Number related
Vn129.1 Robby Computes a Tax 4/5/78 Robby caught on fire again today. He approached me inquiring, “How much is half of 423?” Miriam responded to his question from the other room, “2 hundred and 11 and a half.” I told her to stop butting in and asked Robby how much was half of 400, then …
Vn123.1 Computation Finale 2/12 & 14/78 2/12 Since completing Vignette 121 (Double Perspectives) I have tried to engage Miriam in executing a difficult addition. My purpose was to introduce the idea of a simultaneous, double perspective as what one needs to appreciate carries by challenging her with a puzzle — “What number is 10 when …
Vn122.1 Carrying Bugs 2/5/78 Invited to play at a friend’s house, Miriam waited for Gretchen to drive her there. During this vacuum of activity, I asked her if she remembered how to add with carries (cf. Home Session 23). Miriam reacted impatiently, as though it were foregone that she did. She agreed to solve a …
Vn121.1 Double Perspectives 2/8/78 While school has been canceled this week due to the Blizzard of ’78, the children have spent a lot of time outside, playing on the snow mountains the plows and people have piled up. Inside much of the time, they have followed their own inclinations, playing the card game War, reading …
Vn119.1 Multiplying by Twenty 1/25/78 The children love to get mail and when an envelope comes addressed to them, to open it. Each has a bank account concerning which they receive annual earnings statements. The children opened their mail and puzzled over the contents — a statement of account number, social security number, and interest …
Vn116.1 Transferring a Good Trick 1/3/78 Miriam, not imagining yet that she will one way or another make a living, sees her best hope of getting a lot of money as inheriting my money. Thus my impending demise is a subject on her mind and one that involves her in computations. At lunch today: Miriam …
Vn108.1 Miriam Doesn’t Stop 11/1/77 I have ceased collecting data for this project, have focused my attention on the data reduction problem, but Miriam keeps growing, making breakthrough after breakthrough. This afternoon, for example, I sat transcribing videotapes in the reading alcove. Miriam, waiting in place the ten minutes till Sesame Street should appear on …
Vn105.1 Hotel Magee; Two Microworlds; Decadal Computation 10/20 & 27/77 10/20 With Robby’s introduction of WUMPUS to Miriam yesterday, the mechanically recorded sessions at Logo cease. Vignettes continue to round out and close off at natural stops various themes of the project. The sense of closing off the mechanical recording is that the project has …
Vn100.1 Arithmetic Ripples 9/26/77-10/2&7/77 9/26 Miriam tells me today was her first day of doing math at school. “But we did it differently there from what we [she and I] did here.” She explained that school math was playing with cuisiniere rods. I told her I thought that was great, and asked what she did …
Vn90.1 Meeting Miriam’s Teacher 9/11-12/77 9/11 This Sunday morning, Miriam inquired of me if I knew what kind of a teacher she had. When I admitted I did not, she continued: Miriam Nice. She says if the math problems are too easy, I won’t have to do them. Bob What will you do instead? Miriam …
Vn89.1 The Ten in Fourteen 9/7-10/77 9/7 After considerable confusion at the beginning of yesterday’s arith- metic work (Home Session 18, 9/6/77), in a reprise after games of Tic Tac Toe, I was able to explain ‘carrying’ to Miriam in a manner access- ible to her. I cited a recent comment of hers while doing …
apparently, this file needs to be recreated, from earlier sources. The tags attached to the source suggest it is important.
Vn82.1 Hanging Designs 9/3/77 After today’s session was complete, I asked Miriam why she had not pinned on the wall — as she had said she intended — those designs made in yesterday’s session (Logo 58, 9/2/77). She explained that she had started to do so earlier but needed help. I separated the designs from …
Vn79.1 Sums Over a Hundred 8/29/77-9/1/77 8/29 While we sat at lunch today, Miriam introduced the topic of adding with this claim: “Daddy, if you live for another hundred years, I know how old you’ll be.” When I expressed surprise Miriam demonstrated: “A hundred 37.” Two complications derailed this discussion. Robby introduced my birth on …
Vn65.1 Arithmetic Ripples 8/13/77 1. Miriam brought me this morning a dime she had found in the laundry. My speculation is that it had been left in some pocket, fell out in the wash, and was pinned in and nearly cut in half by the washing machine. How it got on the floor where she …
Vn62.1 Multiplication 8/7 & 11/77 8/7 Robby has many times now seen Miriam on my lap receiving some instruction in addition. Complaining of feeling left out, he has asked for help in math. Robby said he needs help with addition of numbers such as 9 plus 6 and 8 plus 7. I found him a …
Vn58.1 Owning an Angle 8/4/77 As far back as the end of June (in Logo Session 32) making hexagonal mazes has been a part of both children’s Logo work. Before our Connecticut vacation both children worked together generating pictures of mazes (7/8/77: Logo Session 36). During that session, Miriam “discovered” the 60 degree angle input …
Vn55.1 About Taxes 8/1/77 Since the beginning of the High School Studies Program, the children and I have come to Logo to use the system from 8 to 10 am. One consequence is that we occasionally skip breakfast. Even when we do not, the children have become accustomed to mid-morning snacks. The favorite: apple pie …
Vn54.1 More Arithmetic 7/31/77 While I was having lunch, Miriam came (in her bathrobe from the tub) and asked me if I could divide 79. I asked by what. Miriam didn’t answer but moved away. I pursued the question: “What do you know that’s a 79?” Miriam replied, “They said it’s 2 for 79, the …
Vn49.1 Finger Counting 7/24/77 At lunch, I inquired of Miriam how she used to add on her fingers numbers like 2 plus 7. After saying ‘9’ and my refusing that answer, she counted up, i.e. Miriam said ‘7’ then lifting her pinky and fourth finger on the right hand, ‘8, 9.’ I again rejected the …
Vn44.1 A Boring Session 7/12/77 Riding home after this morning’s session (Logo Session 38) Miriam said she thought the work was boring today. When I asked why, she said, “Oh, I don’t know.” I have to look otherwheres for an explanation. Today I tried to exhibit for Miriam the relation between closed polygons and in-going …
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 …
Vignette 23.1 Arithmetic Ripples 6/5 & 11/77 Miriam does not yet recognize the existence of negative numbers. The typical problem this causes her was shown as we rode home from buying a Sunday paper (the children go with me to buy chewing gum). Miriam was discussing making change with Robby. She knew that paying for …
Vn01704 Arithmetic Ripples 6/1/77 When she came home from school, Miriam asked to stay home today. I suggested we do her second adding session. Miriam then countered that we should do math at Logo and use the computer. I agreed. At the lab, while I was logging in, Miriam began playing with a pile of …
Vn01703 Arithmetic Ripples 6/1/77 Miriam was playing in the kitchen with Scurry this morning. Gretchen and I were discussing some topic, and I mentioned a division problem. Miriam piped up, “I can divide, Daddy. . . . 8 divided by 8 is 1.” I congratulated her on her prowess. For Miriam the formula she recited …
Vn017B Arithmetic Ripples5/30/77 As Robby and Miriam came in from play for a little refreshing juice, I heard from the kitchen the squabbling one expects of near-aged siblings: Miriam I can add big numbers. Rob Oh brother! Miriam I can. I can do one thousand and thirty five plus two thousand. Rob Easy. Miriam No. …
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 …
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 …
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, …