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Topic: Please remind me why -3^2 = -9
Replies: 26   Last Post: Nov 18, 2012 7:51 PM

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 Alain Schremmer Posts: 876 Registered: 10/10/05
Re: Please remind me why -3^2 = -9
Posted: Oct 19, 2012 12:03 PM

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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Date Subject Author
10/18/12 Phil Mahler
10/18/12 John Peterson
10/18/12 Guy Brandenburg
10/18/12 Wayne Mackey
10/18/12 Phil Mahler
10/18/12 RotmanJ
10/18/12 Paul Hertzel
10/18/12 Phil Mahler
10/18/12 Clyde Greeno
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/19/12 Wayne Mackey
10/19/12 Alain Schremmer
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/21/12 Wayne Mackey
11/14/12 Beth Hentges
11/15/12 Clyde Greeno
11/16/12 Alain Schremmer
10/18/12 Collinge, Peter (Mathematics)
10/18/12 Guy Brandenburg
10/18/12 Phil Mahler
10/18/12 Alain Schremmer
11/18/12 EddieC
11/18/12 Matthews, George
11/18/12 Phil Mahler
11/18/12 Alain Schremmer