Teachers got the message in meetings and during visits to their classrooms in the days before they were scheduled to administer state exams.

Multiple staffers at Cayuga Elementary said they were instructed by principal Evelyn Cortez to do what they had to do in their rooms to get good scores.

Cortez, reached Friday night, was emphatic: "I disagree with these allegations."

The school, in a tough Hunting Park neighborhood, produced strong test results for several years running, and Philadelphia School District officials noticed. They've rewarded Cayuga with increased flexibility in curriculum and budgeting and public pats on the back.

But teachers, a former staffer, parents, even a student - say those scores were achieved in part by cheating.

And a state-commissioned review of 2009 PSSAs found a suspicious pattern of erasures on Cayuga's fourth-grade reading tests, with the odds of them occurring naturally greater than 1 in 100 million.

"My son came home one day and said his teacher kept telling him to erase his answers and write different answers," one parent said.

The descriptions of cheating on state exams, known as PSSAs, are similar to those detailed to The Inquirer last year by teachers at Roosevelt Middle School in East Germantown.

Both Cayuga and Roosevelt are among the 13 Philadelphia public schools being investigated by the Pennsylvania Department of Education and the state Inspector General's Office for possible cheating on the 2009 exams.

Penny Nixon, the district's chief academic officer, said in an interview that "the district takes these allegations very, very seriously." Nixon said the district had stepped up security for the tests to be administered next month, and also enhanced test-security training.

In 2007, Cayuga did not make AYP, or Adequate Yearly Progress, an important measurement under the federal No Child Left Behind law. That began to change the next year.

Cayuga's 2009 PSSAs had suspicious results in every grade tested, a state analysis found. Experts flagged the school 10 times for statistically unexpected results and earmarked the tests of 18 students as suspicious, mostly due to erasures. The flags do not prove cheating but indicate that further study is warranted.

In 2009, fourth-grade reading scores rose from 53 percent passing to 89 percent, and math scores saw an even larger increase, from 39 percent to 84 percent passing.

No school in the state had more flags for fourth-grade results.

The Cayuga parent whose son complained said his teacher would point out answers she said were wrong. And then she told him which answer was right, the parent and boy said.

The boy was upset, she said. He didn't like the teacher telling him to change his answers.

"You're not supposed to do that," the boy said.

The staffers say tests were manipulated in multiple ways, for several years.

Teachers were directed to give students answers; students were told to change incorrect answers days after the fact. Disruptive students were removed from their classrooms, tested separately with special-education students - who are allowed special accommodations to complete their tests - and encouraged to read questions aloud, they said.

In one instance, staffers saw what they believe was administrators erasing answers in student booklets and changing them.

Before testing time last spring, Cortez even told students to write answers on scrap paper first, then check with teachers before putting them into their PSSA testing booklet, the staffers said.

"The announcement was made over the loudspeaker, to the whole school: 'Students, do not bubble anything in on your books. When your teacher gives you approval, then you may put it in your book,' " one teacher recalled.

"All I have to say is, whatever the allegations they're insinuating, they're not true," Cortez said.

The staffers and parents who came forward to The Inquirer asked that their names be withheld, for fear of reprisal.

One of the teachers who spoke to The Inquirer said Cortez had also made announcements over the loudspeaker telling teachers they were not allowed to sit down during the PSSAs, that they had to walk up and down the aisles of their classroom and help students.

"She said: 'Children, if you need help, you raise your hands. Your teachers are there to help you,' " the teacher said.

State rules forbid teachers from helping students during the test, said Daniel Piotrowski, the district's executive director of accountability and assessment. Teachers can walk up and down aisles during the test, and can make general comments to the class about staying on task, but can't review student work, return a test book to a student, point out an item that's been skipped, or make any kind of signal.

"They are not allowed to give any help on the test. Period. The only things that they can do is read aloud portions of the math assessment," Piotrowski said.

Cortez said the school had a "strong testing system" and observed all state and district procedures.

Accusations of test-tampering at Cayuga are not new, Piotrowski said: "We know allegations against the school in the past were false."

"A lot of times with test-security violations or allegations, people allege things that they think to be true or aren't violations," he said.

Teachers said there was no confusion about what was going on.

They described Cortez directly confronting them, telling them that their students "need to do better," they said. Those who refused to comply with the administration's mandate were moved to grades that weren't being tested, they said.

PSSAs are administered to third through eighth and eleventh graders every year.

The word cheat was never used by Cortez, the teachers said, "but we all knew what she meant," one said.

