Talking about the border we need to cross in this globalisex world. How? By collaboration. Not just collaboration. 'Global' collaboration. Why global collaboration?What requires? Global competence, interctual understanding in a global context, digital citizenship, connected learning, and so on. Some interesting projects are going on - Worthwhile checking the 'Flat Connection' website. Flat Connection is pedagogy which can work well in the ICT integrated languages classrooms.
In my view, the hybrid model (blended learning model: synchronous + asynchronous modes ) would work more efficiently and effectively in a meaningful context for the global collaboration.
You might be interested in reading 2014 Horizon report. Here is the link for K-12.