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 Subject: RE: Fractions, concept and calculations Author: mgre Date: Nov 27 2004
I have just discovered this discussion and am finding it fascinating and
helpful. This is the first year I've been asked to teach math and am teaching a
special ed class of grade 9 students who lack understanding in many areas. I've
been working a lot with fractions.

>I'm with you all
> the way until you got to memorizing with or without >understanding.

I would like to say something on this point especially.

I think memorizing has to go along with understanding. If I, myself, don't
understand something, I memorize or use a working model to make new examples.
For instance, I am self-taught in computer programming and have not had a
teacher to ask questions of. Sometimes I really don't understand what's going on
in an example in the book but I see it works. So when I want to do something
similar in my own program, I use the working example as a model. Of course, I
keep my mind open for understanding and after using the model I'll often have an
"aha" experience - "Oh, I get it! That's what's happening!"

If I don't memorize or use a model I don't really understand, I can't move on.
I'm mired in my non-understanding. So I think sometimes we have to trust that
understanding will catch up.

All this is not to say that we don't try for understanding. We need to
continually find new, meaningful ways to try to impart understanding. When
teaching fractions we need to use real life (can you divide this chocolate bar
evenly among the members of your group? or if I buy a box of 10 pizza pockets
how will I divide that for the 3 members of my family? or using recipes that
contain 1/2 teaspoons of salt, etc), manipulatives, paper diagrams, number
lines, whatever.

I know a girl who has brain damage and needs to be taught over and over again
before she "gets" something. In school, she was taught how to tell time on an
analog clock face drawn on a piece of paper. She learned well enough so that she
could read or draw the correct time on the paper about 70% of the time. But this
knowledge did not transfer to the clock on the wall or to the watch on her
arm.

So I think diagrams, number lines, manipulatives and other "school" things are
not enough. We have to go to real life because that's where real understanding
will come in very handy. Often, students already understand life problems that
deal with fractions and they need to be taught the way to communicate their
understanding in math format.