Shared Pain

If there are isomorphisms related to suffering and pain, then while I like to concentrate on the fact that the misery can take different forms in its target, unfortunately the analogy suggests that the suffering can be reversed.  This is especially true in times of exams.  I had a story I wanted to relate about my own exams, but an email from my colleague Dr. P. N. Philpott made me pause, and think on the pain that students can inflict back on their teachers through their persistent ignorance.  These are his thoughts as they came to him while grading exams, and I suspect everyone that has ever graded mathematics can relate to parts, if not all of it.

It begins:

My god.  Who taught you to write?  A demented chimpanzee with no fingers?

There are days when I wish, among many other things, that I could require students to pass a penmanship test before they dared to hand anything in for credit.  The rise of texting and the decline of instruction in cursive has not helped this matter in the slightest.

I must have not graded you hard enough in Calc I and II if you fail to
remember the fundamental trig identity \sin^2 x + \cos^2 x = 1, how to
expand squares of binomials, or how to integrate constant functions.
It's a mistake I won't make again.

Sometimes they teach us almost as much as we try to teach them.  Here, the lesson is the dangers of assuming these students can retain information seen innumerable times before.  Also:  you've seen these students before and yet they don't understand how tests are conducted in your class?  Sad.  At least if they were new they could argue they didn't know what to expect.

I need a stamp that says "WORD SALAD +0"

I would encourage you to instead take the path of another professor I once knew, who had a reputation for marking off for spelling and grammatical errors on his math tests.  Don't be so kind as to simply insult them, you must hit them where it hurts the most - their grades.

To the precious snowflake who wanted to use the nice big table (in the
room for the use of students who use wheelchairs) while everyone else
suffered with a postage-stamp size auditorium armrest (I said no) and
who just couldn't fit his work into the ample spaces provided, even
with stapled appendices, and needed to submit a homemade blue book
stapled to the exam, thanks so much for making me chew through pages
and pages of your ill-formatted equation casserole and thanks extra
for making absolutely 100% sure your work is nowhere near the problem!
Good thing I don't like to look at the problem while I'm grading it.
Right?

As above, I think you should penalize student further and further the more they inconvenience you.  Stress the importance of clarity of their mathematics and their presentation, and mark off accordingly.

What I love about this whole process is knowing that even though I've
inflated the scores for each problem so much that a dribble of ink or
a drool smear is worth 10 points, I'll spend Friday answering emails
about how I grade too hard and take off points for things that "don't
matter". If you already know "what matters" then by all means, sit
last year's final. We'll just let your course grade be your grade on
that exam.

 I learned long ago that kindness on your part is consistently met with abuse and exploitation on their part.  So you must preempt their whining needs with coldness and hardness, and give no expectation of any leniency.  Then if you ever choose to give them the slightest concession, it will feel as though they have received the greatest divine miracle in history.

I'm going to catch a lot of shit for "not explaining it well enough".
Maybe the quotation marks are inappropriate, since most of my
snowflakes' sense of tact, while vestigial, is developed enough to
avoid this blunder. Because guess what, guys? Education is a two-way
street. If you continue to sit there, blobbily wheezing through your
slightly open mouth, flecks of spittle forming in the corners of your
lips, when I say "Does anyone have any questions about this? Is there
anything I should talk about more, or try to come at from a different
perspective? This is quite an important concept, so we really
shouldn't go on until everyone is sure they understand", you've got
some crust coming at me with "I didn't understand when you explained
it in class". I don't even mention the book any more in this
situation, although it remains a mystery to me why any of these people
buy a $200+ book if they have no intention whatever of reading it.

Clearly your issue is that you still are trying to sympathize with your students, thinking of them as human beings almost on your level.  You should think of them as less than dogs.  For no decent person would abuse a dog, but these students need to be properly whipped into shape.

It's now been a few days, and by far the most frequent answer to my
standard post–exam failure question of "so, what happened?" has been
"Well, I know how to do all the math, but they" (I love that students
refer to the test maker as "they" when they are speaking to the test
maker) "use so many words! Where are all the numbers?" Sorry, sweetie.
Gone are the days when your mathematics examinations consisted of
one-step calculations, all laid out for you with an equals sign and a
blank for you to fill in. In the cold, hard world you've grown into,
you'll have to understand and interpret questions posed by one human
to another. Not your fault you believe that math wouldn't be this way,
exactly; but I'm here to disabuse you of your wrongheaded and mistaken
notions.

