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It is generally acknowledged that one should try to get recommendation letters (for grad school, jobs, etc.) from well-known experienced members of your field, if at all possible (for e.g. see some of the answers to this related question: Do letters of recommendation typically include a biography of the writer?). Of course, sometimes this is not possible.

I am a first-year postdoc (in mathematics, but perhaps this is not relevant), and a masters student in the graduate-level class I am currently teaching approached me to write a letter for them when they apply for PhD programs. I am a natural person to write a letter for them since they are interested in the field that I teach (topology) and I'm teaching one of the three courses they are taking (since application deadlines are quite soon, they won't have taken any other courses here before applying). Of course, I am also a poor choice (which I mentioned to them) as a relatively unknown person with little experience.

While it makes sense to me that recommendation letters from senior research-focused faculty are worth more (since they have greater experience interacting with graduate/soon-to-be-graduate students), there are a fair number of students from relatively obscure 4-year universities who apply to graduate school. They might not have had any access to senior research-focused faculty.

What are some things I should keep in mind when writing a recommendation letter for graduate admissions as a new entrant to my field, or perhaps as an instructor at a relatively obscure primarily teaching-focused school?

Statements like 'they are in the top 7 of all graduate students I've ever taught' carry little weight, since I've only ever taught 7! For what it's worth, the student in question is doing quite well, and my goal is to write a well-deserved relatively glowing letter; I would like to make sure, as much as I can, that my letter is not ignored.

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    I would not undersell letters from a junior letter writer. Consider that a senior-level person who may be writing a few dozen letters. Saying you've worked with a person as your only, I dunno what postdocs call grad students, supports your position in that the reader will know that you didn't just meet them once and write a letter for them, but actually worked with them, perhaps wrote a paper with them. – Compass Oct 22 '14 at 13:48
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    To the downvoter, is there a way to improve this question? – Aru Ray Oct 22 '14 at 21:13
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My advice is to start your letter by explaining who you are and your background. For example, you could mention where you went to graduate school and that you think the student could succeed in that graduate program. This will give the reader a sense that you have some idea of what will be expected of the student in graduate school.

Beyond that, you should focus on the same things that more experienced letter writers do.

You need to explain how you know the applicant and give the reader some sense that you've had enough interaction with the student to be able to judge their chances of success. Simply having had a student in a large class isn't really enough here. On the other hand, "I was Johnny's instructor in a senior level topology class with 12 students. Johnny frequently met with me during office hours to ask questions about aspects of the subject that we were not able to cover in class." tells me that you have had many discussions with the student and really know the student well.

You should comment on both the applicant's intellectual ability and their work habits. Ideally, we want applicants who are smart and work hard. An applicant who isn't very smart but smart enough and who works very hard might be a good candidate for admission to a master's program but might be a very poor choice for a PhD program. An applicant who is brilliant but lazy might start to work harder in graduate school and could turn out to be really successful. Some faculty are willing to take a chance on brilliant but lazy students.

You should talk about the applicant's personality and how they get along with other students and faculty members. No one wants to work with a student who is not fun to be around because they're argumentative or depressed all the time.

You should talk about the applicant's communication skills (both writing and oral presentations) and in mathematics you should comment specifically about their ability to write mathematical proofs.

If it's relevant (and it would be for any area of applied mathematics) you should comment on the applicant's computing skills. What languages and specialized packages have they used in their work with you? Have they been able to produce programs of any substantial size?

You should check that what you've written matches up with the student's transcript and their statement of purpose. For example, don't say that they're one of your top 5% students if their GPA is 3.0. Don't say that Johnny would be a great master's student if he's applying to a PhD program. If the "story" told by the applicant's application file isn't consistent, then I'll be much less likely to admit a student.

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    I would end the letter by explaining who you are and your background - start with the actual letter of recommendation; your bio is, in essence, 'metadata' or 'appendix' that would come after the content as some extra justification on why the actual content is trustworthy. – Peteris Oct 22 '14 at 14:49
  • I agree with Peteris that it makes sense to talk about who you are at the end of the letter rather than the beginning. The point is to say this somewhere in the letter. – Brian Borchers Oct 22 '14 at 14:52
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Providing an anecdote about your interaction with the student which highlights his or her competencies will make your letter stand out, as well as making your letter more readable.

Choose an anecdote that will resonate with the desires of the reader - in this case, finding an articulate, self-motivated and talented researcher.

Far from being inappropriate for reasons of formality, a properly constructed and relevant anecdote about the student will speak volumes to the reader.

"Alex came to me with a particular problem he was facing in understanding elliptical functions. I wasn't able to help him greatly at the time - as it was grant-writing season -- but I suggested that he review Walker et al on the topic and we would discuss it more fully later. Alex returned having not only read Walker, but had downloaded the relevant open-source codes and had made a start on amending them to his problem, solving his original problem and actually identifying a serious flaw in the code which he had started to address".

(Completely fictional. I don't even know what an elliptical function is. Or if there is, indeed, a Walker et al. on the topic.)

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    There seems to be a Walker et al. on any topic. (great example by the way) – xLeitix Oct 23 '14 at 12:23

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