For curiosity, it helps if they're doing something they actually want to do. Being forced to do things tends to kill this off. When kids are into something because they think it's cool and fun and it sparks their imagination, they can go really far beyond what kids are 'supposed' to learn at some age.

I learned very little in school, myself. Instead I read my brother's textbooks long before I was 'supposed' to because I thought it was fun and spent the bulk of my time in school devouring the parts of the library I found engaging.