In classrooms at William C. March Middle School this week, students bantered with their teachers about why their answers to math problems were right, while others diligently scribbled in their notebooks.

They acted out scenarios of bullying and discussed the toll it could take on their peers.

They reflected on the past school year, vowing they wouldn't have another like it again.

For most of the middle-schoolers who spent five weeks of their summer working toward being promoted to the next grade, the interactions reflected a level of engagement they had failed to achieve all school year.

The Building Educated Leaders for Life summer program is showing promising results for Baltimore's most challenging student population, according to the data and the officials who run it.

"These were the kids during the school year who were causing mayhem, and we don't play that here," said Damon Johnson, who runs the program at William C. March, one of two operating this summer. "We have kids who are parents, who have charges and have to come to school with the ankle bracelet monitors on, kids who are 18 in the eighth grade. But they're here, and they're learning."

For the past three years, BELL has tailored its nationally acclaimed extended-learning model to a summer program for city middle-schoolers who were recommended to be held back a grade. This year, 480 students whose families enrolled them attended the programs, which ended Friday.

Since the city partnered with the organization for middle-school promotion, the percentage of middle-school students moving on to the next grade has improved significantly, according to school system data. In 2010, about 29 percent of the city's sixth-graders attending a summer school program were promoted to the next grade; in 2012, 83 percent were.

BELL's report card in Baltimore, based on pre- and post-Stanford Diagnostic assessments last year, shows that all of the students enrolled in its programs gained the equivalent of 9.5 months of skills in literacy and 11 months' worth in math. Students also moved from the 31st percentile in reading to the 44th, and from the 14th percentile in math to the 26th.

The program's operators said that while those results also included elementary students' performance, they are driven by middle-school gains. They expect the same results this year.

At BELL, students are known as "scholars" and are educated in single-sex classrooms of no more than 22 children, which are staffed by at least one teacher and one assistant. Johnson chose a balanced staff of men and women.

"It doesn't even feel like summer school," said De'Aysa Dezurn, who rattled off all of the tests she passed to move up to eighth grade. "It's just a different experience. You think you're just going to do work all day because you're dumb, you've failed. But we actually get to talk to our teachers about what we're doing, and it's fun. It feels like home school."

BELL has operated in Baltimore's low-income communities since 2005, offering after-school programs and expanding to summer learning in 2007. The 20-year-old nonprofit also serves students in the District of Columbia, New York, California, Michigan and South Carolina.

Its model has been recognized for deterring summer learning loss.

Officials with the Baltimore school system, which overhauled its summer programs in 2010, said they partnered with BELL for middle-school promotion because of its unique approach to not only help students with their academic deficiencies, but also the social barriers the face.

The program also fit into the district's emphasis on supporting failing students in its new promotion and retention policies.

Crystal Brice, the district's coordinator for extended-learning programs, said this approach was particularly crucial for middle school students.

"Those three years are critical, and when we looked at the data, we needed to address the number of students who were retained there, and what kind of supports they needed," Brice said. "And not having a program that seems so punitive is very critical in those adolescent years. We wanted to create a place that improved their academic skills, and also build their social skills that are so vital to their success."

Johnson said many of the students who come to the program need extra doses of high standards, support and structure.

Some students said that the program gave them what they yearned for during the school year.