In less than a week my Calculus 2 class will be starting up. As you may have noticed, I've been thinking about ways to run this class differently than I ran it last time. One of the things that has come up in my thinking is how to structure exams. Last semester we had 3 midterm exams and a cumulative final. What I hope to try this semester is two midterms and a non-cumulative final.
First, some background from last semester. Our first midterm covered 2 chapters, the second midterm covered 2 more chapters, and the third covered all but two sections of a single chapter (the chapter on sequences and series). The remaining two sections of that chapter were untested going in to the final. That insured a couple of problems from those sections on the final, as well as all the other material.
What I think I'd rather do is have 2 midterms, covering the same material as the first two midterms last semester, and then have our final exam cover that whole last chapter. Each of these exams will be given the same weight for the overall grade, instead of having a somewhat more heavily weighted final exam.
I think to explain why I like this idea, I need to mention the content that we cover in somewhat more detail. The first midterm covers techniques of integration and a few applications (arc length and surface area for surfaces of revolution). The next exam covers parametric and polar curves (derivatives, areas, and arc lengths) and iterated integrals. The third midterm, last semester, covered sequences and series (definitions and convergence tests) leaving Taylor series for the final.
So, why do I not want a cumulative final? Looking at the 'old material' that students would need to go back and learn, I see a lot of formula memorization. "Make this non-obvious trig substitution when an integral involves...", "to break up a function using partial fractions, do this strange procedure", "the formula for the (arc length, surface area) of a ((polar) function, parametric curve) is ...". These are things I want my kids to know about at the end of the semester. But if they forget formulas, or the appropriate substitutions, I'm perfectly ok with that. They should be allowed, after this semester, to look up all of these things in a book. I expect that the techniques of integration won't be used by hand by students again (unless they end up teaching calc), because they will be permitted to use computers or tables of integrals in the future. And if they are needed, that's what the textbook is for.
Ask any former calc student for a technique of integration. If you're very lucky they'll remember that sometimes something like a trig substitution is useful. Ask them how to find the arc length of a parametric curve. I'd guess you'll see a lot of blank stares. Same goes for polar areas. Why should I test my students twice on material I'm happy to let them forget details of, after demonstrating competence at least once? My vote is for non-cumulative finals.
Thoughts? Why am I wrong?