Aug
14

GEMDAS not PEMDAS!

Filed Under (Mathematics) by on 14-08-2010 and tagged , ,

It was at the first meeting of the Challenger Middle School Mathematics Department that I first heard of GEMDAS. What an obviously good idea!

Remember PEMDAS

PEMDAS is a mnemonic device used to remember the order of operations. The order of operations is a set of rules that specify in which order to perform the mathematical operations in an expression. Such a convention is necessary so that everyone in the world gets the same results when working a math problem (assuming they don’t make a mistake!).

Youre history Aunt Sally (but fess up before you go)

You're history Aunt Sally (but fess up before you go) (Nono via Picasa)

PEMDAS is also remembered as “Please Excuse My Dear Aunt Sally” (what for, no one is quite sure). It means that when evaluating an expression that includes more than one operator, anything in parentheses is evaluated first, followed by exponents, then multiplication and/or division (whichever comes first, left to right), and finally addition and/or subtraction (whichever comes first, left to right). That is the order of operations.

GEMDAS is Better

At the aforementioned department meeting, Ms. Hertzog, a math teacher at Challenger, said something about GEMDAS being superior to PEMDAS because with PEMDAS some learners get it stuck in their heads that parentheses are the only grouping symbols that need to be taken into account, or else they get confused when some other grouping symbol is used instead of parentheses. She made no claim to inventing GEMDAS, but apparently heard about it at a workshop somewhere.

In GEMDAS, the G stands for Grouping symbol, and all the other letters keep the same meanings that they have in PEMDAS.  So with GEMDAS, learners are better able to keep in mind that ALL expressions in, on, or under grouping symbols need to be evaluated first. Grouping symbols include parentheses (), brackets [], braces {}, the vinculum ____ (which is the technical name for what most people call a fraction bar, which is also a repetition symbol used in decimal notation) , and the radical √ (also known as the square root symbol).

Google hits for PEMDAS outnumber hits for GEMDAS by a bit more than 10 to 1 (40,400 to 3,030, as of the date of this posting) so clearly PEMDAS is still a more popular mnemonic that GEMDAS.

I for one am switching over to using and teaching GEMDAS, and I have the impression that all the math teachers at my school are going to do the same so we are using a common vocabulary.  It is traditional to teach and use PEMDAS, but tradition is no reason to keep an old idea around when a better alternative exists. It’s time to get rid of PEMDAS. Long live GEMDAS!

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9 Responses to “GEMDAS not PEMDAS!”

  1.   April C. Sutton Says:
      August 14th, 2010 at 9:32 PM

    Sure does generalize the word “parentheses”. Now we just need a fun little phrase for this acronym “GEMDAS” (Unless there already is one) …Giving everyone my delicious apple sauce…I don’t know. I bet there are some other ideas for said word.

  2.   Mister McIntosh Says:
      August 16th, 2010 at 1:39 PM

    Thanks for checking it out April. I like “Give Everyone My Delicious Apple Sauce!” or “Give Everyone More Delicious Apple Sauce”. Any other ideas out there?

  3.   Tony Scott Says:
      August 18th, 2010 at 4:02 PM

    Try this one:

    Good Education Makes Doing Algebra Simple

  4.   Mister McIntosh Says:
      August 18th, 2010 at 4:26 PM

    I think that is an excellent mnemonic for remembering GEMDAS!

  5.   Shelby Says:
      August 26th, 2010 at 8:14 PM

    Hey mr.mcintosh. So how is gemdas supposed to help you?
    isnt please excuse my dear aunt sally still ok?

  6.   Zach More Says:
      September 7th, 2010 at 7:14 AM

    Just read your post today. It’s funny, I just taught order of operations to my students last week and suggested we use GEMDAS rather than PEMDAS so we were sure to address all grouping symbols and not just parentheses. I find no matter how much I emphasize it I still find students performing M before D and A before S rather than working out M and D from left to right before A and S from left to right. Perhaps we need GE(MD)(AS) or GE (DM)(SA).

  7.   Mister McIntosh Says:
      September 7th, 2010 at 12:02 PM

    Yeah it’s still “okay” but just not as good as GEMDAS for the reasons I outlined in the post. If you are able to wrap your head around the important idea that the P does not only apply to parentheses then stick with it.

  8.   Mister McIntosh Says:
      September 7th, 2010 at 12:04 PM

    Thanks for reading Zach. You point out another problem with the mnemonic method. It goes to show that there is no substitute for true understanding in place of blind use of a mnemonic device.

  9.   Becky Lynn Says:
      September 14th, 2011 at 1:24 PM

    My pre algebra teacher is teaching this right now and this really helped thanks! :D

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