As advocates for years have tried to secure a larger stream of funding for Pennsylvania’s neediest school districts, they’ve had to push back on a constant refrain — that even when some districts get more money, they still don’t get the desired educational results.

But a superintendent called to testify this week at the historic trial challenging how Pennsylvania funds public education sought to show why that argument isn’t credible — describing the scope of the challenges facing her district, and why despite spending more than most, it still can’t meet children’s needs.

“You can’t compare children who live in such economically disadvantaged homes to children who are middle-class and affluent,” said Lancaster Superintendent Damaris Rau, testifying Thursday before Commonwealth Court Judge Renee Cohn Jubelirer in Harrisburg. “The needs are very different.”

Her district is one of six suing the state, alleging that funding is both inadequate and inequitable in part due to the state’s heavy reliance on local property taxes to pay for schools. Advocates hope the trial, which began about a month ago and is projected to last as long as 12 weeks, will lead to a vast overhaul of the state’s school funding system. The plaintiffs include the William Penn School District in Delaware County as well as a mother from the Philadelphia School District.

Lancaster enrolls just under 11,000 students and has $22,000 to spend per pupil — ranking in the top fifth of Pennsylvania’s 500 school districts in per-pupil expenditures. The state average is $19,000. Republican lawmakers who are defendants in the case have described Lancaster as high-spending but low-achieving, arguing that more money wouldn’t necessarily improve outcomes.

But Lancaster also serves one of the state’s neediest populations: More than 90% of its students are considered economically disadvantaged, a larger share than all but six other districts in Pennsylvania, and about 500 are homeless, Rau said. The district ranks fifth for its share of students for whom English is not their native language — 20% of its enrollment. Its share of special education students, also 20%, is higher than the state average.

About 500 Lancaster students are refugees; some arrived from camps where they weren’t receiving formal education. “They come significantly traumatized,” Rau said, citing students from Latin America, Myanmar, and the Middle East, among other areas.

And they have substantial educational needs, Rau said. The district hired 80 specialized teachers to help students who aren’t fluent in English — and many still have high caseloads. Translators are needed for parent meetings. The district hired three former refugees as “cultural navigators” to help work with families. And it lacks enough social workers, counselors, and school psychologists, Rau said.

“When there are not enough mental health workers in our schools, we start seeing the increase in violence,” she testified.

Pennsylvania recognizes that schools with needier populations — whether it be large shares of students in poverty or English learners — require more money. But its funding formula, which targets additional money to districts with those needs, only applies to a portion of what the state spends on education, meaning the aid Lancaster gets from the state doesn’t match what the formula says it warrants.

Adjusting spending based on student need, Lancaster would rank 274th among school districts for how much it spends per pupil, according to petitioners.

Overall, Rau said, attracting teachers is difficult. Lancaster is the second poorest district in its county, surrounded by affluent suburbs, and many teachers prefer to work in a suburban environment, Rau said. The district tries to match starting salaries with its suburban peers, but can’t pay teachers as much over time.

Because the district worries about losing textbooks, children mostly aren’t allowed to take them home at night — which requires teachers to spend more time finding open-source materials they can copy after school, Rau said. Given those demands — and that some teachers have second jobs — Rau said Lancaster has struggled to staff after-school programs.

With COVID-19 relief money coming in, “we told all our schools, ‘Hey, now you can open up after-school programs every single day,’ ” she said. But now “they can’t find the teachers to run” them.

That’s an example of how the cycle of poverty can continue, Rau said: Lack of after-school options may also complicate a parent’s efforts to find work.

And the district hasn’t been successful in halting the “cycle of decline” that many students experience as they progress through school, Rau said. In 2016-17, 1% of third graders tested above grade level in math in a district test, while 19% scored at level, and 81% below grade level. Two years later, 86% of fifth graders — a group that including many of those same third graders — scored below grade level in math, while only 1% tested above grade level. Rau described a similar pattern in reading.

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She blamed the poor showing on a lack of reading and math specialists who could provide extra support to struggling students: The district has four reading specialists to serve 6,000 elementary students, and no math interventionists.

It has some reading specialists at the middle and high schools, because those students also need additional help, Rau said.

“It’s trying to triage where you put your resources. It’s putting Band-Aids, understanding these gaps are getting bigger and bigger,” she said. She said students and parents “get heartbroken every time they see they are not meeting the state standards. ... If you were receiving a letter every year that says your child is below basic [levels], that’s pretty demoralizing for families. And for kids, because they know.”

The district offers school sports programs, which Rau said sometimes sparks the question: “Why don’t you cut all your athletic programs and give the money to reading and math?”

She responds: “Would it be fair that the poorest kids in the entire county ... would be the only one without a football team, without a basketball team, without a soccer team? How is that equitable?”

Even then, she said, the district’s athletic facilities are subpar compared to its peers — just as its school buildings are also in “bad shape.”

Rau, who grew up poor and didn’t speak English when she began kindergarten, said she sees herself in Lancaster’s students and believes they could succeed at higher rates if they had more resources. A former teacher in the South Bronx who moved onto administrative roles in Greenwich and New Haven, Conn., Rau said she had been accustomed to working in school systems that “believed in providing kids resources needed.”

But when she came to Lancaster, she testified, “I realized that was not the norm here in the state of Pennsylvania.”