No Child Left Behind did two major things: It forced states to identify schools that were failing according to scores on standardized tests. Then it told states what to do to fix those schools.

Congress is now overhauling the law. The biggest likely change in any compromise is that the federal government will no longer tell states what they have to do if students in their schools aren't passing tests.

That's partly for ideological reasons. The bill the Senate passed last week to get rid of No Child Left Behind represents the views of Republicans who want to diminish the federal role in education. But it's also an acknowledgment of a big lesson of 13 years of No Child Left Behind: Even if we can tell when schools are failing their students, it's often not clear how to fix them.

How No Child Left Behind tried to fix failing schools

The ultimate goal of No Child Left Behind was that every student would be able to read and do math by mid-2014. The law required schools to test students every year from third through eighth grades in English and math. Schools had to make "adequate yearly progress" toward the 2014 goal.

If schools with a population of at least 35 percent low-income students failed to make progress for two years in a row, consequences started to kick in:

After two years of not making progress, schools and districts had to make it easier for those schools' students to transfer to better schools. If another year went by without improvement, schools had to offer free tutoring as well as the transfer options. After four years, districts had to take "corrective action." They could choose from a menu of options, including replacing teachers and staff, reorganizing the school, implementing a new curriculum, appointing an outside expert, or extending the school day or year. (Some of these consequences are more severe than others, and districts could choose which ones to implement; firing staff is more dramatic than hiring a consultant.) After five years of failing to make progress, the district had to make a plan to restructure the school, by turning it into a charter school, getting a new principal and replacing most or all of the staff, or having the state take over its management. After six years, the school would be restructured.

The consequences didn't only apply if the entire school was falling behind. They also applied if a subgroup of students — students with disabilities, students from low-income families, students learning English, or students from a particular racial group — didn't make progress.

Tens of thousands of schools ended up facing No Child Left Behind's sanctions. In mid-2012, more than 6,000 schools were being restructured, meaning they'd made it all the way through the penalties without improvement. Thousands more had been required to take some of the less drastic steps.

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No Child Left Behind failed to achieve its central goal

It didn't get every child up to grade level in reading and math by mid-2014. But it did produce some improvement, at least in math.

Research, including papers by Swarthmore's Thomas Dee and the University of Michigan's Brian Jacob, as well as by Maynee Wong, Thomas Cook, and Peter Steiner, found that No Child Left Behind improved fourth-grade and eighth-grade math test scores, but didn't do as much for reading abilities. The effects were greatest for African-American students and for students from low-income families.

But that improvement wasn't enough to close the large gap between black students and their peers. Sean Reardon at Stanford found that, nationally, the law didn't achieve its goal of closing achievement gaps, even though some states saw some improvement.

"Comparing the magnitude of these effects is akin to comparing the speed of different glaciers," Reardon wrote. "Some are retreating, some advancing, but none so fast that one would notice a meaningful difference except over a span of decades (or centuries)."

The big mystery: what, if anything, worked to improve schools

Detangling which school improvement steps were effective is particularly difficult, and it makes it hard to prescribe what steps states and districts should take.

Research in North Carolina by Thomas Ahn and Jacob Vigdor found that the most effective interventions were at opposite ends of the spectrum: Schools that had missed the progress goal for only one year and weren't yet facing consequences improved. So did schools that faced the biggest consequence, a total restructuring.

But everything in between — transfers, tutoring, a new curriculum or hiring consultants, threatening to restructure — didn't help much. This could be because many families didn't, or couldn't, take advantage of the options schools were supposed to offer them after failing to make progress for two or three years.

Some studies found that tutoring was helpful, particularly if students attended for more than 40 hours, but many others found no effect. A large study of six school districts in three states found tutoring had no significant effect on students' math and reading test scores. Studies found the same in Milwaukee and Minneapolis.

The next steps — the various "corrective actions" ranging from firing staff to hiring consultants — were equally ineffective, Ahn and Vigdor found. It wasn't until schools had to hire new leadership that schools made meaningful change. But, as the authors pointed out, even if it's effective, it doesn't mean it's efficient. Schools didn't undergo restructuring until after students had been failing to make progress for six years.

The challenge for states now is to try to figure out a way to replicate that result more quickly without the federal government telling them what to do.

What we know about how to turn around a school

Besides the dramatic step of school restructuring, there are a handful of methods that have helped some schools improve. The Education Department's What Works Clearinghouse, which reviews education research to make sure studies are well-designed, has picked out four strategies for "whole school reform" that it says are proven to be effective:

Success for All, created in the 1980s, emphasizes reading and phonics at the elementary school level. It also includes training teachers to better manage their classrooms and teaching students about nonacademic but crucial skills like self-control. It's been found to improve students' reading abilities. The Institute for Student Achievement's Whole School Reform is intended for high schools. It includes a longer school day, a college prep curriculum, and keeping students with the same team of teachers and counselors throughout four years. Studies found that students in schools using the program earned more credits and were less likely to drop out, and were more likely to go to a four-year college after high school. Positive Action, a character development program for all grade levels that teaches children that there is "a positive way to do everything," was found to improve students' behavior as well as their academic achievement. Small Schools of Choice, which subdivide high schools into groups of about 100 students with small classes and counseling teams, improved students' high school graduation and college-going rates.

These interventions are all over the map; they work in some situations, but not in all. Two only focus on high schools. The elementary school Success for All intervention is only about reading, where scores are typically harder to improve, but doesn't do anything for math. Positive Action, meanwhile, focuses mostly on behavior, not on academics.

Schools fall behind for lots of reasons — far more reasons than one set of strategies can fix. Even supporters of a bigger federal role in education now think it's the right call to let states or school districts decide what to do about schools that are falling behind.

No Child Left Behind showed that making every school try the same remedies doesn't necessarily get results. But 12 years of the law left us with a better idea of what doesn't work than what does.