The importance of being earnest

Doomsday averted.

This morning's Writing Intensive Subcommittee meeting was wonderfully productive (we plowed through a TON of tasks), and the pre-meeting conversation I had with the Student Government Association (SGA) rep who's been in conversation with me for the past few weeks (let's call him Kenyon) was even more productive.

I think we're on the same page now. I had a bit of a "come to Jesus meetin'" with this young man, and we were both very honest and open about our concerns. I realized early on that he's more the messenger than the source, and that his intentions are good ones. "We have to be open with each other," I insisted. "We can't sneak around, we can't take part in romantic revolutions are crusades. We have a number of common concerns, I'm sure, and we can work on them together...if we choose to talk to one another about them." He agreed.

He sat in on our meeting, and though I think he's got a thing or two to learn about note-taking, I admire him for following fairly well the course of a rather convoluted proceedings. We hit everything under the sun, from the minutiae of WI proposal wording to the philosophical underpinnings of the WI mission itself...and faculty development and assessment in between. A real trouper!

We agreed by the end of the meeting that it would be worthwhile to establish some sort of "liaisonship" between SGA and ILSOC (or some of the willing subcommittees thereof) in order to open, maintain, and benefit from a dialogue between faculty and students on issues pertaining to ILS and other academic affairs which affect us all. He invited me to attend this evening's meeting of the Academic Affairs Committee of SGA (on which he serves, and for which he's been running his little end-runs).

So I went. I'm glad that I did.

The meeting, held in the SGA offices in the student union, was attended by six members of SGA and me. It was unassuming and informal, as Kenyon assured me it would be. The students took turns reporting on their progress on their individual "homework assignments" from the previous week. One had been sent to data-mine various sets of statistics concerning the ILS Clusters, in the hopes of finding correlation between students' choice of topical clusters and their majors. (Undoubtedly such correlation exists...and as it happens this is one of the students' primary concerns, to which I'll return in a bit.) Another reported on the SACS (Southern Association of Colleges and Schools, our accreditation agency) meeting he had attended. I commended him for his ability to bust out all of the buzzwords.

Kenyon discussed his meeting with me and his attendance of the WI meeting, and I took a moment to explain our feelings about establishing a "liaisonship" between SGA and ILSOC. I'm not sure that everyone at the table was sold about the efficacy of establishing such a dialogue, but one of the student leaders (the Vice President, Samantha), was totally on board. She pleaded vigorously and eloquently for our case, and I'm glad that she did. I think her advocacy helped the case considerably.

As the meeting went on I became a little more annoyed by the continued reluctance of the students simply to come out and say what concerns they were having, and it soon came to the fore why it is they have this reluctance. Historically, it appears, every time they've brought complaints to faculty, they've either (a) been blown off or (b) been told that they need "data" to back up their claims.

So they've been gathering data.

I let them know that they were likely talking to the wrong faculty back then, but that they should feel safe in talking to me and to the other members of ILSOC. At this time, ILSOC consists of very active, engaged, and motivated faculty who are heavily invested in meaningful interdisciplinary learning and fully committed to the spirit of the ILS program. They won't need to sell their story; we've bought it already, and we're eager to talk. I assured the students that we are the people they need to talk to. Samantha was resold, and once again Kenyon put himself forward as a liaison.

After the meeting I lingered a bit and talked some more with Samantha. At long last I learned a bit more about their specific grievances. For instance, it became evident that their primary concern with the LSIC Colloquia is strongly related to our own: uniformity of the quality of instruction across all colloquia. Knowing this, we can talk about it openly and brainstorm ideas together.

It also became evident that the students' primary concern with ILS Clusters is that students aren't getting enough incentive to be daring in their choice of clusters: because they're so pressed to finish their majors with the number of credit hours they're given (lest they pay egregious overage charges), they find they have to select topical clusters focused on topics cognate to their majors. These students would like to see greater incentives (more flexible rules for "double-dipping" courses? Elimination or lowering of overage fees?) offered to students to try out clusters more distant from the safety of their majors, thereby engaging in a richer interdisciplinary learning experience.

Honestly, this perspective is far more mature than that of many members of the faculty, who simply want to scrap the clusters altogether. (Admittedly, this contingent of curmudgeonly academic extremists is getting smaller each year, as the fogyish stalwarts retire one by one.) I was thoroughly impressed with the students' position, and I told them so. We can definitely work with them on this.

Ultimately, as I said above, I'm glad that I went to the meeting. A lot was accomplished, and I'm excited to see the directions in which this heads.

Before I go I should mention one more (not wholly unrelated) incident. Late this afternoon, while sitting in my office, I overheard a couple of my Linear students (sitting in the near end of the Math Lab) quietly voicing their frustrations about not being able to keep up in class because of the way we'd plowed through the definition and derivation of eigenvalues and eigenvectors. I guess we'd been moving a bit too fast. Although I felt a bit uneasy about admitting to my eavesdropping, I sneaked across the hall and joined in the conversation.

