NSF graduate fellowship: how specific should the statement of purpose be?
I think this is an issue that a lot of students struggle with; at least I did when I applied last year.  I was rejected, so probably take what I say with a grain of salt.  They say some things on their website that are important to note.


Keep in mind that NSF does not just seek to fund scientists and engineers; NSF seeks to fund future STEM leaders.
Use appropriate scientific form (hypothesis, figures, references) in the Graduate Research Statement.
Instead of elaborate details on theory, focus on the rationale for your studies and the existing literature as it supports your proposed work.


The students that I know that were given the award properly addressed these issues.  My proposal did focus on one research idea and that was rewarded with comments on the creativity and feasibility of my proposed idea.  One of the critiques I got in my review was "While the applicant does demonstrate an excitement of discovery and should be able to communicate his results to a large audience, ...  Broad societal impacts are not evident with respect to encouraging diversity and enabling the participation of underrepresented groups."

The feedback that I got was based on two scores: Intellectual Merit Criterion and Broader Impacts Criterion.  I would make sure that your students take both into account.  As far as the research proposal goes, I what JeffE said is true.  It is an opportunity for the students to show that they are familiar with the current research and are able to come up with an appropriate idea to pursue.