Teenagers want to take their behavioural cues from older children and young adults, but they simply don't have enough interaction with them so instead take their cues from what they believe to be true via mass media.
Imagine how many fewer 15 year olds would ask "what can I do with calculus" if they had to brush shoulders with 20 year old engineering students and could visibly see what kind of projects you'd work on with a deeper mathematics background?
Cross-polination programs do exist today, but its not the same thing as having it be systemic.