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I am a math professor at an R1 university. I have taken up a new graduate student (my n'th for n<=10), who is mathematically quite strong, but whose writing skills are a couple notches below what I have had to deal with so far.

We have a new result, which he currently is writing up. He is relatively new to English, and his native language is much unlike English. Though one can understand what he says in a conversation, writing a paper is a real struggle.

Most research students that I have worked with start with poor mathematical English skills. Their first drafts have several major problems, and require many rounds of thorough revision. However, there is always at least something which is right from the start. In contrast, this student's drafts appear nearly unsalvageable: they have hardly a sentence in common with any proper exposition. I have lost the track of revision number, but it is likely to be in double digits now.

The student is working hard, and the draft is showing some signs of improvement. However, I cannot shake the feeling that there should be more that I can do than provide extensive feedback. I am also worried that if this continues for another few months, the student can get much discouraged.

I believe that a part of the problem is the sudden jump in writing difficulty. The mathematical content of the paper-in-writing is more complex than it is typical for a first paper of students that I have supervised so far. This makes the writing task harder. I wish only that the student could practice on a simpler, shorter paper first, to provide a smoother transition from writing homework exercises.

I am looking for suggestions. Note that I would like to avoid writing the paper myself (which would be far less work for me than this), for I want the student to learn how to write himself.

What I have done so far:

  • extensive comments on drafts, with some verbal explanations

  • suggested some mathematical readings which I know are well-written (to learn by example)

  • provided general encouragement

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    A key point I can’t see addressed in your question is what your student thinks of all this. Is he aware that his English and writing skills are holding him back, or is he saying to himself “My professor is prejudiced against me, Google Translate says it’s English!”?
    – Martin Kochanski
    Jul 8, 2019 at 17:51
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    @MartinKochanski He is working hard on the writing, so my impression is that it is the former. However, "working hard" is not the same as "making much progress", hence the question.
    – TeacherOfMathEnglish
    Jul 8, 2019 at 17:54
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    Reading is often an important stepping stone to writing; does the student read enough English-language papers in mathematics?
    – Bryan Krause ♦
    Jul 9, 2019 at 15:40
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    Did the student ever take English classes? Or is he trying to learn by himself? Perhaps an "English as a second language" class would be a very useful investment.
    – Aubreal
    Jul 9, 2019 at 20:30
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    @Alexandred'Entraigues For the same reason that students with limited mathematical skills sometimes end up in PhD programs: inability to perfectly assess the "skill", strength in other area that compensates the weakness, competition for stronger/more perfect students.
    – TeacherOfMathEnglish
    Jul 10, 2019 at 19:22

10 Answers 10

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My wife, who was a writing coach for scientists, once had great success with a native speaker of Japanese whose written English was poor. She suggested he write the first few drafts in his native language, so that he could be sure he had the main ideas right. Then he translated his own work into English as best as he could, ready for revision.

Another possible strategy with a similar goal (getting the structure and basic ideas right first) might be for you to sketch a first rough draft, with the theorems in place and some of the expository scaffolding. Then the student could work on fleshing out the proofs and adding details - to be revised, of course.

(I wish I could check that second strategy out with my wife.)

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    This is the first idea that springs to mind. The student is apparently capable of the subject, and assumedly of writing conpetently in their first language, so why not start there and gradually transform it into an English-language text? The last stage would be supported by the suggestions of other answers, like a writing centre or ESL tutoring.
    – Nij
    Jul 9, 2019 at 5:06
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    From a language learning point of view, translating a text from ones native language may not be the best way to learn a language. Ultimately one needs to learn to think in the other language directly, or one will never reach fluency.
    – gerrit
    Jul 9, 2019 at 8:50
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    However, it is much easier to structure an essay in one's native language, @gerrit. And there's no harm in trying both approaches at different times.
    – TRiG
    Jul 9, 2019 at 11:01
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    @GeorgeM I wouldn't suggest a translator. After the native language draft is done the student should do the translation, en route to learning to write in English from the start.
    – Ethan Bolker
    Jul 10, 2019 at 0:46
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    This is the strategy that I use with non-native speakers who get stuck, either in speech or in writing. Say it in [Italian] first and then self translate. It's a slow process, and it's not infallible by a long shot because word-for-word translation has huge pitfalls, but at least they are able to communicate basic ideas.
    – Mari-Lou A
    Jul 10, 2019 at 7:39
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As a partial answer, perhaps your university has a writing Center you could refer the student to for help. For example the University of Wisconsin-Madison has a writing center and Texas Tech even has a graduate writing center.

