“Part of the whole point was you were going to have commonality that would let you compare schools in Chicago to schools in Cleveland,” said Frederick M. Hess, director of education policy at the conservative American Enterprise Institute, who supports the concept of common standards but has been critical of efforts to implement the Core. “We may not see the benefits that folks were hoping to see. . . . The whole notion of commonality, which was so attractive, is more and more a phantasm.”

One of the bipartisan hopes for the Common Core, a set of guidelines for what the nation’s kindergarten-through-12th-grade students should learn and when, was that states would leave behind their patchwork of 50 different sets of standards measured by 50 different tests. It would, for the first time, be easy for parents and policymakers to directly compare student performance in one state to the rest of the nation, and it would be much more difficult for lagging states to game the system in an effort to hide weak performance.

That goal seemed easily within reach in 2011, as 45 states and the District of Columbia adopted the new standards. The Obama administration spent hundreds of millions of dollars to help states develop two new online tests, known as PARCC and Smarter Balanced, that would measure student progress on the Common Core, and most states signed on to administer those tests starting this spring.

But as some states head into their first round of testing, the picture has fragmented amid political blowback from parents and conservative lawmakers who criticize the Core as nationalized education and have found the new course material confounding.

Indiana and Oklahoma have dropped the Core, and four other states are moving to review and potentially replace the standards. Lawmakers in other statehouses are taking up anti-Common Core bills as the legislative season gets underway.

There has been even broader resistance to the common standardized tests. In 2010, for example, there were 26 states aligned with the testing consortium known as PARCC, but that has whittled down by more than half: Now only 12 states plus the District plan to give the PARCC exam to students, according to the Council of State School Officers, an organization of state education chiefs. Mississippi became the latest state to back out of the PARCC testing consortium this month amid calls from Gov. Phil Bryant (R) to drop the Common Core.

Smarter Balanced has seen less attrition, but just 18 states plan to give that test this spring. The states that are planning to administer one of the two tests account for about 40 percent of students nationwide, according to an analysis by the trade newspaper Education Week. The remaining 20 states have chosen their own tests, which could make meaningful comparisons difficult.

Common Core advocates say they never thought every state would sign on to the standards or that every state would agree to one of the two consortia tests. But they also acknowledge that the fragmentation is not ideal, and they hope more states will decide to return to the fold.

“The real issue is what some of these independent state assessments are going to look like, and I think the jury is still out,” said Gene Wilhoit, the former director of an organization of state schools chiefs who played a key role in promoting the Core.

Wilhoit said he had initially envisioned a much more limited number of tests that would allow for a broad comparison of student performance across many states, providing a national picture of achievement.

Although it’s not clear how testing will shake out, Wilhoit said he’s confident that the nation’s focus on Common Core will make it impossible for states to slide by with easy tests that make their students look more accomplished than they are. That has been an issue since 2002, when the federal No Child Left Behind law established sanctions against schools that failed to meet testing targets.

“I am convinced that whatever comes about will be scrutinized to a degree that no one has ever seen,” Wilhoit said. “I think it’s going to be difficult now for any state to hide.”

Some teachers say it’s important to be able to compare their students’ performance with students elsewhere.

Eu Hyun Choi, a seventh-grade math teacher in Chicago, said on a trip to New York for literacy training she realized that, because the two states gave different tests, it wasn’t possible to gauge how her students measured up against those in New York. She feared that her students were being held to a lower bar than their peers elsewhere.

“I just felt like Illinois students were getting cheated,” she said.

The Chicago school system announced this month that it would administer PARCC to 10 percent of its students because of concerns about limited technology access.

Choi said she hopes her students are among those who will take the PARCC exam this year, but she was dismayed to find out that she’ll only be able to compare her students’ performance with 11 other states.

“That’s pretty shocking,” she said.

Other teachers say they don’t care much about the ability to compare test scores across state lines. But they’re tired of the indecision that has come with the political tussles over the standards and their tests.

Natalie Shaw, a second-grade teacher in Indiana — which is choosing an exam — said the turmoil is frustrating. For much of the past year, she said, it has been unclear what Indiana teachers are supposed to teach and what students will be expected to know on spring tests.

“At the end of the day, people just want to know what do they want us to teach so we can make sure that kids are prepared for the types of assessments that are coming up,” Shaw said.

Opposition to the Common Core tests has come amid a broader national debate about standardized testing, which many parents and teachers argue has warped public education. Critics of the Common Core and testing have cheered the fracturing of the testing consortia, but many advocates play down the impact of states withdrawing from the common tests.

“I really don’t see it as a problem,” said Karen Nussle, executive director of the pro-Common Core Collaborative for Student Success. “I think the testing landscape is going to continue to evolve, and I’m really optimistic.”

Nussle and other Core advocates argue that the standards are more important than the tests because they aim to push teachers to better prepare students for life after high school. Most states have retained the standards, although some have backed away from the name “Common Core” because of its political volatility.

Although membership in the two testing consortia has shrunk, there are still large swaths of the country where, for the first time, students will take the same test.

“This is huge, considering the idea of common standards, let alone common assessments, was unfathomable less than a decade ago,” PARCC spokesman David Connerty-Marin said by e-mail. He added that PARCC hopes more states will join the consortia because “students and their families have a right to know if they are on track, and to know how they are performing compared to students in schools across their state and the country.”

Luci Willits, Smarter Balanced’s deputy executive director, said that while cross-state comparisons are ideal, “the real value of the assessment is the quality.” Both consortia say their tests are built to assess students’ critical-thinking and problem-solving skills, providing a more accurate picture of students’ preparedness for college and careers.

Advocates also say they think the number of states administering the consortia tests will grow if states see that the tests are cheaper, and of better quality, than tests that states develop independently.

“States are going to go at their own speed,” said Chad Colby, a spokesman for Achieve, a nonprofit organization that managed the development of the standards.