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Based on the 1995 TIMSS, we identified common standards from the best-performing countries, which we call "A+ standards." We found an overlap of roughly 90 percent between the common math standards and the A+ standards. If the standards of the world's top achievers in 8th grade mathematics are any guide, then the common standards represent high-quality standards.

we find three key characteristics in the curricula of the highest-performing countries: coherence (the logical structure that guides students from basic to more advanced material in a systematic way); focus (the push for mastery of a few key concepts at each grade rather than shallow repetition of the same material); and rigor (the level of difficulty at each grade level). The common core adheres to each of these three principles.

Unfortunately, when one hears that a state's existing standards are better than the common core, it usually means that those standards include more—and more advanced—topics at earlier grades. But this is exactly the problem the common math standards are designed to correct. It is a waste of time to expose children to content they are not prepared for, and it is counterproductive to skim over dozens of disconnected topics every year with no regard for student mastery.

The disappointing reality is that, while improved from a decade ago, most state math standards fall below the common standards in both coherence and focus.

In debating the utility of the common core, it is very important to recognize that standards are not self-executing.

After including both cut points and how far away a state's standards are from the common core (controlling for poverty and socioeconomic status), we found that the two in combination are related to higher mathematics achievement—an even stronger relationship than was the case when only the measure of similarity was included. In the final analysis, however, the key ingredient in the implementation of standards is whether districts, schools, and, most importantly, teachers, deliver the content to students in a way that is consistent with those standards.

As it stands in many classrooms, teachers are forced to pick and choose among the topics as laid out in the textbook, items on state assessments, and the content articulated in state and district standards—expressions of the curriculum that frequently clash with one another. In our recently completed Promoting Rigorous Outcomes in Mathematics and Science Education, or PROM/SE project—a research and development initiative to improve math and science teaching and learning at Michigan State University—we found tremendous variation in the topics covered in mathematics classes within states, within districts, and even within schools. In fact, the content coverage in low-income districts had more in common with the content delivered in low-income districts in other states than with that of the more affluent districts in their own states. Given how haphazardly standards are implemented, it shouldn't be much of a surprise if the relationship between state standards and student achievement is modest. What's remarkable is that the relationship is as strong as it is.

The essential question is not whether the common core can improve mathematics learning in the United States, but whether we, as a nation, have the commitment to ensure that it does.

It remains to be seen whether the right kind of common assessments and supporting instructional materials will be developed.

Probability should not be assessed until grade 7, for instance, the document says, and statistical distributions should not be assessed by materials until grade 6.

In a sign that the new math document will be taken seriously, it has the endorsement of several prominent organizations in the education sphere, including the National Governors Association, the Council of Chief State School Officers, the Council of the Great City Schools, the National Association of State Boards of Education, and Achieve, a national nonprofit that managed the process to develop the common standards. Both the NGA and CCSSO spearheaded that undertaking.

In fact, a group of 20 big-city districts, led by the Council of the Great City Schools, served notice to publishers last month that any materials they purchase must reflect the priorities of the publishers' criteria.

Jason Zimba, a co-author of the document and one of the three lead writers of the math standards, said he anticipates some disagreement.

The other two co-authors of the criteria (and lead writers of the math standards) are William McCallum, a math professor at the University of Arizona, and Philip Daro, an education consultant to states and districts. Both McCallum and Daro also are advisers to Student Achievement Partners.

To be clear, this is not the final word from the standards writers. An "updated" version of the publishers' criteria for math, taking into account feedback, is expected out early next year. In addition, a separate document for high school math will be issued around the same time.

Zimba argues that the single most important element to ensuring the common core's success in improving math education is the emphasis on focus—essentially the idea of covering fewer math topics, but in greater depth.

The criteria document acknowledges upfront that it may be hard for math educators and experts to let go of some topics. "During the writing of the standards, the writing team often received feedback along these lines: 'I love the focus of these standards! Now if we could just add one or two more things,' " it says. "But focus compromised is no longer focus at all. ... 'Teaching less, learning more' can seem like hard medicine for an educational system addicted to coverage."

the new criteria are also aimed at helping to shape professional development pegged to the common-core standards.

The goal of the criteria, the authors say, is not to dictate acceptable forms of instructional resources, suggesting that "materials and tools of very different forms" can be deemed acceptable, including digital and online media.

the guidelines are not binding.

"Ultimately, it's still up to people at the local level. We think it's better to have something to react to than to have nothing out there, ... with people guessing on what they're supposed to do."