Be afraid, but don't be afraid of your fear

Today I had a very contemplative morning. I had a good run, and it couldn't have been a nicer day for it: the air has an early-autumn crispness, and the trees a golden-green that connotes an ageless seasonal change.

I gave thought this morning to an opportunity I've recently been granted, one of which I'll soon take advantage, and which I hope will bear fruit. I can't say much of it publicly yet, but I will say that I became fully determined to make a move this morning when I realized two things:

1. I'm a little afraid of taking this chance, and

2. it's that little bit of fear that's convinced me the chance is worth taking.

I know that if things work out the way I hope they will I'll be presented with entirely new challenges I've not yet faced in my career to this point. I'll be doing a lot of learning on the fly and a lot of playing it by ear. I'll be bearing a great deal of responsibility, but also relying to a greater extent than ever before on others to help me carry out the tasks I'll be responsible for. I'll be delegating, relegating, moving and shaking, and working my tail off.

It's a bit frightening. I've almost balked once or twice because I know that though I'm qualified to take this on, and though I'm as ready as I'll ever be (and as ready as anyone could be expected to be), it'll still be a rough road. I'll definitely be outside my comfort zone. It was only just this morning that I admitted to myself that I've been a little afraid of moving down this path much further.

But you know what? That's a good thing. If we don't put ourselves in that "zone of proximal development," as Vygotsky put it, we don't put ourselves in a position to do much learning or growth. If I only ever do things that I know that I can do, that I'm utterly unafraid of doing, I'm not going to get much out of them.

These twin realizations: the presence of fear and the healthfulness, the appropriateness, of that fear, have moved me forward. I feel stronger and more whole.

There's a parallel in one of my courses right now. Yesterday I spent roughly 10 hours grading (9:00 a.m. to 7:00 p.m., almost nonstop), about 7 hours on Precalculus alone. Their most recent homework sets (especially Homework 6) were challenging ones, involving complicated problems which had to be broken down into simpler subproblems. The students had mixed success in seeking solutions to these problems. Some patiently broken them down and crafted careful solutions; others were less successful, impatiently attempting to swallow the problems whole.

The problems are meant to push the students forward, to move them from a place where they feel comfortable to one where they feel challenged, and maybe just a little scared. I'm confident that the students can do what's asked of them, though, and that they have the skills needed to solve the problems I give to them if they take their time and work carefully. I'm confident that if they take time to contemplate the problems piece by piece, they'll grow in confidence and competence.

I sent the students an email just now, including a model solution to the toughest of the homework problems. Here's some of the text from that email; I hope it helps them place our work together in a healthy context:

...I also recognize that the problems I'm asking you to complete are not easy ones. Each of those on HW 6 likely took you 45 minutes apiece (maybe more) if you did them clearly, capably, carefully, and well, as many of you did. I was impressed with the neatness and precision of some of your answers!

These are not easy problems; they are challenging and probing. It's for the best: I believe that challenging problems are those most worth doing. They push us to our limits and force us to confront fully our understanding of the ideas we come up with together. I'm just relearning now (relearning from you, as much as from any other source) that those things that are most worth doing are those things that are difficult to do, that challenge us, and that, perhaps, even scare us a little.

My reflective morning's brought me other thoughts as well, about which I'll be posting throughout the week. Several stem from my ongoing reading of Parker J. Palmer's and Arthur Zajonc's The heart of higher education: A call to renewal (transforming the academy through collegial conversations) (San Francisco: Jossey-Bass, 2010), the centerpiece of the Learning Circle I've been taking part in (when possible) this semester. The book has great richness, and has led me to reflect deeply; as I wrote to myself at one point "there's poetry on every page!"

In the next few posts I'll talk about what I've learned from an ongoing project about which here I've yet said little, about resistance to curricular change on the part of even the most well-intentioned (and change-oriented) faculty, and about my own elusive "community of scholars" Palmer and Zajonc extol on page 128 of the book I mentioned above. About all of these I've thought today.

As I said, I had a very contemplative morning.

Bile and bluster

I've now had nearly 72 hours to come down from my last post.

In retrospect, perhaps I was a bit harsh.

I mean, I'm pretty sure that my students aren't out to depress me with their eight-o'clock apathy and their poor performance on the exam. ("Did we really make you cry?" asked one of the students in the second section. I think the answer I gave was sufficiently vague so as to leave the matter unresolved.)

At the end of the day, they're good people, they had a rough week last week (didn't we all?), and enough of them have expressed enough remorse over their collective blanking, biffing, and blooping on the exam to make me regret my vituperative post in the wee hours of Saturday night.

