yes, it's been a while;
no, i'm no happier;
yes, I still wonder if i'm cut out for the academic life...
... but let's set aside those irreconcilable issues for now.
* * *
at the moment, i'm having far too much fun devising homework problems for my Numerical Analysis students.
one problem gives them some data points for a unknown function. their task is to show that, given a few hypotheses about the function, why the data cannot possibly come from Newton's method!
Urban teachers have a kind of underground economy, Cohen explained. Some teachers hustle and negotiate to get books and paper and desks for their students. They spend their spare time running campaigns on fundraising sites like DonοrsChoose.org, and they keep an eye out for any materials they can nab from other schools. Philadelphia teachers spend an average of $300 to $\$$1,000 of their own money each year to supplement their $100 annual budget for classroom supplies, according to a Philadelphia Federation of Teachers survey.
~ from "Why Poor Schools Can’t Win at Standardized Testing" @theatlantιc
this article is about how programming, despite the call to arms about learning how to code, is a low-status job.
when i read this post, though, it funded more like the plight of teachers:
.."that we allow “passion” to be used against us. When we like our work, we let it be known. We work extremely hard. That has two negative side effects. The first is that we don’t like our work and put in a half-assed effort like everyone else, it shows. Executives generally have the political aplomb not to show whether they enjoy what they’re doing, except to people they trust with that bit of information. Programmers, on the other hand, make it too obvious how they feel about their work. This means the happy ones don’t get the raises and promotions they deserve (because they’re working so hard) because management sees no need to reward them, and that the unhappy ones stand out to aggressive management as potential “performance issues”. The second is that we allow this “passion” to be used against us. Not to be passionate is almost a crime .."
~ from "How the Other Half Works: an Adventure in the Low Status of Software Engineers" @Michael0Church.
from "Don't Send Your Kid to the Ivy League" @NewRepublic:
So extreme are the admission standards now that kids who manage to get into elite colleges have, by definition, never experienced anything but success. The prospect of not being successful terrifies them, disorients them. The cost of falling short, even temporarily, becomes not merely practical, but existential. The result is a violent aversion to risk. You have no margin for error, so you avoid the possibility that you will ever make an error. Once, a student at Pomona told me that she’d love to have a chance to think about the things she’s studying, only she doesn’t have the time. I asked her if she had ever considered not trying to get an A in every class. She looked at me as if I had made an indecent suggestion.
like any news article on education, one should take this report with a reasonable amount of skepticism ..
.. but being a university educator myself, there's some truth in it. generally my students are uncomfortable when i ask them problems in the exam that don't match up with their textbook problems (even though they are usually combinations of the same problems). the risk of a new obstacle, of not having seen something on which they will be evaluated .. it seems to really affect them.
-----
for instance, last semester i think i spooked most of my linear algebra class with one geometry problem on each exam. [1] at some point several students asked for practice geometry problems.
"everyone's worried about the geometry problem," one of them admitted. i tried to point out that it was only one of at most five problems and that i generally curve the scores ..
.. but (s)he didn't seem convinced.
[1] e.g. "Determine, if it exists, an equation for the sphere passing through the following four points." (i even reminded them what the equation of a 2-sphere in 3-space was!)
.. once, at a party full of mathematicians, a friend was trying to formulate this one lemma. [1] he drew a shape and said ..
.. "ok, so this is a triangle .."
.. but at that point i had one too many and suddenly blurred out ..
.. "no. that's just an approximation of a triangle!.."
.. at which time everyone around just just burst into hysterical laughter.
terrible, unrepentant mathematicians, we were .. :-)
[1] yeah, we were that far in. i truly suspect maths is a language, because many drunken mathmos i know still revert to their mother tongue, after one too many ..
