From Lenka:
I tell Abi: a number is prime if, after I give you that many coins, you can't arrange them in several rows of equal length. Now guess if this is prime...
She "guessed" a corect answer for every set of pennies that I gave her (I tried everything from 4 to 16), just by looking at it and shifting some coins. Having given the answer, she would construct the rows for composite numbers to prove her "guess". Rows were not always on the shorter side: for 12, she used rowlength=4. After a few games, she stopped caring about aligning coins, of even about keeping them "row-like".
She can still occasionally miscount, or skip (say) 17 when counting to 20
Tuesday, December 5, 2006
Songs
Abi likes making up little songs, almost always in English. Here are some recent specimens, with commentary:
I. Mommies are different
From daddies and boys.
Daddies are different
From women and girls.
-------------------------------
When I pointed out the lack of symmetry, she corrected the last line to "mommies and girls" -- the right choice, I would say, from the point of view of both rhythm and semantics. A few minutes later, she proudly announced a variation: "Grandmas are different// From grandpas and boys// Etc."
The song is clearly inspired by a song in the movie "Free To Be You And Me" (the melody is similar too). But the moral is exactly the opposite -- the point of the original song (and the whole movie) is to minimize gender differences: "Mommies are people// Daddies are people//...".
II. Get on to the fast rope
Get on to the slow rope
Get on to the visible rope
Get on to the invisible rope
Get on to the magic rope
--------------------------------------
I asked what the rope was. Turns out that when they go out for a walk with her class, they use ropes with handles to keep everyone together. The kids have a choice of two ropes: fast and slow. I asked who goes on the slow rope, and Abi, to my astonishment, named all four girls in the class except herself. I asked about the fast rope; she said "Me and all the boys" -- though she later admitted that sometimes one of the girls joins her on the fast rope as well. I couldn't tell if she took pride in this or not.
III. Hot Cross Buns
This is not a song Abi made up, and has nothing to do with gender roles. She learned it last year in music class and hadn't heard it since. This morning she said, "Hey mama, remember this song?" -- and sang it. Her melody was:
do re mi
do re mi
mi mi mi mi
fa fa fa fa
sol fa mi
What impressed me was that, although she misremembered the melody, she misremembered it to fit perfectly on the major scale. The last line was especially striking: it's not a logical ending to a song (unless you're singing harmony), but if you start on sol and have to go down two notes, you have no other choice. It seems Abi has internalized this completely.
IV. The Russian alphabet
Abi has known her English ABCs for more than a year now, probably two. But the Russian alphabet doesn't have a nice song to go with it. (It doesn't fit naturally with the ABC tune -- I had tried that last year and gave up.) So although Abi can read Russian, until recently she didn't know the order of the letters.
But now, in her Russian class, they're going through the alphabet, one letter a week. For homework, the kids have to think of as many words as possible starting with that letter. (Abi likes this game and we spend a lot of time each week coming up with words. She always finishes among the first in the class.) They did L last week, which means that Abi had already learned almost half the alphabet. She started trying to fit what she'd learned to the ABC tune, which inspired me to try again too. With this pressure from Abi, I managed to make up something decent, and taught it to her. Today she finally sang it by herself all the way through. So now she knows two alphabets!
I. Mommies are different
From daddies and boys.
Daddies are different
From women and girls.
-------------------------------
When I pointed out the lack of symmetry, she corrected the last line to "mommies and girls" -- the right choice, I would say, from the point of view of both rhythm and semantics. A few minutes later, she proudly announced a variation: "Grandmas are different// From grandpas and boys// Etc."
The song is clearly inspired by a song in the movie "Free To Be You And Me" (the melody is similar too). But the moral is exactly the opposite -- the point of the original song (and the whole movie) is to minimize gender differences: "Mommies are people// Daddies are people//...".
II. Get on to the fast rope
Get on to the slow rope
Get on to the visible rope
Get on to the invisible rope
Get on to the magic rope
--------------------------------------
I asked what the rope was. Turns out that when they go out for a walk with her class, they use ropes with handles to keep everyone together. The kids have a choice of two ropes: fast and slow. I asked who goes on the slow rope, and Abi, to my astonishment, named all four girls in the class except herself. I asked about the fast rope; she said "Me and all the boys" -- though she later admitted that sometimes one of the girls joins her on the fast rope as well. I couldn't tell if she took pride in this or not.