"You've got to let me know," I told them, "if you're having trouble with something."

"I'm just not one of those people who can pick it up really fast," one of them said. "I have to think about it and let it sink in before I understand it."

Although at first the conversation was a bit strained and awkward (I had been eavesdropping, after all), after a bit it warmed up. I agreed to keep tabs on the pace, and to throw in a few more examples and explanations here when needed. They agreed to let me know if things get moving too quickly again.

"I understand that you can't change the way you teach the class for just one person," the more outspoken student said.

"True," I admited. "That's what makes it hard, hearing, as I do, from all of you all of the time. It's awfully hard to teach a course at any sort of pace when I don't want to leave anyone behind. On the other hand, though, I can take your perspective into account and use it, along with everyone else's, to come up with a sort of 'normalized' perspective. If I only hear from the people who are chugging on ahead, I can't help but think everyone's all right with the way things are going. I need to hear from folks like you."

I know it took courage for them to have that conversation with me, and I'm really impressed with that courage. I told them how much I appreciated their earnestness and forthrightness. I think that conversation, a difficult one for both sides, was a fruitful one.

Students, please remember this: there's no shame in taking a little more time to learn something than some of your peers. It's okay to be confused. If anything, there's shame in not owning up to your confusion in the first place.

I guess the moral of the story (by now a twice-told tale) is: if you've got a tale to tell, tell it. Someone will be willing to listen.

How adults do it

I'm pissed.

One of my colleagues on ILS (Integrative Liberal Studies) Oversight Committee with me met with a student representative from SGA (the Student Government Association) about two weeks ago. He met with us because he "had some questions about the clusters [topically clustered courses] as they're implemented" as part of the ILS program. Lexi (my ILSOC colleague) and I left the roughly half-hour meeting suspecting that the kid was looking for some dirt.

Since then it's become apparent, from the minutes of their meetings and various other campus goings-on, that SGA's sending its student representatives to a number of faculty and staff on campus trying to get information on the following components of the ILS program: Humanities, the LSIC colloquia, the ILS Clusters, and the Writing and Diversity Intensive programs. The minutes I've read make it clear that the students are hoping to bring about change in these components of the program. The minutes don't make clear exactly what issue SGA has with these components.

This is what's pissing me off.

The child Lexi and I met with (I'm sorry for the condescension, but that's how he acted, and not at all like adult he was trying to be) had an obligation to speak up and be forthcoming about his purpose for meeting with us. He had an obligation to let us know that the student body has concerns about various aspects of the ILS program, and that they would like to dialogue with us about possible ways to ameliorate any shortcomings they think need addressing.

He was not at all forthcoming about his motives, even as Lexi and I pointed the way to every bit of information about the ILS program that SGA could ever want to read...even as I invited him to the next meeting of the WI Subcommittee (we meet tomorrow morning; I suspect I'll have something more to say after that meeting) and said, in nearly these words precisely: "we have nothing to hide. Every step of the process is transparent. I hope that you'll take a look."

Apparently there is to be no return of the favor.

Pardon my French, but let's cut the juvenile, passive-aggressive cloak 'n' dagger bullshit. You're adults now...or at least that's how we'd prefer to deal with you. Institutional change is not best affected by sneaking around, "gathering evidence," and dramatically confronting your opponent with that evidence in a highly public place. Rather, such change is affected by openness, plain-dealing, and compromise. If you have a problem with the system as it stands, tell us. Tell us, so that we may meet and discuss it. So that we may meet and hash out a plan to deal with your concerns. So that we may make our concerns and motives plainer to you, in the hope that you can see our points of view as we begin to see yours.

Why all of the secrecy and sneaking around? Maybe they're suffering from a romanticized notion of "fighting the good fight" or "leading a revolution"? Committee meetings might be boring as hell, and change at the university level may be glacial in its slowness, but the compromises hammered out in such meetings are far more lasting than ramrodded fiats and ultimatums.

Look, I have problems with the ILS program. It's not perfect, and I can admit that. It's a system designed by dozens of people, overseen by other dozens, and implemented by literally hundreds. Though I feel that for the most part it's working quite well (better than comparable programs at other universities), it's got its flaws.

What do I do about those flaws? I meet with my colleagues, I brainstorm ideas of ways we might address those flaws, I work with my colleagues to workshop a few of those ideas into more robust plans of action, and I help to implement those plans. In other words, I work with everyone else on campus together in order to fix the flaws I and others might see in the system.

That's how adults do it.

To be continued, I'm sure.

Philosophy 101

Well, it's that time again...for one reason or another, I've found it necessary to update my "teaching philosophy," that nebulous document no one's really sure how to write.