In one letter he even displayed contempt for the problem. His friend the German astronomer Heinrich Οlbers had written to Gaμss encouraging him to compete for a prize which had been offered by the Paris Academy for a solution to Fermαt's challenge: "It seems to me, dear Gaμss, that you should get busy about this." Two weeks later Gaμss replied, "I am very much obliged for your news concerning the Paris prize. But I confess that Fermat's Last Theorem as an isolated proposition has very little interest for me, for I could easily lay down a multitude of such propositions, which one could neither prove nor disprove."so i suppose that even the best of us should pick and choose the tasks best suited for ourselves. i wonder, though, what Gaμss thought of the Rιemann hypothesis ..?
~ from "Math's Hidden Woman" @pbs
what really helped, i think, is that it became clear to us that there was plenty we could learn, just by computing explicit configurations.this isn't to say that i didn't guide the discussion, but i felt like the back &-forth today is suggestive, and this laissez faire style might actually work.
the student seemed to feel both awed and excited, that these were strange, interesting, yet accessible things for him. i think he realised today some scope of what was possible for him, that he started to believe in himself.
what if there were ways to become better at solving problems?below are excerpts from an essay i found, through one social media engine or another. what struck me about it was how i've unconsciously kept some of these habits and gotten more insights, in the last few years.
is it more than just a pipe dream to improve oneself?
"A 2004 study published in Naturε examined the role of sleep in the process of generating insight. They found that sleep, regardless of time of day, doubled the number of subjects who came up with the insight solution to a task.of course, this could all just be a manifestation of confirmation bias (or if you will, the fallacy of the consequent). what i do recall, however, are periods of correlation: i was highly uncreative during those times when i was sleeping very little and had no time to exercise.(Presented graphically above.)This effect was only evident in those who had struggled with the problem, so it was the unique combination of struggling followed by sleep and not sleep alone that boosted insight.
..
"There’s a good reason for this: mind-wandering fosters creativity. A 2012 study(results pictured below)found that any sort of mind-wandering will do, but the kind elicited during a low-effort task was more effective than even that of doing nothing .. This, too, is congruent with my experience. How much insight has been produced while taking a shower or mowing the lawn? Paul Dιrac, the Nobel Prize winning physicist, would take long hikes in the wood. I’d bet money that this was prime mind-wandering time."
~ from "The Science of Problem Solving" @rs.io
The answer to this question takes us to the heart of quantum mechanιcs, to the part that popular explanations usually mangle. Quantum mechanιcs wasn't the first theory to introduce randomness and prοbabilities into physics. Ironically, the real novelty of quantum mechanιcs was that it replaced prοbabilities — which are defined as nonnegative real numbers — by less intuitive quantities called amplitudes, which can be positive, negative, or even complex. To find the prοbability of some event happening (say, an atom decaying, or a photon hitting a screen), quantum mechanιcs says that you need to add the amplitudes for all the possible ways that it could happen, and then take the squared absolute value of the result. If an event has positive and negative amplitudes, they can cancel each other out, so the event never happens at all.
The key point is that the behavior of amplitudes seems to force prοbabilities to play a different role in quantum mechanιcs than they do in other physical theories. As long as a theory only involves prοbabilities, we can imagine that the prοbabilities merely reflect our ignorance, and that a “God’s-eye view” of the precise coοrdinates of every subatomιc particle would restore determinism. But quantum mechanιcs’ amplitudes only turn into prοbabilities on being measured — and the specific way the transformation happens depends on which measurement an observer chooses to perform. That is, nature “cooks prοbabilities to order” for us in response to the measurement choice. That being so, how can we regard the prοbabilities as reflecting ignorance of a preexisting truth?
~ via "Quantum Randomness" @ AmericanScientist
For example, everyone knows that scientists overuse the passive voice. It's one of the signatures of academese: "the experiment was performed" instead of "I performed the experiment." But if you follow the guideline, "Change every passive sentence into an active sentence," you don't improve the prose, because there's no way the passive construction could have survived in the English language for millennia if it hadn't served some purpose.(for more articles of this kind, visit edge.org.)
