At a time when many U.S. schools are failing students of color, one school stands out as an unusual success.

But when you realize that the majority of St. Benedict’s students are low-income male students of color, the numbers become groundbreaking. Nationwide around one in four black, Latino and low-income students does not graduate high school, according to the Department of Education.

So how did a school in Newark, run by Benedictine monks, manage to break the mold and graduate almost 100 percent of its low-income students of color?

60 Minutes Students (left to right) Bruce Davis, Andrew Brice, Khalil Flemming and Devionne Johnson.

“The counseling center is critical,” said Father Edwin Leahy, a monk and the school’s headmaster, to the Huffington Post on Tuesday. “I don’t know how people do this work without attending to the kids spirits, psyche and heart. It’s very rare that cognition is the reason for poor academic performance in our experience -- frequently it’s emotional distress.”

In a school where 88 percent of the students are on financial aid, many of them are coming from poor households and neighborhoods, which can make it hard to succeed academically. Experts call it toxic stress: research shows that growing up in poverty often entails excessive exposure to stress and adversity, which can have long-term negative effects on children’s social, emotional and cognitive development, according to the Annie E. Casey Foundation.

St. Benedict’s tackles this issue with deep psycho-social support for its students.

St. Benedict's Prep

“Counselors in most schools are just making sure kids have the right classes,” Father Edwin said. “We have a counseling center with two psychologists, and interns who are PhD or Master’s candidates in school counseling, and four to five different group sessions a week.”

The group sessions are catered to students in specific adverse situations, Fr. Edwin said. The "Blues Boys" is for students who suffer from depression; "Unknown Sons" is for those who don’t have a relationship with their father; "Anger Management" is for those dealing with emotional control issues.

“It works, I can tell you that,” Fr. Edwin said. “It’s about not giving up on yourself. You may fall on your back several times, but you can figure out a way.”

60 Minutes Students seated during morning convocation

The other secret to their success is to let students lead -- literally. The student body is divided into groups of about 25 kids each, in 7th to 12th grade, said Fr. Edwin. Each group has a student leader, and together with the other group leaders, they run the school. They know the grades of all of the kids in their section, and are involved in many of their discipline issues. They set the school schedules and coordinate events -- and they even interview the juniors in the Spring to recommend replacements to the monks for when they graduate.

“When you give teenage boys responsibilities, sometimes it goes wrong, but you debrief them,” Fr. Edwin says. “It’s risky, and most people are afraid to take that risk, and allow kids [that responsibility]. A lot of guys of color feel like nobody pays attention, nobody listens -- so we create situations where they make the arguments, they change the schedule -- that’s important.”

St. Benedict's School Father Edwin

“Benedict's men are different than the guys you see outside,” said Bruce Davis, this year’s senior leader, to CBS’ 60 Minutes. “We learn what we're willing to accept, which is nothing but the best, finishing what we started. The boys press each other to study. The school motto [is] ‘Whatever hurts my brother, hurts me.’"

The big question is, can the model be replicated? Fr. Edwin has gotten calls from all over the country asking that very question. The reality is, he doesn’t know.

St. Benedict's Prep Students backpacking.

“This place is like a diner,” he said. “It’s open 24 hours a day, seven days a week -- because the monks all live here. It’s the same model as the boarding schools in New England: faculty sleeps on the grounds. That creates community. The person responsible for running the place needs to live there -- they have to feel it.”

Financially it would be very difficult for other schools, particularly public schools, to replicate that full-time presence. St. Benedict’s recipe of deep psychological support, a trust in young men’s leadership, and monks on-call 24/7 is unique.

“When you create community, there’s not a big hierarchy,” said Fr. Edwin. “Some call it chaos. But God made something out of chaos, so if it is chaos, well I believe great things can come of it.”