Thursday, December 30, 2010

In the interest of full disclosure

It's been a busy break.

Winter Break started, effectively, just under three weeks ago. In that time I've been almost completely submerged in writing theory and pedagogy, hard at work on my book. I've written about 17,000 words in the past two and a half weeks, so that I'm now roughly 60% done with a first draft of the damned thing.

I say "damned thing," but of course you know I'm loving every minute of it. Some paragraphs are slow going and take me an hour or more to kill, and others just fly from my fingers. It's all fun, though, and I'm excited about how the book's developing. I'm working away at several chapters simultaneously (I've started every chapter but the second and the seventh), and they're starting to grow and to grow together. By the end of next week I hope to have completed first drafts of Chapters 3, 4, 5, and 6. (That'll leave 1, 2, and 7 to go.)

While I'm at it, I'd like to give a massive shout-out to my writing colleague Libby of East Carolina University, who gave me fantastic feedback on my introduction, and excellent ideas for later chapters. She's the first of my colleagues in composition and rhetoric to read any substantive portion of the book, and her reading, and her response to it, has encouraged me greatly. Peace!

Unsurprisingly, in working so closely on the book I've begun to think about ways I can model to my students good writing and good writing process to an even greater extent than I already do. I'd like to offer them a window on my own writing process in whatever way I can. I'd like them to see rough drafts, wrong turns, dead-end ideas, reviewers' feedback, and revision, revision, revision.

Obviously they're not going to give a day-old donut about every single version I write of one or another dry math paper. But it can't hurt to show them some of my first-draft research notes that are little more than mathematical freewriting (see below), or the copious comments and suggested emendations my editor offers me on draft chapters of my textbook. If it accomplishes nothing else, at least showing these things to my students will show them that I too am human, that I too make (often very stupid) mistakes, and that I too am continually growing as a writer and a thinker.

Without further's a sample. Below are the first five out of nine pages of notes I scribbled out the other day as I was working on a paper dealing with the combinatorics of complex polynomials. In these notes, if you look closely (I don't recommend it) you'll see everything I indicated above: wrong turns, dead ends, and idiotic mistakes. (My Facebook friends may even be able to notice on one of these pages the (-1)(-1) = -1 mistake that was the focus of my Facebook status for several hours earlier this week.)

After all, I'm only human.

Coming soon: my thoughts on putting together my first-ever first-year seminar, on Ethnomathematics! This course begins in a little over a week, and I plan on writing my syllabus this weekend. Stay tuned...

Wednesday, December 08, 2010

On behalf of our esteemed colleague...

Now, I've had students get into the Newton v. Leibniz project in Calc I, but a trio of this term's participants took it to the next level.

Hermione, Nina, and Quinn, played the parts of Newton's colleagues John Collins, Isaac Barrow, and Henry Oldenburg, respectively, in my morning section. During the trial they filled the bill impeccably, offering accurate and convincing portrayals as they went, one by one, to the stand in defense of their colleague. Outside of class, too, they stayed in character as they wrote first-person apologia on Newton's behalf. Not only were these letters among the most creative and clearly-written responses to this exercise I've ever received from students...they were also rendered in startling form.

Executed in three distinct antique hand-like fonts (including "Emily Dickinson," modeled after the poet's actual handwriting) upon nine sheets of artificially-aged paper, the letters come to life in striking fashion.

Gimmicky? Perhaps, but cleverly so! The air of authenticity this medium lends is simply marvelous! See for yourself; here's Collins's letter:

The letters themselves delighted me (especially as I found them waiting for me in my office at the end of a particularly long workday), but more delightful still is knowing that the students had gotten this into the project.

Here's Oldenburg's offering, in bold diagonal strokes and terminating in a huge Hancockian signature:

Barrow's script is smaller and more timid, becoming the sort of man who would cede his chair as Lucasian Professor at Cambridge to his promising young pupil:

Who said there's no room for artistic creativity in the calculus classroom? Well done! (Incidentally, I did indeed get permission from my students to post their work.)

Tuesday, December 07, 2010

Making waves

I'm still unclear as to how it happened (something having to do with Reddit), but I'll soon be appearing in an article in The Pipedream, the student-run school newspaper at SUNY-Binghamton. One of their reporters, Zelda, got a hold of my recent post on in-class exams and found it interesting enough to start a conversation around it. She and I had a very pleasant discussion this morning about the pros and cons of various assessment techniques, including in-class and take-home exams.

