David M. Bressoud, October, 2010
This past June, the National Governor’s Association (NGA) and the Council of Chief State School Officers (CCSSO), the state secretaries of education) issued the Common Core State Standards for English and Mathematics. Given the tight timeline—work on these began early in 2009—and the ambitious agenda—to “provide a consistent, clear understanding of what students are expected to learn,” the effort was remarkably successful. The standards for K-12 mathematics can be found at .
These standards were written to address two serious problems in American public education:
- There has been little consistency from state to state in what is expected of students at each grade level.
- The K-12 mathematics curriculum has historically covered too many topics at too shallow a depth, resulting in a situation where too many students fail to develop mastery of the key concepts at one level before moving on to the next level of sophistication.
The intent of the NGA and CCSSO was to produce a small set of core content standards at each grade level that most states could agree to and that would become the dominant focus for Mathematics instruction at that grade level, with a comparable program for English instruction. A large and varied group of those working in mathematics education vetted the standards this past spring to ensure that they do represent our best collective understanding of what content should be expected at what grade level.
The standards are of two types: The content standards are organized by grade level up through grade 8, and into six subject categories for high school: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability. Each grade level or category has about ten big ideas, together with explanations and examples. The practice standards are present at every grade level and category and describe the skills that students are developing throughout their mathematical experience:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
The Common Core State Standards do not constitute a national curriculum. They are intentionally limited to the major concepts that should be the primarly focus of each year, and even there say nothing about how these concepts should be taught. Nor do they specify a particular progression beyond grade 8. The high school topics are grouped into six categories: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability, with a list of big ideas for each category. It is up to the individual state or district to decide how high school students will progress through these topics, allowing either a traditional or an integrated approach. Suggested trajectories are being developed.
There are several other intentional limitations of this document: This is supposed to be a bare bones treatment that will need to be fleshed out and elaborated upon. Also, the content standards are described as “reflecting the knowledge and skills that our young people need for success in college and careers.”  They do not address the knowledge students need to prepare for technical or scientific careers. They also leave to others the task of what this means for the development of curricula, assessment tools, and teacher education. A major conference was held in August under the auspices of the Center for the Study of Mathematics Curriculum to begin the exploration of how these standards can be articulated into a coherent curriculum . This month (October, 2010), the Conference Board of the Mathematical Sciences—of which the MAA is a member—is running a Forum on Content-Based Professional Development for Teachers of Mathematics , tying such development to the pre-service education and in-service support of teachers who will need to work with these standards.
The most significant criticism of the Common Core State Standards arises from the observation that the practice standards have not yet been woven through the individual grade levels or subject categories. They are stated and explained in general terms, but a lot of work will need to be done to provide guidance on what they mean in terms of —for example—introducing coordinate graphing in grade 5 or creating equations and inequalities to solve problems in high school algebra.
In other words, the Common Core State Standards give us a framework within which we can envision and build our future K-12 mathematics education. This task is only just beginning. I am confident that there will be vigorous disagreements over how this should be accomplished, but at least we are starting on common ground.
 Common Core State Standards, Mathematics, www.corestandards.org/the-standards/mathematics
 Curriculum Design, Development, and Implementation in an Era of Common Core State Standards, mathcurriculumcenter.org/conferences/ccss
 CBMS Forum on Content-Based Professional Development for Teachers of Mathematics, www.cbmsweb.org/Forum3/index.htm
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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and President of the MAA. You can reach him at firstname.lastname@example.org. This column does not reflect an official position of the MAA.