PEMDAS is NOT a Word

Here is why I believe that the PEMDAS method for remembering the order of operations should NOT be used:

1.  PEMDAS is not a word.  In general, I believe that for mnemonic devices to have the greatest impact, they should be easy to remember words.  PEMDAS is not easy to remember and PEMDAS is not even a word.

2.  PEMDAS implies to students that there are six steps in the order of operations:  Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, when in fact, there are only four steps in the order of operations.   How can we expect students to properly remember the order of operations if we are providing them with such a misleading mnemonic device?

3.  PEMDAS should not be used simply because it is the way that students want to be taught.  One student told me the other day that he was confused by the way that I was doing the order of operations simply because I was not using PEMDAS.  I told this student that he could continue to use PEMDAS if he wanted to, but he would continue to get incorrect answers (He is one of the students who thinks that PEMDAS has six steps).

4.  PEMDAS simply does not work.  If PEMDAS worked, wouldn’t students actually understand the order of operations?  The fact of the matter is that PEMDAS does not help students understand the order of operations.  PEMDAS did not work for students when they were in elementary school, why should it work for them in college?

I truly believe that my position as a college math instructor requires me to present the material differently than the students saw the material the first time that it was taught to them because whatever they were taught the first time obviously did not stick long term.  Although my ultimate goal is to help students refresh their memory, why should I refresh someone’s memory about something that is misleading and simply does not work?

Below is an example of the Order of Operations using the GEMS Procedure.  I prefer the GEMS Procedure because GEMS is actually a word and GEMS implies that the order of operations actually has four steps and not six steps.

Gems1

To further prove my point, here is an example of a problem that is incorrectly done using PEMDAS versus a problem that is correctly done using the GEMS Procedure. 

Gems2

I know that the GEMS Procedure is not going to become ‘mainstream,’ but I can hope, right?