Progressions for the Common Core State Standards in Mathematics (draft)
The Common Core State Standards (CCSS) in mathematics began with progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by educational research and the structure of mathematics. These documents were then sliced into grade level standards. From that point on the work focused on refining and revising the grade level standards, thus, the early drafts of the progressions documents do not correspond to the 2010 Standards. The Progressions for the CCSS are updated versions of those earlier drafts, revised and edited to correspond with the Standards. Members of the original Progressions work team, together with other mathematicians and education researchers not involved in the initial writing, conducted the work. They note key connections among standards, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics.
The Progressions, funded by the Brookhill Foundation, can be found at The University of Arizona, Institute for Mathematics and Education website. Revision of the draft Progressions are informed by comments and discussion at http://commoncoretools.me, The Tools for the Common Core blog. This blog is a venue for discussion of the Standards as well as the draft Progressions and is maintained by lead CCSS writer William McCallum.
The Progressions provide an extensive overview of the math standards. They include specific examples and explanations of what the standards mean, how they relate to learning mathematics, and why these standards are important. So often, the skeptic reaction to these math standards is, “why is this standard important and why is it important at this level?” This resource provides excellent insight into the relevance of a standard, its role at a particular level (focus), and how other levels continue to develop this standard (coherence).
The resource elaborates on the grade level coordination of standards across domains and connects standards for content and mathematical practices. It highlights key ideas that develop within one domain over the grades, key ideas that change domains as they develop over the grades, and key ideas that recur in different domains and categories.
Although the Progressions are aligned to the CCSS for Mathematics, it is not difficult to connect them to the College and Career Ready (CCR) standards.
The Progressions are intended to inform teacher preparation, professional development, curriculum organization, and textbook content. This resource can provide an in-depth understanding of the standards, how they connect, and their implications in classrooms.
The Progressions are written with a depth that requires organized discussion, sharing, and reflection. Professional development opportunities, in which teachers have the opportunity to actually work on the problems included in each chapter, reflect on solutions, and then review how standards are structured, would be very effective. Identifying the ways these examples might play out in adult education is an important part of the group discussions.
These resources are very important in actually developing curriculum and in evaluating lessons or problems in which CCR standards are identified as part of the design of the lesson. The resources provide math coaches, curriculum specialists, and teachers with specific criteria to determine if the standards are appropriately developed. The Progressions may be helpful for adult educators who are trying to ensure a clear flow of concepts in their curriculum.
The document is organized around important CCSS domains and conceptual categories. Each chapter provides an overview of the domain within the K-12 grade band, explores the standards within each grade, and highlights how the connections between the standards and the concepts progress.
Within each chapter are well-designed problems which are particularly helpful. The problems range from relatively straightforward to more complex, and they address some of the challenges students face at all levels as they achieve a conceptual understanding of the standards. The problems include graphs, tables, or other formats. Examples of student responses or solutions to these problems are also provided. The responses provide an opportunity for educators to examine how students indicate their understanding of a standard.
Since this document describes the Progressions within the CCSS, and there are CCSS standards that were not selected for the CCR, a strong understanding of the CCSS/CCR connection is recommended. In addition, the Progressions are organized by K-12 grade level. As a result, there is a need for adult educators to not only sift through the examples and identify those examples that specifically address the CCR standards, but also to translate the grade bands into CCR levels.