At last!

The syllabi for my Spring 2010 courses have been posted on the now-up-and-openly-accessible course websites for Calc II and Topology. Supplementing these are the omnipresent links to my now-standard writing stylesheet, and for the budding topologists I've included a more-robust-than-ever introduction to LaTeX, now including a guide on inserting graphics files into LaTeX documents.

What about those syllabi? I've tried to take all of the feedback my students offered to me by e-mail (about 20 students eventually got back to me with their suggestions!) as I put them together, and I've tried to stay somewhat true to my goal of de-emphasizing grades (and thereby at least implicitly emphasizing collaboration), all while minimizing the "bureaucratic overhead" that was probably the number one complaint my 280 students had about their course this past semester, as measured by the course evaluation forms I got back a couple of weeks ago.

A few additional comments:

1. Rinse and repeat. I've backed off from explicit portfolio grading, but I've included the portfolio-esque unlimited revision-and-resubmission option in both courses: exams and projects in Calc II and everything in Topology can be revised and resubmitted as many times as the student would like to in order to craft an increasingly correct, complete, clear, and well-composed piece of mathematical writing. These systems of unlimited R 'n' R should help to cut down on the complexity of grading: if you're not happy with a grade, revise and resubmit. Again, if you'd like. And again. And again and again and again. I like this idea in theory and I'm excited to see how well it's going to work in practice.

2. Homework presentations. For the first time in two years I'll be teaching an upper-division course without homework committees, replacing the committees in Topology with "homework presentations" instead. This move too is designed to reduce "bureaucracy" by eliminating the deadlines associated with committee problem submissions and committee presentations, and it introduces a good deal of flexibility: as you can see on the syllabus, any number of students (including a single student!) may opt to join in on a particular homework problem's presentation, and there's only minimal bureaucracy involved in assessing participation in presentations. Speaking of flexibility, I believe the new syllabi offer tremendous...

3. Flexibility in assessment. Though there's no explicit mention of portfolios, in both courses I've left the exact manner of grading up to the students: in the first full week of class one of our tasks will be to decide, as a class, how each sort of assignment will be assessed, and with what weight it will affect students' grades.

4. Homework in Calc II. In Calc II, I will still be requiring homework, but at least half (probably more) of the homework will be handcrafted by yours truly, and I'll include frequent "short essay" questions demanding interpretation and explanation in addition to more traditional problems requiring no more than computation. Although I've still not made up my mind on the matter, I believe I'll grade the homework by giving each problem a number from 0 to 3:

0: no attempt, or a clearly half-assed attempt, made at solving the problem.

1: an honest attempt has been made, but the method of solution is not correct, and/or the student's work is very unclear and logically jumbled.

2: the method of solution is correct, but perhaps there are one or two minor computational errors; the writing is clear and well-composed, but insufficient explanation is given when explanation is called for.

3: solid; there are no errors (save perhaps a transcription error or a minor, minor error in computation), the student's logic is clear and straightforward, and all necessary explanations are sufficiently complete and are given in complete sentences.

It'll probably be a relatively easy matter for most students to get a 2 on a problem, but I'll warn them that getting a 3 is typically going to require careful attention to mathematical exposition as well as mathematical computation.

The syllabus for Calc II doesn't allow for unlimited revision and resubmission of homework problems, but if there's enough call for it, maybe I'll consider it.

5. The "textbook" assignment. The Topology crew is going to follow in the footsteps of this past term's 280 folks in writing a textbook for the course. As I did this past fall, I'll randomly assign topics from each "chapter" to students in the class. As in the fall, we'll meet up at "editing parties," but I'll be making these parties a bit more formal (going so far as to bring homemade goodies to them!) in order to encourage attendance. Finally, I'm taking La Donna's suggestion and writing a template the students will be asked to use in order to craft their textbook submissions; this will encourage at least basic typographical consistencies between the sections of the book.

Incidentally, La Donna and I will be meeting next week to hammer out some more edits on this past semester's textbook. I'm excited to see what we can make of it.

