Three examples:
DC20--He's pg/2E, and it's a push-and-pull to get him to learn things. He'll zoom off with history documentaries and books on tape, learning everything in history, philosophy, and literature. We and teachers just sort of went along for the ride in some of those interests. However, it was a battle to get him to write anything or learn math. However, he had to learn it for school and to understand some of the subjects that caught his interest. I'd consider it hothousing, but it was just for his achievement to mirror his ability and avoid closing off options in the future.
DC17--She's the moderately gifted sort, and she's at a competitive high school, where everyone measures themselves against their classmates (her choice and seems mostly happy about school--left it alone). She sometimes decides to push her limits to compete with her classmates and find alternatives to "catch up." Never had this desire until ending up in this district and missing the gifted cut-off by a point in middle school.
Me as a kid--I was the sort who would read anything in the house and check out more books than I could carry on every subject when we went to the library--wanted to learn everything as deeply and broadly as I could about every subject. I'm still that way, though I've never had pressure from my parents to perform at a certain level. I think I've overwhelmed most of my teachers and definitely my parents since I started learning, and it was usually a struggle to keep up with me.
So, I think it depends on the child. Some need to be pushed to avoid falling behind in areas and limitting what they can do later in life. Some are very competitive in school environments and push themselves to "be better" at something. Some just have an intensity to learn everything, regardless of their environments...
