are the dollar signs worth it?

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."

my younger self used to be so smart ..

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.

ARR, MOAR!.. or: "active" = passive.

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.

An open letter to panicked calculus students, after their final exam.

[to put this in context, i had a more vicious version of this letter in mind .. but after some contemplation, it seemed wiser to be diplomatic.]

---

Dear Student,

This is to confirm receipt of your email which was sent shortly after the final exam of our course. I realise that Finals Week is a stressful time for you, as well as every other student at our University.

Being that our final exam ended very recently, the final exams for our course are not fully graded. In fact, they are not even halfway done. Fair grading, especially that which rewards students for their understanding of the concepts treated in this course, necessarily warrants care, and therefore, adequate time.

That said, barring a rather poor semester-long effort on your part (in which case your grade will be already close to failure) I have no idea yet what your final grade is. Based on the scores preceding this final exam, it looks likely that grades for this course will be put on a curve, and it will not be clear how the distribution will look until the final exams are fully graded.

That said, it is futile for you to ask about your final grade. Either be patient or stop asking because I, your instructor and grader, simply have no answer for you yet. In fact, your (and your fellow students's) sending me these sudden emails is causing a great annoyance to me; it even affects my focus on grading exams, which further delays any outcome you would like to know.

Keep in mind that if you are writing me now, then very likely other students are doing the same. All of you point to extenuating circumstances in your situation, many of which do not pertain to University guidelines for exceptions.

By the very definition, exceptions are rare. Please think twice before you consider your situation a truly rare one.

---
Regarding your inquiry into "extra credit" there is none available. If there were such a possibility, then it would have been properly announced on the course syllabus, as distributed on the first day of classes.

To offer you an additional opportunity now would be unfair to other students and therefore unethical of me; being that it is Finals Week and other students will likely have arranged their schedules to best prepare for their other exams or term papers, to offer everyone a chance for extra credit would be unreasonable.

In particular, I have reiterated the same consistent policy to other students in our course, earlier in the semester, and in light of this, they have chosen to withdraw from this course. So to offer you extra credit would be a disservice to those students who made the most reasonable choice with the options made available to them at the time.

You are asking something unfair and unethical. I will not grant this request.

---
I realise that you may be writing me not on your own rational consideration, but in the heat of panick or perhaps on the suggestion of your parents, your friends, or even your academic advisor. In that sense, it is possible that you initially did not want to send me your message in the first place.

That said, please understand my position in this scenario. The grade breakdown in the syllabus has been clear from the start. Barring exceptions given in the University guidelines, every student is graded in the same way. In particular, that means I grade every student based on his/her written work, and that alone.

So by writing this panicked email to me, you have an answer that you could have deduced on your own. Moreover, the time I spent writing this reply could have been more efficiently spent on actual grading of exams. This means that you have delayed the answer to your question; worse yet, it means that you have delayed a definitive answer to those other students who have the same question; in particular, you have just inconvenienced your fellow classmates.

There has been no benefit to you by writing to me now. This has been a waste of your time and mine.

Sincerely,
Your instructor.

I'd rather students be honest, but if they're going to be efficient about it...

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.