Homework has the following benefits, when done properly:

Promotes independent work
Promotes independent research
Enables parents to talk about schoolwork with children

Self-marking of work allows:
Teacher-time freed up to plan more meaningful lessons with better resources. Trust me, checking endless sums and marking them takes up a LOT of time that could be more gainfully spent.
Student able to see within a half-hour of doing the work if they are correct or not (teacher will check this work, but not every day)
Students able to see where their problem is and so can seek help with this - the child learns responsibility here. The child should also correct the work when self-marking.

Actually, your child can help that "she's bad at math" - by self-marking properly, seeking help and attempting the work rather than just copying an incorrect answer.


And having said that - I'm not a big fan of homework. I can set independent learning tasks in lesson and, if a child actually does the work (I have some very lazy ones who get extra homework to catch up), homework is just more of the same. Some homework I have set includes research and discovery, applying work done in lessons, explaining a physics lesson to a parent, bringing a car that they can modify in for invention week, sums, making posters... most of which can be done in lessons, finding a car does not take half an hour that it was supposed to (but building a lego car may... what a tough homework!), and parents should want to hear about their child's lessons. But I am a fan of self-marking and I do check the self-marking and then correct the work where needed. So long as it isn't every answer that's wrong - I'll call the child in to do the work again one-to-one if that's the case, as they do not understand the work, have not listened to the marking (so probably the explanation of how to do the work as well) and have not done what is expected with corrections.