The Erasmus Student Exchange Programme is one of the most high profile examples of the success of open EU borders, and one in which Scotland is heavily involved.
1,875 students from Scottish higher education institutions represented 13% of all Erasmus students from the UK between 2012 and 2013. 
The programme provides the opportunity for young Scots to study for part of their degree elsewhere in Europe. This provides experience of other cultures and also develops crucial language skills. Such experience is becoming increasingly desirable in the interconnected modern world.
This is well above the level that would be expected considering the size of the Scottish higher education sector and shows just how many Scots have taken advantage of what the EU can offer them.