When students at the District’s Simon Elementary show up for school on time, they reach for a numbered index card. It’s their ticket for that day’s attendance raffle.

The prizes are small — a ruler, a calculator, a bag of candy — but they are enough to trigger shrieks of celebration each morning in the cafeteria, and administrators hope they also are enough to help nudge more children through the front door of the schoolhouse. The reward program is one of the more visible parts of a much broader effort to tackle rampant truancy at Simon and other schools across the city.

Last school year, about 15,000 D.C. Public Schools students — 32 percent of all students in pre-kindergarten through high school — missed more than 10 days of classes without a valid excuse, according to school system data released in January. Nine thousand of those students missed more than 20 days without an excuse.

Total absenteeism in the traditional schools, including absences excused for reasons such as an illness, is even worse. Last school year, DCPS officials said, nearly 40 percent of the city’s students missed at least 18 days of school, a level of chronic absence tightly linked to academic failure. Half of those students were absent for the equivalent of seven weeks during the course of the 36-week school year.

Truancy in the District has long been a significant problem, one that city officials say has dragged down overall school performance and graduation rates, and has sent students into academic tailspins from which they never recover. But it has drawn new attention and urgency since the disappearance of 8-year-old Relisha Rudd, a girl who loved school but who accumulated more than 30 absences at Southeast Washington’s Payne Elementary before a school social worker alerted police last month.

In suburban school systems outside Washington, Relisha’s absenteeism might have been astonishing. But in the District, it was astonishingly normal.

“In some of our schools, the number of kids who have the same number of absences as Relisha is astounding,” said Schools Chancellor Kaya Henderson. “It’s a problem.”

It is impossible for even the most effective educator to change a child’s trajectory when that child doesn’t show up for class. Research has shown that children who miss more than 10 percent of the school year — 18 days of the District’s 180-day year — are far more likely to struggle academically and eventually drop out.

The problem is worst among the school system’s high school students, but it is also a serious issue among its youngest children. Nearly one in five students in pre-kindergarten and kindergarten missed more than 10 days of school without an excuse — absences that often contribute to gaps in knowledge that widen over the years.

“Everything we know about early attendance suggests that it’s critically important to lay the foundation” for future academic success, said HyeSook Chung of D.C. Action for Children, a nonprofit group that has analyzed attendance data from the city’s schools. “We think the parents just aren’t prioritizing, because they just don’t see value. They think of pre-k as babysitting.”

The school system has hired more staff devoted to reducing absenteeism and has intensified its focus on attendance as a key element of evaluating schools and principals. There are signs of progress, especially at the elementary level, where at the end of the first semester of this school year, the rate of chronic truancy had dropped 27 percent compared with the same point last year. Total absenteeism also has begun to drop.

But even with the improvements, children still miss an enormous number of class days, raising questions about whether the District has found an effective approach to reduce absences.

“How do you go after the kids who are not in school? It becomes an insurmountable problem,” said Henderson, who credits the D.C. Council with forcing the school system to confront its truancy crisis but says schools cannot solve truancy on their own.

D.C. Council Chairman Phil Mendelson (D), who has focused on truancy as a way to identify and help children at risk of entering the criminal justice system, said that the city still has a long way to go but that it has made notable progress. Four years ago, he said, children weren’t declared chronically truant until they reached 28 unexcused absences, and the school system had no useful data on the scope of the truancy problem. “All that’s changed,” he said.

Now, because of new laws, the District’s schools must track and report unexcused absences and must take clear steps when children reach certain thresholds: at five unexcused absences, school staff must hold a meeting to identify why the student is missing school and what can be done about it; at 10 unexcused absences, the family must be referred to the D.C. Child and Family Services Agency.

The laws have also tightened the definition of chronic truancy to include students who miss at least 10 days of school without an excuse, and have specified that children should be marked absent if they miss more than 20 percent of the school day.

Officials in high-truancy schools are overwhelmed and often struggle to meet the new requirements, Henderson said. As of early January, fewer than 40 percent of the system’s chronically truant students had been referred to child welfare as required by law, according to school data.

The new expectations have “made us more vigilant and have helped us to focus on attendance,” Henderson said. “But I am worried that I have people whose entire job is the compliance and paperwork . . . and I think that does not then allow us to do the deeper things that engage students.”

Courts also have become more involved, with the number of truancy prosecutions spiking more than tenfold in the past five years.

