I'm sorry OP, but you're going to have to listen to me talk about the acronyms I hate first, to give the readers some context:
- FOIL, of course, implies that the order of a commutative operation matters while not generalizing beyond binomials.
- PEMDAS / BODMAS is bad for a lot of reasons but what gets my goat worst is the fact that it reifies something that is just accepted convention (like, more than normal math is). It also encourages bad notation and the use of the division sign, which deserves to be ironically punished by being divided into several pieces in Dantean hell.
- SOHCAHTOA would be fine... except it's always taught as "Chief Sohcahtoa", which is the type of fetishizing where you just put the concept of Indigeneity into a blender and lap up the festering sludge. (Also this is an essay unto itself but SOHCAHTOA is part of the apparatus that convinces people that trig is the study of triangles and not similarity.)
The worst, though, is CUBES, an enumeration of the process mathematicians allegedly use to solve word problems: Circle the relevant numbers, Underline the question, Box the math verbs, Eliminate extra information, and Solve the problem.
I hate all of these cutesy "how to solve a standardized test problem" acronyms. Like the ghost of Hamlet's father, they recount and symbolize the death of mathematics education, and drive us to madness. But more than that, it's just bad. "Solve the problem" is some real "draw the rest of the owl" cope, and I don't know how "eliminate extra information" comes after "circle the relevant numbers". It has the veneer of promoting understanding, or at least acting as training wheels to that goal, but this shit is how you miss slam-dunks like "If 4 violinists can play Beethoven's Fifth in 30 minutes, how many violinists would it take to play it in 10?". I don't know how you can take a word problem about taking away apples, a clear illustration of subtraction, and alienate the solver to the point of gargling "the math verb take away entails that I must apply the subtraction problem-solving technique in Section 5.1" in their mouth.
In short, I don't really like any math acronyms. I don't know how algebra got all the flak for introducing letters into math when PEMDAS is right there. When they're not racist or embedding the mentifacts of the Christian nuclear family, they're promising students a flash-cards solution to a lapse in understanding.
So I don't like any acronyms. But there are other types of mnemonics-- and the one I like the best of all is that the greater than / lesser than sign looks like a crocodile mouth that wants to eat the bigger number. Or, alternatively, the lesser than sign looks like a mouse who only wants to nibble the smaller number. It's amusing and intuitive, to the point that I still occasionally used it when I was in Real Analysis. And unlike e.g. FOIL, its purpose is to reinforce notational understanding, not replace or obscure generalizable understanding. When I used the alligator 1,000 times my brain rewired it to recall instantly-- "mouth. big. greater.", and I still could bring out the alligator when I wanted a little whimsy. I've had students who have FOILED 1,000 times and couldn't express (a + b + 1)(a + 1) as a single polynomial.
Come, friends. Let us leave the forest of wicked letters behind, with its promise that even the proof of FLT will one day be whittled and vacuum-sealed into a Quizlet's worth of handy tips. Let us leave behind the breathy whispers through the pines asking "r pies square?", begging us to echo back "Two pis r!" And let us create our own small god and embrace her. Mine is a trickster deity named Janus-- one face an alligator, one face a mouse, with a scale in her hand that weighs souls, grams, and other fungible things.