Before I go, I wanted to provide a link to the pedagogical Live Journal authored by my collaborator in crime, Cogswell. He and I will be sharing ideas with one another (often openly on our respective blogs) as we move forward with our courses this semester. I believe he's thinking about using the textbook assignment in his abstract algebra course, but is understandably skittish about the amount of work it might entail (he's the proud father of a brand-spankin'-new baby and has therefore clearly got other major commitments!).

More power to ya, Cogswell!

## Monday, December 28, 2009

### Spring syllabi

Posted by DocTurtle at 11:16 AM 2 reflections

Labels: Calculus II, Cogswell, course prep, MATH 192, MATH 431, Topology

## Wednesday, December 16, 2009

### Course coordination

Cogswell (as he'll be known here), a colleague whom I've met in various places (while a grad student at UW-Madison he spoke in the Group Theory Seminar at UIUC, and later I ran into him while he was doing a stint as a preceptor in Harvard's Math Department), has suggested that we put our heads together as we design our courses for the upcoming semester, and as we put them into action.

A lovely idea! We've got many of the same ideas regarding teaching, and we're eager to try out some of the same methods.

I think our collaboration will be a fruitful one, and I'll look forward to trading traveler's tales with him.

Posted by DocTurtle at 9:45 AM 0 reflections

Labels: Cogswell, course prep

## Friday, December 11, 2009

### Collaboration II: Electric Boogaloo

Today's collaborative extra credit session for Calc I is slightly better attended than Monday's was, with 26 people plugging away at problems while they partake of tooth-rotting holiday-themed treats, 7 more than the 19 who showed on Monday.

I'm not sure if this should be surprising: final exams end this evening, so in a way it's shocking to see so many people still engaged enough to make it to this session; on the other hand, perhaps enough people are desperate enough to do anything to add a few points to their grades that attendance is thereby boosted.

I don't sense desperation on most people's parts, though. Of course, everyone wants to get a good grade, but as a whole the students in these two sections of Calc I have done a good job in focusing their efforts on understanding and not on realizing largely artifical benchmarks of excellence. "I think our class already de-emphasizes grades," one of my students told me just a couple of hours ago as we were talking about my plans to further de-emphasize them next semester in Calc II. "I've felt all along that as long as I'm working on the homework and keeping up then I'm going to get a B."

"For the most part, that's true," I told her. "If you're doing what you need to to stay involved and engaged in class, and you're finishing the homework and doing decently on the exams, you'll get a C or a B, and most people in my classes get Cs and Bs. If you go above and beyond the basic expectations, you'll get an A, but you have to work pretty hard to get a D or an F."

I talked with her a bit about what a portfolio-based course would look like, and I admitted that I still haven't worked out all of the details for myself. "You have to turn in a grade at the end of the semester anyway, right?" she asked. "How would you do that?"

"It would be determined by looking at the products of the work you'd done throughout the semester and making sure that it demonstrates your achievement of various learning goals that we'd agreed upon in advance. Maybe we'd have said 'You need to be able to compute integrals of these types,' or maybe 'You need to show that you know some basic problem-solving techniques,' and I'd look to see that your portfolio contains assignments that show you can compute those integrals, and assignments that show you can solve some complicated problems."

I think we both ended the conversation with a better understanding of what our class would look like if I switched to portfolio-based grading, but I indicated that I'm still not sure that I'll implement that system in Calc II next semester. "I may try it out in my upper-division class," I told her, "and if it works out well there I'll contemplate using it the next time I teach a calc class of some kind."

But is this fair? I think now: one of the aspects of my own teaching I'm most critical of is the relative eagerness with which I apply techniques like inquiry-based learning and discovery learning and whatnot in my upper-level courses and eschew those same techniques in lower-level courses. To some extent this is understandable, since my lower-level courses are generally considerably larger than my upper-level ones, and such student-centered methods are much more easily implemented in smaller classes. Would portfolios present the same difficulties?

I don't think so. So why not go for it? Maybe I'm just clutching uncharacteristically conservatively at tradition, afraid to take that long, long leap all at once, preferring a few baby steps in its place.

I'll sort it out.

For now I'm going to sit back, close my eyes, and enjoy the pleasant hum of my students' voices as they puzzle through their extra credit problems.