She raised good questions, and I hope I gave good answers. Many of my responses were much in line with the ideas I've put forth in the above-linked-to post and in the comments to that post, but there was one point I'd like to elaborate a little more thoroughly.

At one time Zelda raised a concern an unnamed faculty member at her own university had discussed with her when asked about elimination of take-home exams. In essence, the concern is as follows: "getting rid of in-class exams might work well in upper-level courses where students are familiar with the great responsibility placed on them by being granted a take-home exam, but first-year students simply don't have the maturity or the sense of responsibility to realize the gravity of an act of academic dishonesty. How can these students be trusted to take on this responsibility?"

My response was largely in line with elements of the above post and of my teaching philosophy: if we show our students that we trust them and respect them as adults and as co-learners, they will have a harder time betraying that trust. "Won't there always be temptation to cheat, on the part of the students given a take-home exam?" Zelda asked in follow-up. "Indeed," I agreed, "but if they've been made to feel respected, understood, and appreciated, they'll be less likely to follow through on temptation."

To be sure, this establishment of mutual trust, respect, and understanding is not foolproof: there will always be those who cannot resist the temptation to cheat and who therefore abuse the trust being placed in them, but I'm not convinced that the relatively few cases of cheating one might encounter make it worth abandoning take-home exams.

Moreover (and here's the point I didn't make clear in my interview), how are students ever to learn about mutual trust, respect, and understanding if not given an opportunity to demonstrate that trust, respect, and understanding? Put another way, how else will students develop the maturity we ascribe to upper-level students but by demonstrating that they can acquit themselves in a mature fashion when given tasks like take-home exams in courses like Calc I? It seems to me something of a Catch-22 to say that students aren't mature enough to handle take-home exams, while at the same time they can't develop the sort of maturity we're looking for without being given such opportunities.

That said, and as I told Zelda this morning, I don't believe that take-home exams are appropriate in just any class: it takes pedagogical skill, time, and a considerable amount of practice and patience to design and develop the sorts of learning environments in which young students feel trusted, respected, and understood. It takes just as much skill, time, practice, and patience to develop the robust assignments and assessments that abrogate the need for in-class exams. The course I'm plotting is not for everyone, as I indicated to Zelda when she asked if I'd support a campus-wide "no in-class exams" policy. "No," I said. "Not only do faculty as a rule not like to be told what to do (a fact which would make implementation of the policy horrifically difficult), but the policy isn't appropriate for every instructor."

Anyhow, that's the scoop. I'll post a link to the article in The Pipedream when it appears. I'll also soon be posting some delightful documents three of my students produced as part of their Newton v. Leibniz project (I've just gotten permission from all three to post). Stay tuned!

Saturday, December 04, 2010

Observations: a follow-up

[Note: I first wrote much of this post as a comment in response to a comment one of my colleagues from grad school left on my last post; I thought it was strong enough to stand as a follow-up post in its own right. Meredith there left a link to an NPR story on teen neurochemistry some might find interesting.]

My colleague Meredith left the following comment on my last post:

A bit more about those non-traditional students. I would love to see a push on research on the neuroscience of the teenage brain and the "wisdom" of pushing ever-more high school students to take Calculus, at the expense of time spent on functions, trig, etc.

As I hinted in my previous post, it's really no surprise that the nontraditional students are outperforming the younger ones: it happens every semester. The relatively high percentage of such older students at UNCA is one of the things that makes our school such a fun place to teach. Because of the relative affordability of UNCA we get far more than our share of returning students (something one couldn't count on at schools like Davidson, Drake, or Bucknell), and I can't count the number of more mature students I've had whose presence has measurably improved the dynamic of whatever class they're in.

"Measurable"? This semester offers an extreme case: my morning section of Calc I has about three times as many "returning" students as does my afternoon section. Yesterday I noticed that every single one of the fifteen or so questions (every one of them reasonable and deep) raised by students in my morning section during our discussion of integrals was asked by a nontraditional student. Every one. They're simply less fearful of appearing "stupid."

It's this fearlessness that's helped deepen the level of the discussion that goes on in that course and that has ultimately, I really believe, helped lead to the startling difference in grades between the two sections: my morning section's overall course average is almost a full letter grade higher than my afternoon section's. There are other factors which contribute to this differential, to be sure, but it's difficult to discount the involvement of so many older, more mature students.

