Common Core State Standards for Mathematics

The Kindergarten through 12th grade (K-12) Common Core State Standards in Mathematics (CCSS-M) are the result of a collaborative effort between state departments of education, teachers, experts in a wide array of fields, and professional organizations. The standards allow students to become increasingly more proficient in understanding and using mathematics with a steady progression, leading to college and career readiness by the end of high school.

In grades K-8 the grade-level standards are organized by domains and in high school (grades 9-12) they are organized by conceptual categories. These standards include skills and knowledge – what students need to know and be able to do as well as mathematical practices – and habits of mind that students should develop to foster mathematical understanding and expertise. An organizational framework illustrating this blend is found at the beginning of each grade and each conceptual category in the standards.


Expectations

The standards are grounded in evidence, including the best work of states and high-performing nations, frameworks developed for the National Assessment of Educational Progress (NAEP), academic research, curriculum surveys, assessment data on college- and career-ready performance, and input from educators at all levels and from a variety of subjects. High points include:

K-5 Expectations
The K-5 standards are organized in domains: counting and cardinality; operations and algebraic thinking; number and operations in base ten; number and operations – fractions; measurement and data; and geometry. The domains vary by grade-level as appropriate; counting and cardinality is a key domain in kindergarten, while number and operations – fractions is introduced in third grade.The grade-by-grade K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals—which taken together provide students with a strong foundation for learning and applying more demanding math concepts and procedures, and for moving into robust applications.

Middle School Expectations
The 6-8 standards are organized in domains: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics and probability. Having built a strong foundation in K-5, students are prepared for robust learning in geometry, Algebra, and probability and statistics in middle school. Students who have completed 7th grade and mastered the content and skills of the K-7 standards will be well prepared for algebra in grade 8 or after. The middle school standards provide a coherent and rich preparation for high school mathematics.

High School Expectations
The high school standards are organized around five conceptual categories: number and quantity, algebra, functions, geometry, and statistics and probability. The high school standards call on students to practice applying mathematical ways of thinking to real world issues and challenges; they prepare students to think and reason mathematically. The high school standards set a rigorous definition of college and career readiness, not by piling topic upon topic, but by demanding that students develop a depth of understanding and an ability to apply mathematics to novel situations, as college students and employees regularly do.


Standards for Mathematical Practice

The requirements for campus proposals are described in the project’s Request for Proposals (RFP), which was released in December. The RFP will require a brief description of the campus' intended outcomes, its implementation plan, and the approach that will be used for assessing the impact of the reforms when they are put in place. Every CSU campus that prepares elementary teachers is eligible and encouraged to submit a proposal for a grant. The proposals will be due in March, and awards will be announced in April. Campuses will have through June 2014 to complete their projects and reports.

The Common Core mathematics standards include both content and process standards. Content standards include the mathematical knowledge and skills students should learn; process standards specify the mathematical ways of thinking students should develop while learning mathematics content. In the Common Core standards, the process standards are described as eight Common Core Mathematical Practices (see Figure 1) that build on the earlier National Council of Teachers of Mathematics process standards (communication, representation, reasoning and proof, connections, and problem solving) and the National Research Council's five strands of mathematical proficiency (procedural fluency, conceptual understanding, strategic competence, adaptive reasoning, and productive disposition).

 

Figure 1. Common Core Standards for Mathematical Practices

 

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning (Common Core Standards Initiative).

To emphasize the link between the content standards and the Mathematical Practices, the Common Core standards document indicates that content standards—beginning with the word "understand"—are especially good places for making connections between the content standards and Mathematical Practices.

Given the importance of the Mathematical Practices in understanding and implementing the Common Core mathematics standards, it is essential that teachers, teacher leaders, and administrators have a firm knowledge of these practices. Implementing the Common Core Mathematical Practices describes a variety of ways to foster understanding of the Mathematical Practices among future and current educators and suggestions for finding and creating math activities that elicit the Mathematical Practices.

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The Common Core State Standards and Teacher Preparation – The Role of Higher Education

A Discussion Paper from the Science and Mathematics Teacher Imperative (SMTI)/ The Leadership Collaborative (TLC) Working Group on Common Core State Standards

Higher education plays multiple roles in ensuring the success of the Common Core State

Standards. This brief describes an action agenda for the role of higher education institutions in this collective work, including:

  • Aligning higher education curriculum with K–12 curriculum
  • Preparing and educating teachers, both prospective and practicing
  • Conducting research on issues of teaching and learning the Common Core State Standards
  • Establishing and sustaining long-term partnerships with other actors and agencies in the educational system

Download the Role of Higher Education PDF here