In thinking about the redesign of the bioengineering curriculum, I’ve had to pay a lot of attention to what level of courses the engineers would be required to take. Our campus offers physics at three different levels (one algebra-based, the other two calculus-based) and calculus at 4 levels (honors for math majors, for physicists and engineers, for life scientists, and for economists). Do I allow the students to take either of the calculus-based physics courses? Do I allow any of the three calculus classes (excluding the one for economics majors)? I’ve wrestled with this problem for a while (see for example, my post Physics for life-sciences majors from last June).

### In favor of allowing the lower level courses:

Usually there is the most scheduling flexibility for the second-lowest level—the level aimed at biology majors—because that is where the largest numbers of students are, so the courses get offered repeatedly during the year, while the more advanced courses get offered only once. So from a scheduling standpoint, it would be best if students were able to take those courses.

In bioengineering, we also get a lot of students who start out in biology, but who later realize that other majors are more interesting (freshman year everyone thinks they want to go to med school—most have given no thought at all to engineering). Because the biology majors are advised to take the calculus and physics courses intended for biologists, the students have taken only those and not the higher level calculus and physics courses intended for engineers. So a change of major is easier if students are allowed to take the biology-level calculus and physics.

One thing I’m trying hard to avoid in the bioengineering curriculum redesign is “creeping prerequitism”—the tendency for most courses to gradually increase the prerequisites in order to have better prepared students in the course. In many cases the prerequisites are irrelevant to the material of the course (like multi-variable calculus for a data structures course or genetics for a cell biology course), but are just *filter* prereqs, to make sure the students have more “maturity” by having passed a gantlet of other course. Because of these prerequisites (both real ones and filter ones) being added independently by each of the 8 or 9 departments that teach courses required for bioengineers, we end up with a program grossly overloaded with lower-division “preparation” courses, and not enough upper-division “application” courses.

### Against allowing the lower-level courses:

In exit interviews with seniors last spring and this fall, we asked them about their experiences in calculus and physics. Those who had taken the lower level of calculus-based physics course felt that it had been a waster of their time—neither their classmates nor their professors seemed to care much about whether the material was learned, and everything was covered rather superficially. (We didn’t get the same info about calculus, because most had been forced to retake the higher-level calculus class if they had only taken the biology-level one.) So from a pedagogic standpoint the students get a better course if they take the higher level with students who expect to use the material and with professors who expect their own majors to be taking the course.

Some upper-division courses do rely on math and physics skills of the more advanced courses. For example, the upper-division probability and statistical inference classes do rely on students being adept at integration, the statics and dynamics course relies on students knowing Newtonian mechanics well and being able to handle differential equations, and the electronics courses require some skill with calculus and differential equations.

### Concluding thoughts

I read an blog post today by a high-school physics teacher addressing a similar question at the high-school level: Jacobs Physics: How do you tell the difference between AP and “regular” physics?. He doesn’t have to face what courses students are *required* to take, but only which ones they should be *advised* to take, but the underlying questions are the same. In the post, Greg Jacobs writes

If an AP and a Regular course cover the same “standards,” how are the two classes different?

Don’t use standards to define courses; use tests and exams, preferably as written by someone external to the course, to define courses. Once you’re clear on the level, topics, and depth of question that your students will be expected to answer, then you can make up a concordance with any state standards you need to.

…

The AP Physics 1 exam covers much of the same material as regular/Regents. The major difference is the depth of that coverage, as evidenced in the test questions.

A regular question can generally be categorized in a single topic area, and can be answered in one step, or two brief steps, or a one-two sentence explanation with reference to a single fact of physics.

An AP question generally requires cross-categorization across two or three topic areas. Most require multi-step reasoning, or a two-three sentence explanation with reference to more than just one fact of physics. AP questions, for the most part, require students to make connections across skills and topics.

…

As an additional comparison, you might consider a conceptual class. Conceptual Physics can cover many of the same topics as “regular” physics, but without using a calculator. … A conceptual approach provides a greater contrast between AP and non-AP physics.

The key idea here is that the difference between levels is not in what subjects are covered, but in the expected skills of the students after taking the course. That holds true at the college level as well—I can’t decide based just on catalog copy what level of course students need, because the catalog copy only lists topics, not the complexity of the problems that students who pass will be able to solve.

In the interest of minimizing filter prereqs, but making sure that all genuine prereqs are met, I’m suggesting requiring the higher level for the bioelectronics and assistive technology: motor tracks, but allowing the lower calculus-based physics for the biomolecular and assistive technology: cognitive/perceptual tracks. I am suggesting requiring the physicist/engineer track for calculus in all tracks, since it is needed for a higher-level course in all of them. It’s not the same course in each track, but electronics, statics and dynamics, and statistical inference all require greater facility with calculus than the calculus-for-biologists track provides.

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