III. Hot Cross Buns
This is not a song Abi made up, and has nothing to do with gender roles. She learned it last year in music class and hadn't heard it since. This morning she said, "Hey mama, remember this song?" -- and sang it. Her melody was:
do re mi
do re mi
mi mi mi mi
fa fa fa fa
sol fa mi
What impressed me was that, although she misremembered the melody, she misremembered it to fit perfectly on the major scale. The last line was especially striking: it's not a logical ending to a song (unless you're singing harmony), but if you start on sol and have to go down two notes, you have no other choice. It seems Abi has internalized this completely.
IV. The Russian alphabet
Abi has known her English ABCs for more than a year now, probably two. But the Russian alphabet doesn't have a nice song to go with it. (It doesn't fit naturally with the ABC tune -- I had tried that last year and gave up.) So although Abi can read Russian, until recently she didn't know the order of the letters.
But now, in her Russian class, they're going through the alphabet, one letter a week. For homework, the kids have to think of as many words as possible starting with that letter. (Abi likes this game and we spend a lot of time each week coming up with words. She always finishes among the first in the class.) They did L last week, which means that Abi had already learned almost half the alphabet. She started trying to fit what she'd learned to the ABC tune, which inspired me to try again too. With this pressure from Abi, I managed to make up something decent, and taught it to her. Today she finally sang it by herself all the way through. So now she knows two alphabets!
Correction?
Abi and I have been having some discussion about the proper spelling/pronunciation of Oyo Komos. Given that Abi can't properly pronounce (or often neglects to pronounce) L, R, or SH, and that in Russian unaccented vowels are ambiguous, the theoretical possibilities are numerous:
Oyo Komos
Oyo Komosh
Oya Komos
Olya Komos
Orya Komos
I asked Abi before starting this blog whether it was Komosh or Komos. She wavered, but chose Komos. But now it turns out that the first word is probably Oya, possibly Olya (it hadn't occured to me to ask about that). Oh well. I guess whoever first writes down a language gets some leeway with the spelling.
Months later: Josh finally figured out where it comes from! In the summer of 2005, Abi was with Mira at Mathcamp in Portland, OR and went to a mini-daycamp where one of the units they had was Spanish. "Oyo komos" is "Ola, como estas?"
Oyo Komos
Oyo Komosh
Oya Komos
Olya Komos
Orya Komos
I asked Abi before starting this blog whether it was Komosh or Komos. She wavered, but chose Komos. But now it turns out that the first word is probably Oya, possibly Olya (it hadn't occured to me to ask about that). Oh well. I guess whoever first writes down a language gets some leeway with the spelling.
Months later: Josh finally figured out where it comes from! In the summer of 2005, Abi was with Mira at Mathcamp in Portland, OR and went to a mini-daycamp where one of the units they had was Spanish. "Oyo komos" is "Ola, como estas?"
Wednesday, November 29, 2006
The Banyan
From Lenka:
Today I was telling Avi about the Banyan tree in Lahaina: first, a banyan spreads its branch like this (I extend my arm horizontally), then roots go down from the branch until they touch the ground (indicate downward movement with my hand), then a new trunk grows there, a new branch extends horizontally, and so on.
Abi, upon contemplating this: It's like a needle with a thread, as if a banyan tree sews on the ground.
Today I was telling Avi about the Banyan tree in Lahaina: first, a banyan spreads its branch like this (I extend my arm horizontally), then roots go down from the branch until they touch the ground (indicate downward movement with my hand), then a new trunk grows there, a new branch extends horizontally, and so on.
Abi, upon contemplating this: It's like a needle with a thread, as if a banyan tree sews on the ground.
Tuesday, November 28, 2006
The Slaveboy
I was working out a math problem and Abi asked me what I was doing. I said, "It's geometry", which of course elicited the question, "What's that?"
So I drew a square subdivided into four smaller squares and said, "Look, this big square is four times as big as the little ones. Can you draw a square that's only twice as big as the little ones?"
She first drew a 2 x 1 rectangle subdivided into two squares; I pointed out this wasn't a square. Then she drew a square subdivided into two rectangles; I pointed out they weren't squares. Then she gave up and wanted me to tell her the answer.
I showed her Socrates' answer -- connect the midpoints of the large square -- and asked her why it works. She pointed to the eight triangles. I'm not sure she fully got it on her own, but we went over it together: How many triangles in the smaller square? How many in the larger square? I think she more or less got it.
Her other mathematical accomplishments of late include adding two-digit numbers without carry (with no help at all); multiplying 12 by 4 and by 5 (with minor prompting from Josh); and figuring out that "4 years and 3/4" means "4 years and 9 months" (with minor prompting from me).