The problem with any given construction, like the passive voice, isn't that people use it, but that they use it too much or in the wrong circumstances. Active and passive sentences express the same underlying content (who did what to whom) while varying the topic, focus, and linear order of the participants, all of which have cognitive ramifications. The passive is a better construction than the active when the affected entity (the thing that has moved or changed) is the topic of the preceding discourse, and should therefore come early in the sentence to connect with what came before; when the affected entity is shorter or grammatically simpler than the agent of the action, so expressing it early relieves the reader's memory load; and when the agent is irrelevant to the story, and is best omitted altogether (which the passive, but not the active, allows you to do). To give good advice on how to write, you have to understand what the passive can accomplish, and therefore you should not blue-pencil every passive sentence into an active one (as one of my copyeditors once did).
so i spent most of the day LaTeX'ing, which went well enough.
the best thing about writing up ready results in LaTeX is that one feels smart, that maybe all those days of banging one's head against these damned technical lemmas [1] were worth it after all.
..
.. on the other hand, there's something else I should write up, but i can't convince myself to do so:
whenever i think about the proof, I don't feel smart. instead, it just seems .. trivial.
[1] technically, the plural of lemma is "lemmata."
yesterday i printed out some research notes i wrote in february ..
.. all 24 pages of them, just to prove one lemma. [1]
ye gods; the ideas still make intuitive sense, but the proofs are painfully technical .. much more so than i recall. [2]
they're not even a complete set of notes! for the lemma to have a complete proof, i'll have to read another set of 5 pages of notes for a sub-lemma, as well as a short 3-page section of an old preprint of mine ..
no wonder why i couldn't convince myself to work hard in april. after that and then that trip to spain in march, i had little to no energy left.
anyway, it's time to write up the result(s) ..
.. because what currently exists are the notes, not a preprint. there's a lot of exposition and simplification before i have anything remotely readable!
[1] at this point maybe i should promote it to "theorem" status. (before i thought it was .. well, obvious, and the proof would be short.)
[2] one series of estimates involved 4-5 indices. i was comparing intervals at different dyadic scales, as well as the same scale, which explains two indices .. but the intervals aren't nested in one another, which requires two more indices. lastly, these estimates were "fibrewise," so an additional fifth index kept track of which fibre was which.
one of these days i'll start posting regularly again .. and about research too.
until that day comes, however, readers of this blog will have to suffer through the occasional repost about maths education, like this one:
"Lectures Aren't Just Boring, They're Ineffective, Too, Study Finds" by a. bajak @science
The meta-analysis, published online today in the Proceedings of the National Academy of Sciences, concluded that teaching approaches that turned students into active participants rather than passive listeners reduced failure rates and boosted scores on exams by almost one-half a standard deviation.
i don't doubt that active learning causes students to retain information and to improve their understanding of the concepts of the course.
my contention is that the only novelty of this teaching style is that it institutionalises what students should already be doing:
studying.
you see, it's been suggested that today's college students simply don't hit the books as often as previous generations. when i was an undergrad, i was told that 1 credit hour translates to 2 hours of self-study outside of the classroom, in order to keep up with the class.
(by this rule, a full-time student with four 3-credit courses should be studying 24 hours per week; combined with class times, this should be close to the hours for a full-time job .. which is exactly how seriously college should be treated by college students.)
to me, what active learning amounts to is ..
(a) moving the act of self-study from the student's prerogative to inside of the classroom,
(b) eliminating the temptation of distraction (from tv, internet, dorm buddies) by forcing the student to focus on clear goals with immediate rewards/punishments.
in other words, active learning caters to the modern, distracted, undisciplined mind. they are bringing studying back into college by rebranding it as a new, structured feature of a course.
to their credit, proponents of this method are being efficient. I have no doubt that this does encourage (read: force) students to study, inside and outside of the classroom ..
.. but it does so, at the cost of maintaining the status-quo of short attention spans and immediate gratification, while further reducing personal responsibility.
the more i think about it, the less sense it makes:
if you were a mediocre calculus student, then why wouldn't you invest in a complete solutions manual for the textbook of your course?
even if you copied all the answers, the percentage of exam problems similar to textbook problems is rather high .. enough, say, for a C grade or probably a B.
after all, solutions manuals are perfectly legal products to buy. the only setback I can think of is the additional cost.
