WINSLOW, Ariz. — On a desert outpost miles from the closest paved road, Navajo students at the Little Singer Community School gleefully taste traditional fry bread during the school’s heritage week.

“It reminds us of the Native American people a long time ago,” said a smiling 9-year-old, Arissa Chee.

The cheer comes in the midst of dire surroundings: Little Singer, like so many of the 183 Indian schools overseen by the federal government, is verging on decrepit.

The school, which serves 81 students, consists of a cluster of rundown classroom buildings containing asbestos, radon, mice, mold and flimsy outside door locks. The newest building, a large, white monolithic dome that is nearly 20 years old, houses the gym.

On a recent day, students carried chairs above their heads while they changed classes, so they would have a place to sit.