The Common Core State Standards for Mathematics (CCSSM) are part of a broader effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers to develop common state standards in key subjects. The CCSSM specify content learning goals by grade in K-8 and by conceptual categories in the high school grades. In addition, there are eight standards for mathematical practice to be addressed throughout K-12 mathematics education, describing fundamental approaches to, and dispositions toward, learning and doing mathematics. States, districts, schools, and teachers may choose to follow, or not follow, the CCSSM specifications; and those that do will likely differ in how they interpret the standards, what they plan to do in response, and their capacity to implement their plans. As a result, and because of considerable differences among school contexts and student populations, common standards are not likely to lead to the same results, either in implementation or in impacts on students. The goal in this project was to suggest a set of priorities for research that would provide the field with a reasonably broad and deep understanding of the influence of the CCSSM. The priority research agenda recommends a set of case studies, investigations of relationships, and status studies to address three overarching questions: (1) How is the mathematics education system responding to the introduction of the CCSSM? (2) What happens, and for whom, as a result? and (3) How can the CCSSM and future standards be improved? The purposes of this priority research agenda are to inform funders of mathematics education research about important areas of investigation to consider supporting, and to suggest to the mathematics education research community focal areas of study to build the field's knowledge about the influence of the CCSSM. The following are appended: (1) Contributors; and (2) Other Research Areas of Interest for Understanding the Influence of the CCSSM. [This report was written with William O. Fulkerson, Adrienne A. Smith, and Shayla M. Thomas.] (Contains 2 footnotes.)