Building a six-week Calculus 2 course

May 1, 2012, 9:18 am

I took a two-week blogging hiatus while final exams week, and the week before, played themselves out. Now that those fun two weeks are over, it’s time to start focusing on what’s next. Some of those things you’ll read about here on the blog, starting with the most immediate item: my spring Calculus 2 class that starts on Monday.

Terminology note: At GVSU and other Michigan schools, the semester that runs from January through April is called “Winter” semester. The period in between Winter and Fall is split into two six-week terms, the first being “Spring” (May-mid June) and the second “Summer” (mid June-July). It’s quite accurate to the climate here.

Anyway, my Calculus 2 class runs in that 6-week Spring term. If you know anything about Calculus 2, and you have a sense of just how long, or short, a 6-week period is, the first thing you’ll realize is that this is a lot of content to bring to students in a fairly short amount of time. We will meet 9:00am-11:15am, four days a week. So the number of contact hours is roughly the same as a regular 14-week semester — it just takes place in half the time! The image you see above is my game plan for what’s going to happen, and when. It’s so dense that you can almost feel a gravitational pull into the whiteboard.

So, how do you take a course like Calculus 2 — which a lot of people (myself included) think is the hardest of the three introductory semesters of calculus — and condense it into a 6-week period in which there is precious little time for students to assimilate anything? Well, I’m about to embark on a six-week thrill ride of trial and error, but here are the instructional design principles I am employing.

  • Don’t lecture (much). The one thing you dare not do in a class that meets for 135 minutes (!) is lecture the whole time, or even a significant minority of the time. There are pedagogical reasons for this, but you don’t need them — just think about the sheer physical issues. Do you expect students to stay engaged for that long? Do I even have the physical stamina to lecture for that long? Right.
  • Force the assimilation issue. The single biggest issue with this class is the lack of time outside of class for assimilation of information. In a regular 14-week setting, you might be able to justify lecturing by saying that students have lots of unstructured time outside of class to work problems and seek out help. In this setting, you do not have that luxury. The class time itself has to be used significantly for activities that focus on assimilating information — not information transfer, at least not primarily.
  • Assess early, small, and often. Another side effect of the compressed time scale of the class is that students need to know how they are doing in understanding the concepts and processes almost in real time. In a 14-week period, if a student misunderstands a concept, realistically the student has about a week in most cases to find and repair it before it starts to compound. Think about the effect of misunderstanding u-substitutions and how that affects understanding integration by parts, and how much time typically separates those two integration ideas in a 14-week Calculus 2 class. Well, in this class, 1 week of “normal” class time equals 1 day of class time. Students can’t afford to let misunderstandings go unnoticed and unfixed for more than 24 hours. It’s my responsibility as the instructor to give students the framework and opportunities to see how they are doing early and often and in a way that gives grading a fast turn-around time. This precludes typical assessment procedures like big, chapter-long timed tests, which come too late and take too long to grade.
  • Stress collaboration and community. This is going to be a stressful, hectic pace for most students. The human element of the class can be the secret weapon that makes the pace bearable for most students and makes difference between success and failure for at least some of them. The two most important things I want students to realize is that I want them to succeed and that we are all in this together. Those principles are going to be woven into the fabric of the course — daily activities, assessments, everything.
  • Stress connections and concepts. We already know that students learn better when they have an internal framework in which to put incoming knowledge — and we also know from experience that most students don’t know how best to construct that framework. So even though concepts will not be spaced out much in terms of time, a key focus of the class is what the big ideas are and where the minute details fit in terms of the big ideas.

Given that I’m a proponent of the inverted classroom, and given that the inverted classroom focuses on using class time on assimilation-oriented tasks, you might think that I’d gravitate toward an entirely inverted format for this class. But I think that would fail horribly here. There’s just not enough time between classes for students to read material or watch videos and put the basic pieces together before using it in class the next day. I’m a proponent but not an uncritical fan of the inverted classroom. It’s a teaching tool, and like any tool, it works well in some cases and not at all in others.

In later posts, I’ll describe more of the specifics of what I’m planning for this course. In the meanwhile, what do you think about all this? Any advice, warnings, etc.?

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