Sunday, December 31, 2006

Priming the pump

Here we are again!

It's the last day of the old year, and I'm really starting to get things in order for the start of classes, coming up in a little over two weeks.

I've got (and have had for a couple of weeks now) the syllabus for Calc I put together and posted on-line. I've taught that class often enough that I'm sure I could do it with my eyes closed and both arms held behind my back...which is exactly why I need to challenge myself to do it differently, better, this time around. Not that I've taught it poorly in the past, but I believe that now I'm capable of running this course so much better still that it'll make my previous efforts look like those of a first-year grad student. (I ain't knockin' on first-year grad students, some of them are hella good teachers; what they lack is experience.)

What'll be different about this coming semester? I plan on teaching this course in much the same way I've taught the last four sections of Calc II I've had: lots of application-oriented projects (which are, for the first time ever, built into the syllabus), structured team activities, including the ever-popular team quizzes, carrying over from last semester's MATH 365 course.

Then there's 280, our "Foundations" (read: "Proofs") course. To be honest, I haven't given it much thought, though that'll change in the next couple of weeks.

For 368, the course with the hifalutin' name "Theory of Numbers" (it's "number theory," people! "Number theory"!), I'm envisioning something much more akin to a seminar than a lecture. I may just have to take a page from Maryellen Weimer's playbook and let the students come up with their own course, selecting the assignments they'd like to complete from among a smorgasbord I place before them.

There is one goal I want to lay before them and make a sort of lodestone for the semester: what's the largest number you can prove is prime? I might make it a contest between the members of the class, to see who can come up with the biggest provably prime number before the semester is out. This'll spur them into reading about all sorts of primality tests, involving everything from basic modular arithmetic and Fermat's Little Theorem, through quadratic reciprocity and Dirichlet characters, all the way up to Dirichlet's theorem on prime congruences, and the Riemann Hypothesis itself!

Obviously this is a bit to bite off, let alone chew. But I have a feeling we'll get farther if I let them lead the race than if I serve as a pace car.

I'm off for now...I hope to get a working syllabus up for the other two courses before the week is out and I head down to New Orleans.

Sunday, December 10, 2006

The proverbial Morning After

Well, it's all over and done with.

I think.

There are a few minor details to wrap up with one or two folks, but nothing major. The third exams, the last journal entries, the presentations and concomitant posters are all graded and ready to hand back to those eager enough to come and retrieve them. (C'mon, y'all! Come and get 'em!)

Moreover, I've finished grading.


In the end, I'm really disappointed that I've got to hand out grades: how difficult is it to boil down all of the interactions, inquiries, examples, applications, projects, presentations, portfolios, and other assorted whatnots we've collaborated on in the past few months, and end up with a residuum summed up by a single letter?

I tell you what: put simply, it's a bitch.

But it's done. And ultimately many people in the class did very well. There's a pretty large number of As and A-minuses, a fair smattering of Bs and Cs of various sorts, and only a puny handful of anything lower.

Beyond the grades, there are the lessons learned. I hope that in the case of our class we've been able to transcend cliche and put some truth into that truism. I can't speak for the students in the class (I'd love it if they'd take the time to speak for themselves in the comments to this post!), but I know I've learned a lot.

1. I am never, ever going to do this with a class this size again. Ever. I'm figurin' the upper limit for this method is something in the ballpark of 15 students. At that point I could have an eminently manageable 5 teams of 3 folks each. With that small a number of teams, I could make the rounds in the classroom during group exercises and be sure of hitting everyone at least once. I could schedule team meetings more regularly to ensure frequent updates, and the teams would be small enough to allow for easier scheduling of research meetings. We started out with thirty-three students and ended with thirty, and as hair-pullingly frustrating as the size of the course sometimes made the daily proceedings, I'm quite frankly awed that more people didn't drop midway. I have nothing but admiration for the patience and dedication of those that stuck with it.

2. This method of learning is not for everyone. Those that fared best were those who were more used to courses run along these lines, and those whose learning styles are at odds with those assumed by a more "traditional" classroom. For instance, those who identified as "visual" learners were likelier to find our class useful. Others, more used to the run-of-the-mill lecture format, felt a bit out-of-place and longed for those infrequent days when I'd stand at the front of the room and yammer. As the semester wore on, I developed a balance between the applications-based guided discovery exercises I'd envisioned for the course and a more lecture-led semitraditional format, all based upon the worksheets I turned out, one or two per week.

