Few in New York are calling for abandoning the standards. And state officials have not backed out of a national consortium developing exams based on the standards, as their counterparts in states like Georgia and Oklahoma have. No state that adopted the standards has gone so far as to withdraw from them.

The loudest of the complaints is based on New York’s decision not to wait for those new Common Core exams, which are expected to make their debut in 2015, but to begin testing students on the new standards last year. Teachers said they had not been fully trained in the new curriculums, and had not received new textbooks and teaching materials; many still did not have them in the fall. As the tests changed, the scores plummeted: Less than a third of the state’s students passed.

In Albany, leaders of both houses of the Legislature called this month for a two-year moratorium on the use of Common Core test scores in teacher evaluations and in decisions about student promotions or admissions. The state teachers’ union has asked for a three-year pause. The state Board of Regents, which oversees education policy and is appointed by the Legislature, has already voted to delay by five years the date by which all high school graduates must pass Common Core-aligned Regents exams.

The state education commissioner, John B. King, Jr., who reports to the Board of Regents, conceded there was an “uneven” rollout of the standards. Looking back, he said recently, “we could have prioritized parent engagement, and helping parents understand what the Common Core is, and is not.”

Yet he staunchly defended the effort, saying Massachusetts went through the same pains two decades ago after it adopted new standards, and now consistently scores as high as the top countries do on international measures.

Dr. King was booed and shouted down as he made similar arguments at public forums he held around New York in the fall. They grew so testy at one point that he called the remaining forums off before scheduling new ones.