A tale of two issues

One thing is undeniable: grades on Calc II exams have gone down since the last time I taught this course.

By quite a bit.

I don't think the students are any less bright, and I don't think my teaching has plummeted in quality since Spring 2008. The classroom format is nearly identical, many of the activities the same.

What's changed, and changed substantially, is my exam grading policy: instead of allowing a single round of revisions in which students can earn back up to 1/3 of the points they initially missed, I now allow unlimited revisions, with an opportunity to make up every single point missed.

My aim in allowing such revisions is to mimic a not uncommon practice in writing-intensive courses, in which students are allowed a chance to continually revise their written work until it meets whatever standard they hold for themselves: if a student is happy with the C she earns in the first place, she can stop there. But if she's so motivated, she can continue to clean up her work, polish her argument, practice her diction, until she's made the paper the best damned paper it could ever be.

Why shouldn't this translate well into mathematics?

I'm finding, as I mentioned above, that it's having a deleterious effect on the initial grades. On yesterday's exam (the third for the semester, regarding the infamous sequences and series), students averaged roughly 61% between my two sections. Though the topic is an inherently difficult one for beginning students, the exam was not overly long and fairly straightforward. It had no "curveball questions" (for instance, I felt that all four "test for convergence" problems were solvable by obvious choices of convergence tests) and two or three of the problems were nearly identical to those worked out during a review session attended by roughly 30 students the night before. I thought the exam was extremely fair. (Students, if you're reading this, feel free to chime in in the comments section. I'd be curious to know your thoughts on the matter.)

In the past my pre-revision grades have been in the neighborhood of 70% or 72%. What's caused this drop?

My hypothesis: students feel less pressure to do well on the initial go, knowing that they'll have the chance to make up whatever points they miss in the aftermath. Simply put, the stakes are lower, so students don't prepare as well. Granted, you're always going to have those "gotta have a 100" grinds (and I use this term appreciatively!) who'll by god be sure to nail it on the first go-around, but I think it's likely that most students, knowing that the stakes are low, will ease up a bit on the throttle. They'll forgo that preliminary all-nighter, they'll pass on the practice exam, and they'll sleep in an extra hour on the morning of the exam instead of getting up early to pore over integration formulas while they chomp on their Lucky Charms.

For one reason or another, the grades are lower. To me, though, the issue isn't so much the grades as it is the students' learning. I'll gladly accept lower grades on the initial run of an in-class exam as long as I know that the students are still effectively mastering the concepts we discuss in class.

But how to know that they're doing this? I would argue that, the way things are now, I simply can't know this, as the exams are now saying very little about how much students have learned. (It could be very cogently argued that few traditional exams have ever said anything about how much students have learned, but that's a post for a different day.) I suspect that my exams have ceased providing summative feedback of any kind and offer almost exclusively formative feedback. In theory, they may be providing this service very effectively: by bombing this or that question on a particular exam, a student can know exactly what she needs to brush up on before the semester's over, allowing her to very carefully target her studies for the next iteration of the exam revisions, and the next, and the next, until perfection is achieved.

If the exams really are performing this function, offering meaningful contribution to students' understanding, then the revision policy is definitely worth keeping. As my students well know, I don't give a rat's tuckus about grades so long as students are learning.

But are the students really learning? Are the exams, cut free of any indexical mooring they might once have had, performing any meaningful assessment function? How can I tease apart the two matters, grades and learning?

Students, if you're reading this, let me know by commenting on this post: do you feel that the exams (and, more to the point, the revision policy on the exams) are serving a meaningful purpose? Are you learning effectively by performing the revisions? And, honestly, do you feel as though you've slackened your efforts at achieving a high initial score in light of the revision policy? (Topology students, feel free to chime in too, regarding the similar revision policy on our homework.)

Colleagues, if you're reading this, let me know your thoughts as well: do you have revision policies? Do they work? Have you had to relearn how to discern students' mastery by means of exams?

A postscript: I realize I've been incredibly absent from this forum this semester; it's not for lack of things to say. In fact, I've found myself overwhelmed by matters pedagogical. It's a cruel thing that the semesters in which I've had the most food for thought are precisely those in which I've had the least time to reflect on those thoughts in writing. I hope this will change!