State Education Commissioner MaryEllen Elia faced mounting pressure Monday from opponents of the state’s Common Core testing system that was struck by another large wave of student boycotts last week across Long Island and the state.

The latest offensive against the commissioner’s test policies was coupled with criticism of her response to a question about a controversial classroom lesson in the Oswego area, where a teacher asked students to put themselves in the place of Nazi leaders during World War II and argue for or against the extermination of Jews.

During an upstate appearance last week, Elia said she was not familiar with the Holocaust assignment, but she said believed that students should be critical thinkers who can analyze different arguments so they can make their own judgments.

That response drew criticism from civil rights and Jewish groups, as well as from members of the state Board of Regents, to whom the commissioner reports.

On Monday, Elia issued another statement, saying that she had “done my homework” on the Holocaust lesson, spoken to the upstate school system about it and arrived at an agreement that the assignment should not have been given.

Earlier in the day, leaders of a statewide coalition that helped organize the test boycott called for Elia’s removal from office, contending that the education chief had exacerbated parents’ and students’ anxieties over state exams, rather than providing relief. The group added that the commissioner’s handling of the Holocaust controversy “has only widened the divide between Elia and the parents and students she is supposed to serve.”

Elia stepped into the state’s top education post in July 2015.

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On Monday, the commissioner’s aides in the Education Department issued a lengthy defense of her administration, noting that Elia has spearheaded changes in the assessment system — for example, by releasing 75 percent of test questions publicly and involving classroom teachers more closely in vetting test questions.

“Commissioner Elia has made a profound difference in working to improve New York’s learning standards, student assessments and teacher evaluations — all of which were major issues when she became commissioner,” said Emily DeSantis, a department spokeswoman.

Critics, however, have questioned whether Elia’s actions significantly restored public trust in the test program.

Last week, the number of students on Long Island in grades three through eight who refused to take the state’s English Language Arts exam topped 97,000, according to a Newsday survey that brought responses from 116 of the 124 school districts in Nassau and Suffolk counties. The number represented 51.2 percent of Long Island students eligible for testing — the second consecutive year the boycott has topped 50 percent.

Some upstate school systems also reported high rates of ELA test refusals, while others have said their numbers were down somewhat. Elia told Newsday on Monday that the department would release official data on opt-out rates after state math tests are completed next month.

Representatives of the New York State Alliance for Public Education focused much of their ire Monday on Elia’s decision last year to allow students in grades three through eight as much time as they wanted to complete the ELA and math exams.

The commissioner contended that untimed tests were less stressful than those completed under deadlines. Alliance leaders responded that allowing students to spend entire school days filling in test answers actually heightened stress, and they demanded data on how many pupils engaged in such practices.

Jeanette Deutermann of North Bellmore, a founder of the coalition and the group Long Island Opt Out, said in the statement issued Monday that the commissioner “has shown utter disregard for the well-being of children and opened the floodgates for abusive testing practices with little to no accountability.”

The parent-teacher coalition’s statements were disputed by representatives of High Achievement New York, a Manhattan-based statewide group composed of business and civic leaders and some educators and parents. High Achievement contends that, on a statewide level, this year’s ELA opt-out rates were down from last year’s.

“The facts are that under Commissioner Elia, the state has improved the assessments, included teacher feedback, worked with educators and students to help improve proficiency, and listened to concerns from parents and communities,” three parent members of High Achievement said in a joint statement.

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Elia’s initial comments on the Holocaust lesson raised concerns from two Regents board members, Roger Tilles of Great Neck and Judith Johnson, who lives in Rockland County. The Anti-Defamation League and the Anne Frank Center, both based in Manhattan, criticized Elia’s statements.

After the commissioner released her new statement Monday, both organizations expressed satisfaction with the outcome.

Evan Bernstein, regional director for ADL New York, said his group was “pleased that the school district, as well as New York State Education Department Commissioner MaryEllen Elia, ultimately deemed this offensive assignment inappropriate for a classroom setting.”