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Topic: Fractions, concept and calculations

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Subject:   Fractions, concept and calculations
Author: lanius
Date: Sep 30 2004

How do you teach conceptual understanding of fractions? What tools have you
found to be effective, and likewise how do you teach computational fluency with
fractions and what tools are effective?

I'd like to relate a story. Formerly, in Texas, we had the Texas Assessment of
Academic Skills (TAAS) where  students had to pass what was basically an 8th
grade level test in order to graduate. One of the questions always on the test
required them to order a series of fractions from least to gratest -- 2/3,
5/6, 3/4, 2/5, etc. I was teaching a test-prep class to seniors who needed
only to pass the math test in order to graduate, having failed it several times.
I wrote the problem of ordering fractions on the board. The students had some
ideas of getting common denominators, etc. to work the problem, but I asked them
to talk about the problem a bit to see what they understood about fractional
parts. To try to get at what they understood, I wrote 6/7 and 7/6 on the board
and asked them to put those in order. And the students couldn't.

So what does that mean? I felt like they had no clue about what these numbers
meant. So I thought why spend time teaching students to
add/subtract/multiply/divide fractions (which also was tested) when the numbers
held no meaning for them. How could this happen? These students were plenty
bright. I'm sure they'd seen lots of pies cut up all through math classes. Why
didn't they get it? Where was the dis-connect in the understanding?


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