I find that the older I get, the less patience I have for philosophies which read like litanies of pedagogical tricks, no matter how clever those tricks are. I see no reason anymore to brag about "use of technology" or "co-curricular activities" or even "inquiry-based learning" in my statement of teaching philosophy. It's not the place.

For what it's worth (I've nothing to hide), here's my current philosophy, version 2010.1.2 (or thereabouts):

My philosophy of teaching, like my teaching itself, has undergone many changes in the years past. Like those of many novice teachers, my earliest philosophies were tailor-made to fit one or another job description and often relied on catch-phrases like “use of technology” and “collaborative learning.” Embarrassingly recently my teaching philosophy read like a behaviorist’s manifesto, a long list of actions typically taken by me or by my students, actions which merely indicated a certain philosophy at work without getting at the heart of that philosophy. As I’ve grown as a teacher (and scholar of teaching and learning) I’ve been better able to tease out from those actions their essential qualities in order to understand why it is I do what I do, and what it is I hope my students will do with me when we work together in and outside of the classroom.

As a result my philosophy has become more streamlined and systematic, and while it is on its face less “practical,” it still has profound practical implications when put into action. It is no longer so describable by a few pages filled with phrases like “co-curricular activities,” “writing-to-learn,” or even the loftier “inquiry-based learning.” Though all of these feature prominently in my teaching, none is the prime mover, none is the ultimate reason why I do what I do.

If not these things, then what is it that guides my teaching?

My primary goal is to address my students’ affective needs as well as their cognitive ones. Put simply, I believe, and the literature on teaching and learning bears me out, that how my students feel about what they do is as important as what they do in the first place. Students who feel confident about their abilities will pursue greater challenges and aspire toward greater goals than students who lack that confidence. Moreover, confident students will strive toward their goals far more effectively than will unconfident ones. Therefore, instilling a sense of security and confidence in my classes, and in all other interactions with my students, is of paramount importance.

To help my students feel secure and confident, I aim to create a safe learning environment characterized by openness, honesty, and friendliness. Such an environment cannot help but lead to a shared sense of respect and understanding. Such an environment relies on a commitment to clarity and transparency, and this I keep in place by maintaining open lines of communication. I go to great lengths to make sure that my students are always able to get in touch with me in a timely manner, and that the concerns they raise in their correspondence will be met with legitimate concern and care. In this way open communication fosters a deep sense of mutual trust.

Once I have my students’ trust, and once they are convinced that they have mine, we can work more effectively together. But working effectively requires that we have a shared sense of purpose, and I cannot presuppose that my students will come to class with the same purpose I will. Some work is needed on all of our parts to align our purposes. I spend a great deal of time early in the semester learning as much as I can about my students and their academic and life goals, so that I can better make the case that what we will learn together will be useful to them: every aspect of every subject I teach I try to imbue with relevance and applicability. Here my aim is to instill in my students an intrinsic desire to learn, rather than an extrinsic one, for their learning experience will not fail to be a richer one if they see how what we study is inherently useful to them. Put another way, it’s better that my students see how useful a subject is, in actual practice, than that they merely be told of its usefulness, in theory.

Once students are intrinsically motivated to learn, it’s up to me to place before them challenging opportunities for deep learning. These opportunities are often driven and directed by the students themselves. While it is difficult to characterize broadly the activities in which my students take part, they are as a rule

• active and not passive,
• guided by discovery and not prescription,
• concept-driven and not computational, and
• authentic (that is, "real-world") and not artificial.

In every one of my courses, from the first day of class, my students do rather than see. They are encouraged to cooperate and collaborate, and competition of every sort (including for grades) is minimized. I prod them to be skeptical and to ask probative questions, like “why should I care?” and “why is that true?,” and I encourage them to answer these questions themselves before looking to me for a response. With a bit of practice, they end up learning more from each another than they learn from me.

If I am successful in my efforts, my students soon become (often very literally!) the authors of their own knowledge. They allow themselves to become the experts and are no longer beholden to an intermediary who stands between them and their engagement of new ideas.

Of course, no two students are alike: some develop more quickly than others, some are more or less astute, observant, or mathematically apt. Moreover, students at varying stages in their academic careers exhibit a broad variation in maturity and intellectual development. When put into practice, my philosophy must take these variations into account, and I do this by adopting a sort of “dialectical” approach to teaching, engaging in frequent conversations with my students about the pace with which we proceed and the direction in which we travel. What do my students need from me, as individuals and as a class, this week, on this day, at this moment? I can never plan more than a class or two in advance, knowing that on any given day we might linger longer than I’d anticipated on a surprisingly challenging concept, or that an interesting conversation will spiral outward into an engaging and enlightening example.