Posted by DocTurtle at 11:47 AM 3 reflections

Labels: Calculus I, Calculus II, IBL, MATH 191, MATH 192, PBL, portfolios

## Tuesday, December 08, 2009

### Words to watch out for

Here are two tremendously off-putting words one might encounter in reading others' teaching philosophies: lecture (particularly when used without exception as a synonym for "class") and cover (or any variation thereof).

Posted by DocTurtle at 11:04 AM 4 reflections

Labels: bitching

## Monday, December 07, 2009

### Random Walk, Take One

I've got a few photos to share from yesterday's inaugural random walk, sponsored by Algebra al Fresco. In all we had 16 different people take part (never more than 13 at a time), including three members of the general community who found out about the event through local advertisements. Good fun!

First, a demonstration of some of the equipment we used to help us plot our course:

Four-sided dice led the way at each four-way intersection; traditional six-sided dice directed us (with two values for each route) at three-ways. Only once or twice did we have to flip a coin for "either/or" choices.

It being a rather chilly morning (about 30 degrees Fahrenheit at the outset of the walk at 10:15), an early consensus decision was made to stop at Izzy's Coffee Den on Lexington Avenue, where walkers warmed up and partook of toasty caffeinated beverages:

Out on the road again, we stopped at every corner to conference on our next move. One person would roll, and another one or two, before the roll, would call the directions, pointing: "1, 2: that way...3, 6: that way...4, 5: that way..." It was a genuine group effort.

I don't know why La Donna's laughing in the picture below, but she's always laughing at me about something. ("You look goofier than me," she tells me. She's probably right.)

Pauses, though by necessity frequent, were never long, and we were soon on our way again. Below, we stride confidently down College Street, Ino (one of three of my Calc I students to show up...way to represent, y'all!) leading the way.

By my reckoning we took 38 steps, visiting 22 distinct intersections. Of these intersections, 11 were visited once, 6 twice, and 5 three times (none more frequently than this). As anticipated we never strayed off of the map of downtown Asheville I'd printed out for folks to follow as we walked. The furthest-flung intersection we ever reached from our starting point at the southeast corner of Pritchard Park was eight blocks to the east, the roundabout at the corner of College and Oak.

I'd be happy to provide readers with further statistics upon request.

All in all, it was a great social event, a good way to get some exercise on a brisk and beautiful late autumn morning, and a fair bit of nerdy fun. For sure there'll be another in the spring!

Posted by DocTurtle at 3:37 PM 1 reflections

Labels: Algebra al Fresco

### Collaboration takes coordination

We're about 50 minutes into the collaborative extra credit problem session (and potluck) I'd planned in order to give my Calc I students some sort of group-learning activity for the final exam.

So far, they're working together wonderfully.

18 students showed up by the session's beginning, and after a few minutes to organize the foodstuffs and return graded assignments, I pitched to them three problems that are considerably harder than the problems appearing on the exam itself, in the hope that their collaborative effort would make the problem-solving process a relatively easy one. I've asked them to submit their own individual solutions to these problems by the end of the session in order to receive extra credit, but they're allowed to work together in whatever way they'd like to in order to prepare those solo solutions.

Immediately the student broke into three groups, of 3, 4, and 11 students, respectively. (One student has now left, bringing the 11 to 10, and another just arrived, bringing the 3 up to another 4.) At first there was silence as the students started feeling the problems out on their own. Within about five or ten minutes, though, the chatter began, and in the murmurs they made I detected clear signs of honest collaboration: some students understood one part of a problem, and others another. They began comparing their solutions and sharing their methods. One student went to the board to log a tricky computation he'd just performed. "Just so y'all know," said another student, "he's writing up the step in Number 2 where we got stuck."

Another student has now gone to the board to indicate an approach for the third problem.

This is working well!

If only I can get them to eat some more of the lovely guacamole and pumpkin muffins that a couple of the students brought.

Posted by DocTurtle at 12:20 PM 0 reflections

Labels: Calculus I, MATH 191

## Sunday, December 06, 2009

### The calm at the center of the storm

It's early, early, early on Sunday morning on the weekend between the last week of class and finals week. I've had a good stack of grading to get through, but I'm about two thirds of the way through that, and tomorrow morning brings the most recent Algebra al Fresco event, a random walk through downtown Asheville.

