Elementary schoolteacher Ben Johnson helps 9-year-old Evan Bowie with his schoolwork during a class session on the history of Jamestown at Two Rivers Public Charter School in the District. (Astrid Riecken/For The Washington Post)

For a fourth-grade unit about Jamestown, students at Two Rivers Public Charter School studied historical documents, created a timeline of important events in the history of the first permanent English settlement in the United States, researched the groups of people that lived there — Africans, Powhatan Indians, the settlers — and wrote fictional stories from different points of view.

They also took a trip to see the Virginia landmark. It was a memorable experience for 9-year-old Evan Bowie, who was still excited about it a month later.

“We got to spend the night,” he said. “We got to go on ships, and I got to hold a sword and a shield and put on armor.”

The lesson was actually what the school calls an “expedition,” the basis of an instructional model that emphasizes interactive, project-based learning. It is gaining popularity at a time when many parents and educators are concerned that a focus on test-based accountability has promoted rote learning, is taking the fun out of school, and is not preparing students for the real-world rigors of today’s workplace.

Ahead of the enrollment lottery opening in the District on Dec. 14, families are beginning to visit schools and make sense of a menu of different models and curricula: Tools of the Mind. No Excuses. Dual Language. Montessori. Reggio Emilia.

Expeditionary learning, in particular, has attracted attention. Two Rivers in Northeast had the longest wait list of any charter school in the District last spring, with 1,381 names. The next most-popular school, with about 1,200 names, was Mundo Verde in Northwest. Capital City, a charter school near the Maryland border, was in the top 10, with nearly 700 on the wait list. All three have adopted the expeditionary model, which also emphasizes character development and skills such as perseverance and risk-taking.

They are affiliated with a national organization called EL Education, founded more than two decades ago through a partnership between Outward Bound and the Harvard Graduate School of Education.

Phillip Lucas, 9, places sticky notes on the window of his classroom during a session on the history of Jamestown at Two Rivers Public Charter School. (Astrid Riecken/For The Washington Post)

Elliott Vanderbilt, 4, paints vegetables and fruits during an art expedition class focusing on nutrition at Two Rivers Public Charter School. (Astrid Riecken/For The Washington Post)

The New York-based organization is built on 10 “design principles,” including such tenets as “The Primacy of Self Discovery” — students work to discover their abilities, values, passions and responsibilities in “situations that offer ad­ven­ture and the unexpected” — and “The Having of Wonderful Ideas,” which says that students need opportunities to explore their curiosities, time to experiment and time to make sense of what they learned.

Scott Hartl, president and chief executive of EL Education, described “explosive growth” in interest in expeditionary learning in recent years, as states are updating their academic standards and tests to encourage more critical thinking and problem solving.

The organization, which also trains teachers and provides resources to school districts, was commissioned to write a literacy curriculum for New York. It is available for free online and has been downloaded more than 4 million times in slightly more than two years, he said.

The District’s traditional public school system is emphasizing deeper, project-based learning through new “cornerstone lessons” starting this year, with the goal of bringing more uniform and rigorous instruction to D.C. students. The new lessons aim to be memorable or inspiring, to help students make connections to the real world or encourage breakthroughs in their thinking.

Such lessons have long been associated with effective instruction, but school officials said that they want to make sure they are a standard part of every child’s education.

At Two Rivers, eighth-graders read “The Immortal Life of Henrietta Lacks” for a lesson in genetics and ethics and staged a mock trial of Johns Hopkins Hospital, which used Lacks’s DNA without her or her family’s permission.

And first-graders got an applied lesson in economics when they raised money to buy books for children at the D.C. General Homeless Shelter last year. They opened and ran a school store selling popcorn, recruiting investors for their business, tracking sales and returning the seed money with interest.

Esther Espinoza Dilone, 9, listens during a class session on the history of Jamestown at Two Rivers Public Charter School in the District. (Astrid Riecken/For The Washington Post)

Blake Robinson, left, and Elliott Vanderbilt, both 4, attend an art expedition class focused on nutrition at Two Rivers Public Charter School. (Astrid Riecken/For The Washington Post)

“The most exciting learning, the most long-lasting learning, is through these kinds of projects,” said Jessica Wodatch, executive director of Two Rivers.

The expeditions are typically interdisciplinary. Pre-kindergarten students are learning this fall about nutrition. In an art class on a November morning, they told their teacher Leah Carpenter Quinter about some of the food groups they have been learning about, including vegetables, proteins and grains. Quinter told them: “I have some exciting news: Artists often use food in their artwork.”

She showed them still-life paintings and then set them up with water colors to paint their own carrots and apples.

Fourth-grade teacher Ben Johnson, who is teaching the Jamestown expedition for the first time, said he used to work at a charter school that had a more top-down teaching approach. The main difference with this model? “Way more kid buy-in,” he said.

Kennedy Cawley, 9, a student in his class, agreed with the sentiment. She recalled her favorite expedition at Two Rivers — a study of insects in first grade — when she made bug trading cards, similar to baseball cards, with important information on them. She had the ant and the butterfly.

“It was actually fun to do,” she said. “It wasn’t just, ‘This is a bug; it does this.’ ”