Gifted girls in particular often feel insulted and diminished when they're not offered material at the appropriate level, which causes them to shut down. They also tend to be teacher pleasers and social seekers, which motivates them to blend into their environment. So if she's receiving enrichment the school obviously sees something extra in her, and she's got a couple of potential reasons to not be showing them her full potential.
In your place, I would press that psychologist on just what precisely he means by "has trouble processing information." There might be a learning disability he's hinting at there, which could be another valid reason why she's not showing her full potential.
And don't judge your child based on everything you see here. My DD7 isn't studying Algebra or reading War and Peace either. She doesn't know any Chinese, but she's got some conversational Spanish.
