Meditative

Origami is
a contemplative practice.
Fall is paper leaves.

Day One...Again...

Though I've been teaching at the college level for 15 years now, I've never been able to shake those first-day jitters. I have, however, gotten better at managing them and overcoming them and even having fun in the process.

This morning I taught my first Calc I class in...three years, I think? I believe this is the longest I've gone without teaching Calc I since I started teaching in grad school 15 years ago. That remove from the Calc I classroom, I believe, will help me come back to the subject with excitement and an authentic sense of novelty. I'm looking forward to a new format (for me), flipping the classroom and using computer-graded problem sets to give students practice in the basic computations they'll need to know.

Today we spent some time getting to know one another and reviewing some of the mathematical ideas leading up to calculus. I ended class by asking the students to write down (anonymously) any questions they might have about our class at this time...or if they had no questions, just to draw a smiley face.

Their questions, and my answers, are below, in no order other than the order I picked them up:

What's your biggest pet-peeve with your students? Disengagement. It really bugs me when students check out. Regardless of your skill level, give it some effort, please: we all have something we can give to the class, and we all have something we can take away.

Could we brush over some of the topics that were written on the board today, because even if I learned them, I need a little bit of remembering? Though we won't do much formal review in this class, we will do a lot of "just-in-time" review, meaning that as needed we'll brush up on important topics (e.g., trig identities, rules for exponents, factoring methods, etc.) when they come up. If you'd like more help, the Math Lab (located on the third floor of Robinson Hall) has many more resources and assistants who can help you, and you can always sign up with a private tutor. (You can find information about tutors from the Math Lab, too.)

I recently purchased a new Chromebook. Do you think all those softwares will be able to get on it? I'm assuming you're referring to Mathematica and LaTeX. I'm not sure about this, but it's a great question. I believe if you run a flavor of Linux as your OS on the Chromebook you should be able to find both of these applications by visiting the websites I've linked to on the class website. If you run the standard Chrome OS, though, I'm not sure. I'll look into this.

If we want to practice/review some old (algebra or similar) concepts, is there a site for problems? Good question. I believe the Math Lab staff can point you in the direction of some good texts and e-resources for review. Visit them!

Are there any other calc tutors other than the Math Lab? You can sign up with a private tutor, a list of whom is available by visiting the Math Lab.

Explain what the "lab" section of the class is. For arcane bureaucratic reasons, the department must differentiate between the "standard" class and the "lab," but besides the difference in time and place, there's no other distinction. We'll do many of the same things on all days. Just show up, relax, and have fun!

Can I eat breakfast in class? Yup. No worries! Just try not to spill anything or eat too loudly.

What is the meaning of life? Dunno. I missed that day.

:)

Q: What is beauty? What is truth? A: Type "graph " into Wolfram Alpha. I'll get on this at once and report back.

Ready for Calc! :)

How many chapters will be covered? We'll discuss the information addressed by the first five chapters of the textbook. I should point out, though, that I despise the term "cover" in reference to education. It corresponds to a very antiquated notion of pedagogy, in which the teacher "covers" material by talking about it in front of the students, thereby absolving the teacher of all guilt in case the students do poorly on an exam. "I can't believe they did so poorly on this question...we covered it in class!"

Is most of the reading done in class or not? Not. You will be responsible for reading the textbook on your own time. I would guess that a somewhat careful reading of most sections should take you about an hour, and we'll discuss roughly two or three sections per week. You do the math!

:-)

Can we review trigonometry? Pre-cal was a long time ago... See my comment above about "just-in-time" review. We'll definitely review trig and other tricky concepts as needed, when needed.

Ready for calc!

It's gonna be a good class, folks.

What's a guy to do? (A paean for laziness)

Halfway through our winter break I paused in my course preparations, panicking that I'd spent nearly all of my time planning my HON 479 course and had done nearly nothing to prep for Linear Algebra II. Though I had a rough framework for the course's structure (semiregular homework assignments, a few take-home exams, student-led projects, presentations, and discussions), I had almost no idea what content I would include in the course.

