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

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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
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> 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
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
kathleen Offenholley
2/4/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Prof Martin Weissman
2/4/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/5/09
Read order of ops
Beth Hentges
2/6/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
kathleen Offenholley
2/6/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Phil Mahler
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/9/09
Read fraction bar
Beth Hentges
2/9/09
Read Re: fraction bar
Bret Taylor
2/9/09
Read Re: fraction bar
Jonathan Groves
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
kathleen Offenholley
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Phil Mahler
2/7/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/8/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Larry Stone
2/9/09
Read mult and div
Beth Hentges
2/9/09
Read RE: mult and div
Prof Martin Weissman
2/10/09
Read RE: mult and div
Phil Mahler
2/10/09
Read RE: mult and div
Bruce Yoshiwara
2/9/09
Read -2^4 vs (-2)^4
Beth Hentges
2/9/09
Read RE: -2^4 vs (-2)^4
Prof Martin Weissman
2/9/09
Read Re: -2^4 vs (-2)^4
Alain Schremmer
2/9/09
Read Re: RE: -2^4 vs (-2)^4
Jonathan Groves
2/10/09
Read RE: RE: -2^4 vs (-2)^4
Beth Hentges
2/18/09
Read Re: -2^4 vs (-2)^4
Jonathan Groves
2/9/09
Read RE: -2^4 vs (-2)^4
Prof Martin Weissman
2/9/09
Read Re: -2^4 vs (-2)^4
Alain Schremmer
2/9/09
Read Re: -2^4 vs (-2)^4
Bret Taylor
2/9/09
Read RE: -2^4 vs (-2)^4
Daniel Kleinfelter
2/9/09
Read Re: -2^4 vs (-2)^4
Alain Schremmer
2/10/09
Read RE: -2^4 vs (-2)^4
Adam Stinchcombe
2/10/09
Read Re: -2^4 vs (-2)^4
Alain Schremmer
2/10/09
Read RE: -2^4 vs (-2)^4
Beth Hentges
2/10/09
Read Re: -2^4 vs (-2)^4
Alain Schremmer
2/10/09
Read RE: -2^4 vs (-2)^4 [Microsoft Excel]
Matthews, George
2/10/09
Read RE: -2^4 vs (-2)^4 [Microsoft Excel]
Phil Mahler
2/10/09
Read Re: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Jonathan Groves
2/10/09
Read Re: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Sharon Killian
2/10/09
Read RE: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Beth Hentges
2/10/09
Read Re: RE: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Jodi Cotten
2/25/09
Read Re: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Jonathan Groves
2/27/09
Read Re: RE: -2^4 vs (-2)^4 [Microsoft Excel]
Jonathan Groves
2/9/09
Read Re: RE: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/16/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Sue VanHattum
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Phil Mahler
2/18/09
Read Different Orders of Operations Among Machines and Humans
Jonathan Groves
2/18/09
Read Re: Different Orders of Operations Among Machines and Humans
Wayne Mackey
2/18/09
Read Re: Different Orders of Operations Among Machines and Humans
Phil Mahler
2/18/09
Read Re: Different Orders of Operations Among Machines and Humans
Wayne Mackey
5/4/09
Read Re: Different Orders of Operations Among Machines and Humans
martsbradley
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Wayne Mackey
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Phil Mahler
2/18/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Mowers, Kathy \(Owensboro\)
2/18/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Wayne Mackey
2/18/09
Read minus vs. opposite symbols
Larry Stone
2/20/09
Read Re: minus vs. opposite symbols
Beverly R. Broomell
2/21/09
Read Re: minus vs. opposite symbols
Jonathan Groves
2/23/09
Read Re: minus vs. opposite symbols
Dana Lee Ling
2/23/09
Read RE: minus vs. opposite symbols
Bruce Yoshiwara
2/18/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Prof Martin Weissman
2/18/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Wayne Mackey
2/19/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/19/09
Read How Would You Help This Student?
Prof Martin Weissman
2/19/09
Read Re: How Would You Help This Student?
Alain Schremmer
2/19/09
Read Re: How Would You Help This Student?
Wayne Mackey
2/19/09
Read Re: How Would You Help This Student?
Clyde Greeno
2/19/09
Read Re: How Would You Help This Student?
Alain Schremmer
2/19/09
Read Re: How Would You Help This Student?
Greeno
2/19/09
Read Re: How Would You Help This Student?
Alain Schremmer
2/19/09
Read Re: How Would You Help This Student?
Wayne Mackey
2/19/09
Read RE: How Would You Help This Student?
Bruce Yoshiwara
2/20/09
Read Re: How Would You Help This Student?
Jonathan Groves
2/20/09
Read Re: How Would You Help This Student?
Alain Schremmer
2/20/09
Read RE: How Would You Help This Student?
Larry Stone
2/18/09
Read Re: RE: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/19/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
George Alexander
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Wayne Mackey
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/20/09
Read counting on, counting back
Beth Hentges
2/20/09
Read Re: counting on, counting back
Alain Schremmer
2/23/09
Read Re: counting on, counting back
Alain Schremmer
2/23/09
Read Cognitively Guided Instruction
Beth Hentges
2/23/09
Read Re: Cognitively Guided Instruction
Alain Schremmer
2/23/09
Read RE: Cognitively Guided Instruction
Beth Hentges
2/24/09
Read RE: Cognitively Guided Instruction
Beth Hentges
2/20/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Mowers, Kathy \(Owensboro\)
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/20/09
Read RE: Teaching Dev Mathematics Conceptually: practical ideas
Bruce Yoshiwara
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Wayne Mackey
2/18/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Phil Mahler
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Jonathan Groves
2/20/09
Read Re: Teaching Dev Mathematics Conceptually: practical ideas
Alain Schremmer

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