I agree with what Jesse said. As a very shy child, it was very hurtful to know that my outgoing mom wanted me to be more outgoing. From my perspective, she wanted to fix what wasn't broken. She has never really understood me, no matter how many ways I've tried to explain. I even had her read the chapter on introversion in Silverman's book.
I also think it's important to note that being shy/introverted is not some large barrier to success. (It didn't stop me from becoming a litigator, for example.) I vaguely recall reading that there are quite a few closet introverts amongst successful people.
When she is older, the circumstances of your child's life may motivate her to speak in ways that she's not willing to while she's young. This is something she'll have to do for herself; I would not advise forcing her.
And one last thing, don't overlook the connection between introversion and perfectionism. The more confident a person is about their knowledge of a subject, the easier it is to speak about it.
