Luke Matheny keeps getting pulled away. We are on a rented soundstage on the outskirts of Los Angeles’s Koreatown, sitting in director’s chairs in front of a television monitor. A woman standing nearby flips through script pages on a clipboard, and a few crew members mill around with practiced nonchalance. On the monitor is a live feed of four middle schoolers sitting at desks on the other side of a big prop wall. From this set, which looks like a museum piece — presidential portraits, American flag, the words MONROE DOCTRINE scrawled on a dusty blackboard — someone is hollering for Matheny, the 38-year-old director of Gortimer Gibbon’s Life on Normal Street. “To be continued,” Matheny calls over his shoulder as his expansive snarl of dark hair disappears around the corner. I catch a brief glimpse of his pants on the monitor as he strides past the camera.

Gortimer, which debuted last year on Amazon to critical acclaim, is about a 13-year-old boy whose suburban street provides the backdrop for fantastical adventures with his two best friends. Matheny won the 2011 Academy Award for Best Live Action Short Film and hasn’t done children’s television before, but he says he fell in love with the show when he first read the pilot. “It felt like The Wonder Years, but with a supernatural element,” he tells me. Today, he’s shooting an episode in which Gortimer discovers a charmed blazer that makes others see and treat him as an adult. While Gortimer characteristically weighs the implications of his newfound power and hesitates to use it for his own gain, his mischievous best friend Ranger goes on a spree of lottery-ticket buying and R-rated-movie watching.

Gortimer feels stylistically and emotionally different from shows kids have come to expect from Nickelodeon or Disney. It’s sweet in an old-fashioned way, with gentle humor and sophisticated writing. And Matheny is shooting single-camera, a time-intensive process that gives the show a more cinematic look than sitcom-y, multicamera kids’ fare but requires a new take for every angle (which is why he’s constantly scurrying between the monitor and the set). I overhear him telling his cinematographer, Eduardo Enrique Mayén, how to position the children for a B-roll, or background, shot. A moment later he returns, easing his lanky frame into his chair. Somebody yells, “Background!” and on the monitor the middle schoolers begin pantomiming an enthusiastic conversation as the camera glides backward.

The set of Gortimer Gibbon’s Life on Normal Street

Matheny is called away again before long, and in his absence Sloane Morgan Siegel, who plays Gortimer and is zipping around the soundstage waiting for his next scene, takes it upon himself to entertain me. “You don’t know where you are or when you are with this show, so it’s timeless,” he says. “I love that quality.” Siegel, who’s 14, speaks without a trace of slang; dressed in the episode’s magical blazer, with his thick hair parted on the side, he, too, seems timeless.

Gortimer is one of a slate of original children’s shows being produced for Amazon Instant Video, which, along with other streaming services, is dumping money into content for children. Kids watch a lot of TV, which increasingly means watching a smartphone or tablet — in 2013, according to Common Sense Media, 75 percent of U.S. children aged 8 and younger had access to a smart mobile device in their homes. This, combined with young kids’ habit of playing favorite episodes again and again, gives video-on-demand networks such as Netflix, Amazon Instant Video, and Hulu Plus a big advantage over traditional broadcast and cable networks. Executives see an opportunity to shape a new generation’s viewing habits, as well as to turn parents, eager to entertain their kids with nonjunk, into subscribers.

In the streaming world, Netflix is the biggest player: It’s in 36 percent of “high-tech” American households, according to a recent Nielsen report, and accounts for more than a third of North American internet traffic during peak periods. For kids’ content, it’s using its massive programming budget — $3.2 billion in 2014 — to license existing movies and TV series from Disney and other companies and to create original content. One of its primary vehicles for that content is a 2013 deal it signed with DreamWorks Animation for hundreds of hours of new shows based on recent franchises like the Madagascar movies and Puss in Boots as well as classic series like Veggie Tales. Amazon Instant Video, the second-widest-reaching streaming service — it’s in 13 percent of Nielsen households, though growing rapidly — is going after young viewers with equal vigor. In 2013, less than two months after the expiration of a Netflix deal with Viacom, Nickelodeon’s parent company, Amazon licensed a lineup of Nickelodeon’s preschool shows. Since Amazon’s content budget is smaller, it has taken a scrappier approach with original programming, crowdsourcing scripts and putting money behind entirely new, high-quality shows that kids can’t watch elsewhere: like Tumble Leaf, a stop-motion animated series for preschoolers that won five Daytime Emmys in April, and Gortimer.

“We don’t hear ‘no’ a lot, so we’re really not treating it like a normal kids’ show,” says Matheny, who’s directed most of Gortimer’s 13 released episodes. He cites old Steven Spielberg movies — The Goonies, E.T. — as inspiration. Gortimer is funny and almost folksy, but an undercurrent of gloom keeps viewers on edge. In the pilot, a lazy summer day unfolds into a surreal fairy-tale adventure that is interrupted when Gortimer nearly dies of heatstroke in a crawl space. It’s moments like this, when reality comes crashing through, that give the show its power.

Matheny rounds the corner just as Siegel is summoned elsewhere. He settles into his chair and puts on a pair of headphones. Someone yells, “Action!” and the camera captures about four seconds of footage. “OK!” Matheny says, ripping off his headphones and heading back to the set.