So I drew a square subdivided into four smaller squares and said, "Look, this big square is four times as big as the little ones. Can you draw a square that's only twice as big as the little ones?"
She first drew a 2 x 1 rectangle subdivided into two squares; I pointed out this wasn't a square. Then she drew a square subdivided into two rectangles; I pointed out they weren't squares. Then she gave up and wanted me to tell her the answer.
I showed her Socrates' answer -- connect the midpoints of the large square -- and asked her why it works. She pointed to the eight triangles. I'm not sure she fully got it on her own, but we went over it together: How many triangles in the smaller square? How many in the larger square? I think she more or less got it.
Her other mathematical accomplishments of late include adding two-digit numbers without carry (with no help at all); multiplying 12 by 4 and by 5 (with minor prompting from Josh); and figuring out that "4 years and 3/4" means "4 years and 9 months" (with minor prompting from me).
Monday, November 27, 2006
Oyo Komos?
OK, it's 4.75 years too late for a baby blog, but better late than never.
The title, Oyo Komos, is a sentence in Avish, Abi's favorite language. (She consistently claims to be trilingual.) Actually, it's pretty much the only Avish sentence; other words come and go, but Oyo Komos has been there for about a year now. It means "How are you?" If you're doing well, you answer "Oyo!". If you're doing badly, you say "Komos". If you're doing so-so, you say "Komos Oyo". And if you're doing very badly, you don't say anything at all, so the person you're talking to doesn't get upset.
Abi was visiting MIT today, to be a live demo (a real child!) in the class of Josh's colleague Laura on cognitive development. But first, Abi stopped by Josh's office to draw a few pictures on his white board. She wrote "Abi" and "Papa" in a strange font that she claimed was Avish. Many hours later, she recreated exactly the same characters on a restaurant napkin. So it may be that Avish is on its way to becoming a written language.
Last week, Abi found out that Josh has almost certainly gotten tenure at MIT. She understands that tenure is something you get for doing good work as a scientist and discovering interesting new things, and that it means Josh can stay at MIT as long as he wants. But when she walked into his office today, she looked around excitedly and asked: "Papa, where's your tenure?"
In Laura's class, as befits a 4-year-old, Abi passed all the usual false belief tasks -- except for one. She was shown a pen box and asked what she thought was in it; she said pens. Then she got to see that the box actually had rubber bands in it, and was suitably surprised. When asked, "What did you think was in the box before you opened it?", she answered correctly (unlike last year). Finally, she was asked, "If your Mama were to come into the room right now, what would she think was in the box?" Abi thought about it and said, "I think my Mama would know that it was rubber bands." Clearly what we have here is a sophisticated theory of mind, which happens to hold that Mama knows everything.
The title, Oyo Komos, is a sentence in Avish, Abi's favorite language. (She consistently claims to be trilingual.) Actually, it's pretty much the only Avish sentence; other words come and go, but Oyo Komos has been there for about a year now. It means "How are you?" If you're doing well, you answer "Oyo!". If you're doing badly, you say "Komos". If you're doing so-so, you say "Komos Oyo". And if you're doing very badly, you don't say anything at all, so the person you're talking to doesn't get upset.
Abi was visiting MIT today, to be a live demo (a real child!) in the class of Josh's colleague Laura on cognitive development. But first, Abi stopped by Josh's office to draw a few pictures on his white board. She wrote "Abi" and "Papa" in a strange font that she claimed was Avish. Many hours later, she recreated exactly the same characters on a restaurant napkin. So it may be that Avish is on its way to becoming a written language.
Last week, Abi found out that Josh has almost certainly gotten tenure at MIT. She understands that tenure is something you get for doing good work as a scientist and discovering interesting new things, and that it means Josh can stay at MIT as long as he wants. But when she walked into his office today, she looked around excitedly and asked: "Papa, where's your tenure?"
In Laura's class, as befits a 4-year-old, Abi passed all the usual false belief tasks -- except for one. She was shown a pen box and asked what she thought was in it; she said pens. Then she got to see that the box actually had rubber bands in it, and was suitably surprised. When asked, "What did you think was in the box before you opened it?", she answered correctly (unlike last year). Finally, she was asked, "If your Mama were to come into the room right now, what would she think was in the box?" Abi thought about it and said, "I think my Mama would know that it was rubber bands." Clearly what we have here is a sophisticated theory of mind, which happens to hold that Mama knows everything.
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