For the same reason, no two iterations of the same course will look at all alike, and no amount of experience or preparation will fully ready me for the next time I teach a course. Herein is the true challenge my philosophy must face: meaningful teaching is time-consuming and work-intensive. It requires constant vigilance and refinement, because midcourse adjustments are almost unending. It requires humility, and a rather thick skin, because mistakes are often made, and it’s often hard to not take them personally. Finally, it requires seemingly limitless patience and flexibility, because to teach well I must be ready to work effectively with every sort of learner I can imagine…and a few I cannot.

Why work so hard?

I can think of no better way to affect the world in a positive manner than to teach, and to teaching meaningfully. I can think of no better way to spend my time. Indeed, I feel blessed that I get paid to do something which I do well and which I love to do anyway. When I reflect upon my experiences with my students, I realize that I truly am one of the luckiest people on Earth.

Workshop Idea #483 (not really)

I promised that I'd soon share the faculty development workshop idea which came to me during the Tuesday evening session at this year's CWPA.

Scene: lunch. We're at the outset of a half-day workshop featuring a short keynote speech. The speaker finishes her half-hour spiel, the congregants put down their half-empty bags of chips and wipe their mayo-covered hands awkwardly on their blue jeans or tablecloths.

"All right, everyone, groups of three." At each table the six people sitting there split into two groups. While this goes on one of the organizers walks about the room with a bucket full of folded pages. One at a time one person from each group of three picks a page from the bucket. On it is given a writing-related scenario of some sort, a short case study.

"At the end of the final stage of a multistage assignment three students come to you and tell you they can't finish their final draft because etc. ..."

"Your two colleagues who are helping you complete a reading of your department's senior portfolios fall into a heated argument about an apparently irreconcilable difference in grading philosophy. They ask you to mediate etc. ..."

I'm not claiming to have a dozen of these at the front of my mind; a book like Chris Anson's WAC Casebook would make a great source for these scenarios.

Each team now has half an hour to come up with a proper response to the issue raised in their scenario. At the end of that half-hour, the teams will take turns, using five minutes to explain and interpret their scenario (or even to act it out!), and another five to resolve it. Each resolution will be followed by a brief discussion, and after four or five resolutions there will be a break during which those who've not yet presented may reflect on what they plan to say.

Could be fun, relevant, and meaningful, all at once.

I'd like to do this, I think.

Bragging on my students is a full-time job

Before I scooted off to the 2010 Carolinas Writing Program Administrators conference (also known as "the best damned conference on the planet") at Wildacres the past few days I entrusted my Linear students with a task to perform in my absence on Monday, and all signs show that they pulled it off wonderfully.

Their job was to meet as a class, brainstorm topics from linear algebra which would be placed under broader "general headings" (also brainstormed), and assign themselves, in whatever way they felt effective and appropriate, to teams each of which would be tasked with writing a "section" of a review manual on one of the general headings decided upon earlier.

Apparently Ino, never one to let chaos cramp her style, enlisted Iris's help in leading the class through the brainstorming exercise, and they had it all done in short order. She later e-mailed me the list of headings, each with three or four students assigned to it.

I'm delighted that I was able to trust my students to meet without me and get the job done, and I'd like to think that the effort they showed in finishing this job was payback to me for showing them that trust in the first place. I think there's something to be said for the benefits that mutual trust can bestow both on teacher and on students. I trust this particular batch of students fully. They're great.

As I hinted above, I got back in town early this morning (in plenty of time for my 8:00 a.m. Calc I class) from CWPA. As ever, it was a fantastically productive experience. This year's get-together wisely eschewed rigid structure, offering instead ample opportunities for participants to meet in whatever groups and subgroups they felt they needed to.

I spent Tuesday morning talking assessment with folks from Elon, Mars Hill, and Charleston Southern. Our conversation helped me to tease out the issue at the root of what was puzzling me most about our current writing-intensive assessment plan. Namely, what do we do with the assessment data once we've got them? There must be more in store for them than a place in a forgotten file cabinet or a SACS reviewer's dossier. Yet for assessment data to mean much more, they must be highly esteemed by the faculty to whom they're given.

I realized about halfway through the day that faculty need to be helped to see the intrinsic value of both the assessment data and the assessment process itself. If faculty can learn to see assessment as a formative, reflective, and dialogic process involving many inter-interested parties, rather than as a summative, unidirectional, and punitive process instituted from above, they may come to understand its usefulness. As I said to a few of my colleagues at CWPA, it would be great if we could get them to the point where they'd say, "hot damn, data!"

I can dream, can't I?

Although I'd like to think that faculty development workshops can solve all problems, it would be great to come up with a more exciting means of changing faculty perceptions regarding assessment...any thoughts?

Speaking of workshops, I've got a great idea for what I think could be a fun faculty writing workshop, but I'll save that for another post. Now, it's bedtime: tomorrow's another long one.

