3V1416.1

3V1416.01 A Big Penny and a Little One (12/8/81) We went to Boston this day for a pre-Christmas visit. Rob hung around LCSI with me. Miriam took Peggy over to the Childrens Museum. Late in the day, the kids were going out with Greg to buy sodas and Peggy — of course — wanted to …

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3V1275.1

3V1275.01 Computer “rods” (7/20/81) Seeing the trouble she had with the rods always falling over, I asked is a Rods microworld would be easier to manipulate and thus intellectually more accessible to her. So I proceeded to make one, substituting (a later idea) the blinking of numbers in place of partial blanks — that is …

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3V1267.1

3V1267.01 Computer-based cuisenaire rods (7/12/81) Peggy enjoyed playing with the Cuisenaire rods during out experiment P181. Either in that one or the next P182, Peggy first accomplished a set of “stairs.” After the end of the experiment, she continued playing with rods and I heard her mention (at a point where she omitted the 3-length …

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3V1179.1

3V1179.01 Counting Plates with numbers in various ranges (4/15/81) Peggy loves to help empty the dishwasher. After stacking the small plates on the shelves, she began counting: 1, 2, 3, 4, 5, 6, 9, etc…18… She continued from stack to stack, using ‘big’ numbers as well, “eighty, ninety, tendy” repeating them as well as smaller …

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3V1155.1

3V1155.01 Cuisenaire rods: playing with them after experiments (3/22/81) Guessing games Peggy had used Cuisenaire rods in the immediately previous videotape. Somehow she got hold of them again and I became aware that she was laying them out [Bob had, I think, tried to see if she would build a “stair.”] As she did so, …

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3V1148.1

3V1148.01 “Tendy” (3/15/81) While working on dinner in the kitchen amidst a circus of children, I suddenly heard out of the chaos Peggy counting, ‘eighty, ninety, tendy, eleven…’. She trailed off there, perhaps having said ‘eleventy.’ Gretchen

3V1084.1

3V1084.01 Counting Irregularities (1/10/81) Peggy “counts,” ie. recites the number names in a quasi-standard fashion. (omitting “seven” more often than including it.) Although she has put objects in one to one correspondence, she has not done so successfully in the standard sense. She counted on her fingers today showing no non-standard variations. First she counted …

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3V1074.1

3V1074.01 Counting: for hide and seek (12/31/80) Peggy was playing hide and seek with Robby. He was “it” and after finding her [she didn’t really hide, but stood in another room ready to laugh when he appeared] told her to go into the end of the kitchen (by the basement) and hide her face while …

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3V1070.1

3V1070.01 Counting: scrambled eggs super ? (12/27/80) Reading “Scrambled Eggs Super (Dr. Seuss) one page has a line of birds winding back into the distance over a mountain. Peggy spontaneously started counting, at the beginning of the line, ” 1…2…3…4…5…6…[here the line turned and became less detailed]… many birds.” Gretchen

3V1063.2

3V1063.02 Reciting number names: varied responses to correction (12/20/80) I drove to New Haven. Miriam and Peggy came along for the ride. On the return trip, Peggy stood behind and between the two front seats of the Saab, holding on and exclaiming amazedly at nearly everything seen. As I drove from I-91 down onto route …

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3V1058.1

3V1058.01 Counting objects: near standard sequence with omissions (12/13/80) Miriam and Peggy went to visit Mrs. Smith. She keeps toys in her house for children she takes care of. Peggy selected a ring pyramid and Miriam (as she later tells the story) inverted the rings. Peggy began re-stacking the ring and spontaneously reciting number names: …

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3V1056.1

3V1056.01 Counting objects for herself (12/6/80) What I remember as significant about this episode was Peggy’s putting her fingers and the number names into 1-1 correspondence. Now she can “count” (as documented below) but the limits of her correspondence appears to be TWO. But that fact that she attempts correspondence at all shows a preliminary …

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3V1049.6

3V1049.06 Finger Counting: 1-1 correspondence, up to 2 (12/6/80) no further content.

