Even in a country that once attempted to ban alcohol, a stiff drink after a hard day is a widely accepted refuge. It’s rare, however, to find a movie that’s empathetic toward those who go further than that: people like Half Nelson’s Dan, who relieves career stress by smoking crack, or Factotum’s Henry, who decides to skip the job and go straight to the drink. The protagonists of these films characterized not only by pivotal mistakes but also by their reasons for making them.

Half Nelson opens with a shot of its central character’s face, accompanied by the sound of an alarm clock. Dan Dunne (Ryan Gosling) teaches eighth-grade history and coaches girls’ basketball. He’s impassioned about his subject yet somehow he can’t get his class in sync with the official Civil Rights Movement syllabus he’s supposed to be teaching, or engage his African-American and Latino students. The only one he seems to be reaching is 13-year-old Drey (Shareeka Epps), who also plays on the team Dan coaches.

One day after practice, Dan curls up in a toilet stall in the empty girls’ locker room and lights a crack pipe. Drey finds him there, a wordless moment that alters their relationship significantly. Drey’s brother is in jail, keeping his mouth shut to benefit local dealer Frank (Anthony Mackie). Frank is cultivating Drey, hoping to enlist her as a drug courier. Dan intends to prevent this, but as one of Frank’s customers, lacks a certain moral authority.

Director Ryan Fleck, who co-scripted Half Nelson with its editor Anna Boden, knows how this sort of fable is supposed to proceed. The earnest white man redeems the at-risk black student and maybe even picks up some new slang in the bargain. Fortunately for the viewer, Dan is nobody’s idea of a redeemer. He wants to do the right thing, but he just doesn’t have the strength—even when his will isn’t sapped by cocaine or booze. In one of the film’s pitch-perfect scenes, Dan goes to confront Frank, and a battle seems imminent. But then Dan loses his concentration, and Frank offers him a drink.

The lack of resolution can be a drawback. The movie’s ending is underwhelming, although it’s preferable to the sort of big finish that would have fatally disrupted the fundamental tone. And Fleck indulges with an overstated soundtrack, with a few songs that are jarringly out of place.

Elsewhere, however, the juxtapositions work well. A student’s report on the Attica prison uprising, for example, is followed by Drey’s visit to her brother in jail. These are the sort of links Dan wants his kids to make, even if he’s not sure they make any difference. Dan wants not only to live up to their tattered ideals but also go beyond them. Sometimes, though, he just needs to slip out the back door and find a place where he can get stoned without anyone asking why.

Instead, Dan encounters Drey, who has lots of questions he should be prepared to answer. The relationship between the half-defeated teacher and his precariously situated student is the film’s crux, requiring subtle work from Gosling (who was stunning as the secretly Jewish neo-Nazi in The Believer) and Epps (who’s making her debut). The performances are utterly natural, seemingly as offhand as Andrij Parekh’s hand-held cinematography. Gosling’s Dan is an ideologue who’s not sure he can be fully human; Epps’ Drey is the child who forces him to be. It’s a relationship that moves beyond theory, which is exactly where Dan needs to go.

HALF NELSON *** Directed by Ryan Fleck. • Starring Ryan Gosling, Shareeka Epps and Anthony Mackie. • R, 106 min. • At the Osio Cinemas.