Monday, October 24, 2011

Dead Zone

Today I felt like every one of my classes was a bit stuck in the mud. (Oddly enough, my morning Precalc class, often my quietest, was the most lively today.) It was all we could do to keep making forward progress in a couple of the classes, and I felt like I was beating a dead horse more than once.

What to do at such times?

The classical response, at least from instructors in content-driven disciplines: "well, we've got so much to cover that we've got to keep going..."

...but this is wrongheaded. If you press on without pause, it's not like students are going to get any more engaged, and it's not like they're going to get much out of whatever you do together, anyway. In pressing on you'll be doing so only for the sake of pressing on, and any progress you make will be illusory.

This is exactly how it felt in my second section of Precalc, and in Abstract Algebra, in both of which classes we worked with (what I thought were) some pretty neat mathematical ideas: in Precalc we solved a nontrivial optimization problem involving rational functions, and in Abstract Algebra we looked at the subgroup lattices of a couple of groups and examined the asymptotic behavior of Euler's function φ. I don't feel that either class picked up on the subtle beauty in a way they would have had they been in a more receptive mood.

Don't get me wrong: I'm not blaming my classes. Both of these classes are full of wonderful students who are generally unafraid of working together to make a healthy and supportive learning environment. (I've bragged on my Precalc peeps enough this semester for you not to know how much I care about them.) Rather, I think we've just hit that point in the semester, about 50-60% of the way through, where everybody's just DEAD.

It's the Dead Zone. Wearied by exams and essays and due dates and deadlines, overburdened by homework and quizzes and lit reviews and response papers, we're tired and jaded and not having much fun. (Believe me, kiddoes, this "we" often includes me. I apologize if I'm sometimes snappy around this time of the term; it's hard to be irrepressibly chipped every hour of every day!)

On reflection, I've thought of a two-fold healthier response to these Dead Zone doldrums:

1. Play. Put down the pen or pencil, put the paper away. Let's just think of something fun we can do with whatever it is we're working at this very moment. Optimization problems? Let's come up with some kind of crazy variation on the theme, whether we have any idea how to solve it or not. Let's set it up and see if we can work it out, like Ariadne weaving a web through the labyrinth. Are we sick to death of subgroup theorems? Let's break it all down with an explicit or example, or two, or three...let's dissect the dihedral groups until there's nothing left but individual elements...let's take it apart!

2. Reflect. The next step comes as no surprise to those who know me well: once we're done playing, let's take a minute or two to write to ourselves, if only to reflect on what we've been able to discover. Did we reach an end? How? Did we run aground? Why'd we lose our way? What's our play got to do with other problems we might encounter in mathematics and beyond? Write about it, write about how we feel about it. Hell, write about how we feel in general: why are we so dead today?

Too often affective learning goals get lost when we focus too heavily on cognitive learning goals, and that goes double for content-laden quantitative sciences. Let's try not to lose sight of our humanity, and the fragility that comes with it. Let's take care of each other as we come together to learn.

By and large all of my classes this semester are doing a marvelous job at this, and I admire them for it. I never cease to be amazed at the quality of students with whom I get to interact and learn. You're terrific people, all of you!


monalisasmile said...

It is most definitely the dead zone right now, in every aspect of life. The leaves have mostly fallen; the world is becoming bare; the weather is getting colder and the days are shorter.

Classes seem to drag on and homework is piling up. Midterms are always in clumps and usually back-to-back. There are no real breaks these days. Professors assign papers and projects and presentations to do over the weekend and "breaks." I understand it's not called homework for the sake of it, but we do need a break.

I've felt this semester, although hard to jump into in the first place, has been at a much faster pace than normal. And I've really only noticed this with your class. I feel like we "got off on the wrong foot" and now that I'm on track and have my schedule down, I'm still far behind and lost.

Talking among other classmates, they tend to agree that since problem set 3, we have been steam-rolling through information and theorems and proofs; everything is just a blur. Perhaps a thorough recap of what we've done thus far would suffice, and a fun "out of the classroom" project could jolt us out of the lull.

I must admit, this past problem set was pretty awesome. I want to see and feel what we are learning and how it applies to the world. I would suggest more problem sets like that. *If you haven't caught on, I'm referring to Abstract*

But in other news, keep on keeping on!

DocTurtle said...

Hey, monalisasmile: thanks for letting me know! I have a hunch that people are sick of theorems...and I'm all for more "experiential" problem sets. I think that's how I'm going to slant the remaining ones, and the last couple of exams. In these you'll learn by "experimenting," gathering data, and making hypotheses (which you can then test and prove) regarding the data.

I apologize for the "theorem...proof...theorem...proof" nature of the past few weeks. In some sense, it's the nature of the beast: this is inherently a proof-heavy (and theorem-laden) course...but there are ways to lessen the blow, and I'll try my best to do that.

Again, thanks for chiming in! I appreciate the feedback.

monalisasmile said...

No problem, and thank you!