3. This method of teaching is not for everyone. As folks who've had me for other courses can attest, my teaching style is probably best characterized by the word "enthusiastic." A number of other words have been used to describe my teaching (few of which, fortunately, are unprintable), but this is the word which predominates in my teaching evaluations at the end of every semester (runners-up include "approachable" and "accessible"). And honestly, without the charisma and energy that I put into my classes, I have NO IDEA how I would have made it through this semester. WARNING: if you plan on teaching in this manner, make sure that you've got lots of free time, and boundless energy. Even with all of the preparation I did in advance, I was still blown away by just how much I had to do to keep up with the work. A lot of this labor was on account of the size of the course, but much can be attributed to the method alone.

4. Some innovation is appreciated. Team quizzes, for example, went over enormously well. I'm keepin' those: you can be sure that every course I teach from this point forward will include some variant of that activity. This blog's been a popular feature, too. For a while there, before everyone was occupied with exams and presentations and other geegaws, I was getting at least one or two comments per post (and as many as 14 at one point), which ain't bad considering all of the other faaaaaaaaar more interesting blogs there are out there that my students could be reading. (By the way, a shout out to The Comics Curmudgeon, one of the baddest blogs on the internet.) Change of Basis, too, will live on, in modified form, as I move into the planning stages for next semester's classes. Look forward to my continued chronicling of my teaching adventures. There are several of you from Linear who are continuing on with me, either in 280 or in Number Theory...keep reading, folks, and keep posting!

I've learned more lessons than this, but those are the biggies.

I've gotta go for now, but hey, 365ers! I really would like to hear what you feel you've gotten from this class, so please feel free to leave a comment or two on this post: let me know what you've learned, what lessons you'll take with you.

This'll likely be the last post I make on 365 for quite a while, but I'll be back soon with updates regarding next semester's courses. And I'm slated to give a talk on the writing component of our class in January at the big annual Joint Meetings of the American Mathematical Society and Mathematics Association of America. I'll be sure to let you know how that goes. (And yes, Fiona, I'll let you know as soon as I hear about the Information Literacy Intensive status for the class...but I'll be seeing you in 280 in the Spring, so I know you won't be going anywhere!)

Au revoir, then. To everyone in my class: thank you. Thank you for your hard work, your time, your cooperation, your willingness to try something new, your everything. Take care, and have a wonderful Winter Break!

Thursday, December 07, 2006

Math aftermath

Well, we did it! We survived. We finished.

Well, they've finished, anyway. I've got a stack of grading as high as the Petronas towers to clean off. I'm about halfway through the third exams, on which folks are doing uniformly well, and then it's onto the papers and the presentations.

The presentations? They went well, for the most part. There were a couple that could have stood to be a little more robust, a bit more fully fleshed-out, but by and large they were informative, and fun. I felt that there were two that stood out from the others in terms of clarity, content, and comprehension, not to mention preparedness and smoothness of delivery. It was exciting to see the aftermath of everyone's hard work. I'm sure the papers will reflect the same sort of diligence.

For now, I'm getting back to the grading, but I'll check in later with more insights as they come.

Wednesday, December 06, 2006

Today's the day!...

...We get things underway in about an hour now. I've been putting together my score sheets, getting the food ready, setting up tables, and whatnot for about an hour now, and I think we're just about ready. I'm hoping that the next hour will see folks showing up to put their files on the desktop so we can effect smooth transitions from talk to talk.

I'm confident things are going to go well.

Tuesday, December 05, 2006

One more day...

Well, we're finally here. The end of the semester is upon us. Yesterday brought us the last day of class, tonight's will be the final problem session, and tomorrow will see the Symposium on Linear Algebra and Its Applications.

During the past few days I've read through five or six drafts of final papers; written a ton of Mathematica code to simulate moves in Monopoly, to translate between various representations of color, and to analyze traffic flow; and helped several teams plow through some fairly dense source material. All in all, the projects have come along nicely, and I know I'm not the only one looking forward to tomorrow's presentations. Several folks have told me how excited they are, how much fun they've had, and how proud they are of the work they've done.

I don't recall if I've yet mentioned that about a week ago I submitted an Information Literacy Intensive proposal for the course. If we get that picked up, that's one more checkbox all of the people under the ILS system can put a mark in. Woo hoo!

Right now, I've got to go and do a little tweaking with some of the color simulation Mathematica code I worked up the other day. Toodles!