The head of software billionaire Bill Gates’ foundation has admitted the agency underestimated the difficulty of transforming the nation’s public schools, as it poured millions of dollars into developing and promoting the Common Core academic standards and related reforms.

Gates and his nonprofit foundation — which has an endowment of nearly $40 billion and is described as one of the world’s biggest private philanthropies — have taken a verbal pounding in recent years from parent leaders and teachers. Critics contended that new state tests based on the tougher standards imposed undue pressures on students and teachers alike, and parents had their children refuse to take the tests in record numbers.

Sue Desmond-Hellmann, CEO of the Bill & Melinda Gates Foundation, wrote in a letter released this week that the organization “missed an early opportunity” to engage teachers, parents and others in a national drive to improve curriculum standards and better prepare students for success in college.

“This has been a challenging lesson for us to absorb, but we take it to heart,” Desmond-Hellmann wrote in the letter posted on the foundation’s website. “The mission of improving education in America is both vast and complicated, and the Gates Foundation doesn’t have all the answers.”

She said the agency would redouble efforts to provide teachers with high-quality instructional materials to reduce the time they have to spend designing their own lessons. The 22-page letter also spelled out projects the Seattle-based foundation considers successes, in areas including anti-smoking campaigns overseas and control of tropical diseases.

Jeanette Deutermann of North Bellmore, chief organizer of Long Island Opt Out, a regional grassroots group that has encouraged test boycotts, said she was not impressed with the Gates Foundation’s acknowledgment of error.

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“It’s little consolation for the millions of kids throughout the country who have been negatively affected by this,” said Deutermann, a mother of two who helped lead a series of public forums this spring, where speakers frequently criticized Gates and other business and political leaders for what was described as a poorly conceived school reform movement.

The foundation invested hundreds of millions of dollars since 2009 in national efforts to develop Common Core standards and promote their adoption by more than 40 states, including New York. Foundation grants were the largest single source of funding for the drafting of standards under the direction of the National Governors Association.

Another foundation project, “Measuring Effective Teachers,” spent an estimated $50 million and three years in researching the classroom performance of 3,000 teachers. The project concluded that student test scores could be used effectively in producing up to 50 percent of teachers’ job ratings — an idea adopted by New York and many other states in revamping their own evaluation systems.

Many school administrators, teachers and parents protested that the new curriculum standards, assessments and job ratings were rushed into place without adequate preparation. Plunging test scores added to the anxieties, and increasing numbers of families pulled children out of state tests.

New York has seen the nation’s largest boycotts of Common Core tests given to students in grades three through eight, both in the current school year and in 2014-15.

Last month, 89,036 students in Nassau and Suffolk counties — more than half of all those eligible — refused to take state English language arts tests in 108 of the Island’s 124 districts that responded to a Newsday survey. Other large boycotts were staged for the second consecutive year in upstate New York, as well as in New Jersey and other states.