Live, from Wildacres, it's 2010's CWPA!

Yes, it's that time of year again, folks. I find myself up in the woods-covered mountains of Western North Carolina, spittin' distance from the Blue Ridge Parkway, hanging out with a gaggle of composition theorists and rhetoricians with only nominal control of their drinking impulses.

Seriously, these are wonderful people, and as was the case with the previous two years of this shindig (my first time was in 2008), by the dawn of the first full day (now) I've already had a dozen wonderful and insightful conversations. I've gotten a few pointers for my book from the point of view of my friends in writing centers and first-year composition programs, having asked several of them pointedly "so...what would you want to get out of such a book?" I've gotten a few nibbles of interest for the poetry conference, including a few from the writers' workshop that's going on across from us in the other lodge. Mostly, though, I've been talking assessment. (w00t.)

Assessment is the theme of this year's get-together, and we started things off last night with a keynote presentation from none other than Chris Anson, writing assessor extraordinaire. Of course, ever in teaching mode, all through the conversation he instigated I thought not only of the programmatic assessment we're undertaking with the Writing Intensive program but also my own assessment of my students' performance. Am I assessing what I claim to value as learning outcomes for my courses? Am I applying suitable methods in order to help my students achieve those outcomes, both at the micro (assignment) and macro (course) levels? And are my outcomes measurable, reasonable, and meaningful ones in the first place?

I think that the answer to all three of those questions, fortunately, is "yes." I feel confident that I'm doing the right thing, more or less, by this point in my career.

But I could be doing better, and after last night's conversations I am more firmly convinced than ever before that portfolios are the right way to go.

I was complaining to my colleagues Cammie and Nico (both of whom teach rhetoric at Western Carolina University) about how in mathematics assessment of student mastery is all too-often tied to completion of a particular course with a suitably high grade, with little behind that grade other than similarly high performance on exams and quizzes which essentially test rote memorization and unthinking application of various formulas and algorithms. For context: this followed a rather lengthy conversation stemming from Chris's presentation that began with his assertion that it was difficult to assess a student's knowledge of the works of Shakespeare by asking whether the student got a B or better in a course on Shakespeare's writing. Nora (from UNC-Charlotte) countered that such a measure could be an effective one, depending on what exactly you were measuring: it all depends on how it is that B was arrived at.

It was interesting to note that during that earlier conversation Cammie and Nico were musing about how nice it must be in mathematics, where quantifiable outcomes lie so thick you can't but trip over them.

No, portfolios are the way to go. I'm already so repulsed by assigning numerical values to single iterations of students' work that I don't know how much longer I can continue to do it. It almost made me physically ill yesterday to put numbers on the "final" drafts of my Linear students' papers on the geometry of linear systems.

What needs to be done next, if I plan on taking big steps in that direction? I need to convince my students that it's worthwhile and doable (I don't think this will be too hard a sell). I need to firm up each course's learning outcomes (which I already have for most of them) so that they're clear enough to explain to students and solid enough to be measurable. I need to make sure every assignment or activity I craft is explicit in its intentions (I'm already doing this). I need to more cleanly codify the way in which the students' portfolios would be put together, added to, and ultimately assessed.

As I mentioned in the previous paragraph, much of this I've already done. I just have to be more purposeful about it, take a deep breath, and jump.

Okay, the first bell rang about ten minutes ago...I should get ready for breakfast.

More to come!

No regrets

I've said a lot lately about the way Calc I has been going this term, and I've said relatively little about Linear, perhaps because I feel that course has felt fewer obstacles along the way so far. I honestly feel that Linear has been going more smoothly than just about any course I've ever taught. (Fall 2006 Calc II and Fall 2009 Foundations are possible exceptions.) And I'm having a blast in it.

What's made it work so well? The high quality of the students, their outgoing nature, their friendliness, their willingness (nay, eagerness) to work together both in and outside of class...and, I'll own up to it, the course plan I've laid out is working very well.

I'm never planning too far ahead in that course. Rather, I'm responding to the way the students handle each new activity I give for them. If they need more time, we slow down; if they're bored, we speed up. More importantly, perhaps, no activity follows another without a reason for doing so. We introduced inverses because we needed them to solve a particular problem, and we introduced the determinant of a 2 x 2 matrix for the same reason. We defined matrix multiplication the way we did because it made sense to do so, not because the textbook told us to.

Moreover, I've avoided technicalities where I feel those technicalities tend to swamp out understanding and intuition. For instance, without knowing it, per se, the students have now worked with bases, matrix linearity and singularity, and Markov processes, generally without explicit mention of those terms. They don't yet know what a vector space is, nor a linear transformation, yet they do know how to apply the techniques of linear algebra to solve nontrivial problems in graph theory and geometry, and they have robust intuitive understanding of those problems, as well as the nature of linear equations and their solutions. I remain convinced that now, as we're finally getting around to proving conditions for singularity of a matrix (still without using that term), the students' understanding of those conditions is so much deeper than would be the understanding of a typical student by this point in the semester.

