I agree with no5no5. Really is about interest. DD 3.3 is like this. She goes through phases. Sometimes it's math and she is obsessed with it; other times she is my little encyclopedia, memorizing verbatim information from books read to her; and other times she is all about her verbals and developing her second language.
I've lost track of where DD aligns to public school curriculum. Before she turned 2 she was already doing a lot of 2nd grade level work, specifically in math. This structure has changed drastically for us since we decided to go the academic route and place her in a Spanish Immersion program where their academics are 2 years ahead of the public school curriculum here in Texas. I will never forget our walk through of the school this past spring. They explained the advancement of their curriculum and gave examples of what each age worked on. Eye opening for me as I realized that the 3 year olds work at a kindergarten level, yet my DD was already doing a lot of what the kindergarten class did, which aligns to second grade. Our one saving grace (at this moment) is all of it is done in Spanish so she has a little challenge for now. The other savior is the school already recognizes her abilities and won't pigeon hold her to a class just because of her age. When she is no longer challenged, they plan to evaluate and consider grade acceleration.
Now back to your question about do they stay that advanced. I, personally, think it depends on the environment. Case in point, my DD. Before labeling her with gifted, my eyes were closed and I didn't over think all of it. I had no problems running with her interest; basically facilitating whatever it was she was in to and building off of it. IE. shapes led to colors which led to whatever. She might not have been interested in colors but it made sense to provide her that information. Once I stumbled on the term gifted and really read up on it, I freaked out and with held information. I could have tackled multiplication after she started adding and subtracting but couldn't bring myself to do it because I felt like I would be pushing. Workbooks were evil hot-housing material and none would be found in my house! I really took it to the extreme. Where would my DD be at this point if I had just left things alone and facilitated her adventure? Who is to say but it really was when I made the bad decision of putting her in a social preschool that I came around to realize I don't have a child who will blossom in this type of structure and I, myself, had created a similar structure at the house. She became a shell of herself. Now that she is in an academic based program we have our DD back. And when she is interested in learning something I have no problem providing her the info, be it in a workbook, internet, conversations, etc.
Through all of this it wasn't that she didn't advance but I saw it in other ways. Her wit and humor became even more advanced, along with her cognitive skills and language.
