### Abbreviating the Order of Operations

My recent posts about “Dear Aunt Sally” have, I hope, shown how dangerous it is to teach the memory trick of Please Excuse My Dear Aunt Sally — at least without some additional explanation.

Today I propose a way to save Dear Aunt Sally, for those of you who still like her.

As you know, the memory sentence is often abbreviated PEMDAS, which stands for: PARENTHESES, the EXPONENTS, then MULTIPLICATION, then DIVISION, then ADDITION, then SUBTRACTION.

The problem with PEMDAS is that it makes kids think they always multiply before dividing, and that they always add before subtracting.

For students attached to PEMDAS, I let them use it, but I have them write it a novel way, so they realize they must pay attention to the left-right orientation of the operation symbols.

In the new way of writing PEMDAS, I put M and D in the same place, separate by the word “or.” Then I do the same for the A and S. So the whole memory device looks like this:

My suggestion is that teachers who like PEMDAS try this and see if your students start making fewer mistakes with the order of operations.

For those of you who never liked PEMDAS on the first place, I recommend that you check out the order of operations as presently in a clearer way, as it is in my Algebra Survival Guide. To get a feel for that, you can download the chapter of the book on Positive and Negative numbers here. Just click where it says: See Sample Chapters of the Algebra Survival Guide and Workbook.

Then you’ll want to get the Survival Guide for the chapter on Order of Operations, which you can do through Amazon.com, here. Sorry, I can’t make everything available for free … I do have a business to run, with new products I’d like to create and make available.