According to conventional wisdom, Carl Roberson and his twin sister Carol should not be graduating tonight along with 390 other seniors from Ballou High School in southeast Washington. They should be dropout statistics.

Last November, D.C. schools officials said, the twins found themselves homeless and destitute. Their mother had moved to Georgia to recuperate from a mental breakdown, the officials said, and their father, a retired Air Force Master Sergeant, left home. Subsequently, an older brother was jailed on several criminal charges.

Though similar pressures have led countless other students to leave school before earning their high school diplomas, Carl and Carol stayed -- with some timely help from teachers, school counselors, social workers and psychologists.

Their diplomas will be tangible proof of their determination to overcome the odds, they said. To them, the documents will serve as trophies symbolizing not just 12 years of education, but the begining of new life and opportunity.

Both have been awarded athletic scholarships to Livingstone College, a small private institution in Salisbury, N.C., where Carl intends to major in computer science and Carol in pediatric nursing and psychology.

Nellie Grant, counselor for seniors at Ballou, said that the Robersons "are to be commended for the way they have worked hard to graduate this year. They have really pulled themselves up by their bootstraps and kept going.

"You have to have a lot of maturity to keep going against the odds, as they have done. They attended school regularly and kept their grades up even while their family was crumbling around them. They let nothing stand in their way and made stepping stones out of adversity."

School employes worked together and "tried to give them a lot of support, because the role of the school is to help a student reach his potential in every way, academically, socially and emotionally," Grant said.

"Sometimes students need to know that someone cares, that someone believes in them in spite of what they are going through. They need to know that we are here to help them, to talk to them, to listen and to feel with them -- and to even cry with them sometimes."

According to Grant, several other students set to graduate from Ballou during ceremonies Constitution Hall also have overcome great odds. One was severely burned in a fire, she said; another had to deal with his mother's death from cancer.

According to city schools psychologist Marilyn Green and social worker Wilma Prince, Carl and Carol were traumatized and left homeless by the sudden breakup of their family.

They stayed for a while with a relative in Columbia, Md., but had to leave there and had nowhere to go.

Carl Roberson said in interviews that he spent several nights wandering the streets of Washington, hungry and tired, sleeping in the rear seats of city buses.

"There were a lot of weak moments . . . but we made it," said Carl, who at 6-feet-6 aspires to play professional basketball someday. "I spent some nights riding the buses. Sometimes, I didn't have enough money to buy food to eat . . . so I starved."

"Everybody in our family just went our separate ways. I just got really depressed," said Carol, who has undergone prolonged treatment for her depression.

As she recuperated, school became not an added burden but a bright focal point. "At times, it took my mind off the sad things in my life," she said.

Often, youths who undergo family and personal crises that are considerably less severe than those encountered by the Roberson twins find it impossible to cope, and instead drop out of school and hit the streets, school officials said.

Teachers, counselors and social service organizations often fail to reach these youths in time to save them from idleness, drugs or crime.

But psychologist Green and social worker Prince, who together are assigned to serve six schools and thousands of students in some of the poorest areas of southeast Washington, said they were determined to not let Carl and Carol slip through the cracks.

"We got to them in time," Green said. "Sometimes when we find out a kid is having problems it's too late. And sometimes we don't find out until the student has already dropped out."

Often, youths who suffer parental neglect never find a place to live and instead move from one temporary home to another like nomads, Prince said.

Ironically, it is especially difficult to find help for "good kids" who have not been charged with crimes, according to Larry Pittman, a counselor at the Sasha Bruce House, a home for runaways and wards of the court.

Green and Prince convinced officials of Sasha Bruce House, on Maryland Avenue in the Capitol Hill area, to bend the rules to let Carl move in.

Several city agencies specialize in counseling and caring for juvenile delinquents, "but if you are a good kid with adversity and no family support, there's nothing for you," Pittman said.

Green and Prince also helped arrange for Carol to be taken in by a friend, Pamela Finley, who lives at Bolling Air Force Base with her husband and three children.

When family conflicts disrupt students' abilities to attend classes and study, "they need a place to cool off," Green said. "There are countless numbers of kids like Carl and Carol who just need a place to stay, but there are just no places for some kids to get away from home and get the counseling they need. Parents need to be involved in the process, as well."

Green and Prince also helped arrange financial support for the twins. But perhaps their biggest contribution was the time they spent talking to Carl and Carol, day after day, to keep them focused on the goal of graduatingl -- an effort that bears fruit tonight.

"In Carl and Carol's case, there were a lot of people who were able to network and use the resources that were available to help," Prince said. "The sad thing about it is that for every child who is saved, there are hundreds who aren't."