Kaya Henderson was the D.C. schools chancellor for more than five years, until she stepped down in fall 2016. (Jabin Botsford/The Washington Post)

By some key measures, public schools in the nation’s capital look better than they did a decade ago when reformers upended the system.

Enrollment has steadily increased in the past five years, high school graduation rates have improved, and most students are scoring higher on standardized exams. Schools boast state-of-the-art facilities after a rebuilding spree, and the system has invested in rewarding and keeping good teachers.

So why did former D.C. Public C. Schools Chancellor Kaya Henderson feel she needed to boost confidence in the system by giving high-ranking officials special treatment to help their children get into sought-after schools?

All those systemic improvements, it turns out, weren’t enough.

DCPS still suffers from a “crisis in confidence,” as Henderson told city investigators in a report The Washington Post disclosed this month detailing her actions to help certain families get around the D.C. school lottery.

Images can’t be remade simply by having better test scores or shinier buildings. And Henderson believed that having more VIPs in the schools could matter in turning the system’s reputation around.

For decades, DCPS hasn’t educated a president’s child. President Trump and Presidents Barack Obama and Bill Clinton all opted to send their children to private schools. Thousands of other families in the city do the same. Additionally, nearly half the city’s public school students enroll in charter schools.

Experts say school leaders in systems with tattered reputations will try everything they can to change the system’s image. Some say schools benefit from attracting wealthier families into their schools, as Henderson was trying to do, because research suggests schools benefit academically when they enroll students from a wide spectrum of economic backgrounds, from poor to rich.

“Endorsement from parents who are considered peers is probably more powerful than what any principal or superintendent will say about a school system,” said Richard D. Kahlenberg, a senior fellow at The the Century Foundation and an expert on school integration.

D.C. Inspector General Daniel W. Lucas found that Henderson helped well-connected parents bypass the city’s lottery to enroll their children in coveted schools. Lucas found Henderson misused her authority by giving preferential treatment to seven of 10 people who requested special school placements for their children during the 2015 lottery season.

In at least three of those placements, Henderson told investigators that she approved the placements because she wanted to boost the reputation of the school system.

“She felt it looks good for the school district when an elected official reaches out about attending a D.C. public school,” Lucas’s report said of one of the placements.

The report does not name the parents who benefited from Henderson’s actions. However, a former city official with knowledge of the school placements provided documents identifying four of them as City Administrator Rashad M. Young, D.C. Deputy Mayor Courtney Snowden, former D.C. mayor Adrian Fenty and Roberto J. Rodríguez. Rodríguez, who served in the White House as an education adviser to Obama. The former official provided the information on the condition of anonymity because he was not authorized to discuss the matter.

In three of those placements, Henderson told investigators that she wanted influential city and federal workers to have a seat in D.C. schools.

Asked about the Rodríguez placement, Henderson told investigators that when people in the White House send their children to a DCPS school, it “shows high-ranking officials’ trust in the school system, leading to the theory that it will show others should also trust the DCPS school system.”

Henderson declined an interview request, saying in an email that she has been advised by her attorneys not to make public statements until the conclusion of a D.C. Board of Ethics and Government Accountability probe, but she said she appreciates an exploration of “this part of the story.”

While the Lucas report lays bare how Henderson used her power to place the children of those with political clout in sought-after schools, it also revealed her apparent insecurity about the reputation of a school system that is trying to rebuild its image after a decade of school reform efforts that she helped lead.

Most of the 48,000 students in DCPS come from low-income families: 75 percent qualify for free or reduced-price meals. In some schools, all students qualify. D.C. officials are pushing to take advantage of the city’s gentrification and to diversify their enrollment.

Having middle- or upper-middle class families in schools sends a signal to other parents that there is trust in the school system, Kahlenberg said. Research has found that schools with balanced shares of middle- and low-income students do better academically than those with high concentrations of poverty.

Kahlenberg called Henderson’s rationale in trying to attract high-powered families into the school system “half right.” He said he disagrees with Henderson’s methods.

“If her argument is you are trying to instill confidence in the system, then using means that suggest to the average person that the system is rigged backfires,” Kahlenberg said.

Daniel A. Domenech, executive director of the School Superintendents Association and a former superintendent of Fairfax County Public Schools in Virginia, said superintendents sometimes rely on quick fixes to repair their reputations. Having influential government leaders with children in schools can help improve the system’s image, he said.

“You scratch and do the best you can in the short term, as Kaya tried to do,” Domenech said. “But it comes down to improving the system so the kids are getting the quality education that they need, and that will attract residents to the schools.”