I thought that type of analysis was cool; it's what I went to grad school for. OTOH, I was dismayed that this type of insight didn't lend itself to some of the things that were giving me problems, such as graph theory (taken in the same quarter).
Along the lines of early exposure to science, etc. I remember when I was very young, asking my father why traffic jams occurred. I didn't understand why we couldn't drive at 55, even though that's what the given speed limit was, because people kept slowing down. I wondered why we couldn't just be given a "slot" that would allow us to move at the speed limit. (I didn't realize that I was describing is now a principle behind several types of data communications.) He didn't know; he had driven a truck in the Army, but perhaps the mathematics of traffic jams hadn't been solved yet. Anyway, this is the sort of thing I've been talking about – kids I know have parents, or friends of parents who know about science and can tell them things. For example, my choral director's son talks to one of our sopranos' husbands, holder of a Stanford PhD in materials engineering, about Stanford. He wants to study mechanical engineering there. The director knows all sorts of things about the curriculum, down to what the summer programs for kids thinking of studying engineering are like.