3V1049.1

3V1049.01 Finger counting: [I want fifteen childs] (12/6/80) Asked if she thought it would be nice to have a baby, Peggy held up her hand and said, “I want a baby. a boy, and a girl.” holding up a finger for each. We tried again, “Peggy, the baby will be a little boy or a …

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3V1043.2

3V1043.02 Shooting Monsters (22/30/80) Miriam was in the basement watching King Kong on TV. Peggy came into the living room and told Robby there was a monster. He drew out his gun and undertook shooting all the monsters. Peggy was not content with this form of their game. She wheedled the gun from Robby and …

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3V1025.1

3V1025.01 85 dollars (1/12/80) For several months Peggy has been coming out at random times with odd numbers. She will look at a supermarket tag and say with a decisive air “This costs 86 dollars.” to which my usual reply is “I hope not.” Gretchen.

3V1010.1

3V1010.01 Playing with coins: progressive discrimination (10/26/80) After P143 (where we played with many coins) Peggy found the pile of change and asked me to join her in playing with them on the floor. As we did so, Peggy separated them and said, “I’m picking the big pennies out and putting them on the floor.” …

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3V0996.1

3V0996.01 Using incomprehensible numbers: “Eighty” (10/12/80) Miriam reported that Peggy was counting with such high numbers. I recall Miriam saying that Peggy said things like “85, 86” and so forth but have little confidence in that. See note of 10/27/80 on Counting Jumping Jacks.

3V0931.1

3V0931.01 Generalization; logical thinking accidentally wrong: pennies and quarters. (8/10/80) Peggy came running around the table. “Somebody left these pennies and quarters on the table,” she exclaimed as she handed them to me. There were two pennies and, folded up, two dollar bills. So Peggy knows two coin names and knows that both coins and …

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3V0882.2

3V0882.02 Counting: pauses at places where sequence goes wrong (6/22/80) Peggy was up late last night. Around eleven o’clock, while Robby played with Miriam, I heard Peggy counting to herself: “one, two, three, four, five, six, seven, eight, nine, ten, eleven,…eight,…twelve,…nine… ” (where the dots represent short pauses).

3V0865.1

3V0865.01 Counting with Mimi: alternate counting game (6/5/80) Miriam announced a game she and Peggy have been playing – a game of alternate counting. Miriam and Peg count alternately: M1, P2, M3, P4, M5, P6, M7, P7, M8, P9, M10, P11, M12, P12 6/8 note: Peg fast count from 4-11 by herself in the other …

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3V0829.1

3V0829.01 Counting; conventional now to six (4/30/80) Robby and I discussed Peggy’s counting and he informs me she counts now beyond four, to six, quite conventionally. He has waked and heard her counting in her crib “one, two, three, four, five, six, nine, ten” This is further evidence of the influence of hide and seek.

3V0824.2

3V0824.02 Hide and seek (4/25/80) Miriam and Peggy play “hide and seek” — and Peggy’s imitation is prominent. The place she picks to hide is always where Miriam hid immediately before. Counting has resurfaced as an issue in this context. Peggy hides her head and counts (1, 2, 3, 4…) then runs to find Miriam. …

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3V0801.1

3V0801.01 Counting (4/2/80) As I put her floride drops into juice, Peggy counted out as she has heard me do, “One…two….three…” Bob notes Peggy counted: one, two three four (checkers) Gretchen

3V0749.1

3V0749.01 Words and Numbers; primary roots of discrimination (2/10/80) Miriam and Peggy play with my yardstick a lot (a free one from a local hardware store, it has the measure and advertisements on it). Miriam marches around with it on her shoulder: “hup, two, three, four; hup…” Peggy marches too, “hup, two, three; hup, two, …

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3V0747.3

3V0747.03 Number/temporal names (2/8/80) Miriam tells me she has asked Peggy the time and Peggy responded “eleven.” The answer was not correct but was significant as a number name. Peggy may have been imitating a specific response heard from some one else in response to the same question. Miriam asked again of Peggy, in my …

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3V0733.2

3V0733.02 More variations. (1/25/80) Over the past few days, Peggy has been using the words ‘many’ and ‘more’ in various contexts. Example : sitting on my lap, Peggy looked up at the picture illustrating Chaucer’s Canterbury pilgrims, and remarked P : ‘Many (unclear).’ G : What ? What did you say ? P : Many …

