Re: 64 - is this the only number that is both a sq and a cube?

From: Daniel Grubb (grubb_at_lola.math.niu.edu)
Date: 09/21/04 

Date: 21 Sep 2004 15:58:04 GMT

>>He's the norm, not the exception. Hardly any of the students I see,
>>even the better ones, know (x+y)^2 = x^2+2xy+y^2 without multiplying
>>out the factors by "FOIL". These are all students who have been
>>through two years of high-school algebra, or more.

>You think memorizing (x+y)^2 = x^2+2xy+y^2 is more important than
>knowing FOIL? Isn't it better to know an algorithm than a fact?
>Because I was never good at memorizing things, the only thing I
>memorized about trigonometry was sin(0)=0 from which I would derive
>the needed trig identity. As a result, I got straight A's in math while
>failing Spanish.

One of the problems I've run into is that students know FOIL, but get
lost when asked to multiply (2x+y+z) and (3x+4y-5z) because FOIL
only works for *pairs*. So I would say there is a hierarchy of
desirables:

1) Know how to multiply general expressions.

2) Know how to use FOIL

3) Know (x+y)^2 =x^2 +2xy +y^2 and (x+y)(x-y)=x^2 -y^2 and other
simple products.

The difficulty is that many students know *none* of these.

--Dan Grubb

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