Can you request formal testing by the school, especially achievement testing, since that will probably do the best job of showing the school what your child can really do and where she really is operating?
If the school will not test her, would they accept private testing?
What do you want to have happen? Just in-class differentiation? Do you think that will be enough for your daughter? Or if she's operating at or above the 3rd grade level, should you be pushing for more: grade-skipping, subject acceleration, etc.?
Given that your DD's teacher is clearly not on board for differentiation, I'd be pushing for something else. I can't imagine that she's going to get what she needs from a teacher who doesn't get your DD's 6yo-ness is very, VERY different from most other 6yo's! (Been there, done that, hated it when we went through it, too!)
What to push for, though, depends upon your child and where she'd fit best. If she's not fitting in socially because she's "older" than the kids in her grade, then she might do a whole lot better with a grade skip. If she's not fitting in with agemates because she's unhappy and surly as a result, but she's not significantly more socially advanced, then subject acceleration might be better for her. It's also possible that some combination of these (and maybe other solutions?) would work best.
I'll add that you might also consider other educational options. Private schools and homeschooling can provide alternatives that might work better for your child. No pushing there--I'm a big believer in using the public schools as long as they can be made to work for you! But knowing that you have alternatives can help to keep you from feeling like you're in an impossible situation. And those alternatives means that you're not at the mercy of anyone else, which can really affect your feelings about the situation. Coming from a position of strength and confidence is much better!
HTH! Best wishes to you!
