
RE: Teaching Dev Mathematics Conceptually: practical ideas
Posted:
Feb 18, 2009 4:54 PM


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: ownermathedcc@mathforum.org [mailto:ownermathedcc@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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