In the end, I'm a firm believer in the idea that, if these students refuse to learn any mathematics from me, I can at least teach them that it is in fact possible to fail.  I think many of these children go their whole lives coddled, with their self-esteem and ego stroked at each moment.  Enjoy teaching them that those days are over.

Test Faces

Proctoring exams is boring.  If you don't watch them, the students feel like they can push the boundaries.  In no time they'll sneak out pages of illicit notes, or act like you can't tell they're using their phones to search for answers or get help from someone else.  Yet it's not something I can entirely foist off on graduate students.  The lecture hall is too big, there are too many students, and the average graduate student is only slightly more aware of their surroundings than the infants they're supposed to be watching.

So, in the absence of anything better to do, you notice the different faces that students adopt while taking exams.  They range in an amusing spectrum centered around the one that most students have, that of the dutiful and busy face.  This is what you want, the student who knows they have no time to waste, this test is serious business, and so they had better get moving if they want to have a chance at finishing in time.

A little ways away from this norm is the angry face.  I doubt they do it consciously, but I have seen students who frown at their exams the whole way through.  It may be that this is simply what they look like when they're concentrating, but I suspect it's more that they see the test for what it is:  an adversary, and it is a battle they're not winning.  They look like they want to start arguing with the page in front of them, and it likely takes fair amount of restraint for them to not yell at the problems.  I'm sure these people are very pleasant to be around in day-to-day life.

On the other hand, you have the students, the all too common students, who might as well have been given a test written in Sanskrit.  They stare at the page, and you can see their brain has shut down.  These types come in two flavors, both characterized by their vacant stares, hoping that divine inspiration will hit them, or that the answers will magically materialize in front of them.  One stares at the test in front of them, not fully giving up, but their pencil sits limp in their hand.  The other stares off at the wall.  I think the latter is further gone, and probably is more likely to look at their peers' papers given the opportunity.

Then you have my personal favorite.  Take the angry student and the student of the vacant stare, mix them together and push them a little bit harder, and you have the imminent crier.  No student has full-out burst into tears during an exam in my experience, but I have seen plenty who are clearly using all of their mental and physical ability to hold in their tears until they leave the class.  They certainly aren't using any of their power to complete the exam.  These students tend to turn in their tests and almost run out of the room.  It is hard not to smile at them as they hand in their pathetic papers.

Then there is the one which is an endangered animal in my classroom, yet one I saw on this first calculus test.  I hope I misread it, but I believe I saw the endlessly irritating Miss Johnson give this face.  The face of someone who goes into a test expecting a challenge, as they should.  They look dutiful and serious at first, like the bulk of the students.  But then something will happen.  They'll flip through the test, look at the backs of the pages to see if they're missing anything, maybe even look around the class to see if anyone else is in on it, then scribble furiously, a smile creeping over them.  This is the look of someone who knows, or thinks they know, the material far better than they, or I for that matter, expected.

She indeed finished faster than anyone else in the class.  And there are only two kinds of people that finish tests early:  those that destroyed the test, and those that were destroyed by the test.

If she is the former rather than the latter, I am convinced she must have cheated.  If I can't prove it, or find how she did it, rest assured the very least that will happen in the future is a custom exam, just for her.

Safety Nets

The first exam is coming soon.  I look forward to watching their pain, seeing their feeble attempts to get those wheels spinning fast enough to exhibit some pretense of intellect.

It amuses me to see them squirm. They try everything they can to avoid actually thinking.  They are desperate to use calculators, to let a machine do the thinking for them.  They love to just mash the numbers and operands they encounter into their calculators in the hopes of getting something close to correct.

If I allow them to bring notes into the test they will copy every tiny bit of information they've encountered into their notes, until they reach a point where it would require a magnifying glass to make it all out properly.

And yet, no matter how many security blankets or safety nets you give them, if you ask them to do even the slightest amount of thinking for themselves they will panic.  I once heard of a student who was working with the basic equations of parabolic motion.  This student could plug numbers into the given formula, and get out an answer.  However, the moment they were required to solve for one of the coefficients in terms of everything else, they would shut down.  I'm not even talking about trigonometry.  This just required a basic algebraic manipulation of a quadratic equation to solve for one of the coefficients.

