Her students call it “the square world”— a family with two parents who work from nine to five, a home, kids in school, and regular meals.

“It’s everything they think that normal is,” says Magaly Melendez, the education manager of Girls Education and Mentoring Services (GEMS), a New York City organization that serves girls ages 12 to 24 who are victims of commercial sexual exploitation and domestic trafficking. But for Melendez’s students, and thousands more of the city’s homeless and marginalized youth, the square world can feel out of reach.

For Melendez, helping her students achieve in school means first convincing them they belong in the square world. Because of their experiences, “They feel like outsiders,” in the classroom, she says. “We try to show them that they do deserve to be there.”

Melendez says that her students struggle with constant self-sabotage. They lash out in anticipation of a classmate or teacher confirming their greatest fear— that they don’t belong in school. Fighting back against that impulse, she says, “That is every day.”

Amanda Savishinsky, the head of education at midtown’s Covenant House shelter for 18 to 25 year olds, says that her biggest challenge is motivating this population of students to go to school at all. “It is difficult for them to think beyond their short-term goals of housing, employment, and their next paycheck,” she says.

Many students Melendez works with have been out of school for years due to trafficking, abuse, forced labor, homelessness or incarceration. For other teens, the path back to education can be further disrupted by legal issues, sudden court dates for past charges, not having photo identification, or being evicted from a shelter or other housing.

Covenant House focuses on classes their students can take while working full-time. They host evening high school equivalency courses run by the Department of Education, as well as professional training to become security guards, nurse’s aids, or food professionals. These career selections are not accidental. “The goal is to get them to a living wage of $15 an hour,” says Savishinsky, “the fastest and easiest ways.”

Brian Scheibe runs the Introduction to Culinary Arts program at Covenant House where his students receive their food handler’s license, a state requirement to work as a supervisor in a professional kitchen.

When students are admitted into the program, Scheibe says, “I try to make it really special. I’ll type up a letter of acceptance and slip it under their door early in the morning. It might be the first acceptance they’ve ever got in their life.”

Scheibe says many of his students have never had anyone “on their back” before. He works to read their moods and stress levels. On the morning of state food protection exam, the culmination of their course, he knocks on their doors, sends reminder emails, prints out maps to test locations, and pays for the permitting fees with grant money.

“You care a lot,” he says. “You just want them to get it so bad.”

Still, these educators try to be realistic about their ability to control outcomes. Melendez says she sees lots of GEMS girls return to homelessness or to exploitive relationships, in part because it’s familiar. Unlike in the square world, says Melendez, “There, they know what to expect.”

Of the 75,323 homeless in New York City, more than 1,706 of them are unaccompanied youth under the age of 25, according to Department of Housing and Urban Development. The methodology is considered imperfect, and care providers say the number of homeless youth is likely much higher.

“Homeless teens don’t normally present themselves as homeless,” says Carolyn Strudwick, associate vice-president of youth and anti-trafficking programs at Safe Horizons, a program that provides aid and shelter services to homeless teens in Manhattan. “They’re more conscious of appearance and presentation.”

Melendez works with one 19 year-old who is enrolled in a competitive college course for robotics and spends each night on the subway. “She doesn’t miss a day of school,” says Melendez.

There are success stories. Each month Savishinsky meets with six alumni of Covenant House who are enrolled in Mount St. Vincent in the Bronx, on full scholarships. They go over academic goals and review how to save money while studying, to avoid lapsing into homelessness after graduation. Her emphasis is always on long-term thinking.

For these students, it can be difficult to connect with classmates who have had uninterrupted education, are generally younger, and have never experienced homelessness. Savishinsky places her students in a dorm with older learners who can act as mentors.

“We try to keep them as a group so that they can support each other,” she says. “Like a family.”