The Obama administration on Wednesday granted the District and six states relief from key provisions of the federal No Child Left Behind law, including the requirement that all students be proficient in math and reading by 2014.

The law has come under increasing criticism for being unrealistic and overly punitive, but Congress has yet to pass revisions. Last year, Education Secretary Arne Duncan announced that he would lift the most burdensome mandates for states that outlined alternative accountability plans.

Duncan has granted 33 waivers so far, including to Maryland and Virginia. Approval for the District’s plan came after months of revisions.

“D.C. has come a long way since the initial submission,” Duncan said. “There are folks that thought they couldn’t get it done, and they clearly have.”

In Washington, where many schools fall far short of 100 percent proficiency, the Office of the State Superintendent of Education can now set new goals that reward schools for making gains on standardized tests, not just posting high scores.

“It’s better than we had before,” said Scott Pearson, executive director of the D.C. Public Charter School Board, who called the previous system “clearly broken.” State Superintendent Hosanna Mahaley and D.C. Schools Chancellor Kaya Henderson also applauded the new plan.

The aim is to cut failure rates in half by 2017 so that 73 percent of students in public schools are proficient in reading and 74 percent are proficient in math. Over the next two years, the city will begin holding schools accountable for meeting targets in science and writing.

Officials also aim to ratchet up the four-year graduation rate from 59 percent to 78 percent by 2017.

Individual schools will have to cut their failure rates in half, which means that those starting with lower achievement will have to make bigger annual gains.

Based on performance, schools will be placed into one of five categories: reward, rising, developing, focus and priority.

Top-performing reward schools will have the most flexibility to determine how they spend federal funds, whereas priority schools — those with the lowest proficiency or growth, or graduation rates under 60 percent for multiple years — will receive the most intensive and substantial interventions.