[scratches head]
sometimes i just don't understand students.
more than eight years ago in a cold, snowy december I sat alone in a cafe, trying to make sense of what had happened.
a little later, a fellow grad student stopped by, looked at me, and remembering, asked me how it went.
"well," i said, "i didn't fail, but .." [1]
i doubt i finished the sentence. we went back and forth in polarised roles, he attempting to be cheerful, me still down.
i wouldn't feel "up" for a while.
it would take a while of forgetting, earning small separate achievements, before i could look back at it without pain and malaise.
-----
that scene from my life came to mind because right now, i have a similar mood .. only less severe.
today was my last day of class .. until August, anyway.
i don't feel like celebrating, though much of me feels so glad ..
i don't feel mournful, but it feels like I lost something .. maybe a chance to have made a great beginning. instead at best i managed a mediocre but trouble-prone one.
all I feel are regrets .. that i could have done better or more, that I put to much effort in pointless things, that i never really understood or appreciated what was really going on, under my own nose and in my own classroom ..
.. that i just had no real sense of "how it all works."
i feel wrong about many things that don't matter, and i don't know how I feel about the things that do.
all this past academic year had taught me is doubt and stress and futility.
-----
on the other hand, those were the same lessons i learned after my first year in graduate school. knowing that i'd be there a while, i worked at it and eventually it all made more sense .. not quite everything, but it got better.
part of me suspects that there is no purpose in life .. in that there is no one canonical purpose. to quote the existentialists, everyone must choose for himself.
i have not determined my purpose yet, but i believe there is one that suits me, in this academic life. it will take time .. but trusting on the pseudo-repetitiveness of life, it gives me a certain illusion of faith.
so i'm down right now. it won't be forever.
[1] it was right after my comprehensive exam, which was an oral, 1 1/2 hour friendly firing squad of questions. i distinctly remember feeling awful that i couldn't prove certain facts on the fly .. and advantageously yet unfairly, the committee never asked for them.
the more I teach liberal arts students, the more convinced I am that my own history is .. slightly out of the ordinary.
simply put.. mathematicians, let alone academic scholars, are a significant minority of the population .. even when one restricts to the college-attending sub-population of the western world only. we aren't ordinary in the sense that we are probabilistically rare. [1]
i guess that's just one way of saying (read: justifying) that i'm weird and i shouldn't be surprised that my students and i don't understand one another.
-----
today i taught two lectures and it felt like i was instructing two confused yet brick-made walls.
it's a very isolating, unnerving experience. maybe i take too much pride in delivering clear, motivating lectures .. where "clear" means clear to me, but apparently not to anyone else.
i'm not being fair, though. it's not equal footing between them and i, because i'm the one setting the agenda and I know what's coming next; to them, though, i'm speaking a foreign language and during class, it's all they can do to copy what's on the blackboard.
isn't it fair, though, that after most of the semester, that they keep up with me?
put otherwise, if i'm going to interact with a brick wall, why should i leave my office to do so? why should I talk about things i know well when i can explore this i don't know but that i want to?
what's the damned point?!?
[1] the more i think about it, the more irrationally obsessive of a student i must have been. i remember studying with friends for exams by quizzing each other, asking each other how to prove this or that statement on the spot. i remember checking out maths books from the library, reading what seemed fascinating at the time. i remember being incredibly upset that, after two years and then graduating, i couldn't solve one particular open problem that my mentor suggested to me. (as far as I know, though, even now nobody's solved it either.)
i don't regret traveling and writing through spring break. it was a pleasure to see colleagues that are soon becoming old friends, in a city becoming more familiar and pleasantly so. this isn't too say that i could live there .. odds are that I'd bend back to my hard-to-get-a-hold-of, anti-social self.
put more simply, it's better that those colleagues of mine know me as a guest, not a neighbor.