I sometimes wonder how these people manage to eat without stabbing themselves in the neck with their forks.  This may explain the popularity of finger food.

One way or the other, in a few days, I will see how long they can last with no safety net at all.  No notes, no calculators, and most of all no friends to do their work for them.  And I will be there standing over them when they fall spectacularly.

The List

I returned the first homework a couple of days ago.  All was relatively silent, at first.  Most of them just took their papers and put them away, probably never intending to give it another thought.  But then, someone looked and realized that only ten of the forty or so problems had been graded.  You could almost see the dawning realization ripple out from that first person like a wave in the auditorium.  I will never get tired of seeing the look of impotent rage on students' faces as they run up against a perceived injustice that they are powerless to fight.

These reactions, though enjoyable, are fully expected.  What I didn't expect was this little pocket of unflappable bodies in the back corner of the room, centered around that blue-haired cheerleader imp.  That  group didn't seem bothered in the least.  Normally this would be because these children are too distracted, too vacant, too busy talking and texting, to notice if the world is ending around them, much less if they're failing a class.  But I handed back their homework, so I know that this whole group scored very well on the assignment.  Among the highest in the class, no less.

Had they cheated?  Did they get the answers from the internet or some contraband instructor's copy of the book? Or did they have one of their number, or some sucker elsewhere in the class, who carried the burden for all of them?  This self-centered cheerleader already acted like the whole world was owed to her, and it looked like someone was willing to do whatever she wanted after a flutter of eyelids.

No.  I will not allow this to continue.  Now that I've handed back the homework, I have their names.  Paul Moreno.  Nathan Thompson.  Kim Sun.  Scott Castilleja.  And the cheerleader, Lindsay Johnson.  The name even sounds like a cheerleader.  I will find out which of them, if any, is carrying the rest.  I will separate them, turning the weaker against the stronger.  And if the strongest survives, then maybe I will take them in and put them on the proper path.  And if none of them has any ability, if they are all getting their answers from an outside source, then they will be purified, in the same way that an incinerator cleans everything away, leaving nothing behind but ashes.

Our Little Snowflakes

Talk about homework, and the creative ways that students blunder into it like someone putting their head down and running into a brick wall, are all too common among teachers.  I suspect this is because there are altogether too many people in these classes that only made it out of high school by some small miracle, or some large grade inflation.

For instance, after posting about my first homework earlier this week, I received an email from my colleague, Dr. P. N. Philpott.  He had received an email from one of his students:

"I just entered the data into webwork, and the online thing, and it gave me 167 for the variance and 12 something for the standard deviation.

How am I suppose to calculate those then?"

Intro stat, first time I've ever taught a sub-precalc level class.  It's fucking nuts.  I can't believe I ever thought badly of my calc students' maturity or sense of initiative.

The "online thing"?  THE ONLINE THING?  Damn, son.

In such a brief message, there seem to be an impressive number of things going wrong.  First of all, I shed a tear that my colleague has been forced to commit what I consider charity work (or possibly something akin to community service punishment) by teaching not just a sub-precalc level class, but statistics.  There's a reason many schools separate the statistics department from the mathematics department.  If it were calculus-based statistics, or an amusing subject like conformal invariants of random processes, then it would be more tolerable.  But this...doesn't sound much better than babysitting preschoolers.

This class is presumably taken by people for whom this will be their sole math class.  People who have spent their whole life trying to dodge thinking.  This email bears this idea out.  Dr. Philpott understandably has been reduced to an apoplectic rage at the ignorance.  No matter how much you lower your standards, there will always be those ready to disappoint you.

I do find it somewhat sad that these online services and programs have been cropping up in recent years in the futile effort to make it easier or...I shudder to say...fun to learn math.  I expect more often than not, the students try to use them as an excuse to be more lazy, and think even less.  The slightest problem that comes up, they come running to their professor.  It's a wonder they can operate a computer well enough to send an email.

The obvious answer to the question, "How am I suppose to calculate those then?" (while trying as hard as possible to ignore the grammatical error - we can leave that to the English professors to pick it to pieces) is, "You calculate it the way that we discussed in class, which is also the way it is done in the book.  If you have trouble using a tool designed to make your life easier and more convenient, I suggest you build character by calculating every variance and standard deviation for the remainder of the semester using nothing more advanced than a slide rule.  And no, I will not teach you how to use a slide rule."  If they try to ask a follow-up question, refuse to answer until they show you their calculations.

