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 Discussion: Traffic Jam Applet tool Topic: Fractions, concept and calculations Related Item: http://mathforum.org/mathtools/tool/10/

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 Subject: RE: Fractions, concept and calculations Author: ihor Date: Oct 27 2004
Hi,

> All I've been able to do is to give the best
> explanation possible, and let their individual intuition work and develop.
I
> don't think I can teach to improve that.  I can show different, perhaps
> better
> ways to do one thing or another, but the arithmetic of fractions [not
> necessarily the physical representation] does eventually boil down to
> memorising
> method, with or without deeper understanding.

I'm with you all the way until you got to memorizing with or without
understanding.

Unfortunately, most people come away with the latter. I think that is
collectively our fault that we have not been able to come up with better ways to
help students learn it. And you may be right, it may not be possible to have the
majority of students understand what they are doing. Most of them will go
through the motions to pass the test just like all the generations before them.
But I'm an optimist I think more kids can understand and appreciate the math
they are learning and its not just the kids that are good at it or like math. I
watched a lot of teachers over the years who find ways to do it and I think
their teaching secrets (their pedagogical content knowledge) ought to be shared
as much as possible. Otherwise we give up too soon and let average kids go
through those same semi-productive hoops. As a good friend of mine once told
me when he was arguing the point of just getting by: "Look at me I was terrible
at math, but I mangaged to be successful as a lawyer." I would say he became a
lawyer despite the handicap of his math skills and it didn't have to be that
way. (What he really meant to say was that he was "terrible" because he didn't
understand it, not because he couldn't "do it."

>Ability to recognise the same
> pattern and thus the same approach to solution in rational algebra pays
off
> as
> the skill through practice [at what point DO they understand?] puts the
> method
> into automode as the larger problem develops into a solution.  I'm
comparing
> that to practicing scales on the piano. .... however intuitive it becomes, and
not having to think about where to place fingers allows for other, better things
to develop more naturally in the long run.  All can learn to play, but not all
can learn to play well,
> no
> matter the teacher.

One of the most formative experiences of my life was taking piano lessons for 3
years: It was the ultimate drill and kill experience because the teaching was so
uninspiring that I actually avoided contact with any form of music for years.
Fortunately, it was not life threatening... I do enjoy all kinds of music today
and even learned to play a little guitar in my later years. I don't have kids of
my own but I did watch closely my niece and nephews grow up all taking years of
music lessons from a good teacher. Only one of them became reasonably good at
it, but the others enjoyed the experience of learning to play. (I'm
jealous.)

-Ihor