Okay, maybe saving the internet is a bit hyperbolic, but better math instruction could reduce some of the arguing that occurs. Internet trolls and pranksters are an internet hazard that most of us would like to see less of. Trolls are a separate issue. but there are certain pranksters that like to take advantage of the poor math instruction that plagues our country. Exhibit A is the math problem 8 ÷2(2+2) making the rounds on the internet. A significant number of electrons are wasted arguing about whether the answer is 1 or 16. Tempers flare, insults are exchanged, and math teachers take another hit to their already tattered reputation.
The problem is that math teachers, many of whom aren’t very good at math themselves, have created this issue by the very methodology they use to teach. Actual mathematicians have been dragged into the debate to no avail. Some, like Evelyn Lamb, argue convincingly that the problem is in vague notation. Additional parenthesis would clarify which answer is correct. While true enough, I would argue that these order-of-operations debates are really the result of poor teaching. I know from experience because I used to make the same mistake.
Specifically, many elementary and middle school math teachers view math as skills to be memorized rather than a language to be immersed in. The acronym PEMDAS is a perfect example. Most teachers teach the order of operations as 1. P [parenthesis] 2. E [exponent] 3. M [multiply] 4. D [divide] 5. A [add] 6. S [subtract]. Using this method on the above problem gives the answer of 1. But mathematicians know that multiplication is on equal footing with division and that addition is equal with subtraction. The correct way to teach order of operations is: 1. P [parenthesis] 2. E [exponent] 3. M OR D [multiplication or division in whatever order they appear from left to right] 4. A OR S [ addition or subtraction in whatever order they appear from left to right].
Put simply, PEMDAS could also be PEDMAS, PEMDSA, or PEDMSA. My students, all felons, would have a great time coming up with mnemonic devices to memorize all of these choices. Instead of “Please excuse my dear Aunt Sally” of grammar school fame, they came up with “please excuse my dumb ass sister,” for example. Truth be told, they have come up with even more vulgar sentences, but I digress. I shudder to think of what else they could invent given all of the new choices.
Everyone remembers the “Aunt Sally” meme, which is the basic problem of math instruction in this country. Students memorize whatever tricks math teachers give them. But they are helpless when they forget or when they are asked to apply their knowledge to a problem-solving situation. Teaching students how order of operations really works instead of making them memorize a silly sentence would go a long way towards improving math literacy in this country. It would also force the pranksters to find something else to try and start arguments about. If you don’t believe me and learn from my mistakes, then check out the recommendations from the National Council of Mathematics Teachers.
