[TubaMorg]

I am also a graduate student, although my research is more focused on bioinformatics/computational biology, I have found that many of the techniques and algorithms associated with robotics are applicable to solving biological problems. Still this isn't really what you are looking for. I have also spent some time in the HS classroom with my teaching fellowships which is how I ended up becoming involved with FIRST and robotics.

One thing that has really struck me is the way HS students think about and try to solve problems. There is a transition that occurs from freshmen to seniors where there is a shift from concrete thinking to abstraction. This is also a time where teens transition away from their egocentric thinking. Both of these can be well exposed in robotics (especially FRC).

So perhaps develop a project that analyzes the disparities in abstract logic between the younger and older students.