Many people might presume that after some five decades spent in the field of education a person could become jaded or perhaps even cynical. Yet, when clarinetist Alvin Batiste relates a recent, seemingly inconsequential, encounter with one of his students, any doubts about the nature of his continued enthusiasm—or those of other such dedicated teachers—immediately dissolve.

“The thing about teaching is that you truly enjoy—even beyond yourself, even without p...