Mistakes like this drive me batty. I take them super-seriously, and students (based on their experience with previous teachers) don’t know what my durn problem is.

I think that some teachers grade this as correct, thinking “this person knows what she is doing”. But talking to students who make this mistake reveals that they do not, in fact, know what they are doing. My sense is that this sort of mistake is highly correlated with being the sort of student who follows a procedure but has no idea what it means.

However, there are some students who understand perfectly well, and who write like this just because no-one has ever told them it is a problem. I think it is important to explain the difference between “work” (scratch calculations, where, frankly, I might write the same thing this student did) and “solutions” (where each line is a logical statement with some meaning). Showing your “work” is not actually that useful; one needs to show a “solution”.

I like the difference between work and solution. This problem speaks directly to the math practice “attend to precision” – I don’t actually know that you understand this unless you can tell me exactly what your solutions mean, and 0=-2 is not stating that precisely.

Andrew
I agree with you here. This reminds me of students who, instead of writing x < 4 or 6 < x will write 6 < x < 4 and see no problem between the or statement and the and statement. Nor do they often think that it is a big deal to write that 6 is less than 4

The words we use matter and the way we write our answers matters.