The end of the school year is always a hectic time here at komplexify, and so updates are always traditionally a little sparse. Nevertheless, partly to share ideas of pedagogy with the world’s wide web community (and mostly because my therapist says it’ll help with the stress), now seems like a perfect time to reflect on the academic year that was.
A snippet of a conversation I had with Professor X:
X: I think one of the problems with linear algebra is that it’s hard to get students fired up about it. I mean it starts of with elimination… how much more boring can you get.
Me: Well, the technique of elimination is, in fact, the single oldest truly algebraic technique in history. Ancient Chinese mathematicians called it the “Method of Rectangular Arrays,” and were using it before the birth of Christ. The technique is outlined in the “Nine Chapters of the Mathematical Art” — kind of a Chinese “Elements” — and it was pretty much identical to modern Gaussian elimination, except that the work was arranged in columns rather than rows.
Me: Yep. Moreover, some of these rectangular array problems include as entries some of the earliest uses of true negative numbers, long before they ever became accepted in the West.
X: You can take the dullest topic and dress it all up with interesting little details. You’re like the Martha Stewart of math.
When it comes time to teach calculus students about L’Hospital’s Rule, I require that students always indicate in their work every application of it, usually by writing a small “LH” over the equals sign, such as in:
Of course, when I was in high school calculus, my teacher would always refer to the application of to the evaluation of a limit as “hitting it with the L’Hospital stick,” such as in “What do we do with 0/0? We hit it with the stick!” I found this such a charmingly irreverent phrasing of the process that I myself say it in class quite frequently. The phrasing continues to be wildly popular with my students as well, though I suspect its popularity rests less on its charming irreverence and more on its suggestion of wanton violence directed against calculus problems.
It has also, unexpectedly, inspired a great deal of creativity from my students.
For example, last year one of my students at the top of her exam drew the following picture
and then proceeded to indicate every use of L’Hospital’s Rule not by the standard “LH” symbol, but by instead depicting a bat beating the living shit out of the limit in question, such as in:
I immediately fell in love with the symbol and continue to teach it to new generations of calculus students, with the proviso that, while inanely fun to draw, it is anything but accepted notation.
This in turn inspired a student this year to take the L’Hospital stick out of the airy realm of cartoon violence and into the real world of physical assault. Behold the L’Hospital Stick:
Check out the small differentiation operator at the business end of the stick. Thwack!
Not to be outdone, yet another student took the initiative to give the L’Hospital Stick an even cooler name, together with a professional looking logo to match. Check out the next it out:
Apparently, if my students don’t succeed in calculus, they have promising futures in graphic design, carpentry, and/or copyright infringement.
Of course, this year wasn’t just about the students being creative.
One of the most frustrating aspects of grading exams is the number of students who commit heinous acts against algebra over and over again, such as distributing a square root or a trig function, splitting the denominator of a rational expression, or making ghastly cancellations in fractions based solely on typographical similarities in the numerator or denominator. At faculty lunches, we math professors often joke that our grading time would be cut in half if we simply had a big stamp that read BAD ALGEBRA! instead of writing it out each time.
During my first year as a professor at Komplexify U, I went out of my way to point out these common errors and admonished students repeatedly not to commit them. Nevertheless, rather than, say, learn how to correctly do a substitution in Calc II (for God’s sake), I would have student after student commit algebraic heresies so ghastly that Jesus himself would cry, and then bitch endlessly about how they deserved more partial credit than what they earned. I would routinely explain to students that they actually didn’t deserve any credit, based on the foolishness of those errors that four years of high school math should have stamped out.
Nevertheless, the whining and errors persisted, so during my second year I actually made explicit the list of algebraic (and one analytic) mistakes so ghastly to me that, should they occur anywhere in a problem, the sinner would earn no credit for the entire problem. Period. With these so-called Deadly sins (and their consequences) so explicitly spelled out, I was certain that I would stomp out forever the curse of BAD ALGEBRA. Unfortunately, students’ algebraic skills remained as bad as ever, although the policy did have the unexpectedly delightful consequence of stamping out the curse of PARTIAL CREDIT WHINING.
So this year, I went one step further. While we were in China, I had a couple of family seals, or chops as their known, made for the Ladybug, the Queen B, and me. After seeing the fine work that the craftsmen put into them, I had a wickedly awesome idea, and had one final chop made:
The chop — the cylinder on the right with the dragon sitting atop it — makes a stamp depicting a fire-breathing dragon that reads BAD ALGEBRA (in English) above the dragon and You do mathematics badly! (in Chinese) below it. Now, when a student commits one of the Deadly Sins, not only to they continue to lose all the points for the problem, but the act of their mathematical atrocity is marked, stamped with this big, red, fire-breathing dragon cursing at them. Think of it as the insult added to the injury.
Oddly enough, while I used the dragon chop extensively on the first exam, its use declined on the subsequent exams; by the final, I only had to bust it out twice. Ancient Chinese wisdom rocks!
So, to summarize. Applying draconian grading to eliminate college students’ BAD ALGEBRA? Total failure. Covering their exams with unhappy stamps like in kindergarten? Complete success.
I so going to invest in some gold stars and happy stickers for next semester.
Speaking of exams, my philosophy is that college examinations should be as much about synthesis of new ideas as it is the simple recall of old ones. The upshot of which is that I craft notoriously long and difficult exams. Exams that make students cry each semester. I’m not kidding. It is rumored that I sold my sold to the Devil in order to write my exams, but this is entirely untrue: it was merely a minor demon.
