by NCTM President J. Michael Shaughnessy
NCTM Summing Up, May 2011 

Recently, I had the opportunity to participate in a working conference on issues related to mathematics curriculum and assessment under the new Common Core State Standards for Mathematics (CCSSM). Forty-four states have now adopted CCSSM, launched by the Council of Chief State School Officers and the National Governors Association Center for Best Practices in 2010. The Department of Education has funded two consortia to develop assessment instruments for CCSSM. Those assessments will go into effect in all states that have adopted CCSSM in the 2014–15 school year. As we all learn more about the Common Core Standards and the accompanying assessments, it is becoming increasingly clear to me that they provide an opportunity for us to make deep changes in the way that we teach and assess K–12 mathematics in our nation. However, as I travel to meetings and conferences throughout the country, I sometimes hear statements like, “Oh, our state already does the Common Core; it won’t be much of a change for us.” Or, “We’re going to just wait and see what happens.” Let me suggest that both of these extremes—one, an assumption that the changes called for by CCSSM have already happened, and the other, an assumption that they will come about on their own, or that CCSSM will quietly go away—are quite naïve.

Systemic changes in mathematics education will necessarily accompany the Common Core State Standards for Mathematics because these standards are national in character. The individual states themselves, as is their right under our Constitution, have, one by one, decided to accept the Common Core State Standards. This is new in the United States—never before have so many states agreed to base mathematics instruction on a common set of standards. Furthermore, these standards include both Standards for Mathematical Content and Standards for Mathematical Practice, and students’ mastery of both the content and the practices will be assessed in the designs being created by the two assessment consortia. By the way, the eight Standards for Mathematical Practice are not teaching practices—they are student practices—processes that students need to engage in and develop facility with as they learn mathematics and solve mathematical problems. The fact that students will be accountable to the Standards for Mathematical Practice is another systemic change for mathematics education in our country. Although in the past individual states have included performance tasks and extended constructed response items calling for student work and reasoning, such assessments have been inconsistent, and sometimes not persistent, in the United States. This will change.

In light of the national character of CCSSM and the new types of accompanying assessments, we can start doing certain things now as we think about curriculum, instruction, and assessment in the era of the Common Core.

With respect to curriculum, we can begin to examine the materials that we use to see how well they support the content and practice standards in CCSSM. A project is now under way to develop tools that teacher leaders, districts, and states can to use to review curricular materials to determine how well they align with CCSSM—both with the content standards and the practice standards. The tools from this project will be available to the public in the next few months. One caveat in regard to curriculum: this is not the time for states to run off and write their own curricula based on the Common Core State Standards. Quite a number of very thoughtful, carefully tested and piloted curriculum projects and materials have appeared over the past twenty years—many of them, in fact, have undergone several updates and revisions. We actually do have good curricula in this country—lots of them! Although the existing materials will need some adjustments to improve their fit with CCSSM, building on existing materials will be a much more efficient and effective process for states and districts than inventing totally new materials on their own. A move by individual states to reinvent the curricular wheel in a rush to implement CCSSM is ill advised. States would do much better to work together with other states on adapting existing curriculum materials.

With respect to instruction, implementing CCSSM’s Standards for Mathematical Practice will call for engaging students much more in such processes as—

• problem solving;
• communication of mathematical ideas in meaningful classroom discourse;
• making connections across topics and to contexts;
• reasoning about and justifying solutions;
• developing a positive disposition toward mathematics;
• creating and sharing multiple representations of mathematical concepts and procedures; and
• modeling mathematical processes.

Excellent resources are available to teachers for instilling and developing fluency in the mathematical practices in our students. At the high school level, particularly useful resources include NCTM’s Focus in High School Mathematics: Reasoning and Sense Making(2009) and the publications in the accompanying Focus in High School Mathematics series. Valuable resources for teachers of mathematics in prekindergarten–grade 8 include the grade-level books in NCTM’s Teaching with Curriculum Focal Points series. In addition, grade-band books in NCTM’s rapidly expanding Essential Understanding Series provide deep, cross-grade discussions of the most important mathematical content and offer excellent resources for teachers to use as they consider instruction based on the CCSSM.

Finally, with respect to assessment, we need to get a head start to prepare both ourselves and our students for the new types of assessment that will be used with CCSSM. The two assessment consortia funded by the Department of Education, SMARTER Balanced Assessment Consortium (SBAC) and the Partnership for the Assessment of Readiness for College and Career (PARCC), have been sharing their respective plans for assessment with the public, and we should all become familiar with them. Both consortia plan to include extended mathematical performance tasks in their instruments. You can download presentations on both assessment plans so that you and your students can get involved in deeper assessment tasks right away, gaining experience with such tasks well before 2014. Performance tasks are available to the public from the MAP project on the MARS website and can be downloaded for noncommercial use. The Silicon Valley Mathematics Initiative also has made a  collection of assessment tasks that can be downloaded. In addition, NCTM has an excellent portfolio of assessment resource materials, along with accompanying support materials for teachers, including the Assessment Sampler series.

The bottom line for all of us is that under CCSSM, it is not, nor will it be, business as usual. With the inclusion of the Standards for Mathematical Practice, we have been handed an opportunity to make some significant changes in our mathematics instruction. And for the first time we have an opportunity to have cross-state, common mathematics assessment of our students’ progress in both content and mathematical practices. Together, let’s make the best decisions we can as we proceed to implement these new standards.