Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: Teaching Dev Mathematics Conceptually: practical ideas
Replies: 96   Last Post: May 4, 2009 5:07 AM

 Messages: [ Previous | Next ]
 Mowers, Kathy \(Owensboro\) Posts: 22 Registered: 1/30/05
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: 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

****************************************************************************
* To post to the list: email mathedcc@mathforum.org *
* To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org *
* Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
****************************************************************************
****************************************************************************
* To post to the list: email mathedcc@mathforum.org *
* To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org *
* Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
****************************************************************************

Date Subject Author
2/4/09 kathleen Offenholley
2/4/09 Prof Martin Weissman
2/4/09 Jonathan Groves
2/5/09 Beth Hentges
2/6/09 kathleen Offenholley
2/6/09 Jonathan Groves
2/7/09 Phil Mahler
2/7/09 Alain Schremmer
2/7/09 Jonathan Groves
2/9/09 Beth Hentges
2/9/09 Bret Taylor
2/9/09 Jonathan Groves
2/7/09 kathleen Offenholley
2/7/09 Jonathan Groves
2/7/09 Phil Mahler
2/7/09 Jonathan Groves
2/8/09 Larry Stone
2/9/09 Beth Hentges
2/9/09 Prof Martin Weissman
2/10/09 Phil Mahler
2/10/09 Bruce Yoshiwara
2/9/09 Beth Hentges
2/9/09 Prof Martin Weissman
2/9/09 Alain Schremmer
2/9/09 Jonathan Groves
2/10/09 Beth Hentges
2/18/09 Jonathan Groves
2/9/09 Prof Martin Weissman
2/9/09 Alain Schremmer
2/9/09 Bret Taylor
2/9/09 Daniel Kleinfelter
2/9/09 Alain Schremmer
2/10/09 Alain Schremmer
2/10/09 Beth Hentges
2/10/09 Alain Schremmer
2/10/09 Matthews, George
2/10/09 Phil Mahler
2/10/09 Jonathan Groves
2/10/09 Sharon Killian
2/10/09 Beth Hentges
2/10/09 Jodi Cotten
2/25/09 Jonathan Groves
2/27/09 Jonathan Groves
2/9/09 Jonathan Groves
2/16/09 Sue VanHattum
2/18/09 Jonathan Groves
2/18/09 Phil Mahler
2/18/09 Jonathan Groves
2/18/09 Wayne Mackey
2/18/09 Phil Mahler
2/18/09 Wayne Mackey
2/18/09 Wayne Mackey
2/18/09 Phil Mahler
2/18/09 Mowers, Kathy \(Owensboro\)
2/18/09 Wayne Mackey
2/18/09 Larry Stone
2/20/09 Beverly R. Broomell
2/21/09 Jonathan Groves
2/23/09 Dana Lee Ling
2/23/09 Bruce Yoshiwara
2/18/09 Prof Martin Weissman
2/18/09 Wayne Mackey
2/19/09 Alain Schremmer
2/19/09 Prof Martin Weissman
2/19/09 Alain Schremmer
2/19/09 Wayne Mackey
2/19/09 Clyde Greeno
2/19/09 Alain Schremmer
2/19/09 Greeno
2/19/09 Alain Schremmer
2/19/09 Wayne Mackey
2/19/09 Bruce Yoshiwara
2/20/09 Jonathan Groves
2/20/09 Alain Schremmer
2/20/09 Larry Stone
2/18/09 Jonathan Groves
2/19/09 Alain Schremmer
2/20/09 George Alexander
2/20/09 Wayne Mackey
2/20/09 Alain Schremmer
2/20/09 Beth Hentges
2/20/09 Alain Schremmer
2/23/09 Alain Schremmer
2/23/09 Beth Hentges
2/23/09 Alain Schremmer
2/23/09 Beth Hentges
2/24/09 Beth Hentges
2/20/09 Mowers, Kathy \(Owensboro\)
2/20/09 Alain Schremmer
2/20/09 Bruce Yoshiwara
2/20/09 Alain Schremmer
2/18/09 Wayne Mackey
2/18/09 Phil Mahler
2/20/09 Jonathan Groves
2/20/09 Alain Schremmer