Actually, to me, for a country to close all schools with just one reported case seems a bit of an overreaction.
Another problem with closing schools early is that if there aren't that many cases straight away, there is pressure to reopen them. A PP on this thread said their school had planned to close for 2 weeks, but is now reopening this week due to pressure from parents.
Whereas by the end of this week, the situation may look very different and more people might be supportive of school closures. If people aren't supportive, it will be very difficult for a government to keep containment measures going long term.
I do think we need to be taking steps to control things- changing the travel advice, especially RE Italy (and also possibly France and Germany) is an important first step. I also think there's a case for stopping large public gatherings, like in France.
As I've said further upthread, I don't think it is the time for school closures yet- but we do need a halfway house where parents are able to keep kids home easily and more students are encouraged to self-isolate.