Kim Ki-hoon earns $4 million a year in South Korea, where he is known as a rock-star teacher—a combination of words not typically heard in the rest of the world. Mr. Kim has been teaching for over 20 years, all of them in the country's private, after-school tutoring academies, known as hagwons. Unlike most teachers across the globe, he is paid according to the demand for his skills—and he is in high demand.

Mr. Kim works about 60 hours a week teaching English, although he spends only three of those hours giving lectures....