“Why are we celebrating these scores as a miracle, when there is no miracle?” Rosa said she asked.

Another insider said Big Apple officials were urged not to “exaggerate” the results. But Mayor Bloomberg hailed the increase in 2009 as an “enormous victory.” At the time, he had a lot riding on the scores — he was seeking a third term and pushing for legislation to extend mayoral control of the schools.

City officials “got very angry,” the insider said, when Regents Chancellor Merryl Tisch publicly downplayed the results, citing “troubling gaps” between the stellar state scores and lackluster outcomes on national exams.

Mills has maintained the scoring was backed by his panel of experts. But Rosa and other members of the Board of Regents say he kept them in the dark.

“I basically asked, ‘Who sets the cut scores? How is this determined?’ ” said Rosa, who joined the board in 2008. “There was no real explanation. I never got a straight answer.”

Mills and his testing chief, David Abrams, had rebuffed requests in 2008 to investigate the inflation. Faced with a lack of confidence, Mills was “encouraged” to leave in June 2009, insiders said. He declined to comment last week, saying, “I have nothing to add.”

Many city students soon discovered their Big Apple diploma was little more than a piece of paper.

Jasmine Gary, 18, a graduate of Port Richmond HS on Staten Island, was surprised when she scored a 70 on the Regents math exam.

“I don’t know how I passed, because I failed a lot of math classes,” she said.

She applied to CUNY but bombed on the entrance exam. Now she’s required to take a no-credit, $75 remedial class at Borough of Manhattan Community College, but is catching up. “I learn more here,” she said.

Rossie and Angely Torres, 18-year-old twins from The Bronx, earned 76 and 75 respectively on the math Regents at Philip Randolph HS in Harlem. They, too, take remedial classes at BMCC.

“In high school it was just people talking and the teacher would just give us an assignment. It was just to graduate. But here, people work hard and the teacher is more serious,” Rossie said.

Former Chancellor Joel Klein, who left office several months ago to join News Corp, which owns The Post, declined to be interviewed. But he defended his eight-year record via e-mail sent by a city DOE spokesman.

“We’ve long called for higher standards and . . . we still made real gains,” Klein said.

For instance, city fourth-graders have boosted their scores on national reading tests since 2003, though eighth-grade scores have remained flat.

And NYC has outpaced the state’s other big cities, Buffalo, Rochester, Syracuse and Yonkers, the DOE says. In 2002, New York City’s fourth-grade math results were 27% lower than the statewide average, while the other four cities showed a 31% gap. In 2008, New York City was just 8% behind the rest of the state, while the “big four” were 25% behind.

But the more spectacular results have vanished.

The Board of Regents commissioned a study, led by Harvard professor Daniel Koretz, which concluded in 2009 that the statewide grades three-eight tests had become too easy. Mills’ successor, David Steiner, recruited for his experience in teacher development as dean of Hunter College of Education, was charged with making the 2010 tests more comprehensive and less predictable. He also hoisted the cutoff points, requiring students to do more to pass.

Scores plunged. Just 54% of all city students in grades three-eight showed proficiency in math tests last year, compared with 82% in 2009. Reading proficiency citywide fell from 69% to a dismal 42%.

Even so, the tougher tests continued the practice of giving “partial credit” for wrong answers — or no answer at all — if the kids showed some understanding of the concept or did one step right.

On the fourth-grade test, for instance, a kid who answered that a 2-foot-long skateboard is 48 inches got half-credit for adding 24 and 24 instead of the correct 12 plus 12. “They were giving credit for blatantly wrong things,” said a teacher hired to score the tests.

A state report released this month delivered a new blow. It found that most kids who earn less than 75 on the state Regents English test or 80 on the math exam — 65 is passing for both — must take remedial classes before starting college.

That 65 score is misleading as well. It’s based on an adjustable scale — and the state has whittled down the points needed to pass. Back in 2003, students had to get 61.2% of math questions right for a 65 score, the minimum required for a Regents diploma, and 50.5% of questions right for a 55 score, enough for a “local diploma.” Today, students need just 30 points out of a maximum 87 — or 34.5% — to get a 65 score.

“When Johnny or Jenny comes home with a 65 or 70, their parents might think they’ve mastered about two-thirds of the material. In fact, it’s slightly more than a third,” said Steve Koss, a retired city math teacher who has railed against the bloated test scores. “Sadly, most parents don’t understand how the scoring works. If they knew the truth, many would be outraged at what amounts to a fraud perpetrated against them by state and local education officials.”

Last month, the state launched a shorter English Regents exam, cutting it from two days to one, six hours to three, and four essays to one. Instead of three other essays, kids have to write two “well-developed paragraphs.”

To bring matters to the present, the Regents are now debating whether to retain or discard their storied exams, which students must pass to graduate.

But that’s a topic for another post.