Hotly debated Common Core tests take center stage in schools across Long Island and New York this week and next, with a key question being what impact state-declared changes may have on an exam-boycott movement that set national records a year ago.

Thousands of students in a dozen of Long Island’s biggest districts already submitted forms to opt out of the tests, a Newsday survey shows. Administrators said more are expected to do so as the first exams begin Tuesday.

This test season, the fourth since the boycotts began, poses a stark choice for parents and guardians of students in grades three through eight: Will their children take the assessments, modified this year to have fewer questions and be given on an untimed basis? Or will their kids be counted among those who refuse?

While the state Board of Regents put a four-year hold on some education reforms — aiming to calm the rebellion by parent activists and educators — several district administrators who responded to Newsday’s survey said they expect opt-out numbers to grow or remain about the same as last year. Others who responded said they believe the numbers in their districts will be lower.

The English language arts exam is being given Tuesday through Thursday, and the math assessment is scheduled April 13-15.

Jennifer Bradshaw, an assistant school superintendent in Smithtown, noted some easing of parent anxieties since last year in her district, but added, “There remain community concerns about the future of Common Core.”

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The Brentwood school district, the largest of 124 systems across Nassau and Suffolk counties, reported it had received test-refusal letters covering 4,199 students — more than half those eligible to take the exams. Levittown said it had refusal forms for 1,547 students of 2,944 eligible; Smithtown, for 1,609 students of 4,403 eligible, and Middle Country, for about 1,300 of 8,684 eligible.

Last year, according to state Education Department data compiled by regional school officials, 50 percent of eligible students in Brentwood opted out, as did 64 percent in Levittown, 55 percent in Smithtown and 67 percent in Middle Country.

Active boycott preparations are under way elsewhere in the state, especially in the suburbs in the Buffalo and Rochester areas, according to published reports in those areas.

The state’s top education official addressed the matter head-on in a letter sent to newspapers statewide and published Sunday in Newsday.

“Opting out of the 2016 tests is not the answer — tests are an essential part of the student experience,” Education Commissioner MaryEllen Elia wrote. “I’m asking New Yorkers to trust in the adjustments we’ve made so far and the purposeful changes we’re going to make.”

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Boycott leaders dismissed the state’s actions with the slogan “Nothing has changed” and held forums in communities across the Island, from late February through March, to promote their cause.

Jeanette Deutermann, a North Bellmore parent and founder of the Long Island Opt Out network, voiced confidence that the number of students opting out would remain significant. This, she and other activists said, should spur the state’s elected leaders to take further action to lessen fears of testing.

“It’s not going away,” said Deutermann, who also wrote a letter that is published Sunday in Newsday.

Opt-out leaders added that it is virtually impossible to predict whether refusals would match last spring’s record highs. This, they said, is because many parents are expected to submit test-refusal forms to schools at the last minute, as they did last year.

Of 27 districts responding to Newsday’s survey, three believed the number of students sitting out tests will be higher than last year; seven, that numbers would be about the same; and four, that numbers would be lower. The 13 remaining districts said they were unsure of the outcome or gave no opinion.

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Evelyn Nadler, of Sayville, is one parent who has made up her mind.

Nadler, who attended an anti-testing forum in a neighboring community last week, said in an interview that her twin seventh-graders would opt out of the English language arts test for the first time.

She explained that the twins, who have been diagnosed with disabilities related to autism, struggled with such tests in years past and had grown increasingly frustrated.

“I certainly know they’re below grade level — I don’t need test scores to know they’re below grade level,” said Nadler, who works as a classroom aide in a private preschool. “It’s very stressful for them to sit there for the tests.”

Joanna Negro of Huntington, however, was definite that her seventh-grade son will take the tests again, just as he has in past years. Negro, a psychologist, often counsels adolescents in her private practice and finds that the subject of tests comes up frequently.

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“What I tell kids is, it’s OK for the test to be hard for you,” Negro said. “Don’t worry; don’t feel bad about yourself. Do your best. It’s really a test to see how the adults responsible for your education are doing.”

New York State rolled out its first tests based on national Common Core academic standards in spring 2013. The new assessments set off alarm bells from the start: Scores of teachers complained the Education Department had not supplied adequate guides of the brand-new curriculum, and many parents expressed deep concern about age-inappropriate test questions and plunging passage rates.

By spring 2015, opposition had risen to the point that an estimated 200,000 students statewide refused to take the tests. More than 70,000 of those students were on Long Island — epicenter of the biggest test boycott in the country.

The Education Department, in an effort to quiet the controversy, introduced changes in the 2016 tests.

The exams are a bit shorter. For example, test booklets given to third- and fourth-graders on Tuesday will contain four reading passages rather than five and 24 multiple-choice questions instead of 30.

In addition, tests now will be untimed. Students still marking answers to questions after the usual testing period will be allowed to continue as long as they wish, even until the end of the school day. Most districts have set aside the same amount of formal testing time as last year — for instance, 70 or 90 minutes a day for English assessments, depending on age level.

Ivy Sherman, principal of Robert Seaman Elementary School in Jericho, sees the addition of an untimed period as beneficial for children who have trouble understanding the exams’ advanced vocabulary, which she describes as “definitely tough.”

“It’s definitely better than it was,” Sherman said of the revamped assessments.

Another, bigger change this year is that teachers no longer must worry that they might be fired at year’s end because of low student test scores.

The state’s teacher evaluation law, still on the books, holds out that possibility. However, the state Board of Regents, with encouragement from Gov. Andrew M. Cuomo, in December declared a four-year moratorium on enforcement of the law.

Many teachers and parents have contended the moratorium is not enough to ease testing pressures, because the threat of eventual penalties for low scores still exists. Those opponents, including many school administrators and local union leaders, want the law repealed.

Assemb. Todd Kaminsky (D-Long Beach) recently introduced legislation that would do just that. Kaminsky is running against Republican Chris McGrath for a vacant State Senate seat in central Nassau County. McGrath says a win by Kaminsky could switch control of the Senate from the GOP, which is strong on the Island, to Democrats, whose power base is in New York City.

A special election is scheduled April 19. Political leaders are watching the race, not only because of its implications for Senate control, but also as a bellwether of public sentiment on Common Core testing and teacher evaluations.

Lawrence Levy, executive dean of Hofstra University’s National Center for Suburban Studies, said the outcome of the Kaminsky-McGrath race and other campaigns could serve as “signs of whether the moratorium has taken the steam out of the opt-out movement” or whether the movement continues to sway public opinion.

Supporters of Common Core standards say controversy over related issues — the tests aligned with the standards, and teacher evaluations — obscure an important truth: that the standards themselves have contributed to a higher level of instruction in many classrooms.

In the East Moriches school district, teachers and administrators have spent much of the past three years revising curricula to conform to the standards. They cited enriched reading exercises and more advanced vocabulary as a beneficial result.

In a third-grade class last week, students were studying the world’s oceans, learning that the name “Pacific” comes from the Latin word “pacificus,” which means peaceful.

Jennifer Holborow, a third-grade teacher, said the use of such words signifies that classes have moved away from “fluff” that was common before the advent of Common Core.

“If you tell kids being challenged is awesome and fun, guess what, they’ll find it awesome and fun,” said Holborow, who has taught for 21 years. “They’re excited about it.”

Kelli Wilson, who also teaches third grade in the district, said she disagreed with those who say students should opt out of tests because they find reading passages difficult.

“I think kids need test-taking skills,” said Wilson, a teacher for 13 years. “They’re going to take tests throughout their life. They’re going to have to take the Regents, they’re going to have to take the SAT. They need to be prepared.”

With Michael R. Ebert