I have just finished a weekly Skype lesson with a cello student in California. I have Skyped lessons several times before- mainly in the US but I have also taught a weekly lesson via Skype for a year with a student staying in Spain.
Each time I have hesitated. Concerned with sound production, inability to play together and the lack of intimacy that is born in a studio setting. Each time the student has convinced me to try and it has been successful.
I set aside lesson time each week and we run a lesson in the same manner that I do in the studio. Although complexities and the lovely timbres of the cello are reduced across the internet, there is the advantage of hearing something much closer to pure pitch.
We can't play together and that is a disappointment to both teacher and student and I can't offer a shoulder squeeze or high five-
However, to counter these challenges I keep a notebook during the lesson and then email my student their assignments for the next week as well as comments, suggestions and encouragement.
I'm finding that because of creativity and cooperation music can, and does, bridge divides.