College math instructor here; I've taught Calculus III for the past three years. I always feel bad for my freshman students, particularly those in the fall seme

College math instructor here; I've taught Calculus III for the past three years. I always feel bad for my freshman students, particularly those in the fall semester. Some of them are prepared, and some aren't, but almost none of them have a mature understanding of mathematics that we expect in a sophomore-level course. The problem with AP from my observation (at least in math) is that it encourages teaching the test. I'm certain many of them have never seen \lim_{h->0}\frac{f(x+h)-f(x)}{h} before, so how can they suddenly expect to understand the limit definition of a partial derivative either? I took a Calculus course in high school, skipped on taking the AP test, and then took an honors section of Cal I when I got to college to get a deeper understanding (and an easy first-semester A). I feel I made the best decision.