on hope, and the learning process.

Grading upsets me.

I think it's because I am a closet perfectionist, despite my occasional, outwardly relaxed appearance. Details do matter and so does rigor, otherwise I'd be a student philosopher and not a student mathematician. Then again, there are plenty of non-rigorous bits of mathematics done, each and every day. But we're supposed to try for correctness and accurate, logical thinking.

I keep reminding myself that most of my students are about 18 years old, and about 6 years younger than I am. Most of them have just arrived from high school, where mathematics may have been glorified computations, excessive formulae, and few insightful ideas.

They may not have been asked to justify their answers in the way we, as Calculus instructors at UM Mathematics, demand them to justify.

It may be that, aside from logical reasoning when writing essays, they've never been held accountable for this sort of thing. They may not be used to thinking of a generic case, or searching for a pathological situation or worst-case scenario in order to compare with what must "always" be true.

That's a lot of 'may's and it tries my patience. It only convinces me that perhaps I'm not well suited to the life of an educator. I have enough trouble with my own shortcomings, so how do I deal with those of others?

It's not easy to find hope in this line of questioning.

---

I went to a dinner party last night and to be simplistic about it, the other guests were bourgeoisie-in-training: law students, MBA students, and an Urban Planning and PolySci Ph.D. student each.

There's nothing wrong with these people, mind you, because the world has to keep running. Money is an important commodity to everyone, and I say these people are being exceedingly realistic. I just choose not to be one of them, because the world and its people frustrates me too easily and quickly for my taste; more importantly, I don't have a mind for money.

One of the MBA fellows half-asked/half-told me, "You must be really smart, to study mathematics!"

I replied, half-jokingly, "I wouldn''t say that. Nobody's actually good at mathematics. It's just that mathematicians just never give up. We're just stubborn that way, and we just try and try."

(It's not entirely accurate if you believe that some people are either 'naturally' good at maths or have learned to be "good," but in light of how frustrated mathematicians can be as a result of their exertions, there must be a speck of truth in this.)

---

Maybe that's it, then. Maybe it's just enough to try, and by trying, to reach some modicum of improvement. It's evident that my students are trying, either for a good grade or for a good understanding of calculus. The end doesn't matter so much, but they are trying.

That has to count for something: it did when I was such a student and my teachers had to grade my shoddy work.

Hope always lies in possibility. Perhaps my students will make their mistakes now and when their exam comes, they won't make them again. Perhaps they will learn more than simply how to do well on their exams, and appreciate a little mathematics for its own sake, which belies appreciating the fundamental logic and reasoning for its own sake. Perhaps it's worth the frustration of grading.

Those are still a lot of 'perhaps,' so here's to hope. \: