Achieving self-awareness

I handed back the first exams of the semester in my Precalc class today.

By and large they did quite well. There were handfuls each of As and Fs, slightly smaller handfuls of Bs and Ds, and a passel of Cs. It was a nice trimodal distribution, with the middle mode dominating strongly at a mean of roughly 76.2%. The students struggled most mightily with anything involving absolute values, an assessment with which they wholeheartedly agreed when I made that observation at the beginning of class this afternoon. Long division of polynomials? No sweat: they nailed that. Radicals? Not anyone's favorite, but they came out okay on those. Absolute values? Fuhgedaboutit.

I'm not sure what it is about absolute values that proves so tricky to these beginning mathematicians. Admittedly their manipulation involves a good deal of practice and carefulness...but the same could be said of other concepts over which the students have shown a good deal more mastery.

I'm just not sure.

One thing I'm finding out about myself as I teach this class is just how much about mathematics I typically take for granted. I've blogged elsewhere (strangely enough, in this post about absolute values!) about the mathematical concepts I take as given; I'm only just now, in the midst of our first round of testing, realizing the tenuousness of some of my assumptions about students of mathematics.

I have to remember that though these Precalc students are every bit as intelligent as my Calc I and Calc II students, and though they're often exceptional students who are remarkably dedicated to their studies and who put every measure of effort into their educations, they're simply not as experienced mathematically as the students I find in my calc classes. I'm used to starting off the semester with students who come preprogrammed with knowledge of absolute values, of the algebra of polynomials and rational functions, of radical manipulations. And if a student makes it to my class without such knowledge, I've had the right to turn them around and send them down the hall to...

...precisely the class I'm now teaching.

It's new for me, and I know I'm messing up here and there, simply because of its newness.

I'm probably making assumptions I shouldn't make, about the knowledge you might or might not have, about the skills you do or don't possess. How many of you have ever graphed a function before? Probably most of you, but I probably shouldn't make that assumption. How many of you are bored to tears in having to spend an hour and a half going over simple examples of functions and the many forms they may take? Probably most of you...but I'm guessing not all.

I'm learning, folks. I'm learning what I need to say, what I need to do. And I need your help. If any of my Precalc students are reading this, please feel free to drop me a line, or even comment on this post (anonymously, if you'd prefer), and let me know: am I saying enough, or am I saying too much? Am I making any unsafe assumptions?, making an ass out of...you know the drill.

Let me know.

Today's one-sentence essay at the class's close asked the students to define "function," in their own words. Additionally, I asked each of them to indicate whether or not he or she liked poetry. Yes, I'm gearing up to assign another poetry exercise. I'm trying to decide how I'd like to modify this iteration of the assignment: ought I ask them to confine their theme to the topic of "function" in some way? Or should I merely let them traipse about the whole of the realm of mathematics, as I did my Calc I students last Fall?

I'm also toying with an ongoing "Pet Function" project, in which each student will be held responsible for the caretaking of a particular function, whose life cycle they'll sketch as we reach various points in the semester.

That's the skinny in Precalc. The thème du jour in Abstract Algebra was a litany of technical lemmata that read like one of the toledoth passages out of Exodus: "and the existence of cycles begat a decomposition into disjoint cycles, and once these cycles were found, verily the other elements they moved not. Existence begat uniqueness, and so was proven the Fundamental Theorem of Arithmetic, symmetric group version."

The first section hung in there, but the weight of the afternoon's weariness and the length of the week's work and the dark depths of the unintuitive computations we'd had to wade through were too much for the yawning and blinking and note-passing second section. Fuck it, we ended a few minutes early and half a proof short.

Hang in there, folks! Next week we'll cap off the FTA for S_n, we'll meet the alternating groups, we'll start exploring properties of groups in their most abstract form. It's all good.

What else?

In addition to about an inch and a half of grading (Precalc projects, abstract homework) I've got to spend a couple of hours this weekend throwing together a couple more handouts for the Carolina Writing Program Administrators conference to which I'm heading off on Monday afternoon. I've already got a handout that breaks down our (my, Lulabelle's, and Casanova's) views on the "future of writing at UNCA." I just need to gather some qualitative and quantitative data on the previous assessment project...and maybe say something about faculty intentionality. I'll figure it out.

Oh, and! I just found out that I will indeed be co-organizing a short course on designing and implementing writing-intensive mathematics courses at this coming spring's MAA Southeastern Sectional Meeting in Nashville! I'm excited.

Okay, my pizza's coming out of the oven in about five minutes, so off I must be. Take care, Gentle Readers. I'll check in again soon.