Flaws in many students’ test booklets during the English language arts exam last week spurred complaints from frustrated school officials, who say the errors further undermine confidence in the Common Core assessments — already repudiated by Long Island parents pulling their children from the exams in record numbers.

Pages in the test booklet that students use to outline or draft their essays, which are purposely left blank for that, were missing or unlabeled in hundreds of thousands of booklets distributed Wednesday — the second of three days the exam was given in 700-plus districts across the state, the state Education Department acknowledged.

“We apologize for any inconvenience this may cause you and we thank you for your hard work on behalf of the students in New York State,” the agency said in a memo labeled “Important Notice” and distributed statewide. The message was from Peter Swerdzewski, assistant commissioner for assessment, standards and curriculum.

Roger Tilles, who represents Long Island on the state Board of Regents, and Rockville Centre Superintendent William Johnson were among those who learned of the problem with the test booklets and knew of the Education Department’s memo.

“To me, it was symptomatic,” said Tilles, of Great Neck, a veteran of the 17-member Regents panel, which sets education policy and oversees the department’s work.

“You know, it’s just one more nail in the coffin,” said Johnson, a former president of the New York State Council of School Superintendents and a longtime critic of state testing policy.

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One educator who emailed Newsday and asked to remain anonymous said the flawed format caused disruption and confusion among students. The state’s memo detailing the problem did not arrive at schools in his district until after Wednesday’s portion of the test started to be administered, he said.

Officials in other districts said they coped with the error by distributing extra sheets of paper in advance, which students then used as scratch pads to plan and outline their essay answers.

Education Department staffers said the lack of labeled planning pages was reported around 8 a.m. Wednesday by a school administrator in New York City. The advisory memo from Swerdzewski went out around 9 a.m. that day.

Jeanne Beattie, a department spokeswoman, said the booklets were printed by outside companies that subcontracted with Questar Assessment Inc., the Minneapolis-based firm the state signed to a five-year, $44 million contract last year with an eye toward improving the standardized exams.

“We are currently doing a full review of the issue,” said Beattie, adding that no action will be taken until the review is complete.

A Questar spokesman messaged Saturday that “the integrity of the tests was not impacted” by the error. He declined to identify the subcontractor responsible, or to say if New York State would be compensated, saying the firm was focused on this coming week’s tests.

Before the English test is given, many students are encouraged to plan essays before writing them. They are not scored on the quality of outlines or drafts.

State and local education officials characterized the missing pages as the latest in a series of Common Core test misfires that the exams’ critics cite as one reason for students to opt out.

Teachers became aware of the test booklets’ shortcomings on Wednesday, the same day that Gov. Andrew M. Cuomo responded to questions about rising opposition to tests by emphasizing the need for error-free administration.

“Now the state Education Department says that they have corrected the mistakes, and they’re explaining that to the parents,” Cuomo said, referring to criticisms that began three years ago, when Common Core tests were rolled out with inadequate preparation. “But I still think you have that initial sense that was generated that, what are these tests, and they don’t make any sense.”

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The governor, while speaking to reporters in Buffalo on Wednesday, did not mention the latest testing miscues, which were not widely known at the time.

Cuomo’s aides did not respond to Newsday’s later requests for comment.

In a Newsday survey last week, responses from 108 of the Island’s 124 districts showed that more than half the students in grades three through eight eligible to take the English language arts test, known as the ELA, refused to do so. Numerically, 89,036 students of 172,410 eligible in the responding districts — 51.6 percent — opted out of the exam.

A survey at the same time last year, which had responses from 110 districts, found that 71,764 of 168,636 eligible students, or 42.6 percent, sat out the test.

Federal law requires the tests to be administered annually to students in grades three through eight. Math tests are scheduled to be given statewide this week, from Wednesday through Friday.

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Johnson said the test-booklet error is a reminder that the system needs an overhaul.

The Rockville Centre system on Nassau’s South Shore — which in spring 2013 was among the first on the Island to have significant numbers of test refusals — reported to Newsday on Thursday that 1,027 of 1,652 eligible students, or 62.2 percent, opted out of the English test. The percentage was nearly the same as the 62.0 percent in Newsday’s 2015 ELA survey.

Last year, Education Commissioner MaryEllen Elia announced the award of a $44 million, five-year contract to Questar. The previous contractor, Pearson Education, was widely criticized for poorly written test items, including one based on a reading passage about a talking pineapple.

This spring’s tests are largely based on Pearson items, but the Education Department said questions were reviewed by more than 20 teachers from across the state.

Since she became commissioner on July 1, Elia has announced a series of steps meant to ease testing anxieties among teachers, parents and students. Some of the modifications were included in emergency regulations passed by the Regents in December in response to public outcry over the education reforms.

The tests have been shortened, and students are being given unlimited time to complete them.

Questar is continuing to revamp the tests with more input from teachers, a process expected to be completed by spring 2018. At the same time, the Education Department has launched a review of the state’s academic standards based on national Common Core guidelines. The goal is to revise academic standards and tests based on those standards by the 2018-19 school year.

There is scant evidence, however, that any of these efforts have made an impression on parents who are opting their children out of the tests.

“It’s typical propaganda,” said Kim Velentzas of Glen Cove, the parent of a fourth-grader who first withdrew from state testing last year and continues to do so. “The shorter tests are shorter by a couple questions. And the untimed portion for me was a huge negative. We’re hearing horror stories of some kids sitting for six hours. It’s crazy.”

Velentzas was interviewed while attending a Wednesday forum organized by test opponents at the Locust Valley Library. More than 100 parents, teachers and others packed the library’s community room, cheering speakers who were demanding that the state’s elected officials revamp the assessment system.

One of the opponents’ major targets is a state law, pushed through the legislature by Cuomo in April 2015, that requires school districts to base up to half of teachers’ evaluations on students’ test results. Student opt-out rates shot up later that month, and the governor responded by appointing an advisory panel that recommended a four-year moratorium on putting the evaluation program into full effect.

The Regents in December approved the moratorium. But opponents continue pressing for total elimination of links between testing and teacher evaluations, saying the system remains a threat four years down the line.

Tilles said he personally favors scrapping the portion of the testing system that links student scores to teachers’ and principals’ job evaluations, but knows such an action requires a change in state law.

Cuomo has not given any sign that he is willing to budge beyond the moratorium delay. At the Buffalo news gathering, the governor mentioned ongoing efforts to revise tests but made no reference to teacher evaluations.

Cuomo administration officials have said repeatedly that the moratorium provides adequate time for the Regents to improve the evaluation system, and that no change in the law is needed.

“I don’t think it’s going to be immediate,” said Douglas Muzzio, a political analyst and professor of public affairs at Baruch College in Manhattan.