I absolutely agree with Meredith's placement of priority, and I'll bet she'd agree that we need to stop pushing kids straight into college after high school unless they're truly intrinsically motivated to pursue college coursework on their own. Some kids (even very, very smart ones) simply are not ready for college, and go there only because they've been told by their teachers, their parents, and their guidance counselors that it's the "next step."

Often, though, the best next step is to burn off some energy taking a full-time job for a few years, traveling (perhaps in service of a humanitarian organization like AmeriCorps or Peace Corps), or even joining the military for a tour or two. Though I'm not a fan of many of the things the military is called on to do for our country, I believe one of its most beneficial functions is providing order and structure to kids who sorely need order and structure in their lives.

Friday, December 03, 2010


A few random observations about my courses this semester:

1. Ever since our department implemented a writing component in the Senior Seminar, the overall quality of the students' oral presentations has gone up as well. Of course, this makes perfect sense for anyone who understands the concept of writing-to-learn: the students are using writing as a means of engaging meaningfully the topics on which they'll later present...moreover, they're making that engagement earlier in the semester than they normally would, asked as they are to complete a rough draft of their written report by the halfway point of the term, at least a week or two before they must present.

2. As in every semester that's ever been and every semester that ever will be, the "nontraditional" students in my Calc I class are outperforming the young 'uns. The more mature folks (juniors, seniors, and returning students) are the first and most frequent askers of questions and the strongest showers on exams, and they make up the majority of those still completing the homework regularly, despite the fact that it's been optional for a week or more by now.

Though there are a couple dozen Cs and Ds scattered throughout my two sections of Calc I, none of the 15 (out of 65) older students has a grade below a B going into the final exam. While they might not have quite as fresh of math skills (or even intrinsic mathematical aptitude) as do the first-year students, the older folks have vastly superior time management techniques, study habits, self-direction, commitment, and sense of purpose. Those skills and attributes (among the most important ones learned or acquired in college) help them to be, by and large, far more successful than their younger peers in most of their courses.

3. This semester's end-of-term presentations in Linear (the first three of nine given today) are far and away better than those the students put together for the course the last time I taught it...and they students have had less time to prepare them than they'd had the last time, too. Though this is a particularly strong class, I humbly give myself some credit for doing a better job overall in leading this course than I did last time. The exercises and activities I've put together are more authentic and robust, and the ways in which the various components of the course were fitted together simply made more logical sense.

Incidentally, one of the presentations will very likely lead to a rich research project. Ino and I have already discussed (at great length) our plans to parlay her team's presentation on linear analysis of nutritional data into a full-scale publishable project. The sky's the limit, and I'm really looking forward to directing what will likely be my first-ever truly applied math research project.

4. As early as I can next term I need to make a point of helping students get past their own pride when it comes to asking questions in class. Students (especially younger ones) often have a morbid fear of "looking dumb" in front of their peers, and of course asking questions makes one appear ignorant. (As opposed to remaining silent, which leads not to appearing ignorant but simply to being ignorant.) I've got to more actively help students overcome that fear.

To that end, I made some remarks in my second (the quiet) section of Calc I today that seemed to have a positive effect on students' querulousness: before proceeding from a specific example of a definite integral computation to a general one, I said something along the lines of "any questions before we move on? This idea is a crucial one, and it's very important that you have a good grasp on it before we proceed. [Silence. Pause.] How many people are there in here? [Count out loud.] Thirty or so? In a class this size, I fully expect more than half of you, probably 15 to 20 of you, don't understand something about what we just did. I expect that. Typically at this point half of the class doesn't fully know what's going on. I expect that. I'm sure you've got questions. I'm just not sure why you're not asking them. But I really can't do anything about it if you don't ask, so we'll just move on."

Move on I did, and within a minute or so two or three people who almost never ask questions posed a few. I was ecstatic! It's the first time this semester that some of these people have come out of their shells.

I've got to remember that trick.

5. I will never ceased to be amazed by how wonderful are the students I work with on a daily basis. Our students are incredible. They're intelligent, devoted, hard-working, honest, and down-to-earth. They're smart, sassy, funny, and fun. They're some of my favorite people on the planet, and I cherish every moment in working with them. I am the luckiest man on Earth for getting to do what I do, and getting paid for it.