A churl I knew

It's been a rough semester all around.

We're all tired, we're all grumpy, and some of us are acting a bit churlish of late.

I put myself in that last crowd. I know I've been snippier, snottier, and snarkier lately than I typically am, even at the end of a busy semester. (After all, I've lived through busier semesters than this one has been, and have been in less of a foul mood by the end, at that.)

I typically write a post at the end of each semester in which I "grade" myself on my performance in each class during the past term, but I don't feel like doing that just now. I've thought a little bit about why it is that I want to forgo that post, at least for the moment. At first I thought this reluctance to post stems from fear of assigning myself lousy marks...after all, this was definitely a rougher semester pedagogically for me than any semester I can remember...but I don't think this is what makes me hesitate before grading myself.

I think rather the hesitation comes from my state of mind: I don't right now feel like I'm close to the classroom.

This is the first term ever during my academic career during which I've felt less like a teacher and more like an administrator.

And I don't like it.

I don't like what I've become.

It's not that the committee work I've taken on this past year has been overwhelming (I know of others who deal regularly with a far heavier administrative load than the one I've taken on); it's more that I've let myself drift into it too far, into its depths, into its dark waters, and out of sight of the calm cove of the classroom with which I'm most familiar and in which I'm most at home. I fear that I may have too often put my committee work ahead of my students, and this is the most churlish move of all.

I don't like myself for doing that.

I need to get back to where I belong.

I'm glad for the end of this semester, for it can be made to be a turning point, a terminus, a full stop before the next sentence begins: "After the summer was over, ..."

I promise I'll be back next fall, my friends. I promise to be in-the-moment in the classroom, to be on-the-spot during office hours, and to be less snippy, snotty, and snarky wherever you find me.

Before ending this post I'd like to apologize to any of my colleagues and students who've found themselves the objects of my churlishness and frustration, and to thank you all for helping me to make the most we can out of a term during which we've all found ourselves overworked, overtired, and out-of-sync after a string of freakish snowstorms.

To my students: nothing I've ever done gives me greater fulfillment than working with you all on a daily basis. Nothing. Your dedication is indefatigable, and your curiosity infectious. You are almost uniformly the most honest, open, warm, welcoming, intelligent, and human group of human beings I've ever known.

To my colleagues: in your own individual ways you all offer support that sometimes goes unnoticed and unrecognized, yet you keep on offering that support anyway. Without your ideas and your inventiveness I'd be stagnant, and without your help I'd be nowhere. I appreciate all that you do.

Thank you all! I'll be seeing you all soon. And I'll look forward to it.

Patrick is a patsy no more

I'm a nice guy, but I don't like to be made a fool...nor do I want people to think they can make a fool of me.

To the Calc II students who were overheard by Math Lab staff to say, while completing the homework on Taylor series after the exam featuring Taylor series questions had been given in class, "yeah, now we need to learn how to do this stuff, so we can do the revisions!": congratulations! Your flagrant display of immaturity has caused me to completely rethink the revision policy. Sufficiently many of your more mature colleagues have let me know that the revisions truly do help them learn that the opportunity for revision will remain in place, but I fear that offering full credit for unlimited revisions may simply be unfair to those who struggle to master the material in a timely fashion. Look forward to a revamped version of the policy for the Fall 2010 semester.

To the Topology students whose homework is an automatistic transcription of the work of one of your more steady peers in the same class: as I'm fond of saying, I've been in this line of work for over a decade now, and I know the score. I just want you to know that I can tell when a person's work is really that person's work. Don't think you're pulling a fast one on me.

That is all.

Please understand that I'm not angry, just tired, and, honestly, a little disappointed.

And I'm also off to class.

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!