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Re: Please remind me why -3^2 = -9
Posted:
Oct 19, 2012 12:03 PM
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On Oct 19, 2012, at 10:50 AM, Wayne Ford Mackey wrote:
> What if a student has to replace x by 3 in the expression - x^2?
> Shouldn't he or she know the result?
I think that the basic issue here is really the following:
When a student see -3, s/he correctly sees a signed number, that is a
two-part symbol, one part of which codes the size of whatever in the
real world the compound symbol -3 represents and the other part of
which codes the way the real-part entity goes: good / bad, black /
white, up / down, in / out, etc.
But then, when s/he sees -x, s/he naturally thinks that she is seeing
a two-part symbol of which - is the sign and of which x stands for the
undisclosed size. Which is why s/he will tell you that -x is negative.
The fact that x stands for the two-part symbol as a whole is
absolutely not obvious.
This is another illustration of the fact that students expect the
meaning of symbols to be context-free while, in fact, the meaning of -
depends here on whether it in front of a specific number or in front
of a letter.
Regards
--schremmer
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