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From US News & World Report http://www.usnews.com/articles/education/2007/11/02/english-as-a-second-language.html
The fifth graders are learning division in small groups in the Fairfax County, Va., classroom, but Carolina, a girl from El Salvador who speaks broken English, is having a bit of a hard time. She has figured out that 162 divided by 12 equals 13 with a remainder of 6, but she can't come up with a story to write that shows she understands the problem. "No entiendo," she whispers to her friends. I don't understand.
She's struggling, not because she doesn't know the math, but because she can't come up with a story. This is so wrong-headed on so many levels, not the least of which is what it is doing to this girl's confidence in her own mathematical abilities, which could (in another time and place) prove to be exceptional.
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3 comments:
This is another tragedy of reform math. Many English language learners use to look forward to mathematics because it was a language they could speak with their peers while they were still struggling to speak English. In fact, most immigrant children brought strong mathematical skills to the classroom.
My father was one such immigrant. His mathematical abilities opened doors for him while his accent and lack of native fluency tried to hold him back. Being strong in mathematics gave him the confidence and opportunities he needed to become a successful and productive citizen. If he would have had to write stories about a division problem I don't know if he would have been as fortunate.
And what about those children that just don't like to write? You know, the ones who speak English fluently but prefer numbers to words? This puts them at a disadvantage as well.
It really stinks.
Yes and no. I'm sure it can be taught better, but knowing how to contextualize your knowledge is important too. If you know how to calculate 162/12, you should also know that this might mean 162 things split into 12 sets or 162 things grouped into sets of 12. With appropriate instruction, you should be able to identify objects that might be grouped into 12's, and the sorts of sets they could be put in. (162 cookies, 12 on each plate, etc). If I were teaching this class, there would be a brainstormed list of objects and sets they could be put in somewhere in the classroom. Writing a story isn't the only way of assessing the knowledge, but it is useful to know what division means as well as knowing how to do it.
I question how effective these "reverse" word problems really are in demonstrating contextual understanding. I've seen them in action. Even kids who get the math have trouble pulling stories out of their hats. Constructing a story to fit a math expression or even a simple story line is a different kind of skill (and a pretty high level one at that).
It is more useful to be able to translate a word problem into a numerical expression (e.g., setting up an equation). This is the time-honored word problem, and it reliably shows contextual understanding. It's typically the way math is encountered in the other disciplines (engineering, physics) and it's also a lot easier for an ESL student to read a word problem and write and equation than the other way around.
And isn't it more fair to them as well? Why should you get a C in math b/c you can't write the story problem?
[Funny how the language arts classes never penalize a kid because they can't solve a math problem!]
In my 40,000 pupil urban school district, about 30% are ESL. When I was reviewing the new textbooks selected for district secondary math (HEAVILY loaded with text--open them and you think you are looking at a history or geography text, not a math text) I asked the district secondary math coaches how new immigrant students can succeed in math class? They said the new students (even the mathematically accomplished ones) are placed in "transition" math (the lowest math classes) until their English skills improve to the point that they can handle the regular math classes.
How wrong is this?
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