...The idea of a longer day was first promoted in charter schools — public schools that are tax-supported but independently run. But the surge of interest has been spurred largely by the federal No Child Left Behind law, which requires annual testing of students, with increasingly dire consequences for schools that fall short each year, including possible closing. Pressed by the demands of the law, school officials who support longer days say that much of the regular day must concentrate on test preparation. With extra hours, they say, they can devote more time to test readiness, if needed, and teach...