I do not regret the emphases I've chosen to give in this class. I hate to brag, but I've got to say that though we've not "covered" a number of the terms and techniques (for everyone's sake, do not focus your attention on the mechanics of row-reduction and matrix inversion for two or three weeks, people!), I'd bet that the students have a much richer understanding of linear algebra than would students in most Linear courses by this point in the term, and I'd also be willing to bet that that understanding will last, too, and not disappear immediately after this semester's over.

Any takers?

Mystery...solved?

I have a conjectural hypothesis regarding the stronger overall performance by my 8:00 a.m. section. It hit me this morning as I was loitering in the Math Lab about a half hour after class.

Around 9:30 or so, there were seven or eight members of that morning section hanging out in the Math Lab. Several of them stuck around for a couple of hours. This was by no means exceptional behavior: several of them (some of the strongest students in the class, in fact) often spend a couple of hours in the Math Lab after class. Almost every day.

My hypothesis is that after they finish class at 8:00 a.m., many of the students simply have nothing else to do for the next few hours, so, having already dragged themselves out of bed, they figure they might as well get some work done. To the Math Lab they go!

There could be something to this...

Clarification

As I was falling asleep at faaaaaaaaar too late an hour last night (technically this morning...aaaaah, bowling night!), I felt a twinge of anxiety over something I'd written in my blog yesterday. I want to speak briefly to that something.

I realized that both in class yesterday (twice!) and then in my last post here I really gave it to that one response: the "0, 1" answer to the homework question on last week's problem sets. True, the answer is a pretty awful one, but what I should have made clear is that though the answer is awful, that says nothing about the talent or intelligence of its author.

I realize that most of you (my Calc I kiddoes) have probably never been asked to write in complete sentences in mathematics before, and most of you are trained to think of "writing" and "math" as two ends of an academic spectrum. (I'm addressing these issues in Chapter 2 of my book.) Therefore I understand that there's a good deal of inertia you're trying to overcome as you're moving toward writing more robust responses to my homework questions.

I appreciate all that you're doing to get things moving in the right direction. All of you, from the most experienced "math writers" to the least, are intelligent people, and I want to make sure you all know that there's a difference between a lousy answer and a lousy mathematician. We all give the former from time to time, but that doesn't mean that any one of us is the latter.

See you in class!

You complete me

I had a blast in today's Calc I classes: students were engaged and alert, and eager to follow up on some of the missteps made in The Clock Problem. The few students I've talked to who missed the boat on that project were more than happy to make up for it and grateful for being given a chance to revise and resubmit. I look forward to seeing their recovery!

I spent a few minutes at the start of both sections drawing a big fat ol' line between the following two solutions I received to the problem "Find the number of local maxima and local minima the function f(x) = |x| has":

1. "The function f(x) = |x| has no local maxima and one local minimum, at x = 0."

2. "0, 1."

Though technically correct, the second response is dramatically inferior to the first: the first makes sense even when taken completely out of context. More than simply correct, it is complete and perfectly composed. It could appear in a textbook, expressing as it does, in a clear and unambiguous fashion, a true mathematical fact. One doesn't need to know that it was written in response to a homework question, for its truth transcends that humble context. From a practical standpoint, this solution could be used as a useful study tool later on, even without the question which prompted it.

The second solution, on the other hand is practically meaningless.

I asked the students whether they would dare to hand an assignment into their instructor of their LANG 120 (first-year composition course) which did not entirely comprise complete sentences. Predictably, they shook their heads.

So why shouldn't they pay the same respect to their math instructor? After all, aren't they using writing for the same purpose here, namely, to convince, and to communicate?

Moreover, it hit me this evening what the most profound philosophical difference between the two solutions above is: while there's no "movement" in the second solution, the first moves students a great distance, from being consumers, merely reacting to a stimulus given to them by their instructor, to being authors of their own truth and knowledge. The simple act of creating a complete sentence (expressing a concomitantly complete thought) transforms the student's role from a passive one to an active one.

I'm looking forward to tomorrow. I feel like this semester is finally getting into a groove. Stay tuned!

Rediscovery

I'm about 10 hours into an estimated 15 total hours of grading this weekend, and I'd like to pause to make the following observation (I know I've made it in this blog before, but I can't seem to find it in an earlier post), which I rediscover every time I teach Calc I in a Fall semester:

Almost without exception, an older student (a junior or senior, or a nontraditional student), even one who is not a math major or even particularly mathematically inclined, will outperform even the brightest and most math-literate first-year student.

Why?

