It’s easy to understand why Ellis Marsalis seems almost gratified by something his students almost take for granted. “Growing up in New Orleans, there was always some opposition, especially at the university level, to any kind of jazz,” said Marsalis, the city’s foremost jazz educator. “There was also a kind of fundamental opposition in academe to certain kinds of experimentation—anything that wasn’t by the book. Seemingly, a lot of that either has changed or is changing.”

As a pianist, Ma...