Ruth Hopkins, a writer at Indian Country Today, set off a small firestorm last month when she tweeted that a Washington source had told her President Trump and Education Secretary Betsy DeVos“have plans to scrap” the Bureau of Indian Education. There hasn’t been any official indication from the Trump administration that the tweet is correct, but frankly there are few agencies more worthy of elimination than the one in question.

Just ask Keith Moore, who led the bureau from 2010-12. He told me it was “an inefficient, ineffective, poorly structured bureaucracy,” which was also the gist of a memo he sent to Interior Secretary Ken Salazar shortly before resigning. 

The first problem he sees is purely structural: The Bureau of Indian Education is part of the Bureau of Indian Affairs, not the Education Department. This means the same agency that oversees natural-resource use and land development also is in charge of education. Mr. Moore said, “I found it interesting that it was hard to track how the dollars were spent when they were allocated by Congress.” 

Only about 7% of Native children attended BIE schools in 2013, according to Education Week. That’s approximately 48,000 students at 183 schools. The education they receive is abysmal. A lawsuit filed in federal court last month by the Havasupai tribe near the Grand Canyon offers a useful example. The tribe is suing the government over its terrible management at the tribe’s elementary school. In the 2012-13 school year, students scored in the third percentile for math and the first percentile for reading.

The problem is not a lack of funding. Bureau of Indian Education schools spent approximately $20,000 per pupil in 2014, according to an analysis by the Cato Institute, compared with a national average of $12,400. Even so, their graduation rate is 53% compared with a national average of 81%. The agency can’t even keep the buildings from falling down. As then-Rep. John Kline (R., Minn.), explained at a hearing in 2015, “You’ve got collapsing roofs, leaking roofs, buckling floors, exposed wires, popping circuit breakers, gas leaks. That’s totally unacceptable.” 

According to a 2014 report by the Government Accountability Office, the agency was aware that 24 schools had misspent $13.8 million in federal Indian School Equalization Program funding on unallowable expenses. But as RiShawn Biddle pointed out on the blog Dropout Nation, “the agency has done nothing to follow-up on the evidence, either by conducting second audits to determine the weaknesses of the schools’ financial controls, or to sanction the schools and tribes that operate them for the malfeasance.”

Given the management problems at the agency, the situation is hardly surprising. Its 34th director in 38 years was removed last spring for using his influence to give jobs to a relative as well as a girlfriend. 

Rather than be subject to this kind of incompetence and corruption, lawyers for the Havasupai tribe argue that the tribe, not the federal government, should control education.

But schools run by tribes, or state-run public schools near reservations, don’t offer much better education. The high-school graduation rate for American Indians, including those not living on reservations, is 69%. Many schools are plagued by violence and a shortage of teachers. One reason is that tribal leaders are sometimes hostile to the presence of non-Native Americans in the classroom, or even of those who have been educated off the reservation. At Wounded Knee Elementary School on the Pine Ridge Reservation, all of the teachers from Teach for America were fired one year as part of a “reorganization plan,” the underlying implication being that they were interlopers and not welcome. 

As a follow-up to her first tweet, Ms. Hopkins wrote: “If the BIE is dismantled by Trump and DeVos it will hurt Native children & create major job loss on the Rez. We cannot afford this.” Put another way, schools are a jobs program that Native leaders don’t want to lose. 

Even if they were inclined to change, it’s hard to imagine where a geographically isolated tribe like the Havasupai will find qualified teachers. Last year, Sen. John McCain proposed legislation that would create education savings accounts for students enrolled in BIE schools, so they could use these funds to attend other schools. Though Mrs. DeVos doesn’t control the agency, this is the type of legislation she should back. She could also help fund contracts between tribes and successful charter-school organizations to revamp the Native education systems.

Dan Nelson, a facilities manager at one of the schools on Pine Ridge, was recently part of a group of parents and grandparents who flew to Denver to visit some high-performing charters. He told me, “The system that we have been using is tired. The teachers are helpless to control their work environments. They just do what they have to rather than being active in changing things.” 

Mr. Nelson says that at the KIPP Foundation charter school he visited, “the kids have a light in their eyes. That’s what impressed me.” The kids at the schools on Pine Ridge might have that light too, but “it’s dulled by our schools.” 

This is a perfect opening for the Trump administration to make some serious changes to help children. “The only way for us to succeed,” says Mr. Nelson, “is to start from scratch and build the school system the way we want it.” 

Ms. Riley is a senior fellow at the Independent Women’s Forum and author of “The New Trail of Tears: How Washington Is Destroying American Indians” (Encounter, 2016).