As a PE student, I have only taken large classes where the teachers barely gave any attention. I did, however, take an undergraduate honors seminar where there

As a PE student, I have only taken large classes where the teachers barely gave any attention. I did, however, take an undergraduate honors seminar where there were seven self-selected students all of whom were there voluntarily and who got individual attention from the professor. So I think both sorts of dynamics exist in the university (though formal HS probably does little to no "coaching" type activity and math stars coach each other in high school math teams). I don't think very many folks who were herded into the PE classes I've taken learned that much and everyone in the honors undergraduate seminar learned a lot. I can't prove that anyone who wants to can learn strong math but I don't think the results of a typical mass-level math class proves much about this either way. (I too, have taught your typical average crappy undergraduate math class).