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Topic: Fractions, concept and calculations

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Subject:   RE: Fractions, concept and calculations
Author: Mathman
Date: Oct 3 2004
On Oct  1 2004, Teach Math wrote:
> Much of the research suggests that we
> move too quickly to engaging students in computing with fractions
> before they understand the meanings of fractions.

That is so.  One reason is that there must be time put aside to learn how to
search the web and learn other computer skills, or throw dice and learn
something about statistics before they have any sense of what statistics are.
Another reason is the arduousness of having to do more than a question seems to
require.  That is, the age old question "Do we HAVE to do this?" by both student
and teacher; like children learning the piano, they must first learn where to
place their fingers, and so must practice scales and arpheggios.  Since that
turns off a lot of people, then a lot of people simply don't learn how to play
the piano, at least to any pleasing extent.  It's largely a matter of time
spent, and time needed to be spent solving a problem in fractions and then
drawing a diagram to see the results start and finish, then practicing ...daily.
[Oops.  Some might call that "drill and kill".  I still call it "practice".]

A young man early in the days of computer availability turned in a beautiful
graph others had done carefully by hand.  He had learned nothing about graphing
and its interpretation.  Today, young people struggle with algebraic graphing by
pressing keys on a calculator or computer.  I've earned a little tutoring by
having them draw by hand, studying the ups and downs as they work along.
Everyone is in too much of a hurry.  A slow start can save years and years of
work in the long run, as through those years developed skills come into play,
and the seemingly arduous becomes quite natural so that newer work can be
considered in context of the old.  Those who practiced their scales and
arpheggios can concentrate on the music, not where to place their fingers.  [I
dearly wish I had those skills in typing!]


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