The semester's ending well. I've been worried about how my philosophical frustrations from a few weeks back might have been adversely affecting the students in my classes (especially Calc I), as I've feared they may have been buffeted by ever-shifting winds. But signs point to students' weather the storm rather well. One Calc I student spoke of being "inspired," and one 280 student said that, despite the difficulty and relative disorderliness of the textbook project, he learned "50% of his understanding of the concepts from the project." That comment, coupled with the envy my Spring 2009 students have shown for my current ones' getting a crack at this assignment, has convinced me that the same assignment, modified to fix the weaknesses it's shown this semester, should be a part of the curriculum for next term's Topology course.

I've still not put much thought into the precise structural details of that course, but it's starting to come together. It's not going to be as tightly structured, and it's going to be highly collaborative, and all assignments will allow unlimited revision and resubmission. Beyond that, who knows?

For now, it's late, and I'm off to bed. I hope to post again tomorrow with pictures of the random walk!

Posted by DocTurtle at 12:47 AM 0 reflections

Labels: Algebra al Fresco, Calculus I, Foundations, MATH 191, MATH 280, MATH 431, Topology

## Wednesday, December 02, 2009

### There's a first time for everything

I'm a pretty bad "sympathy crier": if I see someone close to me crying, I'm almost certain to join in.

I've had a good number of students cry in my office before (usually out of stress, sometimes out of disappointment), and there've been a few times when I've gotten in on the action.

But I'd never teared up in class before, like I did today when I was telling my 280 students what a wonderful job they've done on so many different things this semester, and how proud I am of them and how much I appreciate all of the work they've put into our course.

To those students: this class is one of the most challenging in our curriculum. I've asked you to prove deep theorems, and to perform complex computations. I've asked you to write proofs, explanations, dialogues, a textbook. I've asked you to review each others' work almost weekly, offering advice to your peers in both in-class presentations and written comments on each others' papers. I've asked you to master a technical typesetting environment, which is in many ways asking you to master a new tongue. You've done all of this willingly, eagerly even, without complaint. At all of these tasks, varied and difficult, you have succeeded beyond my expectations. As individuals and as a class, you've shone. You've soared.

Let me say this again, just so we're clear: I am proud to be your professor. It's working with students like you all that makes me love my job so much and makes me realize that I would never be happier doing anything else.

Thank you. I will miss our class tremendously.

Posted by DocTurtle at 3:41 PM 0 reflections

Labels: Foundations, MATH 280

## Tuesday, December 01, 2009

### Stress sets in

Yeah, we're almost done.

Mercifully, the semester will soon come to its end.

Signs of stress are setting in: even the best students in my 280 class are having a hard time picking apart the problems on the latest (and last) homework set, due on Friday, the last day of class.

Granted, the problems are difficult ones, built upon a vertiginous pile of definitions we've been amassing for the past several weeks: the set of functions from one set, S, to another, T, rests upon the definition of functions in general, which rests on the definition of relations more generally still, which rests on the definition of the Cartesian product. The notation for the formermost set is puzzling, too: since when does it make sense to talk about a set raised to the power of another set? And then you claim that the cardinality of this set is given by some exponential formula involving the cardinalities of the constituent sets?! Interrobang city.

It's late. These kids have given it their all, all semester long, and they're finally getting tired. It's taken them a long time to reach this point, but they're tired. I figure I'll give them a break: we'll spend a little while in class tomorrow planing down some of the rough spots in the hardest of this homework set's problems. They've earned it.

And on Friday, and during the final exam time slot next week, it's back to the book: we've got two more chapters to write and edit, and then the blasted thing is done. A first complete draft, anyway; two of the class's students have already expressed interest in putting some more time into the project over the break, polishing up the pagination, making consistent all of the notation and terminology, and putting together nice pretty pictures illustrating the concepts more amenable to visual expression.

Are these folks awesome, or what? I'm going to try to recruit as many of them as I can to attend the MAA Southeast Sectional meeting at Elon in March...and to try to get at least one of them to speak on the project there, with the others singing the harmonies.

We'll see how that recruiting goes.

For now, it's off to bed. Another long day comes tomorrow, but Calc I should be fun: Riemann sums await!

Posted by DocTurtle at 11:51 PM 0 reflections

Labels: Foundations, MATH 280