Putting this in 7yo terms, "Mommy is making me do homework when I'm supposed to be on vacation. That's NOT FAIR!!"
Ultimately, you have to ask yourself what you're trying to accomplish here. This is a gifted child who is already running ahead of schedule educationally. She can't forget how to learn any more than she can forget how to breathe. So unless there's some kind of specific goal you're trying to achieve, I wouldn't bother. It's not a battle worth fighting.
Last year, we asked our DD what she wanted to do over the summer, and her response was, "Nothing!" No extracurriculars, no camps, just play and travel. So that's what she got.
This year, DD8 was asked to do some work over Spring Break, but that's with a specific goal in mind... in this case, we're homeschooling her into a grade skip as a way to bypass a skip-hostile school district and make them take her as a 4th grader next year. There's a statewide achievement test given to 3rd graders that we've registered her to to take later this month, and in order to close our argument with the school, she needs to excel on that. She needed to finish the last section of social studies over break, so she'd have a week for review before the test.
So that was a battle worth fighting.