While I admit that my exams are challenging (they’re designed to be), the length isn’t my fault. I discovered early on that students chronically underestimate the time it takes them to do problems, so during exams I would give them 15-minute updates to help budget their time better. Of course, I discovered shortly after that I chronically overestimated their patience with my interrupting their work every quarter hour to let them know their impending doom was even more impendier, so I quit doing this and searched for a better way to help students gauge the time during an exam.
Part of the problem, I believe, is that most classrooms at Komplexify U have only one clock in them, and in a feat of engineering improbability, each clock is placed in the one spot in each room that completely blocks it from everyone’s view: on the back wall, or right behind a post, or in some cases, buried behind two feet of concrete. To rectify this, I always use the overhead projector to display at the front of the class a cool clock from this website. Many of the clocks are interesting in their design, but most are either too animated , too vague, or too inducing of panicked fits of erasing to be useful. However, I’ve eventually settled on the this clock for its simplicity; projected at the front of the room it gives everyone a clear line-of-sight to a digital and analog clock.
Of course, during the final five-minutes of the exam, it’s fun to switch over to the doomsday clock, ‘cuz nothing says Finish it up now! than an eight-foot-wide digital countdown tick-tick-ticking away each second. Let the terror begin!
This was a rough year, especially the end of it.
I fell so far behind this semester in all my classes. Indeed, during the last week of class, in order to simply cover the required topics list, I pretty much lectured on new material right up until the moment I actually handed out the final exams. If the class experience can be likened to a train ride (which is entirely appropriate, as we spend the semester chugging along, sometimes swiftly and sometimes slowly, but always forward along the same track of topics), then this semester’s excursion resembled less the amiable 1880 Train ride and more the final scene from Back to the Future III.
One can probably argue that this suicidal race against time was most directly a consequence of week’s worth of cancelled classes during which the Ladybug was diagnosed with a slight case of plague, but I see it instead a consequence of Komplexify U’s brand new technology mandate.
So let me set the back-story.
This year, the Komplexify U initiated mandatory enrollment of freshmen into its “Hybrid-Computer Program.” While it sounds like some kind of sinister plan to assimilate unsuspecting college students into the Borg collective, the “Hybrid-Computer Program” in reality requires all new students to lease for the duration of their university experience a hybrid tablet–laptop from the school, a piece of computer engineering that combines the limitations of both machines with the functionality of neither.
The machines were dumped into the laps of students and faculty without any ideas regarding their actual use decided upon (or apparently even discussed) beforehand, with the explicitly vague directive that faculty (like me) be charged with using them to “enhance student learning.” It’s as if Komplexify U was run by the Guiness brewmasters:
Administrator 1: The number of science and engineering majors are dropping across the state. We need something to attract new students. Something that says we’re hip and cutting-edge!
Administrator 2: Brilliant! We could give new students a “prize” when they enroll. Something future-y and engineer-istic.
A 1: Brilliant! How about personal jet-packs?
A 2: Those don’t exist yet. You’re thinking of The Jetsons.
A 1: Dammit!
A 2: Let’s just give ’em all computers. Lots of schools are doing that.
A 1: Brilliant! But what if they could, you know, change shape and stuff? That’s futuristical!
A 2: Now you’re thinking of The Transformers.
A 1: No, I saw ’em on a Best Buy commercial. Hybrid laptops or something.
A 2: Brilliant!
A 1: But won’t this be really expensive?
A 2: Eh. We’ll just add the costs to their school fees. They’ll never know.
A 1: Brilliant!
A 2: Brilliant!
Apparently, main “enhanced learning” selling point of the hybrid computers (gleaned during an uncountable number of summer workshops and orientations) is that they can convert between a standard laptop configuration to a stylus-based “tablet” form that allows students to write on it just like it’s a pad of paper, albeit a pad that costs $3000 over four years and overheats to the point of malfunctioning after 3 hours of continuous use. Of course, the only “enhanced learning” that matters to the students is their new-found ability to surf YouTube and IM classmates during class itself.
(Of course, truth be told, we professors have only ourselves to blame for all of this nonsense, since when the issues relating to the implementation of the Hybrid-Computer Program were voted upon during faculty meetings, many of us had other, more pressing engagements that prevented us from voting. Like surfing YouTube and IM-ing colleauges.)
The Math Department, begrudgingly accepting this as the way it shall be, has at least been proactive in trying to find sound practical and pedagogical uses for the hybrid machines. In particular, this year all of Calculus courses became tablet-required, the immediate consequence of which is that I, as a professor, now have to deal with students having problems not only with the mathematics, but also with the machine and its software. I in particular reconfabulated my calculus courses to make them more or less entirely paperless and tablet-driven (a pretty ballsy (some might say “stupid”) choice), but grappling with the software hurdles — a task so onerous I’ll defer it to a later post — gobbled up so much time that, by the end of class, I was so far behind and trying to cram so much material into each lecture that students mobbed my office with torches and pitchforks, and broke my arms to prevent me from lecturing again.
So, on the one hand, the Hybrid-Computer program completely mangled my classes and turned the end of the semester into a living nightmare.
On the other hand, considering the fact that I’m not tenured yet and one of aforementioned higher-powers-that-be might actually read this stuff…