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 Subject: RE: Fractions, concept and calculations Author: tracythompson Date: Oct 13 2004
Hi Cynthia,

My name is Tracy Thompson, and I'm a member of the mathtools group. I'm also in
a Master's program in math education at San Francisco State University. Your
message caught my eye, because I'm in a class called "Analyzing Cases of
Mathematical Teaching." We meet every week and use case studies to discuss
student thinking and effective teaching strategies. I forwarded your message to
the class, and we decided to discuss it, because you brought up some great
issues that we all struggle with. We came up with some ideas which I'll try to
synthesize here.

One big issue that came up was that since these were seniors, the decision about
how and what to teach for understanding may be different than if these were
younger students. At this point, the goal may be just passing the test. You
don't have time to re-teach everything. Some ideas:

-The time frame is probably really tight, since they are most likely weak in
many different areas of math. Still, you may want to consider spending a week or
so teaching basic fraction concepts. Draw pictures, use models, and make them
explain their thinking. Use manipulatives, but don't rely on them too much. Have
them really look at the meaning of numerator and denominator. You might go back
6/7 of a candy bar (or gold bar) or 7/6.

-They may have great difficulty with fractions, but they've been exposed to
the ideas for many years. They all know something--they just don't all know
the same things! Try to exploit this for the class' benefit. Put that problem
about ordering fractions back on the board, and have them brainstorm strategies.
Ask them to draw representations of the different fractions. If they don't have
good number sense about fractions, then discussing the relative sizes is really
important.

-Test-taking strategies may be useful if the exam is multiple-choice. You
won't be able to teach them everything they somehow didn't learn in 12 years of
school, but 'psyching out' the test is a powerful tool that they can learn. See
the class (and yourself) as united in beating the test.

-Last but not least, don't give up! Keep the faith. :-)
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,
> 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