International Academy math teacher Angelina Dialel walks through her geometry class at Cardozo High School on Sept. 23, 2014, in Washington, D.C. (Ricky Carioti/The Washington Post)

The Obama administration handed out more than $3 billion to the states and the District of Columbia to help them turn around their worst-performing schools as part of the federal stimulus spending that took place after the 2008 recession.

But most states lacked the capacity to improve those schools, according to a new analysis by federal researchers.

Although turning around the worst schools was a priority for nearly every state, most did not have the staff, technology and expertise to pull those schools out of the bottom rankings, according to a brief released Tuesday by the Institute of Education Sciences, the research arm of the U.S. Education Department.

With funds allocated by Congress under the American Recovery and Reinvestment Act of 2009, the Obama administration spent $3.5 million on School Improvement Grants to states, directing them to focus the money on their lowest-performing schools.

School Improvement Grants had been part of No Child Left Behind, the 2002 federal education law. But stimulus spending increased the budget for the grants sixfold.

Under the Obama administration, schools could receive up to $2 million annually for three years. The money was divided among the states and D.C. according a federal formula. About 1,500 schools received grants.

Any school accepting a grant had to agree to adopt one of four strategies favored by the administration: Replace the principal and at least 50 percent of the staff; close the school and enroll students in another, better-performing school; close the school and reopen it as a charter school; or transform the school through new instructional strategies and other techniques.

While 84 percent of states told the researchers that improving the worst schools was a top priority, 58 percent said it was one of the most difficult tasks to accomplish. Eighty percent of states and the District told federal researchers that their states had at least one significant gap in expertise needed to significantly improve the worst schools.

Preliminary research released in 2013 found that about a third of the schools that received School Improvement Grants improved, a third of the schools performed about the same, and a third got worse.