Jazz and film have a great history together. In the early days, jazz was a boon to the young film industry, providing a seemingly endless collection of tunes for hit musicals. Indeed, in those days a great soundtrack was not merely something to sing; in many cases the songs became a bigger part of the story than the rest of the movie. Look at any Fred and Ginger classic, and you’ll find that the emotional high point is just about always sung instead of merely said.

As the years went by, jazz became less and less a popular music, until what was once the soundtrack of a nation became an esoteric art, shrouded in smoke and mystery and practiced in dimly lit basement bars. At that point, its relationship with film reversed — the music and the people who made it were a dramatic opportunity. There followed a raft of films that used jazz and jazz artists as their subjects, right up through last year’s Oscar-winning film Whiplash, about a talented young drummer and the abusive teacher that pushes him toward greatness.

This week at Amherst Cinema, Keep On Keepin’ On continues that tradition. Screening Monday night at 7 p.m. as part of the Jazz À La Mode film series, director Alan Hicks’ hour-and-a-half documentary is the chronicle of a special musical bond between 89-year-old jazz legend Clark Terry and a 23-year-old blind piano prodigy named Justin Kauflin. Shot over a five-year span, the story of their growing friendship (cemented during what turns out to be a turbulent time for both musicians) also becomes an exploration of how jazz is passed on to new generations of musicians.

For Terry — a trumpeter skilled enough to have played with both Count Basie and Duke Ellington’s legendary bands — teaching is nothing new. His first student, who appears here to talk about Terry, was a 12-year-old kid named Quincy Jones. And while not all of the musicians Terry has mentored have gone on to the heights that Jones has scaled, he leaves little doubt that they are richer for the experience. For Kauflin, whose young career is marked by early setbacks and a nagging stage fright, Terry’s guidance and friendship are both comfort and compass.

Presented in collaboration with New England Public Radio, the screening will feature commentary from NEPR jazz host Tom Reney, as well as a live jazz performance before the screening begins. But for all the talk of music, Keep On Keepin’ On is not just a film for fans; anyone who has ever had a teacher make a difference in their lives will appreciate this story.

Also this week: In wider release, Brad Bird’s new film Tomorrowland comes to area screens. A vision of the future from the director who brought us The Iron Giant and The Incredibles, it pairs a crusty, aging inventor (George Clooney) with a scrappy young girl set on solving the mystery of the place known as Tomorrowland. The feel of this sci-fi Brigadoon, a land caught in a sort of parallel universe, is inspired by Walt Disney’s famous theme park. Bubbling over with goodwill and the curves and chrome of the 1950s, Bird’s outlook on the future is refreshingly upbeat in our Hunger Games age (tellingly, one of the first images of the place is of someone zipping by on a jetpack — few things so definitively describe optimism about the future as a jetpack).

Bird has never been a glass-half-empty type. But much of his best work has been animated, a form that is perhaps more forgiving if a film dips toward sappiness. On the other hand, his animated work stands out precisely for the strength of its emotional impact; The Iron Giant remains one of the few films guaranteed to make me cry before it is over. It’s hard to say if Tomorrowland will have that staying power.

In the meantime, an animated short that Bird devised for the film, but eventually excised from the final cut is available for viewing online. It is the origin story of Plus Ultra — a secret society formed at the 1889 World’s Fair by Thomas Edison and Jules Verne, among others — told in a visual style reminiscent of the Atomic Age and narrated by Orson Welles sound-alike Maurice LaMarche. If you find yourself standing on line for a Tomorrowland screening, this three-and-a-half-minute short is a nice way to get in the spirit for what’s to come.•

Jack Brown can be reached at cinemadope@gmail.com.