Two multi-billion-dollar competitive grant programs are a big part of the legacy left by U.S. Education Secretary Arne Duncan, pictured here in a 2014 visit to a D.C. school. He plans to step down next month. (Cliff Owen/AP)

A national program that pumped a record $7 billion into failing schools — and became one of U.S. Education Secretary Arne Duncan’s signature policies — has yielded mixed results, according to a new federal analysis released Thursday.

Students in about two-thirds of the schools studied posted gains on math and reading tests, but one-third showed no improvements or even slid backward.

Schools that participated in the program the longest showed the strongest improvements in math and reading. The average high school graduation rate also increased for schools that received School Improvement Grants (SIG).

But the government analysis is incomplete.

Almost 1,400 schools received grants from 2010 to 2013, but the report does not include data from about half of those schools. Federal officials blamed the gap on several factors, including the fact that some states switched to new tests during the study period, making it impossible to compare student test scores over time. Meanwhile, the analysis does not include performance statistics from the two most recent school years.

“Here we are, five years into the program, and it’s hard to look at it as a success,” said Andy Smarick, a former federal education official and a partner at the consulting firm Bellwether Education Partners.

When Duncan announced the investment, “he was talking about transformational change,” Smarick said. “We’re just not getting evidence that that’s what the program produced.”

The head of a major teachers union was more blunt. SIG was a “terrible investment,” said Randi Weingarten, president of the American Federation of Teachers, adding that she thinks federal dollars would be better spent on community schools and career and technical education programs.

Under the SIG program, schools could receive up to $2 million annually for three years.

The Education Department also on Thursday released a report on the Obama administration’s $4 billion Race to the Top competitive grant program, describing how it ushered in sweeping policy changes in many states, including some that proved controversial, such as new teacher evaluations tied to student test scores.

It also offers a few data points: In the District and 11 states that received Race to the Top grants in 2010, graduation rates rose from 76.5 percent to 79.9 percent. In addition, students in those jurisdictions are taking and passing more Advanced Placement exams now than they were four years ago: Students passed 770,000 AP exams in 2014, up 21 percent from 2011.

Kevin Huffman, the former education commissioner in Tennessee, said Race to the Top galvanized policymakers in his state to make real change. Tennessee has had some of the country’s largest student achievement gains on national tests in recent years.

“In Tennessee, kids are learning more than they were before the grant,” Huffman said.

The picture is not as rosy nationwide: In 2015, math scores on national tests ticked downward for the first time in two decades, and reading scores were stagnant.

In a speech at a Boston school on Thursday, Duncan argued that the two grant programs unleashed innovation in classrooms across the country. Duncan, who plans to step down next month after seven years as one of the most influential education secretaries in history, considers the programs part of his legacy.

He chose Massachusetts as a backdrop for his remarks in part because that state revamped education policy and dramatically boosted funding in 1993, but results were not immediate. He drew parallels between that example and his own programs.

“Here in Massachusetts, it actually took several years to see real improvement in some areas,” Duncan said. “Scores were flat or even down in some subjects and grades for a while. Many people questioned whether the state should hit the brakes on change. But you had the courage to stick with it, and the results are clear to all.”

Duncan spoke at Jeremiah E. Burke High School, one of the worst in the state in 2011. Then it won $1.7 million in a school improvement grant, which it used to reinvent the school, said Headmaster Lindsa McIntyre. The school day was lengthened by an hour, classes were restructured, teachers were given a period every day to plan and collaborate, and counseling was provided to students, most of whom had experienced gun violence, homelessness or addiction.

This year, Burke was honored as Boston’s most improved public school. About 70 percent of students are proficient in English, 67 percent are proficient in math and two-thirds are graduating on time. Suspensions have dropped from 525 in 2009 to 25 this year, McIntyre said.

“I would not have been able to do that heavy a lift without some sort of support,” she said. “The SIG money provided me with the opportunity to redesign how we were going to operate as an urban school.”

But Smarick said the federal government could have spurred more consistent improvement by helping to fund new charter schools instead of trying to fix dysfunctional existing schools and systems.

“Year after year after year, we’re getting the same findings showing that this is not a turnaround program,” Smarick said. “For decades, people said more money and more urgency is going to turn around our low-performing schools. For whatever reason, this administration and Secretary Duncan believed that their money and their urgency was going to be better.”

The school improvement grants mark the largest federal investment ever targeted at failing schools.

A large chunk of the grant money came from the American Recovery and Reinvestment Act of 2009. The grants had been part of No Child Left Behind, the 2002 federal law, but stimulus spending increased the budget for the program sixfold.

Any school accepting a grant had to agree to adopt one of four strategies: 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. The vast majority chose the last option; it was the least disruptive.

The U.S. Department of Education did not track how the money was spent, other than to note which of the four strategies schools chose.

One problem flagged by federal researchers earlier this year was that most states lacked the capacity to improve their worst schools.

Take Westinghouse High, located in one of Pittsburgh’s poorest neighborhoods. It was among the first wave of schools to receive school improvement money.

School district leaders planned to transform Westinghouse with single-sex classes and longer class periods, but the plan was so poorly executed that the school scrapped it just weeks after the 2011-2012 year began, kicking off a tumultuous period of declining enrollment and frequent principal and teacher turnover. Westinghouse’s performance was not captured in the new federal analysis; none of the SIG schools in Pennsylvania are part of the study because the state high school exams changed in 2013, making it impossible to compare test scores over time.

In a recent interview, Pittsburgh Superintendent Linda Lane called the failure “one of the hardest experiences of my professional career.” But she said she learned from it and that she thinks Westinghouse – which recently won its second school improvement grant — is now ready to capitalize on the money.