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Thousands of students are moving up to the next grade this fall even though they failed last year’s state reading and math tests.

Caught between two sets of conflicting test standards — one produced by the city, one by the state — over 10,000 students were wrongly labeled as passing or failing.

Some of them, about 1,807, will get to skip the last week of the summer session, which they had attended unnecessarily. The new state standards show that these students passed their exams.

But the vast majority of them, about 8,500, were initially told they passed and will shortly learn that they actually failed. City education officials have decided to promote these students to the next grade level, though in a typical year they might have been held back.

A teacher emailed to say that a few eighth graders at his school were told they passed the test, but the state’s cutoff scores now show that they failed. Still, they will begin high school in the fall.

On the flip side, the school sent a fourth grader to summer school for initially failing the test, meaning the boy could not spend the summer with his father. Now, the new standards show the student didn’t need to attend.

The problem began when a new exam schedule and the state’s decision to adjust test standards meant the exam results wouldn’t be released until late July. With summer school beginning in June, schools had to know which students to require to attend, so the city set its own preliminary cutoff scores.

The state’s cutoff scores came out yesterday and they don’t quite match up.

“I think it’s fair to say we were surprised at how many kids we under-identified,” said Department of Education spokesman Matt Mittenthal.

For the reading test, in particular, the state set higher cutoff scores than the city’s own estimates for grades three through eight. Of the students who were wrongly identified as passing, 7,000 of them met the city’s standards in reading, but not the state’s.

The city also lowballed the math test for third and eighth graders, but overshot for grades four, five, and seven. About 1,000 students in grades three and eight will be told in a few weeks that they failed the math test, though the city initially passed them. And about 1,807 students in grades four, five, and seven, will get letters today telling them they can leave summer school early, as the new standards show that they are proficient.

Mittenthal said that students who failed the test according to the state’s standards, but passed the city’s bar, would be promoted and given additional help next year.