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3V0700.2

3V0700.02 Knives and spoons: learning the word “fork”; called initially a spoon; when I named the object as fork, she called it a “foon”; counting incident. (12/23/79) When the dishwasher cycle ended, I asked Miriam to put away the dishes. Helpful Peggy was easily recruited. She started selecting silverware from the dishwasher and carried it …

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3V0674.1

3V0674.01 COUNTING (carrying two cookies) [one, two, seven] ONE, TWO, SEVEN (11/27/79) Peggy came into the study (living room) with cookies in hand (one each) and said to me “two”. She continued beyond me, saying, “One, two, seven”. [FOOTNOTE: Later note on date written up: 12/6 This evening, I asked Miriam is she had been …

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3V0611.1

3V0611.01 Counting cookie request [one…two…two ?] 9/25/79 This morning, Peggy asked for a cookie. As I gave it to her, she said “One,… two…. two ?” She waited until I gave her a second cookie. Gretchen.

3V0594.2

3V0594.02 ONE, TWO: [one, two]: note on standardization of Peggy’s counting 09/08/79; You can’t avoid counting, and it’s hard to avoid instructing those who don’t know what you know — but we’ve been trying to avoid instructing Peggy. The children are persistent, at odd moments that we can’t witness. So Peggy’s idiosyncratic counting [one, one, …

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3V0585.1

3V0585.01 TWO : [two]: counting puddles; spontaneous use: 08/30/79; The kids and I went down to Bishops “Pick your own” raspberries. While the older two picked, Peggy and I walked up and down the dirt road to one side of the bushes. It had rained recently, and there were puddles. Peggy and I pointed them …

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3V0531.1

3V0531.01 COUNTING: beginning of notes. Cookies, hands, and counting (7/7/79) During interviews at IBM, Moshe Zloof raised the question of whether or not, in effect, counting is innate. I told him the question was a big one about which I felt no one could speak with authority but that I had very strong prejudices. As …

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LC1bT21

LC1bT21 Protocol 21 Included Text Pages (8) Included Materials (3)

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LC1bT20 Protocol 20 Included Text Pages Included Materials None

LC1bT19

LC1bT19 Protocol 19 Included Text Pages (7) Included Materials (2) Addendum 19-A1 Addendum 19-A2

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LC1bT13 Protocol 13 Included Text Pages (7) Included Materials (6) Figure 1 Addendum 1 Addendum 2 Addendum 3 Addendum 4 Addendum 5

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LC1bT02 Protocol 2 Included Text Pages (2) Discussion Protocol 2.1 Included Materials (3)

Vn10601

Vn106.1 Tic Tac Toe and Nim 10/22/77 Relevance Miriam’s Tic Tac Toe play shows an opening game played only with Glenn before and some surprising rigidity. When we play a subtraction arithmetic form of Nim, Miriam adduces “going second” as the efficient cause of her winning game 2. This appears to be as a consequence …

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Vn13301

Vn133.1 4/28/78-5/8 & 31/78 4/28 The calorie counting continues for me, and the adding for Miriam. The sum of Addendum 133 – 1 is interesting because of its error: the left justification of 3 and 4 digit addends in the same vertical grid. Despite this mal-arrangement, with its implication that the place-value basis of column …

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Vn13201

Vn132.1 BIG-SUMS Extension 4/21 & 22/78 4/21 “Oog. I’ve got to add all these big numbers.” So I called to Miriam’s attention a situation in which one could make use of the kinds of skills she had developed in adding multi-digit addends: I was summing the number of calories in my day’s diet. Miriam asked …

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Vn13101

Vn131.1 Miriam’s 7th Birthday 4/8 & 9/78 4/8/ Miriam began planning her birthday party several weeks ago. On the 3 x 5 cards of Addendum 131 – 1, she listed the friends to bo invited, the candy, and her selection of party games. The children were all from her class at school. The games are …

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Vn13001

Vn130.1 4/3 & 10, 11/78 4/3 Miriam noticed a sum in Home Session 7 as I worked on a paper and asked if she could do it. When I wrote the sum on the black board, Miriam added right to left with carries, thus: 1 3 7 4 1 + 2 5 3 0 _____________________ …

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