GEMDAS not PEMDAS!

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!