Most school children these days are not being taught this type of subject matter in our classrooms. Those topics that you listed that you talked about are prerequistes to classes such as calculus, physics (quantum), trig, math analysis and the like. We are not at the top of heap when it comes to academic achievement. I'm not saying that we don't have students that reach this level; it's just that we don't have as many as we'd like to believe.
atp