Tuesday, December 9, 2008

More on Math

AJ and his teacher are continuing to struggle with math. They really just don't understand one another. But now when his teacher doesn't get why he is making mistakes, she has started sending things home to me to go over with him, which allows me to figure out what the problem is and explain it to her, so hopefully communication will continue to improve.

This week, Mrs. F. sent AJ home with a worksheet on a estimating addition, something they've been working on in class. AJ has been struggling with estimation, because he doesn't see the point of the technique, where they round to the nearest 10 and then sort out the ones to get the total. He doesn't like the imprecision of estimation and it takes him longer to do it than it does to add the "normal" way, so he's been assuming he's doing it wrong and keeps coming up with these crazy algorithms that aren't really functional but which explain whichever problem he's working on. Once I explained to AJ that his class was learning a bunch of different ways to add and this was one way, then he was fine. He is a kid who needs to know why he's doing something before he can understand it. I know, because I was a kid like that too.

This morning I was tutoring his reading group. They were looking at an interview between a modern Wampanoag and a pilgrim interpreter from Plymouth talking about the way their respective people did things in the 1620s and creating a Venn diagram based on what they learned (the second grade is very bigg on Venn diagrams). One of the questions asked how many were in their respective settlements and the pilgrim replied "9 score." So we talked about what a score was and I asked if anyone could figure out how much 9 score was. "9x20!" AJ barked out without hesitation. But he was crushed when another kid got the answer before he did. If he can't be first, he doesn't want to participate. While I'm sympathetic to that point of view, I also know how paralyzing such self-expectations can be (talk to me about my decade-old dissertation some time). Still, when such pressure is internal, what's the best way to help ease it?


FreshHell said...

I also had trouble with "the point" of certain calculations. I mean, if I don't need it, why do I need to learn it? I understand that better now (though admittedly not always) but it was tough to feel that I was learning something "useless". As for the "if he can't be first" thing, I wonder if that's more prevelent in only children? They are used to being ostensibly first, they have no competition at home, whereas siblings are constantly vying for everything: attention, the last cookie, etc. That when they're at school, they're used to that kind of give and take. You can't always be first even if you know the answer. I don't know if that's true - probably a generalization - but that was my first thought.

Anonymous said...

The "estimating" thing sounds totally moronic to me, but that's not very helpful. Poor AJ--I really feel for him.

Jeanne said...

Walker has eased up on the having to be first thing, which I think is partly a boy thing. I think what helped most was his gradual realization that it's more fun to have good mathematicians to compete with than it is to get all the answers right and be first.

There's a wonderful Venn diagram in the illustrations of an ABC picture book we have, showing correspondences between vampires and voles.

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Anonymous said...

I agree with freshhell about being an only child probably playing a role in this situation.

In the "short term loss/ long term gain" category, I'd say to keep putting AJ in situations where he won't always be first. One of many reasons why we love our school is that D#1 isn't always first. Sometimes this is frustrating for her, or she'll work too fast and not do as well... but being reminded that she isn't the only one in the class who is smart has been a painful but important learning curve for her.

Mrs. PQV

Harriet said...

I hadn't considered the only child syndrome, which I am usually quick to cite, but I think you may be right about that. And actually, the child who got the answer faster is a good match for AJ in many respects. They are the only two doing advanced math in his grade and they are both doing advanced reading. AJ is a little ahead in reading, the other boy is maybe a little ahead in math, but mostly, I think, because he's more focused. AJ is quicker to figure out how to find the answer, but the other boy is quicker with calculations. They actually make a good team. And they are good friends as well -- they have many of the same interests and like to play together. So I hope that eventually AJ will learn to work with him and to learn from him as well.

The estimating is irritating, cranky, but I kind of appreciate the overall cause. Everyday math emphasizes knowing multiple ways to approach a problem -- frequently they have to show several different ways to arrive at the answer. So they are all dealing with it. And while it may seem annoying now, ultimately it seems to give them better problem-solving skills. Additionally, the goal of the estimating in particular seems to be to give them the tools to do fast calculations in their heads, which is something that isn't always taught and which is incredibly useful. While knowing these reasons may not help him with short term frustration, at least they seem to him like plausible reasons to learn a new method.

And Jeanne, that ABC book sounds fabulous. AJ has a math ABC book (more of a math book organized alphabetically-- definitely aimed at those older than ABC learners) where V is for Venn diagram. But it is sadly lacking in both vampires and voles. More's the pity.