The only place you need to really be careful is the subway. I was getting onto a train in rome at the spanish steps station, and 3 girls tried to rob me
Hey - the Spanish Steps is where we had our problems with some kids. We fended them off with the gallon jug of wine we had with us on our way back to play quarters in our bathroom! LOL!! (we were 16-18yo kids then!).
To the OP - i'd ask the teacher. I'm hoping he has experience or can contact the coordinator for recommendations on bringing it. I know i'd want mine with me, but i'd also feel like i would have to bring it with me most times.
Have fun though!!!!!