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.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

3 thoughts on “What Is Calculus I Like?”

  1. I am tempted now to indulge in my memories but this is probably not very helpful – as I am from Europe and more than 25 years have passed since my related experience as a student.
    I loved calculus – but I was among those ‘several’ students you mentioned. Probably this was due to the fact that I had also picked a high school focussing on science, and so I had already been exposed to very rigorous proof-based math in school. Most students freaked out when having to prove something so meticuously that seems to be ‘obvious’. (Anything related to continous and differentiable functions for example).

    Probably I should check curriculums – I had learned about vector calculus in the first year, e.g. Gauss’ and Stokes’ Laws. As I understood differences between US and European educational systems so far, European programs are more specialized right from the start whereas US colleges provide a more well-rounded education.

    But one thing baffled me: Though I really loved calculus, its rather unwordly nature and the proofs – I did not see how useful that stuff is going to be (in physics). I re-learned physics-related calculus again in the lectures on theoretical physics (incl. less rigorous proofs) but only then I really got where this was heading at. Of course I am a bit biased here.
    So it might be great to emphasize the applications for physicists and engineers instead of presenting pure mathematical aspects only.

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    1. I appreciate any thoughts. My Calculus I experience was all in high school and in very odd circumstances compared to most students.

      I do remember calculus as I learned it being … not quite separated from its primary use in physics, since the program I was in tried to coordinate the calculus and the physics classes so we got the tools and the real-world motivation more or less together (though I remember being introduced to small-angle approximations, like turning the sine of theta into theta, in physics class and thinking that seemed mathematically sloppy; it was just too far away from Taylor series and the like where that’d get at least some slightly more rigorous excuse).

      But there were still disjoint passages, particularly when we got into sequences and series, where it seemed like there was this sudden rush of inexplicable rules and problems that seemed to go into great detail on problems that, once solved, got us … not much of anything obvious. That might have been me failing as a student, certainly, but I suppose every subject needs to be introduced with at least some taste of “and if you learn to do this, you’ll be able to do this interesting thing” mixed in well enough.

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