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    Even community colleges have writing centers these days. If the OP's university doesn't have one, the student may do well to sign up for a writing class at the local community college which would give him access to their writing center.
    – user104070
    Jul 9, 2019 at 23:47
  • This class will help students whose English is already at intermediate level or higher. Pretty hopeless in cases where a student cannot write a single coherent English sentence. In speech, there is often context and a non-native speaker's gestures and facial expression will provide essential clues that enable us to guess with a certain degree of accuracy, meaning and intention. But this interpretative skill becomes almost useless when the speaker's communication/message is transcribed, then we only have context to go on.
    – Mari-Lou A
    Jul 10, 2019 at 7:34
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    Another way to put it: This is not your job; send your student to somebody who does have this as their job.
    – Anonymous Physicist
    Jul 10, 2019 at 11:19
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    This was my first thought. I've worked in several writing centers, and I've had many graduate students over the years who came in for recurring visits. A good tutor or consultant will give scaffolded feedback that, over the course of a few months, will most likely make him into a stronger writer. Ideally this student would have multiple points of contact: an advisor can focus on discipline-specific writing skills, a writing center can focus on building general writing skills (from planning to sentence mechanics), and perhaps a graduate writing group can help him with motivation.
    – TaliesinMerlin
    Jul 10, 2019 at 16:12
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I'm not offering a full answer, but your question really moved me. I am a non-native English speaker, who studied at LSE (a while ago now), and did well. However, a few of my classmates, also not first-language speakers, did find it heavy going - all were bright enough to take content IN, but getting it OUT was an issue. I saw their frustration and often embarrassment, which is exacerbated by the fact that they were top performers at their home universities. I offer this - which is fairly non-academic advice, I'm sorry - if you want to really help, encourage your student to use English more in their day-to-day life, and to get themselves into all-English settings. One of the challenges with big, high-profile universities (esp. in the States) is that there are such large foreign communities that, as a student from, say, China (I'm not) - I would be able to basically remain in a Chinese-speaking bubble. This is, of course, wonderful in many ways, but it also means that I never cross the bridge (only done by being immersed in a linguistic environment, which is rather uncomfortable for a while) to the land where I now feel the new language is also a part of me. Once once this transition is made, I can deal much more comfortably with such abstract topics as you suggest.

Your student needs the playful interaction of everyday messiness, not because they need to use nuance and idiom in the paper, but because their English-worldscape sounds, to me, still quite small. It's an issue of confidence, not perfection.

Now, it does not sound like you have the time and resources to do this, and besides, ordering their nonacademic life is quite outside your ambit. So I don't think this can be of much help; but I do think that, in an ideal world, this is where the answer lies.

Finally, this is not meant to be pro-English. In fact, native English speakers have it worse, because you get by in so many places in the world using only English, it's rare to find an academic also able to ply their trade in another language. Moreover, and as academic you be most likely only ever targeting English journals.

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    Yes, immersion works.
    – Peter Mortensen
    Jul 9, 2019 at 14:08
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    a +1 to this answer, with the added caveat that conversational English is very much unlike academic writing English. One would need exposure to both (both formal and informal).
    – Tasos Papastylianou
    Jul 10, 2019 at 9:37
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Have them write up mathematically simpler things first, to reduce the English complications.

Giving fairly-formal oral presentations, on relatively simpler things, can also "expose" in real time issues with formation of sentences.

I do also encourage my students, native English speakers or not, to write as-simple-as-possible sentences, thinking in terms of subject-verb-object, rather than lengthy compound-complex sentences. (Many textbooks and papers are bad models in this regard.)

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    Something absurdly simple perhaps, such a proof that the square root of 2 is irrational, and go through it with him carefully. But make sure he knows why he’s doing it, and what the aim is.
    – Martin Kochanski
    Jul 8, 2019 at 17:55
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    As a non-native speaker myself, I have to disagree. Grammar, sentence structure, and vocabulary are all things that aren't that different between a new result or an easy old result. The student doesn't seem to have a problem with the mathematical concepts themselves but lacks the feel for the language; reading a lot of well-written texts (even/especially fiction), possibly along with (non-mathematical) ESL classes, will probably help them much more.
    – Guntram Blohm
    Jul 9, 2019 at 7:28
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    @GuntramBlohm I have to disagree with your disagreement. Difficult proofs are difficult to write even for native speakers, and new grad students are often very poor at writing proofs -- this may be surprising if you've never worked with grad students in a mathematical subject. The student here is trying to run before they can walk by trying to write a difficult proof in a language they're not very good at yet. This answer tries to address one of the two problems the student is facing at the same time.
    – David Richerby
    Jul 9, 2019 at 10:40
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Ideally, the student needs a tutor, preferably someone trained in ESL (English as a Second Language) and also familiar with the student's native language.

Ideally, but probably impossible to find, is someone conversant in mathematics.

The student probably needs a crutch, but also a plan to be able to throw away the crutch before he graduates.

This isn't, of course, a zero cost solution, but it might be worth it if the student truly has promise to contribute.

Of course, writing in the student's native language is another possibility, but it would, then, be hard for you to evaluate it. A colleague with the required language and math skills might be able to do that. This might be preferred if the student intends to return to his native land eventually.

