Discussion:  Research Area 
Topic:  Why (numerical) algebra is arithmetic backward 
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Subject:  Why (numerical) algebra is arithmetic backward 
Author:  Sonny 
Date:  May 26 2004 
showing that
(NUMERICAL) ALGEBRA IS ARITHMETIC BACKWARDS. Example: If you make 8 payments of
$75 each, that
accumulates to 8 x $75 = $600. Conversely, you may incur an obligation of $600
and wish to know
how much you must pay in eight equal payments. That is the (numerical) algebra
problem of
8X = $600, with solution X = $75. This understanding motivates students by
showing them that
they already know a method which, turned around solves another type of problem.
It also explains
that the "X" in (numerical) algebra is a set of numbers which conditionally
satisfy an equation.
In a file at this Website, I quote the Danish theologian and philosopher, Soren
Kierkegaard:
"Life can only be understood backwards, but must be lived forward." And note
that algebraic
exercises can prepare one for nonmathematical procedures in life. In another
file at this
Website, I note the comment of Morris Kline in his "Mathematical Thought from
Ancient to Modern
Times", V. I, that the first people (Babylonian Priests) to develop predictive
science  namely,
predicting phases of the moon, lunar and solar eclipses, etc.  were the
first people to develop
(numerical) algebra. This material is also ONLINE in Spanish:
http://.../jonhays/algepagina.htm.
 
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