Only for geniuses, eh?

As regularly as the spring rain, memes of the following sort show up on social media.

As a math teacher, I don’t know whether to laugh or to cry. Adults—sometimes hundreds or thousands of them—argue about the correct answer to this “problem” and others like it.
Let’s be clear: this is a question about the order of operations in arithmetic. In the Province of Alberta (my home) this is expected of all Grade 6 math students. So, Facebook is clogged with adults working below 6th grade in basic number sense. Ok I do know. It’s cry, not laugh.
What sense can we make of this? Do adults not remember their elementary-school arithmetic? Apparently many do not. But some of the comments are also telling. It appears that many were taught methods that almost work, but don’t quite.
The acronyms BEDMAS or BODMAS are often taught to children.

Exponents (or pOwers)

If you follow BEDMAS, you’ll be right most of the time. It’s fine for the above problem. There are no brackets or exponents, so you divide 7/7 and multiply 7×7, turning the problem into 7+1+49-7=50. But there is a problem with BEDMAS/BODMAS and that is that the acronym suggests that division has priority over multiplication and that addition has priority over subtraction. This is not true.
Once brackets and exponents are cared for, you work left to right. If you come to a multiplication or division, do that before continuing with the addition or subtraction. Schematically, the problem above simply becomes 7+(7/7)+(7×7)-7, which is pretty easy mental arithmetic.
Even calculators can make errors.


If you’re not working left to right, you run the risk of making the error on the left.
Regardless, what am I on about here?
First, order of operations is elementary school arithmetic. It should not pose a problem for adults. But it does. This points to a serious educational deficiency—for the adults. This is not a problem of “new math” or “constructivism” or “Common Core”. The people getting it wrong online are, by and large, from earlier generations of failed arithmetic education.
But it’s clearly a problem, and I think I know why. It’s a problem of assessment. You see, if students (in any generation) get most of the questions right, they get a good grade. I suspect that the adults who can’t solve simple order of operations problems never could do it well. But they got all the easier questions right, so no one bothered to dig deeply into their failure on the one or two harder items on the test. Yes, this is just speculation on my part, but I’m willing to bet that it explains a good deal of the problem.
But there is a positive note to all this. Adults are arguing about math in their spare time.

They care. And that’s encouraging.


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