-----
those things said, Easter is coming and the university will be closed for chose to a week.
there are so many things to do .. but i'm getting out of practice and growing soft. i get tired more readily.
so i think i'm going to take a vacation, go up north for a day out two and go hiking as i fancied once. maybe i'll watch the latest superhero movie at the cinema. maybe I'll finally meet friends for lunch as i promised, long ago.
more likely, though, i'll spend two days on a research bender, writing up a quick-&-dirty draft of a note.. /-:
i think it accurate to say that I spent the whole day trying not to think too hard about one problem.
in retrospect, i should either have worked as hard as I could have, made some small progress .. even a wrong turn would have been one more lesson in which way not go turn again ..
.. or not worked at all on it;
i guess I never learn.
my memory of Spain it's behind fainter and fainter.
being my Nth trip there (with N > 2) i've stopped picking up souvenirs .. so the only memento i have from the trip is a LaTeX draft in dire need of revision.
i haven't started counting the days until the end of the semester, but i'm getting there. the thing about having had a week off from teaching is that it skews my expectations: lately i've tried (unsuccessfully) to convince myself that a weekend is two days long and plenty of time to accomplish something small.
[ to be cont'd ]
So in a few days I have to return to real life.. that means finally grading these exams, prepping another exam for another class, getting back to a scholarly journal, to colleagues in my department about a potential project and journal club, and so on.
Why do I feel alone in my endeavors? Why do I think I'm so ineffective and inefficient?
I feel refreshed.. but the sort of relief that will quickly deplete itself in a week's time and stress. My one track mind is a disadvantage in this modern society, where one had to stick to a multi-tasking schedule of barely controlled confusion..
In my previous travels to attend conferences or visit colleagues,I used to bring printouts of preprints (most of them by others, not me) as well as a few books and a laptop.
Experience has shown me, however, that most of this stuff is never used.
These days I bring a netbook, the preprints stay in PDF form [1], and there's room for both my running shoes and climbing shoes.
[1] .. and the books are digital, too.. though legal copies are harder to come by.
So I lost a debate with my co-authors, but it doesn't bother me. I guess it shows that we work well together and that I can trust them to tell me when I'm wrong about something.
The important thing about maths is that one remains with what is correct. Often it means that one has to be wrong on occasion, and to realise why. More and more it seems important to me to fail, if only to be aware of how far I am pushing what I knew and what I really understand.
It also seems that the way American universities are structured doesn't allow for this. Sometimes I wonder how new mathematicians come out off the woodwork, and if this explains why it takes so long to get the hang of research... that is, if one ever gets the hang of it.
I like Europe. I didn't realise the extent to which I missed it, how the universities work.
Of course life is always more appealing as a guest.. but being in Spain reminds me of those years in Finland when I was a semi permanent resident and slowly becoming a local. I wonder often enough if I should have stayed and tried for a permanent position.. maybe teach a course or two, co-advise a student, convince my sponsoring department that I might be a good guy to keep around.
Odd. I'd be scared to death of advising a Ph.d. student here in the States, but in Finland it would be more doable.
My recent posts have been rather bleak, haven't they? I guess I'm still not fully used to professorial life; sometimes I wonder if it will ever feel normal.
That said, it's Spring Break and I'm away for the week, visiting my co-authors in sunny Spain.
I feel life my old self again. Ideas are coming out: a few good ones, lots of bad ones too. There's a good chance we'll finish off the guts of one manuscript.. and now I'm thinking about how to start another one.
So maybe I was wrong before; sometimes I can get my act together, finish what I started.
I'm supposed to go to the airport in two days, in order to cross the ocean and to keep a promise to a few colleagues. (Being that I don't keep many of those, it's rather crucial that I do so when it counts.)
Still, I'm easily exhausted. If I could say that I am exhausted right now then I would.. but the fact is that I'm not.
I know that I can still work, still have enough energy to keep the collaboration going if I budget enough effort per day of the visit.
I liken it to surviving on 5 1/2 hours of sleep per night: after a while it feels normal but you could swear that you used to be faster and sharper and maybe you're just "getting old" ..
I also know that once I come back, then I'll spend a few days feeling exhausted and bitter at having to readjust to my old routine.. to the extent that I'll probably swear that I'll never travel mid-semester ever again.
