Some American children are now getting lessons on Skype with less expensive foreign teachers:

Chess in cyber space: a smart move?
By Gillian Tett
Financial Times
July 25, 2014

Quote
At my daughter’s chess tournament, for example, I listened to other proud parents explain that their would-be chess prodigies are being tutored by chess masters to improve their game. No surprise there – New York is a wildly competitive place. But these teachers are not sitting in Manhattan or even in America. These days parents are tapping the most brilliant chess brains in places such as India, Bulgaria or Moscow, to deliver online tutorials for their offspring via Skype. “It’s cheaper to get a tutor that way and you can get a real master,” one father proudly explained.
I've seen articles about children getting tutored academically on Skype.