I am a mathematics grad student who is often the primary instructor for undergraduate courses, and I have been asked by one of my previous students to write a recommendation letter for REUs, which are summer research programs for undergraduate students. This student was in a ``Introduction to Proofs'' course that I taught. I know that recommendation letters from grad students for grad school are looked upon poorly; is the same true for REUs? Applying for REUs is rather different than applying for grad school, so perhaps it is more accepted in this case.
If the best option for this student is to have me write the letter, what should a good letter from a grad student focus on? Since I don't have as extensive a teaching record as a professor I can't realistically compare them to other students I have had-- is it enough to talk about their excellent performance in the course I taught?
In case anyone is concerned about the student, I brought up the issue of me being a grad student when they asked for the letter, and after guidance from a faculty member they still think my letter is their best option (a professor is writing a letter as well). Of course, I'll ask someone at my institution for advice also.