NEW DELHI (AP) -- Their classroom is a flattened patch of dirt and rocks under the elevated rail tracks. Their blackboards are rectangles painted on a chipped concrete wall. Their teacher is a shop owner with no formal training, but a conviction that education is their only hope.
For some of these dozens of children of poor migrant workers in India's capital, this makeshift, open-air school under the rumble of mass transit is the only school they have. Others who attend overcrowded and dismal government schools come here as well -- to actually learn.
India's Right To Education Act promising free, compulsory schooling to all children ages 6 to 14 was supposed to take full effect March 31, but millions of children still don't go to school and many who do are getting only the barest of educations.
So every morning, more than 50 children gather under the bridge for two hours of lessons at Rajesh Kumar's informal school. They sweep the dirt flat and roll out foam mats to sit on, just meters (yards) from the bushes were several men had been squatting and defecating minutes earlier.
The students, ages 4 to 14, study everything from basic reading and writing to the Pythagorean Theorem.
Those who also attend government schools say classrooms there are packed and that teachers, when they show up, just come in, write a problem on the board, and leave.
"They teach much better here," said Raju, 12, the child of flower pickers. He also attends fifth grade at a government school in a class with 61 other students. There "they hardly teach anything," he said.
Under the Right to Education Act, passed in 2010, enrollment has increased from 193 million to 199 million, and the government has invested more than $11 billion extra dollars in upgrading the school system.
Still, about 3 million children remain out of school, according to the government; Private groups put that number at about 8 million. There also remain at least 700,000 teacher vacancies, and many of those who are employed don't have the proper training, according to the government.
Despite the new investments, schools appear to be getting worse.
According to the 2012 report by the non-profit education group Pratham, nearly 68 percent of third graders in government schools can't read at a first-grade level, up 10 percent from two years ago. Math proficiency had similarly plummeted, according to the report, which is based on assessments of about 700,000 children across the country.
The government needs to focus not just on hiring new teachers and building new schools but on providing a good education to Indian children, said Rukmini Banerji, a Pratham official.
"It looks like we are far from getting there," she said.
Government officials say their own surveys show some improvement, though overall learning levels remain low.
"The rapid expansion of primary education and introduction of a large number of first-generation learners in the school system has posed a major challenge for learning outcomes," India's Human Resource Development Minister M. Mangapati Pallam Raju told Parliament last month.
Kumar's school under a bridge stands as proof of the hunger for learning among those either left out of the system or disappointed by it.
One day in 2008, Kumar said, he spotted children playing in the dirt as he walked to the train station and asked their parents why they weren't in school. They complained the school was too far and their children would have to cross a dangerous highway to get there. If he was concerned about their education, he should teach them, they said.
The next morning, he came back to teach his first lesson to five excited children. Within six weeks, there were 140, he said. They were the children of construction workers and bicycle rickshaw drivers, of farm laborers and roadside vendors, the poorest of migrant workers who came to the capital because opportunities in their villages were even worse. Many of the parents were illiterate and couldn't even sign their names, he said.
"To change the future of these children, education is the only weapon," Kumar said. "If they go anywhere in the world, if they have education, they can achieve anything. And without education, they can do nothing."
An Indian donor, seeing an Associated Press photo essay on the school, gave the children socks, shoes and Angry Birds backpacks. He hired workers to level the ground under the bridge and bought the foam mats the pupils sit on.
On a recent spring day, the kids sat attentively, practicing reading and writing with workbooks. A second volunteer teacher whom Kumar recruited chalked algebra equations on a blackboard. A college student on break helped tutor the children.
Kumar, 42, who teaches Monday through Saturday and gives no vacations, stood at the blackboard and in a singsong voice led the younger children in math problems. He called students up to the wall to do simple subtraction and gently patted one girl on the cheek when she got an answer right. She ran back to her seat, beaming.
Every few minutes a train passed overhead, largely ignored by the school below.
Pammi, a 12-year-old girl who, like many of India's poor, uses only one name, was illiterate and had never been to school until she came here six months ago. Now, she can read and write, she said.
Nishu, 5, went to a government school for one month, but cried all the time and told her family the teacher beat her. Her family, unhappy that the little girl had to cross a highway to get to school, pulled her out, said her grandmother, Rekha, 60, who sells vegetables from a basket she carries on her head.
"My granddaughter is very, very smart," Rekha said as Nishu practiced writing her ABCs on a slate. "I don't want her to go anywhere else. I want her to stay and read and write here."
Kumar works to enroll the students in government schools and said he got 130 into the state education system.
"They can get a degree there. I can't give them that," he said.
But many of those kids come back to study with him as well.
Bharat Mandal, 15, wakes up at 3 a.m. to help his parents farm roses for four hours, and he goes to government school in the afternoon, but he still attends Kumar's school in the morning because "I get to learn," he said.
"I get answers to my questions here. In school there are too many students and the teachers just come and then leave, so my questions aren't answered," he said.
Noorbano, 32, had no idea how to register her four children in school when her family moved from the state of Uttar Pradesh to a shack surrounded by a sea of orange marigolds and pink roses near the banks of Delhi's fetid Yamuna River.
Noorbano, a flower picker, sent them to Kumar's school in 2008 and a year later he got them into an official school. Their mother was not impressed.
One day, she brought her son to school and the teacher yelled at her for not sending him before. He's here every day, she responded, it's you who are never here, Noorbano recounted.
She still sends her children to Kumar, and now has dreams almost unthinkable for the offspring of manual laborers attending government schools.
One son will be an engineer, another will be a police officer, a third will be a doctor and so will her daughter, she said.
"For my children, there's God, and there is him," she said, pointing to Kumar.
But Kumar fears his project is precarious.
He needs more volunteer teachers because of the mass of students, but doesn't know where to find them. And his unregistered school is squatting on railroad property.
"Whenever I am asked to leave this place, I will have to," he said. "Right now, the children are studying. We will take each day as it comes. As long as it remains possible, let's take advantage of it."
Follow Ravi Nessman on Twitter at twitter.com/ravinessman