My Other Class

Ah, yes.  I am in fact teaching two classes this semester.  In addition to teaching first semester calculus, I was given a small concession in being allowed to teach a graduate topics class.  That means I can talk about whatever I want.  The students who show will either do their best to not get lost, or possibly try to impress me if they want the chance to work with me in the future.  Not that there's much chance of that.

So for the past couple of weeks I've been going through the four different proofs of the Weierstrass preparation theorem found in Raghavan Narasimhan's Introduction to the Theory of Analytic Spaces.  The theorem itself is beautiful and powerful.  It gives the ability to (up to multiplication by a unit in the proper sense) write an analytic function of several complex variables as a monic polynomial in only one of the variables whose coefficients are analytic functions in the remaining variables.

The four proofs cover a total of twenty pages in the book.  But above and beyond that endurance test for the students, they also have to contend with the fact that (while recently reprinted and cheaper to buy than it generally was ten years ago) it is typed lecture notes from over fifty years ago, printed with none of the modern smoothness that even your average undergraduate can produce after half an hour of learning LaTeX.  Even if the text was crystal clear, they typeface is a bit difficult to work through.

That, and it's always fun to see who is and who isn't capable of dealing with the concepts of germs of analytic functions.  Their beginning classes in complex analysis must be getting better, because not all of them were mystified by the idea.  Maybe it won't be a total loss.  If they can get through this beginning section, maybe I'll need to reward them with something a little lighter.

Or maybe I'll see what other suffering they can endure.

Homework

Ordinarily, I wouldn't assign homework.  They have a book, they have lectures.  If they wanted practice for the exams, they are welcome to do as many or as few problems as they want.  But the department requested that I assign homework, to help keep the different sections of calculus somewhat in line with each other.  I didn't fight it too much, as I saw the potential for fun to be had.

I know that more and more these days teachers are moving to online assignments because the grading is all done automatically.  But I prefer using a real grader, and not just because I am an old man who resists change and technology.  I love the fact that the grader's allotted time on the clock each week is limited, so for a class of this size, he only has the time to grade about ten problems from each assignment.  This gives me the delight of giving them large assignments, but only a handful of the problems are graded, and they never know which ones.  The problem that took them hours to work on could be skipped entirely, or the simple problem at the end they skipped could be graded in detail.  There are so many ways this can frustrate the students.

I also enjoy denying the students the ability to waste my time.  I suspect they come into this class from a high school experience where everyone held their hand and made sure they turned in everything and any little tiny hitch in their schedule was met with exceptions and special treatment.  Last week, when the first assignment was due, I must have had half a dozen students come to me wanting an extension on their homework because their financial aid hadn't come through yet, and so they weren't able to get their book.  I told them that not only was the book on reserve in the library, but they were sitting in a room of a hundred people who had their own books, and surely some of them would have been willing to share.

The look of dejection as reality sunk into their thick skulls was delicious.

Limits

Ah, limits.  The conceptual hub about which the entirety of calculus, and a great deal of analysis, revolves.  Any reasonable person would agree that something this important, this fundamental, should be given a thorough, honest treatment.

The students did not seem to agree.  As soon as I wrote down the epsilons and deltas in the definition, there were murmurs of protest.  As I used the definition to find a limit on a simple polynomial, the protests hit critical mass.  Lecture came to a grinding halt as the confused students became angry when someone said this seemed a bit advanced for a freshman class.

Really?  Who are they to judge what is appropriate?  Are they hoping this will be like a Saturday morning book reading in the local children's library, all simple words, colorful pictures, and happy endings?  It's not as though I have even deviated from the material in the book.  This stuff is all in their text, so as far as I'm concerned it is all information they are responsible to know for the test.  Nothing says I have to spend time in class on concepts proportional to space spent in the book, I can emphasize what I like.

Students only like things that are easy, or things they already know.  The more they protest, the more they are showing me they have room to learn.  Perhaps after the first test they will learn their will be a direct correlation between how much they protest in class, and how much this type of problem appears on the test. I look forward to the pleasant surprise of the first test.