Kathleen McCall:
Occasional�� Muse�

2004-09-17 - 6:29 a.m.

Limited Vision

One of the most interesting things about working with kids has been watching the changes in their thinking over the years. I am watching one group of kids, kids I've known for four years, chewing through a review of fractions. Chewing it right up, for the most part. Because it finally clicked, finally fit in with their worldview and their understanding; they finally developed the puzzle piece that goes NEXT to that one, so now they can see where fractions fit and what they are, and they can slot them in and move on to the next thing.

I don't think it has a lot to do with the fact that we've taught these kids about fractions for over four years, although I'm sure that counts. Been over the logic of the thing, using all kinds of tools and toys and spoken and written and graphic explanations; been over the rules for handling them mathematically, again using all the methods we have. For some kids, I've been through it extra times during the summer, or extra times privately. I'm sure it does some good, I'm not discounting the teaching. But it seems that you put the information IN, and it's simply going to wander around, bumping in to things and getting its shoes all untied, until there's a place that's really READY for it. Being ready is the thing that the kid does all on his or her own, and seemingly without much effort.

I saw a film last week that talked about the supposition that the natives could not see Columbus' ships arriving, because they simply did not have any knowledge with which to connect those ships. The ships didn't fit with anything they already knew in any way, so the brain could not process their existence. I don't know if this is true, but it's a fascinating thought - the question then being, of course, what is it that is true yet we cannot see NOW because we have nothing with which to connect it? What is my brain aware of, but filtering, because it doesn't yet fit with my worldview? And, given what I see of children and development, what information is floating around in my brain because I'm not yet ready to slot the information into the rest of my knowledge?

Physiologically, I suppose I'm not still developing, really, but I think I am changing, which ought to count for something. There's still plenty of chance, I hope, to add new information, and rearrange what little I already have. I hope this is true, because I still want the chance to understand probability, and it's confounding me. I always loved statistics, and I think I OUGHT to be able to understand the concepts, but trying to help Older Daughter with her homework last night was beating me up. I kept getting a hold on the concept and beginning to explain it to her, and then I'd realize halfway through that I was wrong and have to backtrack and qualify; then I'd realize THAT was wrong, too, and the whole thing was like trying to catch trout with my bare hands. Blindfolded. I obviously don't have the place for these concepts to lodge and hold STILL for a while.

So. If the Happy Ice Cream Cone Company says that out of a hundred boxes of cones, only one box will have a broken cone, and you buy a box and get it home and it has a broken cone, and you take it back to the store and exchange it, are you more or less likely to get another box with a broken cone?

Of course; it's obvious; no more or no less, exactly 1/100th of a chance that you'll get a box with a broken cone, same as before. That's a no brainer, right?

But wait. This isn't like dice, is it? Because you already BOUGHT the one with the broken cone from that store. They had a hundred boxes, say, and you got one with a broken cone, wouldn't that REDUCE your chances of getting ANOTHER box with a broken cone out of that same group of a hundred? What are the chances that you'd get TWO boxes with broken cones? They have to be lower, don't they?

Poor Older Daughter; she's used to depending on me to help with her math. But she's hit Columbus' Ships for her mother. I can't quite get a grip on this stuff. If you tell me which answer is true, I can support it. I could support either answer. Which makes me eligible for the debating team, but not the Math Club.

Perhaps probability is something that I'm destined to "get", to click into my available knowledge and understand, later in life. Or perhaps it will always sail just out of reach.

Note: I asked the kid to make SURE she got the answers to the homework and understood them so she could come home and explain them to ME. So when I picked her up at school and asked her, she said, "There is no right answer - it could be either way, depending." So there you go. Those ARE some big ships.

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