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    A tutor doesn't need to be private, see the above answer about writing centers. Some universities may also offer translation help for foreign academics, and the student may be able to be rolled into that general category.
    – user104070
    Jul 9, 2019 at 23:29
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Recommend the student to take an advanced English grammar and vocabulary course, at CEFR C1 or C2 level. My English is fine but if I were tasked with writing a scientific paper in German, I would probably make grammar and prose errors averaging more than one per sentence, unless I spent a huge amount of time double checking everything. A CEFR C2 course is aimed at reaching a level of fluency in writing comparable to a native speaker. They might need to take a C1 course and pass the C1 exam before entering C2, but C2 would be really good to have. The university probably offers such courses.

This will be much easier if you are located in an area where English is the primary language of communication, but even elsewhere many big cities will have CEFR C2 English language courses, and otherwise student can take such a course online.

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    If the student is a student in an English-speaking country, they should be able to sign up for such a course as a natural part of studying there
    – user104070
    Jul 9, 2019 at 23:34
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    @GeorgeM This is true, and possibly in non-English speaking countries too (but maybe not all universities worldwide offer quality C2 education).
    – gerrit
    Jul 10, 2019 at 7:27
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You could rewrite the paper with the student. This will expose the student to their mistakes (which they'll hopefully identify themselves in the future) and to good writing (which they'll hopefully strive towards in the future). Unfortunately, it is a highly labour intensive approach. As an alternative, one of your better students could rewrite the paper with the student (possibly in exchange for co-authorship, which seems reasonable, given they'll be rewriting the paper).

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    Rewriting the paper with the student is what Frank Harary used to do, and not just with foreign students. The results were good, but, as you said, it's a very labor-intensive approach.
    – Andreas Blass
    Jul 8, 2019 at 18:30
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    What do you mean by "rewriting" the paper? You mean physically sitting at a computer together and writing? Because currently, in addition to feedback about overall structure and grammar, etc, my feedback also includes replacement sentences and sometimes paragraphs. If I simply rewrite it offline, then I am afraid that it will not teach the student to write their next paper.
    – TeacherOfMathEnglish
    Jul 8, 2019 at 18:57
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    It is exceptionally difficult for anyone, even a native speaker, to learn from extensive comments on drafts. (I have experience of receiving and later on in my career of giving them). I learned that better progress is made if you start by focussing on the logical structure of the argument - maybe by drawing linked boxes on a blackboard - and only then moving on to sentences and grammar.
    – JeremyC
    Jul 8, 2019 at 22:09
  • @TeacherOfMathEnglish By "rewrite the paper with the student," I meant physically sitting at a computer together and writing.
    – user2768
    Jul 9, 2019 at 7:53
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    That is a good method of learning a language (not sure if it's the fastest one, though). That's how I was learning Japanese: I would write a short essay first, at home, then print it on paper, bring it to the class, fix it together with the teacher (crossing out, circling and drawing arrows to indicate which moves where, changing or adding some stuff), I take it back home, stare at it for a while, incorporate the corrections into my original text, print it on paper, repeat. Would take several weeks for a single paragraph at first (with a class twice a week and my level close to zero).
    – Headcrab
    Jul 9, 2019 at 8:21
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Have them take a look at this online course by Berkeley: Academic and Business Writing

edX may very well have exactly what they need if this isn't quite it. It's remarkable how much information and graded instruction is absolutely free or low cost on this platform by Harvard and MIT.

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  • Not enough up-arrows to click here :-)
    – user104070
    Jul 9, 2019 at 23:35
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Here practice makes mastery. Let your student be exposed to a lot of articles similar to those he has to write, and ask him to try to copy their style.

Also, review his writing with him and point out different ways to express his ideas that fit better in your context

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TL;DR

Suggest him to write a blog or more simple content, like technical reports.

As you said:

I believe that a part of the problem is the sudden jump in writing difficulty.

This is a big challenge. Writing regularly on a blog will help him to gain experience and writing skills. He might start trying to explain his work for a non-math audience, and then try to go deeper and details and complexity, as the paper requires.

You can also ask him to summarize his weekly work/research in a report (article-like or free form), just for getting used to different writing styles and contexts.

For now, if there is no hurry with that paper he can keep iterating or if the paper is unsalvageable, you can kindly suggest him a different paper structure to start from or divide it into more manageable parts for him.

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  • Yeah, only what he needs is feedback on his writing, and a blog will no provide that.
    – user104070
    Jul 9, 2019 at 23:46
  • I disagree with you. As the OP consider there is a sudden jump in writing difficulty, the student needs to practice in a more simple context. He will receive feedback not just from the OP, but from other people who read what he writes. Obviously, you can learn how to drive doing it in a motorway and receiving feedback, but it is not the best way to learn it.
    – gustavovelascoh
    Jul 10, 2019 at 10:55
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    If his English is that bad, he won't get any feedback at all as nobody will be able to bear reading it
    – user104070
    Jul 10, 2019 at 17:31

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