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 Discussion: Roundtable Topic: Fractions, concept and calculations

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 Subject: RE: Fractions, concept and calculations Author: pammeyepoo Date: Jul 21 2009
On Sep 30 2004, lanius wrote:
> Greetings,

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?

Thanks,
Cynthia

Sadly, I have seen this occurrence time and time again. This is an actual
metacognition strategy that I teach the students to do so they make sense of
these combination of digits and symbols in front of them.
What I began to do was to purchase measuring tapes used in construction-type
projects. You can get them fairly inexpensive at dollar tree, and other dollar
stores. However, you must ensure that the increments are marked visibly on the
tape measure. I attempt to get AT LEAST sixteenths. Give the students everyday
items to measure, then have them order them from least to greatest. There is
also the additional visual backup of the items: what LOOKS like it is the
smallest? Does the measurement back that up. The visualization assists in the
transition from concrete to semi-abstract to abstract. Once those images are
in the mind, an abstract visualization occurs. Yes, I am an Intervention
Specialist, but it works for bright students just as well.

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