The position of the Trump administration on these schools is unclear; officials at the Interior Department did not immediately respond to requests for comment on Monday.

After visiting the Standing Rock Sioux Reservation in North Dakota while president in 2014, Mr. Obama pledged to break the cycle of poverty among indigenous children, in part by giving tribes a leading role in their education, which is something that many tribes have long asked for, as a matter of sovereignty.

His administration spent hundreds of millions of dollars to address decades of poor choices at the department’s Bureau of Indian Education, which funds and operates Havasupai Elementary and 182 other tribal schools in 23 states. Some schools have been connected to high-speed internet or undergone critical repairs, though there is still a lot to be done.

A report by the department’s inspector general, released in September, found mold and asbestos in common areas, faulty electrical systems, structural problems and other deficiencies in schools throughout the system.

In its effort to transfer more authority over schools to the tribes, the administration started a program to train indigenous teachers to teach in indigenous schools. Ahniwake Rose, executive director of the National Indian Education Association, an advocacy group, said this was an important first step.

Her hope, she said, is that the idea of choice, so fervently embraced by Betsy DeVos, who has been nominated as secretary of education by President Trump, ultimately translates into “giving tribes the choice to run their own schools.”

Native American children have a large gap to bridge. In general, their schools are poor-performing. The high school graduation rate among those enrolled in bureau schools is 53 percent, nearly 30 points below the national average.