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Topic: Please remind me why -3^2 = -9
Replies: 26   Last Post: Nov 18, 2012 7:51 PM

 Messages: [ Previous | Next ]
 RotmanJ Posts: 95 Registered: 12/6/04
RE: Please remind me why -3^2 = -9
Posted: Oct 18, 2012 12:38 PM
 att1.html (16.1 K)

Phil and all:

The expression "-3^2" deals with the order of operations; the most advanced operations are always done first unless a grouping symbol 'forces' a lower prior operation to be done first. Since exponentiation is more advanced than the sign of a number, the exponent only applies to one symbol (the 3) when there are no grouping symbols.

Instead of banning this type of problem, I believe that we should ban "PEMDAS" or anything like it. The use of overly simplistic rules (often stated as a sequence of nouns) discourages learning and encourages memorization. If a large rate of correct answers is the only criteria, just have students use a calculator and train them on use of parentheses. If we are teaching mathematics, we should focus on understanding the priority of operations. What Phil internalized was this understanding; saying 'PEMDAS' does not provide any of the understanding to our students [I normally spend about a tenth of my time in class trying to undo the damage of PEMDAS. Undoing partially correct information is terribly difficult!]

Even if we never showed "-3^2", students would still be evaluating x^2 for x=-3; knowing that this means squaring a negative is a part of basic literacy in mathematics.

For those with an interest, I've posted some "anti-PEMDAS" comments on my blog (www.devmathrevival.net ). You can use the search box on the site to find them.

Jack Rotman

Professor, Mathematics Department

Lansing Community College

(517)483-1079 rotmanj@lcc.edu <mailto:rotmanj@lcc.edu>

www.devmathrevival.net

From: owner-mathedcc@mathforum.org [mailto:owner-mathedcc@mathforum.org] On Behalf Of Wayne Ford Mackey
Sent: Thursday, October 18, 2012 12:11 PM
To: Guy Brandenburg; john.peterson20@comcast.net; Philip Mahler
Cc: mathedcc
Subject: RE: Please remind me why -3^2 = -9

It should be read as the opposite of 3 squared. Since 3 squared is 9, the opposite is -9. The "-" sign is used in 3 different ways. In front of a natural number it means negative or minus, in front of anything else it means opposite and between two things it means add the opposite.

wayne

________________________________

From: owner-mathedcc@mathforum.org [owner-mathedcc@mathforum.org] on behalf of Guy Brandenburg [gfbrandenburg@yahoo.com]
Sent: Thursday, October 18, 2012 6:04 AM
To: john.peterson20@comcast.net; Philip Mahler
Cc: mathedcc
Subject: Re: Please remind me why -3^2 = -9

It's a convention. In a case like that, one really ought to use parentheses to make the meaning clear, since a lot of people, not just youngsters, will get confused.

If one intends to say (-3)*(-3), then write (-3)^2. If one means - (3)*(3), then write - (3^2).

Writing -3^2 is simply asking for confusion.

Guy Brandenburg, Washington, DC
http://gfbrandenburg.wordpress.com/
============================

________________________________

From: "john.peterson20@comcast.net" <john.peterson20@comcast.net>
To: Philip Mahler <mahlerp@middlesex.mass.edu>
Cc: mathedcc <mathedcc@mathforum.org>
Sent: Thursday, October 18, 2012 6:05 AM
Subject: Re: Please remind me why -3^2 = -9

Phil,

-3 means -1 x 3, so -3^2 is (-1)(3^2) = (-1)(9) = -9.

John Peterson

________________________________

From: "Philip Mahler" <mahlerp@middlesex.mass.edu>
To: "mathedcc" <mathedcc@mathforum.org>
Sent: Thursday, October 18, 2012 5:37:07 AM
Subject: Please remind me why -3^2 = -9

I have been teaching a long time, and I know from experience that 50% of students will tell me that -3^2 = +9 on a test or a final, despite having discussed it a few times in a course.

When I first started teaching I taught calculus and precalc. Piece of cake. Then I started with an Algebra I class and couldn't connect at all for the first week or so. I was ready to believe I couldn't teach. I simply could not explain how I got the right answers when evaluating expressions... Then I discovered the order of operations (PEMDAS to some). A definition of the order of operations which I had so internalized that I didn't know there was a rule for it. Since that discovery I've been a wonderful teacher. :-)

So... I must be missing something that so many of my students think -3^2 is +9. What is the rule I have never discovered?

Full disclosure: I think -k^2, k a constant, should be banned from mathematics texts and tests. -x^2, x a variable, evaluated for say -3, absolutely (no pun intended) but not -3^2.

Phil

Date Subject Author
10/18/12 Phil Mahler
10/18/12 John Peterson
10/18/12 Guy Brandenburg
10/18/12 Wayne Mackey
10/18/12 Phil Mahler
10/18/12 RotmanJ
10/18/12 Paul Hertzel
10/18/12 Phil Mahler
10/18/12 Clyde Greeno
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/19/12 Wayne Mackey
10/19/12 Alain Schremmer
10/19/12 Clyde Greeno
10/19/12 Alain Schremmer
10/21/12 Wayne Mackey
11/14/12 Beth Hentges
11/15/12 Clyde Greeno
11/16/12 Alain Schremmer
10/18/12 Collinge, Peter (Mathematics)
10/18/12 Guy Brandenburg
10/18/12 Phil Mahler
10/18/12 Alain Schremmer
11/18/12 EddieC
11/18/12 Matthews, George
11/18/12 Phil Mahler
11/18/12 Alain Schremmer