```Date: Nov 18, 2012 2:48 AM
Author: Guest
Subject: Re: Please remind me why -3^2 = -9

7-3^2 means 7+-3^2 means 7+-1*3^2The point is that it is all convention, there are reasons for choosing the conventions we do.I am one who usually uses the "flying hyphen" to indicate a negative or opposite sign.I have seen one elementary curriculum that used a hat to indicate negative numbers.BethOn Nov 15, 2012, at 1:36 AM, "Clyde Greeno" <clydegreeno@cox.net> wrote:Beth, thanks for responding!My #s are below- --------------------------------------------------From: "Beth Hentges" <Beth.Hentges@century.edu>Sent: Wednesday, November 14, 2012 10:15 PMTo: "Clyde Greeno" <greeno@malei.org>Cc: "Wayne Ford Mackey" <wmackey@uark.edu>; "Alain Schremmer" <schremmer.alain@gmail.com>; "Philip Mahler" <mahlerp@middlesex.mass.edu>; <mathedcc@mathforum.org>; "Clyde Greeno @ MALEI" <greeno@malei.org>Subject: Re: Please remind me why -3^2 = -9> (-3)^2 is clear> > -(3^2) is clear> > We have to choose which we mean when we write the following.> > -3^2> # So far, so good!> The reason we choose -3^2 to mean -(3^2) is because we do powers before multiplication and because -a = -1*a.# And the reasons for that rule and for that equation are ????It seems as though you are trying to *conclude* what is actually a grammar-rule of the written language. The "powers before multiplication" is just such a grammar rule, and it gains no rational support from the equation. Nonetheless, I can believe that your use of that equation very well might help train students to calculate, better ... even without grasping the commonsensibility of it all.# The mathematical issue with your equation is that it does the usual curricular "slight of hand" by ambiguously using "-" with two differing meanings ... while many students use even a third meaning. Within the context of linear number systems. "-1" means "1 below 0" ... while "-a" means "the negative/opposite of a" ... while students routinely take "-" to mean "subtract a."# In the case of 7-3^2, many students take the "-" to mean subtraction. Then their question becomes, "Does it mean (7-3)^2? [as 4^2]  ... or 7-(3^2) [as 7-9]?" Would your equation lead some to interpret it as 7(-1)*(3^2)? Of course  an instructor  might simply *define" subtraction so that the meaning of "7-3" is 7+(-1)*3. But would that be common-sensible to students?# So the instructological question is whether or not your students actually grasp and apply your theorem: neg of (a) = (1-below-0)*a. Even if not, they still might use your symbol-switching device for more systematically calculating, correctly.# But as yet, I fail to perceive how your equation makes algebraic formulas any more commonsensible than would a good treatment (much better than usual) of how to use parentheses in accord with the syntax-conventions that currently are in commonplace use throughout the field (and in most calculators).Cordially,Clyde> > (-3)^2 = (-1*3)^2 , and the parentheses tell us to do the multiplication first.> > -(3^2) = -1*(3^2), and the parentheses tell us to do the power first.> > -3^2 = -1*3^2, and we do powers before multiplication.> > > As for PEMDAS, I use PEMA.  Otherwise, students think PEMDAS says to do multiplication before division.  Also, when I write it in words, for the E for exponents (which really should be another P for powers), I write, "Do exponents and roots from left to right."  So, even if I did use PEMDAS it would be PERMDAS.  Then, we also have to be careful with absolute value as well.> > Beth in MN***************************************************************************** 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 *****************************************************************************
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