After a few moments (okay, maybe a few hours), the panic passed. I realized the futility of overplanning, a futility reconfirmed by the survey of my Linear II students' background I performed on Monday. The 23 students in that class come to me having taken Linear Algebra I from no fewer than five different faculty members in my department, as long ago as two and a half years back. These faculty include me and one of my colleagues who shares my penchant for student-centered, application-based teaching, a couple folks who typically offer a blend of applications and theory (one with a much more student-centered approach than the other), and a fifth who focuses exclusively on abstraction and theory and whose teaching style can only be described as "traditional." Needless to say, my 23 students come to me with extremely diverse linear algebraic backgrounds. It's unlikely that, beyond a few basic principles (row reduction, linear (in)dependence, bases, determinants, eigenvalues and -vectors, etc.) they all will have studied, they'll have any content knowledge in common. In the end there's really very little I can do to accommodate them all: no matter what static plan for the course that I could come up with, it would no doubt lose some and bore most of the others.

This realization was liberating. Instead of putting forth a particular course of study, I could let the students take the lead, offering them the chance to investigate topics in which they are interested, sharing their investigations with each other in the form of in-class presentations, discussions, and problem sets. I'm going to ask every student to take a turn, working with one or two of her or his peers, leading the class in the study of a topic of her or his choosing. For those who might not know what direction they'd like to head in, I made a list of potential topics, many of which likely made an appearance in some students' first-semester Linear I courses:

• orthonormalization methods
• orthogonal systems of polynomials (e.g., Chebyshev polynomials, Hermite polynomials, and Legendre polynomials)
• Gröbner bases
• LU factorization
• abstract vector spaces and modules
• network flow analysis
• unitary and Hermitian matrices and their applications
• finite element methods (e.g., in atmospheric science)
• Google's PageRank algorithm
• the basics of functional analysis
• linear codes and linear cryptography
• applications to differential equations
• linear programming (e.g., the simplex method)

To help everyone get to the point where we can approach some of these topics, I'm spending the first week or two on review, wherein the students are taking turns, in groups of three or four, presenting on the various "basic principles" I listed above. It's going well so far. "Is this useful at all?" I asked after a couple of presentations this morning. "Should we keep doing this?" There was almost unanimous agreement that yes, we should. So we'll keep it up.

How'll it go? Who knows? Not me. I'm excited to find out, though.

Day Two

Two days down. Day Two was a doozy.

The Honors Program has become a victim of its own success, in a way: so many students are now pursuing Distinction as a University Scholar that I'm finding it necessary to offer not one but two sections of HON 479 this term...and perhaps in (nearly?) every term for the indefinite future. Of course, by the time that I realized the need for a second section of the course (about halfway through last semester's advising period), it was really too late to find another instructor to teach that section, and besides, I'd prefer to have a single instructor for both sections, for consistency's sake. Of course, that meant that the instructor for the first section would also be the instructor for the second section, even if it meant (as it did) teaching a course over the normal load. Of course, that instructor is me.

Genius that I am, I scheduled the two sections to meet back-to-back, 100 minutes apiece with only ten minutes in between, every Tuesday and Thursday. Today was our first meeting. By the end of the first section my throat hurt, and by the end of the second I had nearly no voice: there are so many moving parts to this class that I've just got to spend much of the first class meeting pointing out just how all of those parts fit together and more in a meaningful way.

Throw in a minor student medical emergency, a pressing tech issue facing the school's student-run TEDx chapter (for which I'm the faculty adviser), various administrivia and bureaucratic bullshit, and a two-hour sojourn in Asheville Catholic School's gymnasium, where I helped a friend out as a middle-school science fair judge, and you've got a hell of a day. I'm sore-throated and brain-dead, and I'm tired as hell.

But I'm happy. I've got high hopes for this term. I feel like last semester gave me a good grip on 479, and I had a fantastic first meeting of Linear Algebra II yesterday (the 23 students in that class had five different instructors for Linear I!), a course which I'll be teaching from a nearly total project-based perspective.

Life is good.