Ren-
Most of the folks here have kids that are older than yours, so we can relate to the young gifted child who craves stimulation. Are you asking if this interest in learning is normal for a "very" gifted 3 year old? Or do you want to hear how people have fed that need?
It really sounds to me like you are doing a great job of responding to your daughter's cues. IMHO, it's all about following the child's lead. Sometimes a gifted child will want more, more, more, and then go into a period of apparent dormancy when they process all that they have taken in or work on a different (maybe physical or social) sort of skill.
What "works" is going to be unique to each child and family. We happen to live in a rural community so there's not a lot of enrichment in terms of cultural experiences. We go to museums a few times a year, and maybe a children's theater production or two. It's a half hour ride to the closest mall. Our family spends much more time hanging out at the horse barn where my dd rides, tracking wildlife in our backyard, and playing board games. It's all that the kids know and they are happy and don't feel deprived. We're well known at all the local libraries and our homeschool group has a busy calendar.
Our environments are vastly different, but they both can meet the needs of our little ones. At age three, everything is new and exciting. I don't think it matters too much *what* they are learning, as long as you take time to discuss things and answer their questions. Three is actually a favorite age for me. My youngest is fast approaching three, and I am looking forward to it!
