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 Subject: RE: Fractions, concept and calculations Author: ihor Date: Oct 21 2004
I'm afraid that I'm one of those people that has to hang their head in shame
because over the last 30 years or so of playing this math teaching game I've
have not been able to come up with a magic elixer that will cure the fraction
malaise of many of my students both young and old. But your email did give me a
chuckle and I appreciate that.

Back to the dirty work of helping students learn fractions. I think context is
crucial in how we teach fractions to children. At the 6th grade level I'm
discovering that many kids don't have a good intuitive sense of how fractions
work. That's why I submitted Fraction darts as a resource to the mathtools
collection. By simply trying to hit the target they think about how to make
fractions smaller or larger . One thing It does do is confront  the
misconception that increasing only the denominator makes the fraction larger.
Students are puzzled and interested by that because they want to be able to
control where the darts goes. It seems like an insignificant experience, but I
believe it has powerful ramifications. Howard Gardner in the Unschooled Mind
first gave me the idea that confronting misconceptions was a useful context to
create. He called them Christopherian Encounters as in Christopher Columbus who
confronted his misconception that the earth's circumference was closer to 18,000
miles and therefore making his intended objective closer than it really was. But
that's another story.

I'm interested in hearing from others about effect ive strategies they have
tried to get students to get a better a intution for fractions rather than just
clever way to remember the rules.

Thanks - Ihor