## Monday, October 28, 2013

### Keep Change Change

Here's another one of these stupid memory devices that I guess some pre-algebra instructors use to get their students to hobble through their class, but then put them on the wrong path later on. It's a reminder specifically for how to subtract a negative number: +9-(-4) = +9+(+4) = 13, or -3-(-6) = -3+(+6) = 3, stuff like that. The "keep change change" mnemonic supposedly gets them to cancel the two juxtaposed negatives (and not the one in the first term).

But like PEMDAS, this sets up a terrible habit, and masks the real meaning to the writing. The actual story is that a negative functions like multiplication, and flows left-to-right the same as we read in English. Yes, students in algebra are routinely stumbling over negatives in general and the subtraction most of all. But when I try to clarify it, usually some student now goes "oh, it's keep-change-change". Then I ask them to simplify an expression with three or more terms in it, like +9-(-4)-(+3), and at that point they have no idea what to do. They don't see that juxtaposed negatives are cancelling out, just like a multiply. The mnemonic that get them through pre-algebra with only two terms at a time was a waste, and has set them up for failure later on.

I've only heard this brought up by students in the last 4 years or so (not before that). Initially I suspected that the mnemonic was specific to where I teach, because the initials happen to be the same as our school. But when I do an online search it does show up in a small number of hits elsewhere -- well: actually just once at algebra-class.com and then once as an answer to a Yahoo question (possibly  those two items might be written by someone that went to our school?).

So my question: Have you ever heard of this "keep change change" nonsense anywhere else? Did you ever hear it before, say 2008?