The comments on this post from yesterday begin a good discussion of the role of content in a college course. Specifically, James Fadden asks the questions: "Where does this pressure to get through content come from? And are there things that I (as an instructional technologist) could do to help to relieve some of this pressure?"

As to the second question, I’m not sure — I think this pressure is mostly due to the structural nature of a college’s curriculum, and not so much the fault of the way in which that structure is instantiated through teaching. Or at least, this problem (and I do think it’s a problem) has to be addressed at the structural level first, and only then can people like James can really begin to help.

As to the first question, I have two thoughts about that, some of which are echoed in this comment. .

**First:** The pressure to get through content comes from legitimate prerequisite needs of various courses. Calculus II for example really does require a lot of content from Calculus I. Students have to learn how to take derivatives and learn the basics of integration before they are ready to do things like infinite series or trigonometric integrals, and if the class doesn’t make it through this stuff in Calculus I, then they’re going to be screwed in Calculus II, or else the Calculus II course is going to have to be watered down. And Calculus III requires a solid knowledge of derivative and integration techniques. So there is a sense that content has to be covered because certain courses are sequential.

**Second:** The pressure to get through content comes from a flawed understanding of what learning a subject really means. Specifically, we tend to view content as something resembling a virus and learning like an infection, where students "get" the material if and only if they are "exposed" to it. (I’ve had physics professors complain to me that students haven’t "seen" hyperbolic functions in my class, as if people learned things by *seeing* them.) We consider a subject to have been thoroughly taught if the professor can provide evidence that each element in a particular subset of the textbook’s index has been allotted a nonzero amount of class time. We structure courses and teach them mainly with a view towards absolving ourselves of blame if students don’t learn — "Well, if they didn’t learn *u*-substitution, it’s not my fault, because *they certainly saw it in my class*."

Of course the student has responsibilities here — they can’t be satisfied with merely "seeing" material any more than we profs can; students have to dig deep, work hard and take advantage of opportunities in order to learn the subject matter deeply. But what does it mean to learn a subject deeply? However we may answer that question, I think we would all say that it does not mean mere exposure to material. And yet, this is probably the driving force in how we structure and teach courses.

I’m starting to ramble, so I’ll just say: We need to start making course goals look less like the textbook’s table of contents and a little more like learning. That involves mastery of content, but it also involves (and "mastery of content" involves) paying attention to things like process skills, problem solving, communication, scientific inquiry, and so on — things that are not content but which are inextricably linked to content, and which live longer in the students’ minds than content. This requires more time and therefore less content. But my guess is that if you look at a lot of courses objectively, rather than through the lens of tradition and personal preference, you’ll find a lot of ballast. (Calculus I is full of that.)

Tags: Calculus, higher education, college, teaching

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Yes. Given that you’re teaching Calculus, and I teach applied math (business), I suspect you have even more problems than we do, and that’s saying something. On the whole prerequisites thing, we teach an intro to business problem solving course that also functions as a gateway course. This means we have to teach them problem types they will see in management, marketing, finance, accounting, and decision sciences, which makes coming up with course content more painful than it needs to be. The gateway part, well, there are a lot of students who want to major in business. There are a lot of those students who don’t realize how math intensive business is. They have a romanticized idea of business, I suppose. Many are under the impression that marketing, probably the most data-analysis intensive field in business, is all sitting around coming up with ad campaigns and being creative. A gateway course is not just a “weed out” course; a gateway course is as much for students, so they can decide if they really do want to do a business degree.

Thanks for the insight…

While not addressing the secondary question (How can I help?) Better understanding the source of the pressure I can see some cracks in the More Content Armor that I can work on (and write about).

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I always say that one of the best classes I ever took in college was my multi-variable calculus class. We learned everything 3 ways: using calculus, using math/arthimetic, and by creating a sketch or accurate drawing. It was the first time I could see connections in a meaningful way. I suddenly understood that complex formula for the surface area of a sphere — it comes from integrals. I loved that class because it opened my thinking and I could draw on my understanding in almost all of my math and science classes. It created meaningful learning AND covered the information we needed for the next classes.