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

 Messages: [ Previous | Next ]
 Jonathan Groves Posts: 2,068 From: Kaplan University, Argosy University, Florida Institute of Technology Registered: 8/18/05
Different Orders of Operations Among Machines and Humans
Posted: Feb 18, 2009 11:32 AM

> We've seen in these (very helpful for me) discussions
> that things like a/bc
> and a/b(c) are handled differently by different
> pieces of technology. Indeed
> I would get nervous if I saw the expression a/bc
> somewhere.

Even among mathematicians (not computer algebra systems or calculators or the like), the expression a/bc can mean one of two things. PEMDAS says this is (a/b)c, but I think I have read somewhere that many (maybe most) mathematicians take this to mean a/(bc) since this source (I wish I knew what it was) says many (maybe most) mathematicians perform all multiplications before any divisions. Considering that I have heard from a few sources that some students outside the U.S. have learned it as PEDMAS (all divisions done before any multiplications; one here on Math Forum mentioned this recently), this source might have been discussing American mathematicians. So unless you're writing to mathematicians or students whom you know would not misinterpret a/bc by whatever convention you're using, it's probably best to use parentheses in all cases. I usually do myself so that the meaning, whether it is (a/b)c or a/(bc), is absolutely clear to myself and to my readers.

By the way, Eric Schecter on his common errors in undergrad mathematics under order of operations dicusses some of the differences in conventions among machines and humans; the link to his webpage is http://www.math.vanderbilt.edu/~schectex/commerrs/#Operations. He too recommends not writing a/bc or ab/cd (except dx/dy for the derivative, of course!) because of the different conventions. (He does have the "My Dear Aunt Sally" interpretation wrong, at least according to the way I learned it; I learned it as doing all multiplications and divisions in the order they occur so that a/bc is (a/b)c, not a/(bc). How many here have learned it according to the way Schecter describes it?

> Also, the infamous -3^2, which I still would like to
> ban as an ill-defined
> expression, or at least so confusing it's not worth
> the trouble.

Schecter, on his same webpage, says mathematicians generally see -3^2 as -(3^2) so that it's -9. As far as I know, I don't know any mathematicians or mathematics teachers do see this as (-3)^2=9.

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