Yesterday I met with colleagues in the department and we talked about PDEs.. rather, they did and I was trying to decipher what the underlying mechanisms were.
I am and will always be an analyst; these guys really think in terms of physical principles and what the equations are supposed to mean. I suspect that we'll keep a truce and the compromise of that truce will be geometry.
Anyway, my point is that the whole time I was absolutely ambivalent: I simultaneously thought (a) this is pretty damned cool and (b) fvck: I have.. aw, fvckity fvck! [1] .. that many incomplete projects right now and I'm supposed to learn.. no, have learned.. these disparate things; how can I juggle this one too?
Whether or not I am exhausted, I feel exhausted. So let this be a lesson to you young researchers: even if your intentions are good, never promise more than you can deliver.
[1] at last count, i have $5 + 3(\frac{1}{4})$ collaborations and $3$ solo projects; a $\frac{1}{4}$ of a project means that there is a decent lemma or two, but no real theorems yet. As for the topics, they vary from geometric measure theory and PDEs to fractals, sub-Riemannian geometry, and minimal-like surfaces .. to even Banach space differentiability! On top of these, i suspect that one collaborator is trying to convince me that dynamics is interesting.
If I could do anything right now then I'd..
taken from tours4fun |
..first take a week off to go hiking, maybe rock climbing. Maybe Zion, where I'd carry a rope and harness, my own water and in doing so, suffer the weight of existence. I'd do nothing but cross sand and boulders, shoot photos, and make campfires and sit in front of them, starting into the randomness of their flames and sparks. |
I'd hunt the hidden moon by day, feel stones at my feet, be guided by the wind at my back and the mountains that frame the land-scape. I'd imagine myself made blind by an oppressive sun, finding a path of least resistance, some kind of order amidst the entropy that is desert.
Then dried by desert heat, seeking life and creation .. I'd spend a month doing nothing but writing.
There are too many manuscripts to revise, ideas to shape ..good ideas to initially obscure and when the shortcomings are clear, to revise into clear, intuitive shape.
In leaving Finland there were too many things left incomplete, plenty of angry impatient collaborators.. or at least, should be angry and lack any more patience.
I would become strange for a while, shaped by self-imposed solitude, transforming into something less than human.. if only to create maths that I hope will transcend my mortality.
if i could .. [sighs]
every time i have a proof by picture,[sighs]
it takes 4-5 pages of $\LaTeX$ to write out the details!
there are students *everywhere* in the department.needless to say, 'tis the season of midterms .. and as time goes on, fewer office doors will be open. probabilistically, it's only a matter of time before someone stops by my door and asks me a maths question ..
i hear many young voices from the few office doors that remain open.
the math help room is full of people.
young men and women have taken over the couches in the middle, watching a tutor intently as she's explaining demοrgan's laws on a nearby whiteboard.
what if i .. just didn't show up?.. but then i sighed and realised that, deep down inside, i respect responsible people that can be counted to show up when they need to show up, and that i want to think of myself as such a person. that said, there is only one way to get what you want ..
what's the worst that could happen?
i've told my students that before, and that achieving their goals is conceptually simple but emotionally nontrivial. those things said, that means that i have to do the same ..it isn't easy. it takes a commitment and somehow we educators do it .. but like anything worthwhile, it shouldn't be easy .. and for me, it isn't.
life would be so much easier if one could pick and choose one's convictions, at moment and whim. it is far harder to be consistent.
"Adding up the numbers in a sub-sequeηce gives a figure called the discrepaηcy, which acts as a measure of the structure of the sub-sequeηce .."as for how this came up ..
~ from " Wikipedia-size maths proof too big for humans to check" @newscientist
Erdös thought that for any infinite sequeηce, it would always be possible to find a finite sub-sequeηce summing to a number larger than any you choose - but couldn't prove it.
