That kind of inconsistency in educational standards is what the Common Core — academic guidelines for kindergarten through high school reading and math that were adopted by more than 40 states — was intended to redress. But Ohio is not alone in adjusting the goal posts. In California and North Carolina, state officials reporting headline results lumped together groups of students who either passed or nearly passed the tests. And in Florida, the education commissioner recommended passing rates less stringent than in other states.

“This was exactly the problem that a lot of policy makers and educators were trying to solve,” said Karen Nussle, the executive director of the Collaborative for Student Success, a Common Core advocacy group, “to get a more honest assessment of where kids are and being transparent about that with parents and educators so that we could do something about it.”

Image Notebooks required under the Common Core. Credit... Andrew Spear for The New York Times

The Common Core was devised by experts convened by state education commissioners and governors to set uniform benchmarks for learning. But as it has been put into place, it has faced increasing backlash, both from politicians, who argue that it infringes on states’ independence to determine education policy, and from parents and teachers, who object to the more stringent testing that has come with the new guidelines.

Before the Common Core, each state set its own standards and devised its own tests. Some states made the standardized tests so easy or set passing scores so low that virtually all students were rated proficient even as they scored much lower on federal exams and showed up for college requiring remedial help. Here in Columbus, the school district is still recovering from a scandal in which many principals removed low-performing students from enrollment records in order to improve school ratings.