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Topic: Re: factoring, FOIL, technology, etc.
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Posts: 243
Registered: 12/6/04
Re: factoring, FOIL, technology, etc.
Posted: Jun 13, 1995 2:22 PM
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The issue for me is whether students can manipulate algebraic expressions
with purpose, depending on context, understand that they can be pulled
apart and put together, and so on. The students I get now in college know
(if they and I are lucky) a few standard techniques that they *always* use
whether or not it's appropriate (e.g. they never write 1/sqrt 2, because
"you never put a square root in a denominator" -- somehow they're convinced
that (sqrt 2)/2 is correct, and 2/sqrt 2 isn't), but generally do not have
what we might call algebra sense -- the same understanding of rational
functions that they have of rational numbers. This means things like the
general notion of factoring and some facility outside of basic quadratics,
simplifying expressions when desirable, complicating expressions when
desirable, common denominators and common multiples, primes, and so on.

I would guess that this algebra sense can only come about by their own
manipulations of algebraic expressions, but don't see the calculator as the
enemy -- as always, wise use of technology may be helpful. If anything,
technology can allow us to shift away from hammering away on the 2 or 3
techniques we've always hammered away on and lift the vision a bit.

Of course I don't teach at this level myself, so maybe I'm just full of hot
air. I'd be interested in hearing from the folks who do teach this, from
upper grades in elementary on -- how do you develop this "algebra sense"?

Judy Roitman, Mathematics Department
Univ. of Kansas, Lawrence, KS 66049

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