Asking for a Letter of Reference

A letter of reference is a lttle different from a letter of recommendation, and a reference is not a guarantor.

reference:
  参考、参照、参照できる人、参考になる人など

letter of reference:
  参考になってくれる人からの参考になる（手紙などの）文

つまり、推薦状でもなく、保証人の申し出でもありません。

You provide a letter of reference to give someone an idea of what sort of person you are.
人柄を考えるときに参考になる為に、この文を送ってもらいます。

A referee is completely irrelevant to letters of reference. When you think "referee", think of the guys who call the plays in football and other sports.
"Referee"  と言うのは全く関係ありません。審判のような者です。

[This is not exactly true in the field of law. I'm talking about letters of reference for school and job applications.]
[法律の分野ではちょっと違うことがある。入学志願届けや求職の応募などの話です。]

So I have put together a little sample conversation to help understand the concept and the usage.
以下は概念とその利用について説明するための対話実例です。

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Hana: Professor Williams!

Prof.: Uh, hello.

Hana: Do you remember me? Hana Kinoshita.

Prof: Uhm, sorry, give me some more clues.

Hana: I took your class in foreign language teaching methodologies at Nanboku University seven years ago.

Prof.: Nanboku University ... Ah, yes, I remember teaching there. I was also teaching at Touzai University at the same time.

Hana: Oh, dear. I was hoping to ask you for a letter of reference.

Prof.: You would get a better letter of reference from a tenured professor, I'm afraid.

Hana: But I was hoping for a letter of reference for the methodologies class. I'm applying for post-graduate teacher training at a college in the US.

Prof.: Well, if I were at my desk where I could look at my records, I might remember better. Can you send me an e-mail to refresh my memory?

Hana: Oh, well, I guess I can.

Prof.: And maybe you should get a letter from one of the tenured professors, as well.

Hana: I'll try. Can you write down your e-mail address for me?

Prof.: Got a pencil?

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Don't worry. Forgotten but not forgotten.
忘れていると思うのは仕方がない。記録はあるはず。記録を見たら、思い出せるでしょう。ただし、さらに一人、違う人にも頼んでもいい。

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To: jill7williams (at) groupmail.net
From: hana.yesterday (at) rose.readmail.ne.jp
Subject: Letter of reference I asked for today

Dear Prof. Williams,

Thank you for taking time for me this aftenoon.

I was a student in your foreign language teaching methodologies class at Nanboku University in 2010.

One of the things I remember you teaching were methods of engaging the student. You demonstrated how pretending to forget what words mean can be used to invite the students to help in class.

I really appreciated the teamwork assignments. You had me leading a team twice, once in techniques for elementary schools and once in techniques for high schools.

Sometimes it was hard for me to finish on time because I was also taking a class in using novels as a teaching tool, and had to demonstrate use of four novels for that class over the semester. You helped me several times when I was having trouble getting projects ready to turn in.

I need a letter of reference for Southwestern Teachers College in New Mexico. Could you write one for me? I am asking one of the tenured professors, as well, at your suggestion.

The address to send the letter to is

Admissions Office
Southwestern Teachers College
Santos Pisces, New Mexico 99999
USA

Please let me know if you can.

Respectfully yours,

Hana Kinoshita

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That's a little formal for e-mail, but this is a formal request.
e-mailにしてはやや形式に染まったものですが、礼儀に従うところです。

Note that prompting the memory, as Hana does here, is okay, especially because Professor Williams asked for help remembering.
華さんがここで思い出してもらうために情報を足しているのは特に問題ありません。ウィリアムズ教授が「手がかりください」って言っているし。

Asking the professor to say specific things is usually considered a breach of protocol.
教授に書いていただきたい内容を特定するような発言は気をつけるべきです。礼儀だけではなく、ルール違反になりかねるのですから。

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To: hana.yesterday (at) rose.readmail.ne.jp
From: jill7williams (at) groupmail.net
Subject: Re: Letter of reference I asked for today

Dear Hana,

I have checked my records and refreshed my memory.

I recall encouraging you to work hard on the novels class.

I also recall you falling asleep a couple of times in class because you had been practicing late for the drama club. Remember to use those drama techniques in your classes.

I will be happy to send your letter of reference (and I won't mention the falling asleep in class ;-).

I checked the address for Southwestern Teachers College. The best place to send letters of reference for graduate school applicants is the graduate admissions office, so I will send it there.

Let me know how things go at STCNM.

Sincerely,

Jill Williams

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This is where Hana's involvement ends.
これ以上は、華さんが関わって行けません。

The letter should usually be sent by regular post (physical mail) directly from the professor to the school.
大概は、教授本人がこの letter of reference を直接その学校に送るべきです。

If a professor can't send a positive letter of reference for some reason, the professor should decline, to allow the student to find someone who can.
なんらかの事情があって生徒のためになる letter of reference を送ることができない場合、教授は控えて、生徒が別の方に、参考になる人になってもらえるようにするべきです。