City lawyers say that they only prosecute as a last resort. The cases­ can be dismissed if parents complete community service and ensure that their children go to class.

D.C. Superior Court Judge Kimberley S. Knowles dismissed one such case Friday. The mother of a habitually truant 7-year-old had spent 10 hours volunteering at a day-care center, and her child’s attendance had improved.

Outside the courtroom, the woman’s court-appointed lawyer, Wole Falodun, said that in his experience, absences often pile up because working parents leave their children in the care of other adults who fail to ensure that the kids get to school.

“Most of the time it’s economics,” Falodun said. “The parent is working and whoever they have in place making sure that their child goes to school does not follow through.”

Truancy has complex roots, according to educators and social workers, who say that older students often feel frustrated by their inability to do grade-level work, while younger students miss class for all kinds of reasons. Some parents don’t want to send their children out in bad weather, and others rely on older students to babysit for younger siblings. Some parents are chronically ill, or they are homeless or lack reliable transportation.

Malik Thompson said he missed months of ninth grade after his brother, who had been diagnosed with schizophrenia, was struck and killed by a Metro train about four years ago. Thompson said he eventually received a letter saying he had been “unenrolled.”

“I was going through shock and depression,” said Thompson, now 18. He tried two other D.C. schools before withdrawing to finish his diploma through a home-school program. He said he thinks that he would have reacted differently if he felt he had allies at his school.

“What happened to me was unique but not exceptional,” Thompson said. “Schools at the end of the day should really be communities, so people feel attached to the school, so they’re willing to share and open up and get support.”

National attendance experts cite New York City as a model for how communities can address poor attendance, pointing to a massive effort that then-Mayor Michael Bloomberg launched in 2010.

While the District has focused largely on attacking truancy, New York has targeted students who accumulate large numbers of absences of any kind, excused or unexcused. A citywide task force designed an approach that made a significant dent in absenteeism at 100 pilot schools, especially among poor and homeless children, and is now being rolled out to schools across the city.

Under that model, schools track all absences and analyze data at weekly meetings. They work with outside agencies to connect families with social services, and they offer incentives and public recognition for excellent attendance. Perhaps most important, they find one-on-one mentors for chronically absent students.

Hedy Chang, a national attendance expert who has worked with school systems including the District’s, praised New York’s approach as one that allows for earlier and more meaningful intervention, before a child’s chronic absence turns into chronic truancy.

“It’s much less expensive to make sure that your kids are there starting in kindergarten and have a chance to do well, and don’t end up being a challenge in middle school,” Chang said. “We’re missing this opportunity to take a far more cost-effective approach to make sure that more kids don’t fall through the cracks and have a chance to succeed.”

D.C. Council member and mayoral candidate David A. Catania (I-At Large), who wrote two recent truancy-related laws, said he doesn’t disagree. “Absolutely I believe we should move beyond truancy to total absences, but the situation was so dire that we had to start somewhere,” Catania said.

School system officials do not publish chronic absence data but say they are beginning to study it. They do publish in-seat attendance, a measure of school­wide absenteeism that includes all absences. But high in-seat attendance can mask the severe absenteeism of individual children.

D.C. schools are using some of the same techniques that worked in New York, including incentives and recognition. And thanks to a new program administered by the Justice Grants Administration, dozens of elementary and middle schools are linked to community-based organizations that can help find and address the root causes of the most difficult truancy cases.

Simon Elementary partners with the Far Southeast Family Strengthening Collaborative, which sends a representative to weekly attendance meetings meant to identify which students need extra attention.

“We’re really on top of our families and trying to figure out exactly where the obstacles are,” said Simon Principal Adelaide Flamer, who tracks each classroom’s weekly attendance on a spreadsheet showing how many days each student has missed.

Morning raffle prizes are just part of the effort to stem Simon’s truancy rates, which spiked to more than 30 percent two years ago. That rate fell to 22 percent last year, and this year the school appears on track for much greater improvement.

Photographs hang in the lobby showing students who had perfect attendance for the month. Each day, staff members reach out to parents of absent students, and an attendance team of teachers and support workers meet weekly to discuss how to help struggling families get their children to school.

The toughest ­cases are turned over to the family collaborative, whose employees make home visits to learn what city and social services a family might need. One such visit uncovered a plumbing problem that kept the family from washing clothes; the children were missing school because they had no clean uniforms.

Now the plumbing problem has been fixed. “The children are coming to school now,” Flamer said. “That was a real success story for us.”