One of my central frustrations with my kids' school is the low expectations regarding completed homework. For one, homework is not even graded (homework is not allowed to be part of report card grades believe it or not!). For awhile I tried to be hands off with regards to homework. I wanted it to be my kids' responsibility. I was also under the impression that the teacher was checking the homework and would correct mistakes and make kids redo sloppy work. I was very wrong about that. I had no choice but to become total hands-on with homework and I set a "Quality Work Only" rule for homework. On day one of this new policy I made my daughter erase and rewrite her answers to a few questions because the handwriting was awful. Before going off to do it she whined the following horrible words to me - BUT THE TEACHER DOESN'T CARE! Exactly, that why I am making you redo it!!!
I first heard this detestable sequence of words from a student I was tutoring who attended a local Catholic School. My student was correct - THE TEACHER DIDN'T CARE. I explained to her, and to my kids later, that my philosophy is that turning in quality work is about respect -self-respect and respect to your teacher (regardless of whether the teacher cares). Sometimes I get annoyed with the amount of time I have to spend monitoring homework, but if I didn't than who would know if they are learning math or spelling? The teachers literally do not check the work. For example, in my daughter's 5th grade math class the kids pair up and check each others work. My daughter tells me that they assume the answers are correct if both kids have the same answers. If they have different answers they can ask the teacher to go over it. So the teacher assumes that kids can't have the same incorrect answer? I think this is just lazy.
Part of a classical education is adherence to the principle of quality work. That does not mean perfection - an impossible expectation, but putting in the effort to show your best work for that time and place. Messy handwriting, incorrect answers, and overall sloppiness should not be allowed to go back to school, in particular if your kids' teachers do not correct it. I've found that if I am consistent with my expectation of quality work than the kids are more likely to do it right the first time so the amount of "do-overs" has diminished quickly.