Someone I know recently took an online intermediate algebra course to preparefor college algebra.
Thus course had 70+ sections, each with 10-30 poblems, beginning with set-builder notation and going on to associative/distributive/commutative laws, etc. and in general proceeding axiomatically.
Most college math courses proceed axiomatically, to maintain rigor.
But in the same high school courses this is intended to replace, the emphasis is on 'learn this useful formula and apply it 30 times until you get it'.
In my experience, the best students, who would actually appreciate the rigor, never take the rigorous college courses, but instead do great in high school and move directly into college-only courses such as linear algebfa and vector calculus. While those who take intermediate or college algebra in college tend to be put off by the overly rigorous approach.
My questions are:
Is there a significant difference in the rigor of these courses as taught in college and high school (i.e., is it not just my imagination)?
If there is a difference, is there any published research supporting such a difference, or statements by those in charge of curriculum at an jnstitution giving an explanation?