The teachers who came forward to The Inquirer say they refused to cheat.

"I said, 'I'm not losing my pension and my teaching certificate for anybody,' " one said.

But students have made it clear to these teachers that others have given them answers, the teachers said. Some students have resisted taking tests because other teachers helped them in the past, they said.

The school's 400 kindergarten through fifth-grade students - 94 percent of whom live in poverty, 21 percent of whom do not speak English as a first language - are suffering, the teachers say.

"The kids will say: 'I'm advanced. I'm proficient.' And they just don't have the skills," a teacher said.

After a staffer called the district about the suspected improprieties last year, officials were sent to Cayuga to monitor testing procedures. Cortez still insisted that teachers "help" students, the teachers who spoke to The Inquirer said.

"She said, 'Nobody will be in that room with you,' " one teacher said. Then she told teachers that testing books would be in their room all day. That would be a violation of state protocol, and teachers took it as a sign that Cortez wanted them to cheat, they said.

One day last spring, one teacher said, students were called out of the teacher's classroom two by two. The PSSA math and reading sections were done, but other sections of the test were being administered.

When the students began to file back into the teacher's classroom, the teacher asked them what they were doing.

"They said: 'I had to fix my test. I multiplied and I was supposed to divide. They gave me the calculator and I divided.' One of the kids said, 'You only have to go down there if you get stuff wrong,' " the teacher said.

Piotrowski and Nixon said they had not heard the specific allegations the teachers and others are making.

"These would be like the silver bullet. . .," Piotrowski said. "But I've not heard of any of these. These are not things that have ever been reported to our office, neither for this school, or for some of these things, for any school."

Nixon herself is the former principal of a school flagged by state investigators. During her time at Wagner Middle School in West Oak Lane, investigators flagged the school for a high rate of erasures in 2009. The chances of those erasures happening naturally were astronomical, the report said - nearly 1 in 10 quadrillion.

"I stand behind the scores," Nixon said. "I stand behind the great work that we did at Wagner Middle School."

At Cayuga, the teachers said they finally came forward after years of frustration and worry because of conditions at the school. Cayuga, like public schools across the city, has been hit hard by budget cuts. It has lost teachers and support staff. It has large class sizes, scant supplies, little help for struggling students, and a lack of any real discipline policy, they say.

And the pressure is not limited to PSSAs, the teachers said. They've also been told to inflate students' reading levels, and to photocopy predictive and benchmark tests designed to gauge students' progress, then take them home and prepare lessons designed to teach students how to answer the questions that will appear on those tests.

"It's accepted," one teacher said. "That's just what we do."

Another former staffer corroborated the teachers' stories. The staffer saw 2009 school surveillance video that showed what the staffer suspects was answer-changing by Cortez and others.

The staffer, who left last year, said the video showed Cortez entering an empty school before dawn one day during PSSA testing, entering the locked room where completed tests were kept, and exiting with a box. Cortez then returned with a cart and took two more boxes into her office, the staffer said.

"I don't know what went on in that office, but I can only imagine why you're there that early - before the building engineer got in, at 6 a.m.," the staffer said. "It's not fair to the kids."

Another teacher's suspicions were raised when Cortez - who normally arrived at the school closer to when students did, after 8 a.m. - began coming in early. That practice lasted only as long as PSSA tests did, the teacher said.

That tape no longer exists; surveillance video is routinely destroyed after a time, staffers said.

But it was the subject of much speculation at the school, the staffer said.

"We all talked about it - 'Why was she there at 5 a.m.?' She did whatever she had to to make AYP," the staffer said.

Cortez said she did not recall the incident.

Two Cayuga parents said they had other worries about what's going on at the school - bullying, discipline problems. And now, "we've seen some kids who can't even read and they're passing the PSSA," one of the mothers said.

"There's something funny going on to make the scores that high," another mother said.

The mother whose son didn't like being told to change his PSSA answers voiced her concerns to Cortez and the boy's classroom was changed, she said. No further action was taken, the mother said.

It's an untenable situation, teachers said.

"I am a good teacher," one said. "My kids can do decently on their own without anybody's help. But what she wanted was the impossible."

Contact staff writer Kristen Graham at 215-854-5146215-854-5146 , kgraham@phillynews.com, or on Twitter @newskag. Read her blog, "Philly School Files," at www.philly.com/schoolfiles.

The Inspector General's Office has set up a hotline for teachers with information about cheating to call. It is 888-448-2435888-448-2435 . Information may be provided anonymously.