>>43
The symbols aren't abstract, the applications are (you abstract the calculus in order to apply it). I've seen many people who can do a calc problem even some word problems, but can't tell you why the derivative or the integrals are found the way they are, or even what they mean (these people generally quit right after calc 2 and go into their respective fields). Rote learning will actually get you through a lot more than one would think. As long as the person has "good study skills" (flash cards, a lot of practice with the same types of problems (so that they memorize the procedure and technique, and not the necessarilly the logic), good notes [or lots of notes], cheat sheet, etc...) they can memorize anything. They only stumble if a question is asked in an unfamiliar way, or if a conceptual question relies on a good understanding of several other concepts, or some similar situation (even then though, they'd all throw a fit about how the teacher didn't tell them they had to know that or something). They probably won't do as well on tests as a student who actually knows the material, but they will ace the homework (where as the student who understands the material will probably put off doing it), overall they'll get a passing grade (which for them is acceptable).