My daughter has no idea how to LEARN that which she does not know. She has no idea how to work for understanding. Period.
This point is really important. I had the same problem, my daughter has the same problem...etc. This is why I see acceleration in the US as a least-worst option rather than a good approach to educating gifted kids. Public or private, our education system tends toward the superficial. IMO, this problem is driven by the fact that we've become so hooked on shallow standardized tests on the one hand, and, well, actually a lot of other problems on a lot of other hands. So more slightly harder but mostly superficial stuff still doesn't teach a HG+ kid how to
stop, think, and solve. You need confidence for that, and you only get the confidence with experience. TBH, I think that the lack of imparting this skill in our most talented students is one of the greatest tragedies of the US education system.
In addition, the way that schools are set up makes acceleration not necessarily the best option. I know that this idea isn't popular here, but my son had a lot of trouble fitting in when he was a little 11-year-old in a class full of adolescents. Placing kids with others who are older (or much older) creates its own problems. At the same time, DS understands that
not skipping him wouldn't have been any better, because of the whole boredom/study skills thing.
Personally, I don't like the idea of painting acceleration as a wonderful solution. It isn't. The age-grade thing makes it a mixed bag. Also, my kids may be capable of understanding ideas that are beyond the norm for their ages, but that doesn't mean that they have executive function skills and other attributes that older kids have. Many teachers don't understand the difference, which also creates problems.