...says she hates school, mostly refuses to do her homework, and has become an emotional, angry wreck at home.
Although the teacher is wonderful, has advocated for her own children, and DD adores her, the fact that the teacher may be seeing a different child at school than you are at home complicates matters. Sounds like kiddo may benefit for evaluation for a possible grade skip before she becomes a social isolate. Just my 2 cents.
One thing we do with my children is home education, during which they get to learn about their own interests and challenge themselves in math at home.
Agreed. Many families do this and call it "after-schooling", enrichment, or having an enriched environment (lots of library books for example).
We've also talked about the purpose of school... Nobody's telling you to enjoy something you don't enjoy.
I agree with the work ethic, coping mechanisms, and many of the thoughts expressed. At the same time children benefit from capitalizing on their educational opportunity to learn all they can, at a rather challenging/stimulating level, so they do not learn to passively underachieve. If a child consistently knows the material being taught in the grade-level curriculum, that child may benefit from advanced academics. There is research on underachievement. There are books written for general audiences including parents... Delisle is just one well-known author of books & articles on underachievement.
Helping gifted kids avoid underachievement and dropping out is why we advocate for gifted kids. We call this helping them reach their potential so they may be part of the population of productive adults that you mentioned.
Anecdotal evidence suggests that kiddos may erupt with outbursts prior to giving up, checking out and underachieving. Working extensively with kiddos at this stage to help them build vocabulary to enable them to express what is bothering them, may provide parents with insight as to the child's lived experience.