It's simple: lengthier life experience, superior time management, and stronger study skills.

By the time they've finished a year or two of college, or after they've had several years of real-world experience, students have (by necessity) developed means of managing their time. Some (most?) of my nontraditional students are holding down 20-to-40-hour-a-week jobs, taking care of families, sometimes large and extended ones, and somehow keeping up with one or more difficult college courses. (To my freshmen: if you think you're busy, think again. As busy as you feel you are, I'll tell you this: you're not. You'll find that out in a year or two, trust me.) To do all of this they've got to have some way of budgeting their time, and they've got to be serious about their studies.

They do, and they are.

This semester's no exception: I've got several nontraditional students in my morning section of Calc I, and they're performing wonderfully. Not only are they doing well on all of the assignments, but they're clearly grasping the concepts and challenging themselves to really learn them rather than simply memorize a couple of formulas and move on. I'm immensely proud of them all.

I'd like to give a little speech to my first-year students (I know a few of you are reading this blog, and I hope you'll take heed...and I hope you'll tell your first-year friends what I've said).

Ahem...

...On average, the "big kids" are doing much better than you are. This isn't surprising, because it's nothing new: they always do. It isn't because they're smarter than you are. (They're smart, but you're just as smart.) It isn't because they've seen this stuff before. (Generally speaking, you all have more, and more recent, experience with calculus than they do.)

It's because they know that it takes a little work to do well, and that it takes a little dedication. That it takes a desire to actually learn rather than to simply fill a seat and get a grade. That it means taking an active rather than a passive role in their own educations. That it means managing your time, starting early, and earnestly seeking help when it's needed (by and large they do; by and large you don't). That it means working for a few hours sometimes when you'd rather be playing instead.

They believe me when I say I want to see complete sentences, when I say I want to see your work, and when I say that radicals are better than decimals. And they give me those sentences, that work, and those radicals, not because I asked for them but because they realize why I asked for them in the first place. They produce homework and papers worth reading, worth keeping, worth studying from, worth not throwing away or losing under your bed.

I'm not saying all of this to make you feel bad, but to point out that no matter how well you're doing you can do better, and I hope that you do.

You can get started sooner on the homework, and you can take care to produce nicer drafts. You can take the lead in groups activities, and you can dare to ask and answer questions in class. (Do you notice who's doing most of this right now?) You can take the time to write in complete sentences, to double-check your graphs, and to use your notation clearly and consistently.

You can do better. You can do it. Give it a shot. I'll always be here to help you, and I'll be cheering you on every step of the way. I've got your back. Let's do it.

What a difference a day makes

A good night's sleep and a tall stack of calculus papers later, and I'm feeling a bit better.

This morning's chore was to respond to the 40 calculus papers which I'd merely glanced at last night. (Then I'd done a spot-check to see which ones would need the most ameliorative attention.)

They were, by and large, wonderful. Some of the students had a hard time explaining the importance of finding a horizontal tangent (there was occasional "cart-before-horsing," when students said something along the lines of "we need to find the point where the function is minimized because that's where the tangent is horizontal"), and there were some minor slips in notation (like when students reused the name of the function itself, C(x), for the slope of the tangent line), but all in all the papers were solid. I'm requesting that four of the students send me their papers electronically, so that I can post them on the website as models.

I'm happy.

What of the other 12? I've decided I'm simply not assigning a grade to them. I've written something along the lines of "please come and see me so I can help you hammer this out." Most of them will, I hope, and once they've worked up a more complete solution, I'll respond to it.

It's one step closer to portfolios. I'll get there soon.

Quandary

About an hour ago I said the following out loud: "The last thing I want to do with these papers is grade them, yet the grade is about the only thing many of the students want to get out of it."

"By 'grade,'" I clarified, "I mean rate. I want to respond to them. I wish I could just bring the students in and talk their papers over with them, hand them back, and be done with it, maybe after one or two more rounds of revision."

Maybe I'll do that, after all. Maybe I'll move to a portfolio-style grading system right now.

I don't know.

I'm feeling somewhat cynical about my job right now.

Is the 12-15 hours I'm likely to spend in responding to students' work this weekend worth the reward I'll get for it?

For the roughly 80% of my students who clearly take pride in their work and give it all that they can and are getting a great deal of out of the courses I'm guiding them through, sure: the reward I get from them is a feeling of fulfillment, acknowledgment that I'm doing my job well, and that they're holding up their end of the bargain.

For the other 20%? I'm not so sure about that.

I've received 52 completed "Clock Problems" (the first written assignment of the semester for the Calc I students). Of those, 40 of them clearly put a fair amount of effort into solving the central problem posed to them, applying (with varying degrees of carefulness and correctness) the methods we've developed in class together for the past two weeks. The others...not so much. Of these 12, maybe half of them have some inkling of what it will take to present a reasonable solution to the problem; the other half are clearly out in the cold and have gained little, if anything, from the work we've done in class for the past two weeks.

