What Is Calculus I Like?

Although I haven’t got a mathematics class to teach this term, at least not right now, I have thought a bit about it and realized that I’ve surprisingly missed a nearly universal affair: I haven’t had a Calculus I course, the kind taught in big lecture halls capable of seating hundreds of students, literally several of whom are awake and alert and paying attention. The closest I’ve come is a history-of-computation course, with a nominal enrollment of about 130 students, and a similarly sized Introduction to C; but the big mathematics course college students are supposed to get through so they learn they really don’t like calculus, I haven’t done. While I was teaching assistant for some Calculus I courses, I never had professors who wanted me to attend lecture as a regular thing, and I just came in to do recitations.

More, I never had Calculus I as a student. I was in a magnet program in high school that got me enough advanced placement credit that I skipped pretty near the whole freshman year of the mathematics major sequence, and I could jump right into the courses with 30-to-40 student enrollments like Vector Calculus and Introduction to Differential Equations. That was great for me, but it’s finally struck me that I missed a pretty big, pretty common experience.

So I’m curious what it’s like: what the experience is, what students are expecting from their professors, what professors expect from students, how those expectations clash. I know the sorts of class methods I liked as a student and that I like as an instructor, but not how well that fits the attempt to teach a hundred-plus students who are just there because the school requires the passing of some mathematics courses and this is the one they offer 140 sections of.