As hundreds of newly anointed graduates of John Jay College of Criminal Justice made their way across the commencement stage at Madison Square Garden on Wednesday, the college’s president, Jeremy Travis, beamed with pride at one particular student. The graduate, a 34-year-old Bronx woman named JoAnne Carpenter, had taken a remarkable, circuitous route to the ceremony.

In the years leading up to the festivities, Ms. Carpenter nearly fell through the holes in the threadbare safety net of social services. Her mother struggled with drug addiction, and her father deserted the family for years. By 16, she was a mother to a baby boy whose father also abandoned her.

Ms. Carpenter followed a familiar descent into a trying circle of group and foster homes, but she clung to the hope that she could reverse her course through education.

“I knew school was the only way out,” she said. “I just kept telling myself the obstacles would make me stronger.”