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This summer, I am teaching 8-week calculus courses that meet a total of 16 times in 210 minute class periods. This sounds insane to me since Return of the King is only 201 minutes long, but it is the plan.

It seems to me that when the class period is this long, it will be essentially impossible to "cover" 1/16 of the course material in a class period, since so much of the material builds on previous material. When the fourth(!) hour of class begins, the material from the first hour will be very difficult for students to access.

How can a calculus course be adapted to this format? I would like answers from people who actually have experience teaching calculus in this kind of extreme fast-paced format.

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    $\begingroup$ The cinematic version of ROTK is only 201 min, but the Special Extended Blu-Ray Edition is 263 min, so you really have no excuse. $\endgroup$
    – user378
    Apr 27, 2014 at 16:16
  • $\begingroup$ "This sounds insane to me since Return of the King is only 201 minutes long, but it is the plan." Then why do it? $\endgroup$
    – Pieter B
    Apr 27, 2014 at 23:59
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    $\begingroup$ For the purposes of this question, let's assume that I will be teaching it in this format. The merits of doing so are worth discussing, but not here. $\endgroup$
    – Chris Cunningham
    Apr 28, 2014 at 2:20
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    $\begingroup$ 3 1/2 hours is way too long to be sitting down in a chair trying to listen to someone talk about something without moving. You need to take breaks. Probably more than one per class period. Have them take a quiz every class period. That way, if they're falling behind, they know it by the next class, at the latest. If you take 2 different 10 minute breaks, and allow 10 minutes for a quiz, you still have 3 hours to fill. You could use each of those hours for a separate topic, and the breaks could indicate to the students that we're doing something different now. $\endgroup$
    – Michael Shaw
    Apr 28, 2014 at 3:43
  • $\begingroup$ I've taught physics with a somewhat similar schedule over the summer. There are some advantages. The students tend to be more focused on learning your topic. However, taking breaks is good advice. Otherwise, I'd just teach it normally and tell them sometimes it's not going to make sense until they get home and do some homework to get it to gel. The expectation it makes sense in class as you go is probably unrealistic as a global goal. $\endgroup$
    – James S. Cook
    Apr 28, 2014 at 4:51

2 Answers 2

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Concurring with @vonbrand, try to split the material "sideways", so that the subsequent hours do not depend on supposed (instantaneous) mastery of the first hour, etc.

I've taught summertime classes that met two hours a day, five days a week, instead of what would have been a single hour on MWF, for a full term. When I was young and foolish, I thought that in the upper-division courses of this sort it would be better, since there'd not be such gaps between episodes. But, in fact, exactly as the question anticipates, it was horrible. Not only is there the literal incapacity to adequately assimilate the first hour's material as prerequisite for the second... but there is another terrible problem, namely, few students are acquainted with such a pace and all it entails.

Thus, many students, perhaps a majority, can't help but use their usual "pace" even in doubly or triply speeded-up courses. This includes procrastination at the very beginning, typically, ... which, while unwise in ordinary circumstances, creates an impossible situation in speeded-up instances. Even the students' "catch-up" chops are woefully inadequate for a speeded-up situation, since they are usually not-so-good at catch-up even at normal speeds.

I suspect all-the-worse if you don't actually meet with the students every day, because many will misinterpret the "off-days" as days to not think about your course, etc.

In particular, I'd suggest nearly-oppressive amounts of homework to get their attention on the off-days, or they won't take you (the course) seriously. And, again, in your three hours, as you anticipate, it would be foolish to hope for immediate assimilation. As @vonbrand suggests, making things not too-intensely depend on each other is highly desirable. (Thus, the traditional "strict logical ordering" is infeasible.)

A very unfortunate and impractical pedagogical situation, for sure.

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Never been in such a bind teaching (as a student I had a full term compressed into some six weeks once, but I don't remember much of that), but I'd look for ways to split the subject "sideways", I.e. make it into two or three concurrent courses on related subjects. So you can switch subjects and don't wear out your students (hopefully with a short break). Alternate between covering the material and solving problems using what was covered in groups or open discussion.

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    $\begingroup$ For example, my calculus teacher taught series and non-trivial integration concurrently. Up to a point, they're pretty independent, although after a while, you can integrate the terms of a series, etc., which led to a nice convergence (no pun intended) of material. $\endgroup$
    – wchargin
    Apr 28, 2014 at 0:07
  • $\begingroup$ Just leaving a note while I am thinking of it -- I tried this over the summer and it was very successful. For American "Calculus 2," I highly recommend starting with L'Hopital's Rule and Improper Integrals, then you can just spread the sequences&series all throughout the rest of the semester. $\endgroup$
    – Chris Cunningham
    Aug 20, 2014 at 1:33
  • $\begingroup$ Updating this one more time -- I now split my Calculus 2 "sideways" even in the normal 16-week semester, with Sequences and Series taught a little bit every week. Class periods have a break in them that indicate it is time for series at the end of class. Really the two 2014 answers to this question form the outline of my whole Calculus 2 course. $\endgroup$
    – Chris Cunningham
    Apr 25, 2018 at 15:12

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