It sounds like a dream for some working parents: school for 12 hours a day, starting bright and early at 7 a.m. and ending after dinner, at 7 p.m., all completely free.

One elementary school, Brooklyn Charter School, is experimenting with the idea as a way to tackle two problems at once. The first is a sharp decline in students in urban schools. Families are leaving city public schools around the country, including in New York City, which has led some districts to consider merging schools or…