Arbitrary mnemonics

A mnemonic is a mental trick to help you remember things. People use them all the time for all sorts of things, like the traditional colours of the rainbow (ROY G BIV), the order of the letters in the English alphabet (a song to the tune of Twinkle Twinkle Little Star), the order of operations (BODMAS or PEMDAS), which months have 31 days (“30 days hath September…” or your knuckles), and which kind of camel has one or two humps (Dromedary starts with D which has one hump; Bactrian starts with B which has two humps).

The purpose of a mnemonic is to connect something that is hard to remember to something that is easier to remember. If you can remember the mnemonic and the connection, then you can remember the thing. They are especially useful for things that are arbitrary, where there is no obvious or no particular reason why they are the way they are (such as the number of days in each month).

However, there are a lot of things that most people don’t need mnemonics to remember, and it seems to me they tend to be the things that make sense to them — things that are already connected to other things in an obvious or natural way. Indeed, the very connectedness of things to each other is what causes the sensation of understanding. You feel you understand things when they are highly connected to other things, and you often don’t have to try to remember things that you understand.

So, a mnemonic helps you remember arbitrary things, and un-arbitrary things often don’t need much assistance to remember because they make sense.

What happens if you advocate that learners use a mnemonic for something that is understandable? I think that it sends a signal to learners that the thing is arbitrary — because they know implicitly that arbitrary things are what mnemonics are for — and since it’s arbitrary, they shouldn’t attempt to understand it. So they don’t try. They just try to remember.

For example, to remember which of sin(.), cos(.) and tan(.) are positive for angles in which quadrants, many people use the mnemonic All Stops To Central (or something similar), to remember it’s all of them in Q1, only sin(.) in Q2, only tan(.) in Q3 and only cos(.) in Q4. But I have met so many learners who have not the slightest clue why this is the truth, and don’t even expect there to be a reason. The fact that it’s a mnemonic signals to them there is nothing to understand. On the other hand, when you remind them that sin(.) is the y-coordinate of the matching point on the unit circle, and the y-coordinate is positive in the top half of the circle, you can see the light go on and the sigh of relief that they don’t have to try to remember any more.

So my advice is just to be careful with mnemonics. I would recommend not introducing them too early. Help your learners try to make sense of things as much as they can, and when there are a few spots left that are arbitrary and they have trouble remembering them, then you can introduce a mnemonic to help remember. Otherwise, you may signal to them that what they are learning is arbitrary and they shouldn’t attempt to understand it.

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