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Seizing the Moment for Mathematics

[By William Schmidt, Education Week, July 18 2012]

For years now it has been clear that the U.S. mathematics curriculum is a mile wide and an inch deep, and that the fragmented quality of mathematics instruction is related to our low ranking on international assessments. Nearly a generation after the first Trends in International Mathematics and Science Study, the nation's governors and chief state school officers, in concert with other stakeholders, have fashioned the Common Core State Standards for mathematics that may finally give American students the high-quality standards they deserve.

These new math standards have attracted some criticism, however. Aside from more abstract arguments, a number of specific claims have been leveled against them, including that they are untested; that they are not world-class; and that some existing state standards are superior.

As part of our ongoing research, [see http://www.achieve.org/common-core-math-standards-implementation-can-lead-improved-student-achievement ] Richard Houang and I recently concluded a study of the math standards and their relation to existing state standards and the standards of other nations. Drawing from our work on the 1995 TIMSS, we developed a measure of the congruence of the common core to all 50 state standards in effect in 2008-09, as well as to an international benchmark. We also examined the relationship of each state's math standards to the common standards and how each state performed on the 2009 National Assessment of Educational Progress. Although, we can't project the success of the common math standards with certainty, it would give us reason for optimism if states whose standards more closely resembled those of the common core performed better on NAEP.

What did our research uncover?

The common-core math standards closely mirror those of the world's highest-achieving nations. 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. Of course, as a nation, we shouldn't just slavishly replicate whatever we find other countries doing. But when we look across a number of very different countries-all of whose students do better than ours-we find the same curricular characteristics over and over again. The only sensible course of action is to take a close look and see if important lessons can be learned.

In doing this, 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. As it stands today, we simply hope that students will somehow "get it" at a later grade, and yet we know that far too many students never do. 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.
SIDEBAR: "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."

In debating the utility of the common core, it is very important to recognize that standards are not self-executing. For example, states with very strong standards but very low thresholds for "proficiency" on the state assessments are, in effect, sending a message to teachers and districts that their standards aren't to be taken that seriously. In that way, proficiency cut points can serve as a rough measure of implementation. 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. [http://www.promse.msu.edu/ ] 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. The adoption of the common core doesn't represent a success, but an opportunity. It remains to be seen whether the right kind of common assessments and supporting instructional materials will be developed. It is very much an open question whether states will devote the energy and planning required, especially in a time of fiscal constraint. And, most urgently, we don't yet know if teachers will receive the preparation and support they need to teach mathematics in a fundamentally new way.

The common core offers the opportunity to revolutionize math instruction in this country, to improve student performance, to close the gap between the United States and its competitors, and to ensure that every American student has an equal opportunity to learn important mathematics content. But it is only a chance, and it is imperative that we seize it.
William Schmidt is a Michigan State University distinguished professor and co-director of the university's Education Policy Center. He holds faculty appointments in the departments of education and statistics. He is a member of the National Academy of Education and a fellow of the American Educational Research Association.

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