Plagiarism always prompts an annual ritual of reflection for me. I’m lucky it’s basically annual; it could be twice a year, since there are two semesters, but it’s really a December problem. Why? No one dares plagiarise with me in May 🙂

In December, though, people don’t know me well enough yet. They think I won’t notice that the words they typed don’t answer the question I asked in the assignment, or they think it’s the right way to do things (?!) despite all the conversation to the contrary in September and late November, or they think I don’t actually read what they write. In December, it’s dark and students want to get out. They’re nervous and doubt themselves and their writing skills. They realize approximately 36 hours before the assignment is due that writing math is not like writing English, and they fall back on the sentences of someone in the first 10 Google search results.

I’m sure I don’t catch everyone and everything. But I have an ear for language: I can tell when someone’s writing like they talk, and when they’re not — and I talk to every student I’ve got. (It’s a luxury to have <40 students a semester and be able to learn names and talk to every one!). I notice when the cadence changes, when the vocabulary shifts. Every year there are sentences that I’m sure, sure, a student didn’t write themselves, but I can’t find that sentence out in the world. And every year there are sentence that I’m sure a student didn’t write and that come up in the sources they cited or in the sources I find that they didn’t cite.

(Yes, I spot-check citations. I’m not perfect — in one paper, I thought to myself, “Wow, it’s really interesting that someone named Nakamoto wrote about linear regression *and* about Bitcoin!” and not until the next read did I realize this student was sprinkling citations randomly throughout her paper. Really randomly. It’s as if citations were sprinkles on a cupcake — they make the cupcake look good & it’s the density that matters, not the placement. This student cited Nakamoto’s paper on Bitcoin to justify her use of linear regression, an article about the internet of things to bolster the discussion of currency exchange rates, a review of a book about statistics that included linear regression in the name to support her equation for log returns, although maybe by now I’m permuting things myself. The references were often relevant to the paper; they were just randomly sprinkled around like decoration and after four rounds of revision I didn’t really force any improvement….)

Anyhow, back to plagiarism. There’s almost always a reason given. “I was nervous, I didn’t know, I thought their wording was better, I figured since they were published they were right.”

I try to address all these concerns beforehand. “Send me drafts & I’ll pre-grade it! I’ll help you with wording! It’s ok if it’s not perfect! Writing math is hard — I expect it to be awkward when you’re learning!”

Most students believe me, at least eventually. Many send me their drafts & I’ve caught some plagiarism or near-plagiarism there, and if it’s in a draft I just let the student know & they re-write it & it’s fine! Learning experience for all, round of applause.

But there’s always someone who doesn’t believe me. No drafts or as few as possible. The desperate hope, as far as I can tell, that if the work is turned in at the last minute I’ll just give it an A without looking closely. And then usually the cascade of emotions afterward, when I give the work a poor grade.

argh.

PEOPLE! In general, I hate grading with the passion of at least ten suns. I’d like to poke a fork in my eye every time I’m marking exams, ok? My whiskey consumption goes up slightly at equidistributed intervals during the semester, corresponding to midterms and other exams — it’s always one problem that does me in, really, the rest’s not so bad. Grading makes me see in acute relief what I should have taught differently, spent more time on, etc.

But reading student writing, engaging in a dialogue and finding out what students have learned and thought and discovered? That’s actually interesting and fun and enjoyable, if students actually learned and thought and discovered! Basically the only reasons I’m still in academia are the joy of discovery and the dialogue through the written word. I love interacting with people through writing, and that includes editing and feedback and then discussion afterward. I’m far from perfect. I’m not always a consistent editor and I’m not always the most careful reader. But I really do engage with my students’ papers and the work I do with coauthors and colleagues. I like it, it’s that simple. And so as I’m having a conversation with your paper, I’m going to have questions and go search for them. I’m going to listen to the rhythm of your voice and see what it has to say both through what’s said and what’s not said. I’m going to notice if you don’t answer my questions, at least if you don’t distract me with something more interesting. And I’m going to notice if it’s not you talking to me, or if it’s not you talking to me.

I’d rather have your crappy English-math sentences than what you think of as someone else’s perfect reflection. Their reflection probably isn’t that good, anyway, and I’m not interested in anyone’s thoughts but yours!

The end of the semester is upon me (and many others). It’s time for editing papers and reviewing lots of things, as well as working on my own writing. I’ve got three senior project students, three other research groups, and my own papers-in-progress. Some themes recur.

Big analogy: You’re waltzing or salsa-ing at a delightful party. Pick the music to suit your paper.

• The paper author is the leader in this dance. A good leader shifts pressure back and forth from the base of the palm of the hand to the fingers, and up and down, to tell the following dancer what he intends, three-quarters of a beat before it is to occur. I’m not a great dancer, but when I am partnered with a great lead, I know exactly what’s coming and I can do my best to execute — and I end up looking like a good dancer! In the math paper, tell the reader what move is coming. It is ok to say, “Now I’ll define factorials, which are the number of ways n objects can be arranged in order.” If the reader knows what is coming, she can prepare, and she’ll feel successful!
• Build trust with your reader/follower before asking for faith. Before you can carry out fancy moves, you need trust with your reader/dance follower. Don’t ask the reader to read three pages of complicated stuff without telling them where you’re going. Do tell them explicitly where they’re going first. Don’t confuse motivation with explicit signals like this — telling your dance partner, “This will be great in an hour!” is not the same as telling your dance partner, “You will twirl and then we’ll go backwards for a measure.” The second builds trust. The first sounds good, but the reader may not trust you yet.
• The number of words you write is proportional to the faith you ask. Reading takes time, as does dancing, and time is something we can’t recover. If I’m not dancing with the person I’m in love with, I like best dancing with someone who alternates between fancy moves & relaxing bits. Dancing salsa with someone who never does turns or twirls is boring. Box stepping through an entire waltz is boring. Too many words without math ideas is boring! One easy way to start dealing with this is deleting words if they aren’t necessary. “In some sense these are dual to one another, where we define dual to mean…” -> “These are dual to each other: define dual as…”  “We will present a defintion…” -> “We define…” It helps you get to the fancy moves faster 🙂
• It’s a party! Introduce your guest to everyone! References and citations are not just for information you used to do the math. They’re also resources for the reader if she’d like to learn more or follow up on a tangent or know who else worked on this. So introduce your reader to everyone else at the party! and use names! Rather than, “See [1],” it’s so much more hospitable to say, “To read more about algebraic varieties, see the excellent book by Smith, “An Invitation to Algebraic Geometry.””
•  Seriously, introduce your guest. Here are the people I hang out with (mathematically) all the time and their related papers. Here are the folks I totally disagree with in approach, but we talk about the same math. Here are the people who did the original work on this problem — it was 40 years ago but they can still dance! Here are some good additional resources. Besides being hospitable, references show that you have a command of the field, they make other authors feel good (someone read my paper?!), they allow the reader to potentially notice that there’s a set of articles on the same topic but in math physics that you never heard of and you should really get introduced…!

Ok, that’s it for now. I’m by no means a perfect writer, but it’s a skill I work on regularly. Good luck!

(Yes, I know my dance example here is super heternormative, but trying to do something clever about it would not help the reader or the message…)