Records from Einstein High provide telling details about what students miss: One senior skipped algebra 36 times last spring. Another racked up 47 unexcused absences in English. Still another was gone for more than half a semester of chemistry.

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Roughly 40 percent of Einstein’s Class of 2018 missed large chunks of instruction last school year, not showing up for some classes 10 to more than 50 times in a semester, documents show.

The extent of the absenteeism at Einstein raises questions among some educators about the integrity of grades and diplomas in a school system regarded as among the nation’s best. The issue arises as diploma scandals have roiled school systems in the District of Columbia and nearby Prince George’s County, Md., where investigations have been conducted and changes made.

But the absenteeism also touches on broader questions nationally about the value of attendance and the push to award diplomas. Rising graduation rates have been touted across the country as badges of school success.

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With graduation season underway in Montgomery County’s 25 high schools, questions persist about what should be required to earn a diploma.

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“If 40 percent of the kids were absent to that degree, are we okay with it as a community?” said Christopher Lloyd, president of the Montgomery County Education Association, the teachers union. “And if the answer is, no, what in the world is happening?”

Lloyd described the numbers as shocking but said they also reflect policy changes that have made it easier to pass courses, recover from failing grades and be out of class — even though schools routinely say students must attend classes.

In Montgomery, educators in a string of high schools have told The Post that attendance practices are lax, vague or inconsistent. Some say they feel pressured to give makeup work, extend deadlines, excuse assignments or find other ways to help repeatedly absent students pass — and that the problem is not just a matter of seniors’ losing interest as their high school days wind down.

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The Einstein documents obtained by The Post create an unusual snapshot of absenteeism — with absences noted student by student, course by course — providing far more detail than is offered by state data and showing that scores of diplomas were at risk if students failed to earn credit.

Montgomery school officials did not dispute the veracity of the records but said many students face pressures outside the classroom. Einstein students who received diplomas passed required classes, they said. Schools Superintendent Jack R. Smith said that time in a classroom seat is not a state requirement and that there is “no evidence of wrongdoing on the part of anyone” at Einstein.

“We want kids in school,” Smith said. “We’re working hard to make school a place they can be, both through engagement and through removing barriers to getting there, whether it’s transportation, whether it’s food, whether it’s changing schedules because they have a child or they’re responsible for younger siblings or they have to work.”

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Smith said school officials “hold our diploma very important as a critical indicator of real success in school.”

School officials said attendance issues are not limited to the Kensington school. County data show that unexcused absences were abundant among last year’s seniors.

The data show that some 1,800 graduates countywide last June had at least 20 unexcused absences in at least one class. And that was in one 90-day semester.

Some schools stood out: At John F. Kennedy High, 33 percent of the senior class hit the 20-absence mark. At Northwood High, it was 36 percent. Gaithersburg and Watkins Mill high schools posted rates of more than 40 percent.

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Montgomery school officials emailed the Einstein families about The Post’s story in advance of publication, emphasizing that documents were “leaked” and describing efforts to tackle absenteeism and engage students.

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The Einstein email acknowledged that some staff members felt uncomfortable and pressured as administrators communicated about protocols that were new and that allowed students multiple opportunities to show their academic gains before graduation.

School system administrators said they found no grade ma­nipu­la­tion.

School system officials emphasized in interviews that unexcused absences do not directly factor into course grades. That’s part of the system’s “standards-based” approach, which focuses on student learning, not attendance, they said.

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They also said there is no numerical limit on unexcused absences.

“If I can go to class 40 percent of the time and earn a B,” that would not automatically lead to failure, said Jennifer Webster, director of school support and improvement for Montgomery high schools. “It’s about the grade. It’s not about the number of absences.”

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She said the school system has moved away from a punitive approach. “What we are committed to is intervening for students who have excessive absences, so that’s where we’ve put our energy,” she said.

But many Montgomery educators argue that attending classes and learning go hand in hand.

They criticize Montgomery’s approach: Warnings go out at three unexcused absences in a class and again at five, when students and parents are notified that an attendance intervention plan should be developed. Counselors or administrators are involved. If attendance does not improve, the policy says, students are “in danger” of failing a course.

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The records obtained by The Post for Einstein include only students who have at least 10 unexcused absences in a course — twice as many as the policy’s threshold.

“The policy is intentionally nebulous — for the purpose of graduating students,” said a county teacher who, like many other educators, spoke on the condition of anonymity for fear of retaliation. “When these students graduate, what are we saying? The diploma means nothing, and you don’t even have to show up?”

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Montgomery County’s graduation rate — 88.4 percent in 2018 — has been strong for years, with some high schools exceeding 95 percent. Einstein’s rate was 83.7 percent last year.

Longtime Einstein Principal James G. Fernandez, who recently announced his retirement, declined to speak about absences or related issues, school system officials said.

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Frederick M. Hess, director of education policy studies at the American Enterprise Institute, a Washington think tank, said Montgomery’s problems suggest a broader phenomenon.

“My best guess is you’d see a lot of this pattern because it suits everybody’s needs,” he said. “Kids want to graduate. [School] district leaders are under pressure to raise graduation rates. Teachers don’t want to be called out for causing problems or failing lots of students. There are lots of incentives to push kids through to graduation and very few to ask hard questions or keep them back.”

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Montgomery was once tougher with attendance, but its old “loss of credit” policy was scrapped in 2010 amid concerns that it took a particular toll on students of color, led to some students giving up and was at odds with the system’s move to standards-based grading.

Now, the school system says it focuses on attendance intervention plans, and some educators use a special grade — E3 — to convey that a student is failing because of absences.

Leah B. Michaels, head of the English department at Richard Montgomery High in Rockville, said state and county data suggest an attendance crisis.

“The school system’s attendance policy is vague and not consistently applied from one school to the next,” she said.

