Charter school operators across the country have been grappling with a vexing problem: graduating large numbers of students who go on to college, yet flounder when they get there and never earn a degree.

It’s an issue Achievement First — a national network that operates 19 schools in Brooklyn — is trying to solve by experimenting with a new model that gives students more control over their own learning. The model, known as “Greenfield” for its open-minded approach, was first piloted in Connecticut. But starting next school year, it will roll out for the first time in New York City at a new Brooklyn middle school.

“What a lot of alumni revealed to us were gaps in student agency and student choice in what they were learning in the lower grades,” explained Amanda Pinto, an Achievement First spokeswoman. Though virtually all of the network’s students attend college, Pinto said, only about 50 percent graduate.

The model is designed to prepare students to handle self-direction years before they’re in college. It uses a curriculum that emphasizes personalized learning, where students guide themselves through different units of study and are responsible for mastering each piece of content before they can move on (an approach that has earned both hype and mixed reviews).

Zachary Segall, who will serve as the school’s inaugural principal, said students will have two 40-minute blocks of dance and art classes four times each week, will set their own goals throughout the year, and participate in “expeditions” that allow them to explore interests outside the traditional curriculum. That could include something like podcasting, Segall said, or architecture.

“Part of the model is addressing the idea that our students need to be prepared for college, and not just prepared academically,” Segall said. The new school will be called Achievement First Aspire Middle School, and will open in East New York this fall to serve the students aging out of the network’s local elementary school.

Achievement First is known for high academic expectations and a style of discipline that “sweats the small stuff.” Whether the approach will help the network get more of its students through college remains to be seen.

Pinto pointed to some signs of success: The Greenfield model yielded higher math and reading scores at the pilot school in Connecticut compared to other schools in the network that didn’t use the model. But she acknowledged that the approach is still in its infancy.

“‘Good enough’ is never good enough when you’re talking about getting kids college success,” Pinto added. “Time will tell.”

Correction: An earlier version of this story said students will have two 40-minute blocks of dance and music classes. In fact, they will be dance and art classes.