Report card

So how did I do?

As the semester draws to a close, I'm reflecting back on how well my classes went this term.

Useless, I know: I'm so self-conscious now about asking loaded and essentially pointless questions like "how did I do?", knowing as I do that the best measure of the success of a class is not whether the professor's plans were executed smoothly, not whether her or his lectures were flawless, but rather how much the students were able to learn from the class.

I know this, I know this, I know this. I know that to ask how I "did" as a teacher without knowing precisely how much my students have learned from the class assumes that effective learning is a result of effective professorial procedure, so assessment of that procedure yields an accurate measure of quality of learning.

Yet, as a product of the product-oriented academic establishment that continues to pile everything up into one heap to stamp it with a single letter grade (even while talking from the side of its mouth about portfolios, peer assessment, and learner-centered methodologies), I can't help asking: how well has it "gone"?

I'll soon find out from my end-of-term-evaluations how my students feel, but for the time being I include below some self-evaluation.

Calc I. Overall grade: A-

I feel this class has "gone" quite well. There's some room for improvement, but all in all I can't complain.

I've not taught Calc I for a year and a half now, and after having led four sections of Calc II, one of Calc III, and one of Advanced Calc, all since last teaching Calc I, I wasn't very fresh. I found myself stretching to come up with new ideas for mini-projects (that part went okay, I think), and awkwardly incorporating the team quizzes born in last semester's Linear Algebra class.

What's "gone" well? Class meetings in general have been smooth ones, and I feel that my presentation of the underlying concepts (for what they're worth) has been strong. The smooth flow of class truly has been the work of the students, who've shown nearly no inhibitions when it comes to working together, both in and outside of class. I feel I've developed a good rapport with most of the students, a sort of trust that makes our interactions more fruitful.

What's "gone" not so well? I feel that perhaps I've lingered too long on some topics. I'm not sure I've made as strong an effort as I should have to engage the students outside of the classroom, or to encourage them to do the homework. The "random grading" that I've done for the last four sections of Calc II hasn't gone over so well with the Calc I class, if one is to take any message from the relative infrequency of homework completion. I may rethink this form of assessment before Fall comes. But what will work best to get the students to do the work? Homework quizzes? Grading all of the homework?

Of course, as I've said at length above, it doesn't matter how well I "taught"; ultimately, the question that must be asked is "how well did they learn?" Only the students can answer this question. (Students: thoughts?)

Foundations. Overall grade: B

I started out the semester with exceedingly high hopes, and I'm not altogether certain I've met the goals I'd set out for myself (thus the relatively lackluster grade). I think what's hurt me most is my underestimation of the difficulty of the concepts we've covered: I've forgotten just how difficult it is to master the idea of induction, or how it's far from clear at first what is the structure of a proof by contraposition. I've forgotten that the idea of "relation" isn't immediately intuited, but rather takes time to understand. I've forgotten what it's like to be a budding mathematician, that in the beginning more than at any other time the art takes a great deal of patience and hard work to master, that that mastery comes more easily to some than to others, and that most students will struggle with it. As a consequence, I think I might have assumed that my students are at a higher stage of development as learners than they truly are, opening a chasm between me and my expectations on one side, and them and their abilities on the other. Might this be what's led to the recently-ballyhooed decline in attendance towards the semester's end? (It's hard to stay engaged if your efforts end only in frustration.)

Granted, it was my first time teaching this course at UNCA (and my second time teaching such a course anywhere), so I suppose I'm allowed to err in my assessment of their level of development as learners. I'll know this more well going into the same course next Fall.

Nevertheless, I can think of several students who have excelled as independent learners, who, I feel, have gained immeasurably from the class. I hope they recognize themselves.

To repeat a useless question, for what it's worth: what's "gone" well? The general dynamic of class, with its highly participatory nature, has been a healthy one, by and large. I've had compliments on this dynamic from a number of students who have found it effective, who have said that it makes them feel less anxious about the difficulties in approaching the math, having others to share those difficulties with. Overall, this class, which I've managed in more or less the same way I led Linear Algebra last semester, went far more smoothly than the latter class. (I have a feeling the few students...four, I think...that I've carried over from that class to this one would agree with me.) Students were more engaged in this current class, more eager to contribute, and less trepidatious, and I myself felt more at ease. I felt comfortable with the amount of "lecturing" that I did. I felt this balanced well with the student-centered portions of the class.

What's "gone" not so well? I'm not sure I did as well as I might have in managing the student homework presentations, particularly as regards students' peer evaluation of these presentations. For instance, I didn't challenge the students to challenge each other's solutions, I didn't force them to take the responsibility for the mathematics presented. I think I spent too much time worrying about how long the presentations were taking, and not enough time worrying about how well the students were guiding themselves and each other towards stronger, clearer proofs.

I'm also not sure that I did as well as I should have in demanding boilerplate proofs of everyone. But should I have asked for this?

It's like this: if I've got a student whose grasp of the most basic logical conventions, even at this end of the semester, is, to put it nicely, minimal (and there are a few such students in the class), the last thing I'm going to be worried about in their proofs is whether they ended their sentences with periods. Although good grammar leads automatically to stronger proofs, if the student's handling of the concept "if/then" is nothing more an awkward pawing, no amount of textual emendation short of out-and-out rewriting is going to make a clear proof out of a mish-mash of barely coherent semi-mathematical ramblings.

I'm not sure I'm making any sense.

Again, students: what do you feel?

Number Theory. Overall grade: A

Easy A. With knobs on. I've loved this class, I can't point to a single thing that I feel has gone poorly. The smallness of the class (not to mention the inherent motivation of the students) has led to nearly seamless in-class activities. The students' homework presentations have been strong ones, almost without exception. The worksheets I've constructed based on the text (the first text I've used in years that I feel strongly positively about) did a good job of distilling the essential information into class-long activity guides. The students have cooperated well with each other, have shown genuine interest in the subject, and have unswervingly followed my lead into some pretty dense and detailed detours (like the theory of arithmetic functions and basic analytic number theory). I've already heard from several of the students that they agree with this assessment: they've learned a lot, and they've had fun. This has been one of my favorite classes yet at UNCA.

There you have it. I hope my students will read and feel free to post their own comments (even if anonymously).