On these 12 solutions I'm writing "Please come and see me at once: you can do much better than this, and I want to help you do so." I plan on offering them a chance to revise, and strong encouragement to do that.

I feel like I'm talking in circles right now.

I spent the afternoon at the writing across the curriculum workshop my colleague Betty Lou (of nearby Montreat College) and I organized (it was originally scheduled to run in January but was canceled twice on account of weather). It was a wonderful little get-together bringing folks from four different campuses together under one roof. The very convening of this group of people was worthwhile, and the conversations were enlightening and engaging.

The discussions about writing-intensive courses I shared with my colleagues at the workshop helped me to realize how leviathan is the task I've set out for myself: in teaching both Calc I and Linear as though they are writing-intensive courses, I'm effectively teaching writing-intensive courses with an enrollment of 102 students right now.

It's no wonder I'm tired.

Would I be happier teaching at a school where I'd teach two courses per term, each capped at 20? I could make use of every problem-based learning, inquiry-based learning, application-based learning, discovery-learning, writing-intensive, student-centered teaching technique I'd like to, and they'd all be effective, simply because the classes would be of manageably small size. And I wouldn't drive myself insane in teaching that way.

I'd find that sort of opportunity at Bucknell, or St. Olaf, or Carleton, or Harvey Mudd. And the students I'd be teaching wouldn't all be working 20-30 hours a week, would likely be more intrinsically motivated, and wouldn't need as much coaxing and cajoling to get them on board with my methods.

Then the populist in me kicks in and says "don't the students who can't afford to go to such schools deserve a crack at learning through the same techniques?"

And I am where I am again.

I feel like I'm just talking in circles again.

I'm going to stop for now, before I begin making even less sense.

I'm going to write "please come and see me" a few more times, and then relax for the night.

Here's to a more upbeat tomorrow.

Feedback so far

It's been a few days since I put a "Suggestions" envelope outside my door for the Calc I kiddies to use as a means of providing anonymous feedback on how the class is going.

So far, here's the feedback I've received:

1. Candy and soda!

2. More donuts π

Stay tuned.

Peer review review

Today's meetings of my Calc I class are devoted to giving the students a chance to conference with the folks who over the past weekend performed a peer review of their work on the first class project, The Clock Problem (an optimization problem involving an idealized cost function).

These student meetings this morning, by and large, were brief, but they seemed amicable. I emphasized, as always, the need to be respectful and helpful in providing feedback to one another (it's as pointless to say "good work!" as it is to say "this sucks!"), and I hope that emphasis paid off. We'll see how it goes in the second section, which meets in under an hour.

I'm curious to hear others' thoughts on peer review: students, if you're in my class, drop me a line in the comments section and let me know how you think this particular peer review activity has gone (has it helped? Would you have structured it in a different way?). Other folks: if you have any insights on peer review in mathematical fields, please let me know. I've done a bit of it in various courses, but am always looking for new ideas.

Humbled

It's always humbling to get good (read: "thorough" and "direct") constructive feedback.

Like the feedback I just got back on my first draft of More Than Numbers's intro from my consulting editor.

I plan on using my experience in getting this feedback as a teaching tool for all of my classes: "you think you've got work to do?"

An observation and a question

Observation: every one of the students in my morning section (8:00 a.m.) of Calc I submitted homework (which is graded) this past Friday...that's 32/32. Four students in my afternoon (12:45 p.m.) section did not submit homework...that's 30/34. Though both sections have stellar students, the homework completed by the morning section is also decidedly stronger than that completed by the afternoon section, on average: roughly 84% to roughly 70% so far.

This is not the first time I've taught two sections, one early, early morning and the other later in the day, and found that the morning section's students outperformed the later section's.

Question (two-part): Is there really something to this observation?...and...if there is, why the discrepancy?

I suspect that perhaps the folks who sign up for an early-morning class in the first place are going to be the type of folks who have the extra drive and determination to stay on top of things and see them through. Maybe there's something more, though.

Thoughts?

Why I teach the way I do

So I'm already having a pretty good day (making progress on Chapter 3 of my book, getting great ideas to use in Linear Algebra, enjoying working with a few of the Calc I students in the Math Lab), and along comes an e-mail that pretty much made my week.

To all of those who are reluctant to make the switch to student-centered, problem-based learning, behold the benefits:

"So I just sat down to finally ponder #4 and as I was drawing out a graph, or rather trying figure out which graph I should draw I had one of those major AHA!! moments. The average velocity calculation is the slope of a secant line to the graph s(t)=4.9t^2 !!! I love it when things start to fall into place, especially mathematically. Honestly, I feel elated."

Honestly, I feel elated.