Discussion:  All Topics 
Topic:  Formulas 
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Subject:  RE: Formulas 
Author:  Mathman 
Date:  Mar 14 2005 
> On Mar 11 2005, RedCisc wrote:
> Please excuse me, I am new to
> teaching math and not prepared as a
> math teacher. Our school has
> so many students in developmental math
> and not enough math
> teachers; I was drafted from Computer
> Technology. What is
> transposition?
Is 'transpostion' an Aussie term? I don't think
> I've ever heard it before.
No. I'm English born [oldschool tie and all that] and now, the large part of
my life, Canadian.
My introduction of this sidetopic stems form the fact that I think that many
students get bogged down with, and are far more prone to error when they have
mroe written work to do than is really necessary. Although the transposition
stems form the balance of an equation, it is far easier to manipulate quantities
when one uses that instead of going to the fundamental principles all of the
time. As follows:
1. Do the same to both sides [properites of blanced equations.]
3x + 2 = 8
3x + 2  2 = 8  2
3x = 6
3x / 3 = 6 / 3
x = 2
2. Transposition:
3x + 2 = 8
3x = 8  2
3x = 6
x = 6 / 3
x = 2
They amount to the same thing, but the former is way more bulky to manage when
the formulas or equations are much more complex, although this simple example
isn't the best to show that. Also, and I've used the example of the Special
Theory of Relativity development to make the point, no author of an advanced
text in his right mind would go through the elementary process of "doing the
same to both sides." So, the student is preparing to *read* later texts more
readily when trained properly to do so [even if not going so far as the above
example.]
I do not advocate transposition alone, but as an end result. The fundamental
properties give the reason for being able to do it that much more efficient way.
It does require training and efort, but it pays off big time in the long
run.
One problem all around that students have is "insight" which is not gained until
they have had the prerequisite practice, and that makes the interim difficult...
and so it is ...difficult. The only analogy, and NOT practice for this
requirement, I can think of [and you'll forgive me] is a game called Sokoban.
To solve that efficiently it has to be thought through thoroughly before you
even start. There's the rub.
David.
 
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