Date: Oct 18, 2012 5:37 AM
Author: Phil Mahler
Subject: Please remind me why -3^2 = -9

I have been teaching a long time, and I know from experience that 50% of
students will tell me that ­3^2 = +9 on a test or a final, despite having
discussed it a few times in a course.

When I first started teaching I taught calculus and precalc. Piece of cake.
Then I started with an Algebra I class and couldn¹t connect at all for the
first week or so. I was ready to believe I couldn¹t teach. I simply could
not explain how I got the right answers when evaluating expressions... Then
I discovered the order of operations (PEMDAS to some). A definition of the
order of operations which I had so internalized that I didn¹t know there was
a rule for it. Since that discovery I¹ve been a wonderful teacher. :-)

So... I must be missing something that so many of my students think ­3^2 is
+9. What is the rule I have never discovered?

Full disclosure: I think ­k^2, k a constant, should be banned from
mathematics texts and tests. -x^2, x a variable, evaluated for say ­3,
absolutely (no pun intended) but not ­3^2.

Phil