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10 Oct 2005 - 22:15 What I Learned in Elementary School for me to blooki. Here's the first:
I've thought about this observation every day since reading Aharoni's article. I probably can't explain why. At least, I can't at the moment. (Good thing I'm not taking the Regents, I guess.) But it reminded me of a post Carolyn wrote early on:
Catherine mentioned that she is a fan of tile fraction manipulatives over the more usual 'pie' manipulatives:She said that her daughter didn't get anywhere using the more-common circular, 'pie chart' fraction manipulatives; she needed to see rectangular fractions. I have no idea why this would be, but it 'felt' right to me, so I searched for rectangular manipulatives and found these.I prefer tile manipulatives too, for what I think are solid pedagogical reasons, and here is why: if you want to talk about improper fractions -- fractions greater than one -- with your kid, then the pie-shaped manipulatives add potential for confusion because you can't make a single connected object that represents a quantity greater than one. If you want to represent, for example, 3/2 with pie manipulatives, then you'll have one whole circle and a half circle. You can tell a kid that that represents a single object, the quantity 3/2, all you like; but to him it will look like two objects. Fractions are confusing enough without that. Conversely, you can make a single line of tiles that is as long as you like. So unless your child is really off and running with the pie manipulatives, I'd recommend the tile manipulatives.
These are the fraction tiles I like:
You can order extra tiles, too, which I have done. I've used these over and over again, with Christopher, and with at least two of his friends. Worth their weight in gold.
Aharoni article, part 1
Aharoni article, part 2: America's 'new math' goes to Israel
Aharoni on the fifth operation of arithmetic
Ron Aharoni on teaching fractions & forming units
What I Learned In Elementary School by Ron Aharoni (AMERICAN EDUCATOR)
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