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When the charter school movement first burst on to the scene, its founders pledged to transform big urban school districts by offering low-income and minority families something they believed was missing: safe, orderly schools with rigorous academics.

But now, several decades later, as the movement has expanded , questions about whether its leaders were fulfilling their original promise to educate vulnerable children better than neighborhood public schools have mounted.

When Richard Buery took over last year as the head of policy at KIPP, the nation’s largest charter network, he began to ask the same questions.

He was used to challenging charter schools after years as a top deputy to Mayor Bill de Blasio, who is skeptical of the schools.