Montgomery school system officials underline the many reasons students miss classes: family and economic stresses, child-care duties, jobs that cut into time for school. Some parents may be less aware of the need to submit notes to excuse the missed time; students 18 and older can write their own notes.

At Einstein last year, about 40 percent of students were from low-income families, and 17 percent were English-language learners.

One graduate of Einstein’s Class of 2018, who spoke on the condition of anonymity because of concerns about retaliation if he spoke publicly, said his chronic absenteeism partly reflected financial struggles. He came to the United States from El Salvador as a child and has tried to pick up work — cutting grass, shoveling snow — to help his father support their family.

“I just wanted to take myself off of his plate — to work for myself,” the student said.

The student said high school, including chances to make up for failing grades in “credit recovery” programs, gave him “the stuff I needed.” Now, he is pursuing an associate degree.

But one of his classmates considered the school’s approach more damaging. He said that being frequently absent was viewed as a “victimless crime” at Einstein. “It’s not,” the student said. “Kids are being cheated out of why they’re at school.”

The student, who spoke on the condition of anonymity because of the issue’s sensitivity, said he wasn’t “wishing other people not graduate” but thought students who missed too much class would suffer in the long run.

He wondered what a diploma means.

“My high school diploma is worth as much as this other kid’s even though the kid came to school once a month and I came to school every day,” he said.

School systems throughout the country take varying approaches to absences, but experts say chronic absenteeism can threaten student success and undermine efforts to reduce achievement gaps that leave black and Hispanic students lagging.

Missing even five days in a high school semester increases the likelihood of failing a class or not graduating, said Elaine Allensworth, director of the University of Chicago Consortium on School Research.

“You can’t do the work if you’re not there; you fall behind if you’re not there,” she said. “Even students with strong test scores, they miss class and they fail.”

Robert Balfanz, a Johns Hopkins University research professor, said high school students with frequent absences are more likely to drop out, and those who manage to get to college are less likely to finish. “You pay the price somewhere,” he said.

Researchers say there is a strong link between poverty and absenteeism, and many of the Montgomery high schools with high rates of absenteeism have greater percentages of economically disadvantaged students.

Maryland education officials have recently intensified their focus on chronic absenteeism, which they define as being absent for 10 percent or more of school days for any reason, excused or not.

Every Maryland public school is rated — with one to five stars — using a formula that includes chronic absenteeism as one factor. Data posted in December show eight of Montgomery’s 25 high schools had rates of 30 percent or higher.

At Magruder High School in Derwood, 43 percent of high school students were chronically absent, the county’s highest.

This was hard to fathom for Cynthia Simonson, a data-minded Magruder parent who is a vice president of the countywide council of PTAs. She had never seen numbers on the topic, she said, even though she routinely pores over school system reports.

She wondered whether the problem was seniors’ skipping school, but when the issue came up at a January PTSA meeting, an administrator told parents that absences among freshmen were a particular concern, she said.

“I was surprised,” Simonson said. “What explains that many kids being out that many days?”

Montgomery officials said they have been studying student engagement, with a focus on chronic absenteeism.

Though Maryland has one diploma, its school systems handle absences differently.

In Worcester County, home to Ocean City, students fail a class after they accumulate 11 unexcused absences, a spokeswoman said.

Procedures in Prince George’s County call for zeros for class work given on days that students skip.

Baltimore city schools do not factor unexcused absences into student grades, with the idea that grades reflect mastery of content, not student behavior.

The state is considering whether to create a minimum attendance standard to “ensure equity across the state and the integrity of the Maryland high school diploma,” said Justin M. Hartings, president of the Maryland State Board of Education.

In Montgomery, several principals have expressed concerns about the difficulty of improving attendance, said school board Vice President Patricia O’Neill. While she did not have details about Einstein, she said, excessive absenteeism leaves her wondering about grades.

“It seems incongruous that you could pass high school math and not be there,” she said.

The documents obtained by The Post show that 115 Einstein seniors were frequently absent in math courses and that at least 88 missed senior-year English classes required for a diploma. Others were often out during science, social studies, art, physical education or Advanced Placement classes that may — or may not — have been required for graduation.

The combined effect for one semester: more than 13,700 class periods missed.

“The accountability piece for student attendance is gone,” said Russell Rushton, who was head of the math department at Walt Whitman High School in Bethesda until his retirement last June.

Rushton recalled that at his high-performing high school, 23 seniors in his classes were at risk of failing because of absences last spring. Many had more than 20 absences, passing only after doing significant makeup work, he said.

Many teachers argue that most absences are not related to extenuating circumstances. Rather, they assert, many students miss classes because they see few consequences.

Some teachers see the fallout in the Montgomery County graduates who arrive at Montgomery College unprepared every year. Nearly 70 percent of those students in 2018 needed to take remedial classes in math and 37 percent in English, college officials said.

Teachers may deny credit for assignments on days when students have unexcused absences. But Brian Donlon, a social studies teacher at Richard Montgomery High, said that in his experience, few students end up failing their classes after being frequently absent, because teachers are encouraged or pressured to extend deadlines and accept late makeup work.

He and other teachers also question the role and rigor of credit recovery programs that allow students to make up for failing a course.

“Kids are not having authentic learning experiences, because they are in and out of school so much,” Donlon said, “and we are not preparing them for the next level, whether college or a job, because we are allowing them to engage in a level of absenteeism that won’t work at their next endeavor. They are being set up for failure.”

Teachers at three county high schools said they find the situation so dispiriting that graduation ceremonies leave them conflicted.

Though they commend students who worked hard to earn diplomas, they feel frustrated watching frequently absent students cross the stage.

One remembers catching a colleague’s eye and exchanging a knowing glance. “How’d that happen?” the teacher remembered wondering.