Please Excuse My Dear Aunt Sally (PEMDAS)--Forever!
You don't have to be a math whiz to know that 4 - 2 + 1 equals 3. Yet I was working with several students recently who said it equals 1. And it wasn't their fault. Nor was it their teacher's fault. Nope, the blame in this case and in countless similar cases I've encountered over the years rested squarely with the fictitious Aunt Sally of "Please excuse my dear Aunt Sally" (or PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction) fame—the acronym intended to help students remember the order of operations.
The problem with PEMDAS is that it excludes the "from left to right" requirement for multiplication and division (#3 below) and addition and subtraction (#4 below). Students, as a result, think multiplication always precedes division and addition always precedes subtraction. This explains why students in the above example said 4 - 2 + 1 equals 1 rather than 3 (i.e., they simplified 2 + 1 first rather than 4 - 2).
So then, if not PEMDAS, how should you teach the order of operations? Well, the reality is that the order of operations isn't so much something you teach but rather one of those conventions in math that students simply must memorize. You can help by posting the rules in your classroom, spelled out as they are above--without any misleading acronyms. Also give students lots of practice simplifying expressions like 4 - 2 + 1 where they can see why it's important to follow the order of operations.
But before you do anything, be sure to break the big news to students: dear Aunt Sally has indeed been excused—and she won't be coming back.
Image provided by GECC, LLC with permission.