Meanwhile, my 280 class has been doing wonderful things I fear I've not yet lauded enough. I'm very happy, for instance, with their Professional Proof Analysis papers, particularly insightful comments from which I've selected and compiled to share with the class as a whole. A sample:

"I think [the structure of the Hass and Stewart proofs] reflects a contemporary view that introductory Calculus is more about using Calculus than deeply building an understanding of why it works....[T]o the exploring student, it suggests the text is offering statements like this is true and here is why, instead of by using these ideas we arrive at this helpful result to introduce the material."

And:

"Along with the actual analysis of the proofs, I believe it is worthy to acknowledge that the Weir and Thomas proof was composed by three authors, as opposed to the one author each of the other had. This is important because it allows for immediate revision of each author’s ideas to produce a tighter, more inclusive proof (I now see why work in groups during class)."

We've been working on order relations for the past couple of classes, and a couple of the students seem to have a particular knack for this stuff. Timofei has even expressed interest in signing up for a reading course on lattice theory with me next semester. I think that would be wicked awesome. I pulled Davey and Priestley (Introduction to lattices and order) off the shelf to browse through it with him after class yesterday, it would make an excellent text for a reading course, and he could get it cheap cheap cheap. I don't think it'll take much convincing to make him take the plunge. I've got a soft spot in my heart for order theory, I don't think I'll ever leave it alone for long.

So what's going on in the pedagogical scene, besides the day-in-day-out of my classes?

Yesterday we had our first post-season meeting of the self-authorship Learning Circle. I and three others assembled to share our "homework": each of us was to produce a short narrative describing what self-authorship meant to us (perhaps from the point of view of a practitioner within our respective discipline), illuminating it for the benefit of one of our peers who may never have heard of it.

My narrative on self-authorship in mathematics was informed heavily by my ongoing experience in this semester's 280 course. My description came off sounding a bit clinical in comparison with Thibault's downright hortatory "manifesto" (his word, not mine) on self-authorship in theater. Echoing Goethe, he indicated the fundamental need for a student of theater to be true to one's self. Meanwhile Nola's narrative struck me as a bit more catholic and all-encompassing, with an emphasis on the mutuality of the relationships arising in Baxter Magolda's Learning Partnerships Model. I liked aspects of all three narratives. In discussing them, I found particularly insightful Nola's observation (as I described to her my experience of watching my older students interact with my younger ones) that Vygotsky's "zone of proximal development" is arrived at in the Math Lab.

I see the same dynamic in the conversations between the students taking part in our Math Problems Group (which convened a couple of hours ago this evening): the difference in ability between the weakest regular attendees and the strongest is noticeable but not overwhelming, and all of them possess the background needed to interact proficiently (if not fluently) with one another, yet a few have perceptibly stronger skills than their peers and often serve as coaches for the others.

Tonight I served up a particularly nasty Putnam problem from last year's exam (one that only a handful of the top solvers in the country scored well on), and I let 'em at it. It took 75 minutes to arrive at the rudiments of an argument, though by well before then they'd convinced themselves that they had the right answer. It was fascinating watching them at work, watching them scratch away on their paper, listening to them communicate with one another and share their ideas. Three of the attendees independently arrived at the same conjectural solution, allowing for minor variations on a theme. While Nadia continued to work on her own, Nikolas met up with Beulah and Simon and formed a consensus on a particular formula for the number we sought. Soon Nadia gave up on her computations and joined the others, and they spent another fifteen minutes clarifying their thoughts, and then another fifteen minutes spinning their wheels before we decided to table that problem and start another easier one, a simple problem on graceful graph labellings. As I suspected, this last problem only took Nikolas about five minutes to solve, and we ended the night on a high note.

Now?

I.

Am.

Tired.

Well...

...we'll see how the calc kiddoes are doing tomorrow. I've talked with a few of them about test corrections, including a couple more who agreed that it wasn't that hard an exam, they just had the mother of all brain farts last Thursday.

I'm not sure what it was about last week (something in the air?), but I don't think there was a single person worldwide who was in top form.

Except maybe Matt Ryan.

But that's a different story.

Anyway, before this becomes a football blog, I'd better call it a night.

I'll try to get another post in tomorrow to talk about seven gajillion and one ideas I got from Quimby in Fayetteville. I'd also like to talk about my interview tomorrow with one of the new Writing Center student consultants, the status of the Robert Moses Learning Circle I've put together for our department, the NSF grant I'm nearly done writing, and my final decision to run my upcoming graph theory course using the Moore method.

Stay tuned!