It is relatively easy to show by hand that any way you arrange 12 +'s and -'s always has a sub-sequeηce whose sum exceeds 1. That means that anything longer – including any infinite sequeηce – must also have a discrepaηcy of 1 or more. But extending this method to showing that higher discrepaηcies must always exist is tough as the number of possible sub-sequeηces to test quickly balloons.
Now Konev and Lisitsa have used a computer to move things on. They have shown that an infinite sequeηce will always have a discrepaηcy larger than 2. In this case the cut-off was a sequeηce of length 1161, rather than 12. Establishing this took a computer nearly 6 hours and generated a 13-gigabyte file detailing its working.
it's a more expedient answer during those times when you don't feel like explaining your research to someone who doesn't seem particularly adept at basic algebra, simply wants to be friendly, subsequently asks about your work, and only expected a simple answer (but as to why they expected such a thing is beyond me). [1]that kind of answer gets misconstrued, if you're not specific. occasionally i'm asked if i teach junior or (senior) high school.
"oh, 13th through 16th, and the occasional 17th grader." (-:
if the students aren't paying attention to you, then what's the point of putting in the effort to teach them carefully?coupled with the constant excuses of "i had to miss class because .." or "but my high school teacher told me .." it's enough to make you wonder how students ever learn mathematics at all, and if you were some sort of social mutation to whom maths was somehow natural ..
..if you're a good teacher, then you always get through to your students and they can succeed.i believe that as much as if you work hard enough, then you can become a multi-millionaire. it is surely possible, but the odds are bad and most of the time, circumstances don't favor that outcome.
i can give the best lectures that i can .. that i care to give.some of my colleagues may argue that if the student is committed, then s/he will put in the effort to get what they can from our lectures and the course in general.
when i do, then i feel expert and in my full powers. many of my students would look up to me and i receive their esteem. simply put, it makes me feel good.
it will probably impress the students, put me in a good light, and continue to give me good evaluations. it will be good for my career if i keep doing this, and only make stronger my case for tenure.
the question is whether that really matters.
if my students don't get anything out of the clearest, most intuitive lectures that anyone can give, then really: what's the point?
awareness, i believe, is not only a personality trait; with time, it can be learned. the awareness that is relevant to a student in my course is being aware of what problems are hard, why they are hard, and what steps are needed to overcome these difficulties. the point of the clarity in my lectures is so that my students can cope with the more difficult aspects of the course, by means of a few basic but useful principles.so it's not clear to me:
study habits are precisely their namesake: they are habits, and they can be learned too. some students never learn these habits to do well at the university level [1], which means that it is up to me and other university instructors to promote these habits. in particular, it means convincing students to change their ways, which often means that they should do things that they are not comfortable doing or simply don't want to do, like ..
.. reading the textbook ..
.. asking questions, answering questions ..
.. "showing enough work to demonstrate understanding of the problem, the solution, and related concepts to them" [2] ..
that said, commitment is a two-way street. who in their right mind would commit to responsibilities that offer no reward, tangible or otherwise?
.."so what do you do all day?"lately i've felt like answering:
"i've been trying to build impossible geometric objects, in order to show that certain mass distributions [1] cannot possibly exist."as you may guess, my recent obsession has to do with finishing a proof by contradiction .. which i suspect is a means of inference that most people are uncomfortable with.
come on: everyone knows what vector addition is!.. thinking about it, maybe i should have done exactly that! [1]
do i really have to go over the first section of the first chapter?
surely there is a more efficient way .. maybe i should have built a worksheet, have everyone work it out in a few minutes, go over the answers, and then go on to something more interesting ..
tomorrow is my first day of teaching for the spring semester;oh well: my classes meet in the afternoon, so i guess i'll write them tomorrow morning.
today i spent 8 hours in the office, i was busy all day ..
.. and yet i still haven't written out my lecture notes!
i didn't go to the office,i wanted to, i tried to write up notes for a research idea. there ended up being a flaw in the argument and so i thought, off-&-on about the problem ..
i didn't answer any student emails that i didn't have to answer.
i didn't make sense of my life,
i didn't travel out of town,
i didn't make any new goals.
for the most part, i didn't want to do anything.
