Each year, students would enter Rob Barnett's 12th-grade math class at Eastern High School struggling with fractions and basic division. The students worked hard and improved, but mastering probability and statistics in a single year when they started grade levels behind proved grueling — and not always possible.

So at the end of the course, Barnett said, a crushing dilemma confronted him: Should he pass these students even if they hadn't earned it or flunk them senior year, leaving them without a diploma?

"This student has been passed along by so many teachers and now it's up to me to decide whether this student is going to pass or whether I need to put my foot down and say that you don't really understand math the way you are supposed to," said Barnett, who no longer works for the school system. "It's about a system that cares more about passing than teaching them."

A damning city report released Monday portrayed a systemic culture of passing students in D.C. Public Schools, revealing that teachers felt pressured to award diplomas even if teens failed to meet graduation requirements.

Overly empathetic teachers graduated students who came from challenging backgrounds, despite those teenagers scarcely attending school, the report found. And other D.C. educators said if they wanted a favorable annual job review, there was a limit to the number of students they could fail.

The report, which was commissioned by the Office of the State Superintendent of Education, detailed an urban school system that seems to be driven by a quest to improve graduation rates. Out of 2,758 students who graduated from a D.C. public school last year, more than 900 missed too many classes or improperly took makeup classes, undermining the validity of their diplomas, the report found. D.C. schools recorded a 73 percent graduation rate in 2017, a record high.

At Barnett's Eastern High, nearly 45 percent of last year's graduates appeared not to meet graduation requirements, according to the city report. At Anacostia High, it was 70 percent of students.

"Throughout the course of this investigation, [D.C. Public Schools] staff expressed concerns that it was increasingly difficult to fail students, contributing to a culture in which passing and graduating students is expected of administrators and staff, sometimes at the cost of academic rigor," the report said.

The graduation controversy comes as the D.C. school system has been touting its successes, with Mayor Muriel E. Bowser (D) in October calling it the "fastest improving urban school district in the country." Now, city leaders must contend with a different reality, one depicted in granular detail in the investigation released Monday.

At a monthly meeting Tuesday, Bowser assured the D.C. Council that she and the schools chancellor were committed to transforming graduation practices, and said she wanted more accurate graduation rates, even if they don't portray a rapidly improving school district.

"None of us around the table who have been very committed to the transformation of our schools wins with fake numbers, and certainly our children don't win with fake numbers," Bowser said. "That is my commitment to make sure we know when we present information . . . that everyone has a true reflection of what we have been able to learn."

Experts say the investigation should prompt lawmakers to put less emphasis on graduation rates.

"Diplomas are now high stakes because we're judging states and schools and districts based on their graduation rates, so the fact that some people are cheating to get there is not surprising," said Russell W. Rumberger, director of the California Dropout Research Project at the University of California at Santa Barbara. He urged policymakers to take a more holistic view to determine whether they are prepared for life after high school.

The graduation scandal could undermine the legacy of the ­high-profile reforms enacted by former schools chancellor ­Michelle Rhee and her successor, Kaya Henderson.

Catharine Bellinger, D.C. director for Democrats for Education Reform — which has long supported Rhee — said that the report is not an indictment of Henderson's tenure and that graduation rates are just one of many measures of success.

"These failures in our high schools have existed for decades, and it's unfair to our students that we have not addressed these," Bellinger said. "But the reforms of the last decade have jump-started progress in D.C. elementary schools and high-performing charter schools."

The investigation was prompted by a November article by WAMU and NPR that said Ballou High School in Southeast Washington gave diplomas to seniors who did not meet graduation requirements. Although the article focused on Ballou, the report from the state superintendent's office examined attendance and grading practices across the city, determining that truancy is more severe at neighborhood schools such as Ballou than in charter or application schools.

Those interviewed for the superintendent's report told investigators that because of the District's evaluation system, known as IMPACT, they felt pressure to pass students, knowing it influences the salaries of teachers and administrators.

Some school leaders told investigators the school system gave them graduation targets that would be impossible to reach without violating district policies.

Teachers at two high schools said in interviews with The Washington Post that they were urged to create "makeup packets" for students who missed days of class, and were required to document interventions before giving a failing mark.

At Roosevelt High, teachers told investigators that "school administrators exercised intimidation paired with heavy paperwork burden in order to dissuade teachers from failing students in support of graduation rate goals."

Brittaney Woods, who taught at Dunbar High for seven years before departing last spring, said in an interview with The Post that many of her colleagues complained they were forced to create makeup packets for students who had not shown up for entire school quarters, even though district policy calls for flunking students who miss that much class.

"A lot of teachers had a problem with this," Woods said, adding that the teachers said it made it difficult to motivate students who did show up to class. "How do I get students who are there every day to take this seriously?"

Fenit Nirappil contributed to this report.