[Re: the title, I know I’m not the only one who has seen “vertical” misspelled in every possible way.]
It’s easy to say that this is sloppiness on the part of the student. And maybe it is. But it’s the sort of sloppy mistake that I would rarely make, and that beginners often make, which leads me to think that there’s something else going on here as well.
We’ve talked about reading on this site before, and it’s something that I don’t know a ton about. But it seems to me that part of “looking for and making use of structure” is something like what I’m trying to get at. If you’re really experienced at math, then you start seeing a problem like this as rigidly structured into two separate and equal expressions. I’d bet that for a student that doesn’t have a lot of experience with these sorts of problems that sort of structure is less apparent, and this sort of mistake is less apparent.
Did that make any sense?
[Thanks to Nora for the submission!]