Let’s be blunt: I’m not good at giving feedback. I tend to lay things out with little (read: zero) padding. My former linear algebra* students will understand what I mean immediately. Did you include a meaningless sentence? Did you try to prove linear independence and instead show me that 0 = 0? Here’s what I think of that:
I’m lucky to have an REU group that takes my criticism in stride. They realize, I think, that it’s the math that matters. My comments, though critical, are not judgments of the students. Anything that obscures the math (or worse, misrepresents it!) is a problem. Too much detail is as bad as too little detail, but these are subjective norms decided by the mathematical community. Yep, proof is a social construct. What makes a proof good is much different than whether it’s a proof.
There are many ways in which I think I’ve been a solid REU mentor, but the place where I give myself the harsh feedback is in my transmission of this sense of style. Partly, this is because every mathematician has a personal aesthetic. One’s criteria for “goodness” comes from reading papers (and liking the style of the papers that he or she finds easiest to understand), from writing papers, from having papers refereed (and then refereeing papers). And there’s a difference between a paper that’s pleasant to referee and a paper that contains useful (again subjective!) mathematics.
So, I’m left with this unresolved question: How do you begin to help students develop their math paper writing skills? It’s much harder than just writing up proofs that happen to be true. I don’t really feel like I’ve been helping the students learn anything except how to use the “todonotes” package in LaTeX. Your comments are welcome. Feel free, too, to rip on my writing.** If I can dish it out…
*At Hamilton, linear algebra is also the “intro to proofs” class. As such, it’s writing intensive. This designation means that I grade proofs assignments once or twice a week. At my lowest point, I’ve written “duh” on a paper (and I won’t do that again in linear algebra; senior theses, however…). I have not yet written “aardvark barf” on a paper, but I do remember that particular biting comment making several appearances on drafts of my dissertation.
** I specifically avoided using my Grammarly plugin and my spell check so you’d have plenty to criticize!