Search All of the Math Forum:

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

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

 Messages: [ Previous | Next ]
 Alain Schremmer Posts: 838 Registered: 10/10/05
Re: -2^4 vs (-2)^4
Posted: Feb 9, 2009 10:56 PM

On Feb 9, 2009, at 10:22 PM, Bret Taylor wrote:

> My two cents.
>
> I use several different "techniques" to try and convince my
> students that -6^2 = -36.
>
> But, this one seems to work the best:
>
> -a = -1*a
>
> So,
>
> -2 = -1*2
> -5 = -1*5
> -dog = -1*dog
> -& = -1*&
>
> therefore, -6^2 = -1*6^2
>
> And, since we do multiplication after exponentiation, -6^2 = -1*36
> = -36.

Whether or not -6^2 = -36 is completely a matter of linguistic
convention. It is certainly NOT a matter of logic. Just try to
formalize the above.

It is of course true that for this or that reason, this or that way
of coding may or may not facilitate computations. For instance, if,
in analysis, f(x) is the preferred notation, in algebra, fx and even
xf have very strong proponents.

It may or may not be worth class time to show that agreeing to read
the - as affecting 6^2 is better suited to the computations we will
be likely doing in the foreseeable future than looking at - as
automatically being the sign going with the 2. But one could
certainly argue that, inasmuch as we are dealing with signed numbers,
it is better to see the - as the sign of the integer whose size is 2

In any case, though, it is completely misleading and immensely
counterproductive to " try and convince students that -6^2 = -36".

Regards
--schremmre
****************************************************************************
* 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