the monument, we
could see up and down the coast line, and in the Thames River (/thæmz/
not /temz/) below a Nautilus class nuclear submarine. I pointed south
to the green hangar of Electric Boat, wherein are produced most of
America’s nuclear submarines, where 2 years ago we had witnessed the
launching of the submarine Philadelphia. Back at ground level we found
in the museum the essential toilets, interesting uniforms, muskets,
dolls, and a model of the Fort itself as it was on the date of the
battle.

What remain now of the fort are earthworks, scattered stones, and
an ammunition dump close by the old cannon emplacements overlooking the
harbor. The children raced over the ravelin and in the main gate, past
the plaque commemorating Colonel Ledyard, to the dungeon and the secret
passage through the south rampart. Raymond and Robby scaled the ramparts
and ran about in the moat. Miriam complained at being left behind
as they refought the battle in their imaginations.

Another submarine came gliding down the Thames. Miriam asked me
about the funny smoke stacks. Robby explained what I did not know:
they were underwater launch tubes for Polaris missiles. In the middle
of their morning’s play Robby asked, “Dad, who won the battle of Fort
Griswold? The British or the Americans?” I answered that the British
had defeated the Americans. Robby turned to Raymond. “We’ll be the
Americans the British didn’t defeat.” And they resumed their play.
Recall the rebels’ song in which Ireland is a land

. . . where the past has been lost and the future is yet to be won.
Recall not only the songs, but also the bombs and deaths of innocents.

We bought sandwiches from a shop I knew and divided them in Ledyard
Park. The children played after on one of the best equipped playgrounds
we’ve visited. Miriam ran to ride on the spring mounted toy elephant
and cried, “Daddy, now I know where they put them.” (Cf. Vignette 45)
Miriam assumed her favorite playthings, missing from the town beach in
Guilford, were transported to the park in Groton. In this playground
on can see the impact of EB’s Triton submarine contract. Not only has
Groton been immune to the 2 year real estate depression which plagues
south central Connecticut, but even the parks and playgrounds show the
presence of armament money. As Aeschylus observed, Plutus is the
ultimate god of war, who changes men for gold.

Raymond decided we should visit the Mystic Aquarium instead of the
beach at Rocky Neck. Aside from the sharks in the central tank, only
the trained animal show held interest for the children. Miriam liked
best the high jump of Sassy the dolphin (20′ above the water surface)
and recalled seeing a similar show the summer before. We went home by
way of an ice cream parlor and finished the day with a swim at the
beach of our lake. Raymond, aged 9 and taking regular lessons, swims a
little. Robby appeared to be inspired by his example. Miriam continues
to imitate the splashy surface appearances of swimming but can’t
penetrate the appearances to the activities unseen.

Relevance
This vignette recounts a day of our vacation presented more from
my viewpoint than most others in this series. It may indicate how the
children and I can simultaneously enjoy different aspects of one situation.

Fort Griswold – 1

Vn 52-1 Fort Griswold

Fort Griswold – 2

Vn52-2 Fort Griswold

Fort Griswold – 3

Vn 52-3 Fort Griswold

Vn05301

Vn53.1 A Birthday Party 7/28/77

Robby’s birthday comes in August. Connecticut friends whom he
would like to have at a party can not come to Boston. When he suggested
an early party during our vacation, we agreed. Preparations for the
party focused on choosing activities and procuring treats and prizes.

If you have ‘prizes’ at a party, you must have one for everyone
and the question devolves to one of who gets first pick. The ‘activities’
became a means of deciding the order of selecting prizes. Robby
suggested a foot race and pin-the-tail-on-the-donkey. Miriam, younger
than all his friends and predictably last in a race, objected. She was
declared ‘judge’ and assured she would receive a prize for that office.
Robby took some cardboard (left over from manufacture of the go-cart of
Vignette 50) and drew thereupon a donkey. He made a selection of tails
to be affixed with tape (I balked at the idea of children pinning tails
on the timber walls of our house). When Robby decided the prizes should
be “matchbox racers” (at $1.20 apiece), it was clear he had proposed
enough games. The party was to conclude with an ice cream cake and a
selection of favors. (The items selected were the same as those
distributed at a party for Raymond’s brother — Hershey bars, bubble gum,
a balloon). The chosen hours were 2 to 4 pm. (These hours had been
the standard for parties attended by Miriam and Robby that year).

Six children were to be present. Miriam had to be there. Raymond
was his best friend. David and Vi were friends from a baby-sitting
playgroup he had been a member of. Who else should come? On the way
to Guilford, Robby said he might not have anyone to play with because
he couldn’t remember his schoolmates very well. On our first day in
Guilford, Robby encountered Michael on a walk and the 2 played that day.
After playing with John, a boy who lives across the street, he decided
playing with him was boring. Thus Michael was weakly preferred to John.
Robby called his friends and made the arrangements. David would arrive
late because of a conflict with his swimming class.

The day of the party I picked up Raymond by car and returned home
by 2:05. Robby and Miriam were awaiting guests at the end of the drive.
Raymond joined them while I put the car away and went inside. Before
the party, when he started wondering what presents he would get, I
asked Robby what was more important to him — that his friends come to
play or that he get presents. Robby said he really didn’t care about
the presents. Raymond came to the party without a present; he had
thought he was just coming over to play. I had told him not to worry
about it. He was Robby’s best friend and it was most important that
he come.

About 2:30 the 3 children entered the house. No other guests were
coming, a dreadful situation. Robby called Vi, who had forgotten about
the party and promised to come right over. No one answered the tele-
phone at Michael’s house. With Vi now definitely expected and David
known to be coming later, the 3 children occupied the interval by exam-
ining the prizes. They decided that half the 12 prizes (matchbox
racers) should be reclassified as favors and allocated them accordingly.
Robby asked me: “If Michael doesn’t come, can I have his two racers
because he won’t be bringing me a present?” This seemed reasonably
fair to the other 2 children and to me. Robby tried calling Michael
again with no response, and declared the two left-overs to be his.

Vi entered with the first present, a nicely wrapped package con-
taining a bottle of bubble bath in the shape of a brontosaurus. Robby
was pleased. Shortly after, David arrived. His present, the second
and last, was a nicely wrapped package containing a bottle of bubble
bath in the shape of a rocket. Robby: “Oh well, I guess I’ll have to
take lots of baths.” The 2 most recent arrivals inspected their favors
and prizes. All 5 children then fell to making their balloons scream
by letting the air escape through the neck stretched flat. At my
suggestion, the children took Miriam’s beach ball to play in the yard.
The game of choice was ‘keep away.’ I forbade them to keep the ball
away from Miriam (their original plan, since she objected to the game,
probably suspecting that end). Their alternate game pitted Robby and
Raymond against Vi and David. Miriam sulked and sat on her swing.

After a half hour’s play, the children came in for the cake. At
4:10, expecting the party to end with the last of the cake, I was
surprised to hear cries that I had promised to take the children over to
the playground for the prize selection race. I did so, but warned the
children that their stay would be very short because Raymond had a 4:30
deadline at home. The race was run, prizes were distributed, and all
were content except Miriam; David chose the racing car she wanted.
After we dropped David, Vi, and Raymond off at their houses, I told
Robby how unhappy Miriam was. He agreed to work out with her some
distribution of their six racers which she would consider satisfactory.

Relevance
This party was one arranged by the children according to their
ideas and reflecting the way they coped with unexpected contingencies.
Robby has said since how much he enjoyed the party. Miriam suffered
the younger child’s burden of being left out and left behind.