Several of the students who have come to my group as summer students are planning to submit NSF graduate fellowship applications in the coming weeks. However, one question that I am not sure about is how specific the statement of purpose needs to be.
When I applied for the NSF fellowship (going on fifteen years ago), I had absolutely no clue what I wanted to do as a student, other than it was computational rather than experimental. Therefore, my application was all over the place, talking about three different types of projects I might want to work on as a graduate student (and I ended up choosing none of them in the long run!).
However, I get the impression that today such an essay wouldn't be suitable for the application, and that a more narrowly tailored essay is required. At the same time, there's also the challenge of ensuring that the research problem can be done at the school one has chosen, and not narrowing things so specifically that the student is too "boxed in" or too opaque for a review panel to see the merits of.
So how should students thread the gap between vagueness and specificity in writing these and other fellowship applications?