I’m currently reading “Why Don’t Students Like School?” (second edition) by Daniel T. Willingham. While there is a lot of good stuff in this book and I’m feeling fired out about setting my educational train back on its tracks, I winced at his cheerleading for mnemonics.
And then: I reframed.
He suggests the use of mnemonics for the memorization of information that would otherwise be fairly meaningless. His examples involve lists of jargon, which brings mnemonics like HOMES to mind.
He does point out that mnemonics are meant to be scaffolds to help retention of material that students are otherwise in the process of learning, but might need that extra support. They are useless without an understanding of the underlying material, and there doesn’t seem to be the suggestion that they ought to be used in place of understanding.
This is precisely my annoyance with PEMDAS, for instance. Students learn it or its various international versions (BODMAS, GEMA), or even phrases like Please Excuse My Dear Aunt Sally, and then insist that the “order of operations” is PEMDAS.
First and most obviously, that’s not even how acronyms are meant to work. The Great Lakes are not HOMES; HOMES is an easy way of prompting memory to find the names of the Great Lakes (Huron, Ontario, Michigan, Erie, and Superior).
But more importantly, HOMES is useful because there’s nothing inherently meaningful about the five names of the lakes. Sure, it happens that Lake Michigan is the only lake that doesn’t touch Ontario, Lake Ontario is the only lake that doesn’t touch Michigan, and Lake Superior is the largest of the five. And Lakes Huron and Erie are named after two of the local indigenous tribes. But other than that, the five names are fairly arbitrary, and hence can be difficult to remember.
The Order of Operations, on the other hand, is not arbitrary in the same way. It does come from a mathematical convention that, unless otherwise noted, exponential operations are evaluated first, then multiplicative operations, then additive operations. We could have decided on a different priority, but this particular priority is indeed meaningful.
It would be better to learn this priority, and it doesn’t strike me as that much more complicated than the acronym PEMDAS. Meanwhile, PEMDAS introduces the additional problem that MD and AS have the same priority. I have seen people online claim that the priority between multiplication and division is actually different in BODMAS countries than in PEMDAS countries. This comes from a misunderstanding of how the acronym works. (This is why I believe if we’re going to use any acronym at all, it ought to be GEMA: Grouping, Exponentials, Multiplication, Addition.)
I’m more sympathetic to mnemonics like SOHCAHTOA and All Students Take Calculus, although the former bothers me deeply because of its association in the US with a racist narrative with Chief Sohcahtoa.
But here, again, the mnemonic should be a scaffold that is later removed, not a permanent memory guide. Once the trigonometric relations are properly understood in terms of the motion of the sun across the sky, from east to west, where the sine is the height of the sun and the tangent is the angle of the head looking at it, the information carried by both of these mnemonics follow naturally from that understanding.