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RE: Teaching Dev Mathematics Conceptually: practical ideas
Posted:
Feb 18, 2009 4:54 PM
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At one point, according to what I've seen there was a movement to try to use different symbols to mean "the opposite" and "minus." It didn't catch on, obviously. In one case, the opposite was higher on the line and smaller than the minus. I cannot reproduce it on the keyboard.
-----Original Message-----
From: owner-mathedcc@mathforum.org [mailto:owner-mathedcc@mathforum.org] On Behalf Of Philip Mahler
Sent: Wednesday, February 18, 2009 3:45 PM
To: mathedcc@mathforum.org
Subject: Re: Teaching Dev Mathematics Conceptually: practical ideas
On 2/18/09 3:32 PM, "wmackey" <wmackey@uark.edu> wrote:
> Well, I don't think the expression -3^2 is undefined if - is properly
> defined. It should be read as the opposite of 3^2 which is clearly
> negative 9 or -9. The - symbol has three different meanings depending
> on context. In front of a natural number it means "negative", in
> front of anything else it means "opposite". If it is between 2 things
> it means subtract. Since no books except mine bother to define the
> symbol it leaves everyone confused.
>
> wayne
I like the fact that you confront this situation head on. You are saying, I
think, that - in front of any expression where it doesn't mean subtraction,
or not in front of a single numeral, means -(expression). In some ways it
implies a symbol of grouping. I guess it could be extended to even a numeral
since the opposite of what a numeral represents is a negative number?
That can add a little extra work to something like -6(-4), since you have to
think of it as -[6(-4)] rather than the product of two negatives. But of
course in practice it probably would not be an impediment, people would just
think of it as the product of two negatives, and I grant it helps immensely
with -3^2. Though demonstrably one cannot depend on entering -3^2 into
calculating devices and getting the defined result. But at least it tells
one to enter it as -(3^2).
I might be able to live with that because that just might stick with
students (I imagine that is your experience?). And I realize that everyone
else on the list lives with -3^2 without a problem already. :-)
Phil
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