AMMAN, Jordan (CNN) -- In the sunbathed schoolyard of the Shmisani Institute for Girls in Amman, Jordan, principal Sanaa Abu Harb makes an announcement over the speaker system.
Iraqi students at the Shmisani school in Amman gather around a teacher. One in 5 students there is Iraqi.
"All Iraqi girls come outside now. All Iraqi girls. Iraqi girls only!" she repeats several times, making sure the message is clear and waving away Jordanian pupils attracted by the commotion.
Dozens of girls in green apron-like uniforms pour out into the courtyard and cluster on the top level of a stone staircase overlooking a concrete playground.
Harb wants the CNN crew to see how many Iraqi refugee girls her school is accommodating. This school year, she says, 145 students are Iraqi -- roughly 20 percent of the students at this state-funded institution -- with another 40 Iraqi children on a waiting list. Watch Iraqi girls describe a long way from home »
The reason behind the jump in the number of Iraqis at the school is a new government policy: For the first time since the start of the Iraq war, Jordan is allowing all Iraqi children -- regardless of refugee status -- to enroll in state-funded schools.
Simply, this means that even illegal refugees with no paperwork can send their kids to school with no questions asked.
The move is cementing a massive population shift in the Middle East. More than 2.2 million Iraqis have fled the violence in their homeland, most of them seeking refuge in neighboring Jordan and Syria, according to humanitarian officials.
Jordanian Minister of Education Khalid Touqan says he expects Jordan to accommodate 40,000 to 50,000 Iraqi students this year. That's more than double the number of Iraqi children enrolled in public school two years ago.
Harb, on the front line of the phenomenon, says the influx is putting a strain on her school. Even with some U.N. and U.S. aid to Jordan, there's still not enough money.
"We need more teachers here, more resources, more buildings, more chairs for all Iraqi students and our students," she says.
In a nearby neighborhood, in the study room of the Ahmed Toukan School for Boys, a handful of Iraqi kids talk of their experience living far from home. Seated at a rectangular table covered with a red and white tablecloth, the boys tell stories of horror and displacement.
Eighteen-year-old Qutaiba lost five immediate family members before moving to Jordan to try to live a normal life. Matter-of-factly and with a straight-ahead stare, he repeats the number: "Five members."
Most of the boys and young men from Iraq have missed several years of school -- up to a four-year educational gap that will delay not only their high school graduation, but also their entry into the workforce.
All say, though, that they feel lucky to have gotten out, even if the violence in their country means always having to be on the move, ready to live far from home and away from loved ones.
"It's not strange for me to be in the middle of people I don't know," says eleventh grader Ziad Tarek Al Shamsi. "I had friends in Iraq when I was small, I left them. In America, I left them. I came here, I left them."
He pauses: "But you have to miss your country."
The United Nations High Commissioner for Refugees estimates up to 250,000 school-age Iraqi children are in Jordan.
Many of them are enrolled in private institutions. But as families run out of money they had when they left Iraq, they turn to public schools.
Even so, more than a month into the new academic year, fewer Iraqi families than first anticipated enrolled their kids in schools this year. According to the charity Save the Children, 21,000 Iraqi children have so far enrolled in Jordanian classrooms.
As a result, the government extended the deadline for student applications and cut down on the required paperwork for Iraqi families.
The lower registration numbers were attributed in part to illegal refugees' fears of being identified through their children's school records.
Regardless of what the final number will be this year, the population shift in the Middle East is, according to UNHCR head Antonio Guterres, the largest urban refugee situation in the world.
Iraqi families are changing the social fabric of Jordanian society. About 10 percent of Jordan's population is now made up of Iraqi refugees -- the estimates range from 500,000 to 750,000 of them.
The schoolchildren are living examples of how the Iraq war may permanently change the Middle East.
"Iraqi children will be incorporated and integrated within our mainstream line of education," says Touqan, the education minister. "We will not run a parallel system of education." E-mail to a friend