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Topic: Fractions, concept and calculations

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Subject:   RE: Fractions, concept and calculations
Author: Mathman
Date: Oct 28 2004
On Oct 28 2004, ten frame lady wrote:

A gentle hint:  Please do edit out unnecessary text.  A page or two need not be
left in for a one line response.

> OOPS! There is a typo in the division explanation.

When we divide
> 8 by 4 to get 2, the quotient means that there are 2 groups of 4 in
> 8 (NOT 2 groups of 8)!!

On Oct 27 2004, ten frame lady
> wrote:
> Oh, my goodness! Don't give up on your students' ability
> to make
> sense of fractions!

I never did!  ...not even in thirty odd years of sucessfully teaching the
subject [mathematics] in all grades and at all levels of ability.  Please don't
even suggest that.  I do still suggest that there are those who gather concepts
in more time than it takes others.  I also say that there exist indeed *all*
levels of ability in every subject/study/occupation, and that you would not pay
a cent to watch me play hockey.  If we do not recognise some limitations, then
we fail those who we are trying to teach by pushing them far beyond their true
capabilities, and it is the nature of teaching presently that courses have been
watered down incredibly to accommodate.  That does no-one good in the long
run.  There is sometimes a realism that must be addressed as well as a wish.  To
use a rather worn expression, "There are only so many ways to swing a cat."
I've had a class of over 30 general level students solving two equations, two
variables four different ways ...all of them, every last one.  I've also had one
who *would not* let go of a calculator to divide a decimal fraction by ten.  I
do not give up one the "students' [plural] ability to make sense of fractions",
but am very realistic about expectations for the few.   I also have a deep
abiding understanding that fractions give inordinate problems to students on the
whole, and an understanding of their importance in later study.  That problem,
incidentally, is compounded by the introduction of studies in probability
injunior grades, taking the time needed for necessary practice leading to
understanding.  I play classical piano, and know that I did not understand the
structure, the power, the emotion of the works of the masters while I was a
child practicing my scales.  But if I had not practiced those scales still
lacking that understanding at that time as a child, I would not have gone on to
do so.


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