In 2008, when Katherine Sprowal’s son, Matthew, was selected in a lottery to attend the Harlem Success Academy 3 charter school, she was thrilled. “I felt like we were getting the best private school, and we didn’t have to pay for it,” she recalled.

And so, when Eva S. Moskowitz, the former city councilwoman who operates seven Success charter schools in Harlem and the Bronx, asked Ms. Sprowal to be in a promotional video, she was happy to be included.

Matthew is bright but can be disruptive and easily distracted. It was not a natural fit for the Success charters, which are known for discipline and long school days. From Day 1 of