a thoughtful web.
comment by Devac
Devac  ·  733 days ago  ·  link  ·    ·  parent  ·  post: An Axiomatic Approach to Algebra and Other Aspects of Life

Grading those exams is painful because the class uses online math homework, so for many, the first time they have to write a proof for another human is on that exam. Each answer you have to read closely to see if they understand the ideas but can't explain them well or if they just wrote random words on the page.

Damn, my most sincere wishes of good will toward you should manifest in some sort of alcohol in front of you about now. Not to mention that this format just feels wrong. Making an exam on something that most people never attempted before must look to students completely arbitrary on top of that. Like a medical school that ends with a pie eating contest to determine who gets to become a doctor.

Anyway, you and I should be thankful that we've had something of a nonstandard education in math, and do our best to help others see what we see.

The thing is that I wasn't all that aware about the gap. But I do agree, the least we can do is to show that maths is not about learning some schema but about actually deducing solutions and formulating proofs. Hell, now I feel like I should rewrite most of the complex numbers primer that I made since I have assumed that the reader is prepared to do some heavy lifting instead of (at least that's how it seemed to me) being 'spoon-fed'.

On that note, it's probably for the best that I didn't share most of those Maths for Project Euler sheets. After about second part I have started shortening proofs and fell into the mathematicians mindset of "but that's a trivial step, removed". XD

lm  ·  733 days ago  ·  link  ·

Like a medical school that ends with a pie eating contest to determine who gets to become a doctor.

This is a disturbingly apt comparison.

Hell, now I feel like I should rewrite most of the complex numbers primer that I made since I have assumed that the reader is prepared to do some heavy lifting instead of (at least that's how it seemed to me) being 'spoon-fed'.

I say leave it as-is. At least part of the problem I see is that bad math education tends to hand people properties that seem to have appeared from thin air. On the other hand, if you say, "why is X true?", then that gives an explicit clue to people that they should (if interested) sit down and try to work that out.

Proofs are tricky things to write, but I do prefer a proof written to explain, rather than simply to derive the conclusion. A little exposition here and there can go a long way towards showing others the relationships you see. I am hardly innocent here, though!

I do need to work out a good way of writing proofs in LaTeX. It feels like mine always get compressed into a paragraph of math symbols. Maybe I just need to focus on writing a sentence or two of exposition per step and make one paragraph per conceptual step.

Devac  ·  733 days ago  ·  link  ·

I do need to work out a good way of writing proofs in LaTeX. It feels like mine always get compressed into a paragraph of math symbols. Maybe I just need to focus on writing a sentence or two of exposition per step and make one paragraph per conceptual step.

I assume that you want it for notes and not publications, right? I have been using this style for student physics club handouts and it seems pretty well received. Sometimes with margin notes, if I had some general remark about the proof as a whole but could not figure out how to fit it into the text.

lm  ·  733 days ago  ·  link  ·

Oooh, alignat looks nice! I'll keep that post in mind next time I write a proof (which will hopefully be soon--I've got a little side tangent that I've been working on here and there that I'd like to get online sometime soon). Thanks!