Re: [eddra] Algebra

["Dr. Leo Casey" <LeoCasey@AOL.COM>]

In his book _Radical Equations_, Bob Moses makes a telling point about the
different intellectual structures of arithmetic and algebra to explain why
some students have a difficulty making the transition from the former to the
latter. Arithmetic, he points out, focuses on the question of "how much?"
while Algebra takes up the question of "what direction?". Some students get
caught in the "how much" question, not realizing that a different question is
now being asked. It seems to me that a lot flows from this difference, such
as the more abstract nature of Algebra -- although not so abstract that it
can not be easily grounded in practical contexts, such as rides in subways
and buses.  It also follows that there is a certain amount of disconnect
between the skills of the two subjects, although I don't see how could do
Algebra without a basic grasp of adding, subtracting, multiplication and
division, as well as fractions.

I do think that Moses is on to something important with his insistence upon
numeracy as an educational foundation, and a basis of modern citizenry,
although there is an [understandable?] tendency on his part to overstate his
case. In this respect, I do not agree with the view that Gerry Bracey has
stated, on occasion, that argues against the importance of learning algebra.

Leo Casey
United Federation of Teachers
260 Park Avenue South
New York, New York 10010-7272 (212-598-6869)

Power concedes nothing without a demand.
It never has, and it never will.
If there is no struggle, there is no progress.
Those who profess to favor freedom, and yet deprecate agitation are men who
want crops without plowing the ground. They want rain without thunder and
lightning. They want the ocean without the awful roar of its waters.
-- Frederick Douglass --