The Common Core Standards for Mathematics define what students should understand and be able to do in their study of mathematics. The mathematical standards stress conceptual understanding of key ideas while continually returning to organizing principles (the basics) in order to structure those ideas. The Common Core Standards for Mathematics are meant to ensure that all students have the opportunity to learn and meet the same high standards in order to gain access to the math knowledge and skills necessary in college and careers.
Within the Mathematics Common Core Standards there are two types of standards: Standards for Mathematical Practice and Standards for Mathematical Content. Mathematical Practice standards stay the same for each grade level but the practice of these standards may look different as students get older. Mathematical Content Standards change with grade level.
Standards for Mathematical Practice
There are 8 standards for mathematical practice:
- 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.
As students’ math abilities mature they should have both a deeper understanding of each of these math standards and be able to display them in a more mathematically mature way.
The overall idea of these mathematical standards boils down to that students should be able to both know and understand the concepts of math they are learning. According to the Common Core Standards for Mathematical Practice, students must be able to get the correct answer to a math problem, but also know why that is the correct answer and why a certain formula will give them the answer they need.
Standards for Mathematical Content
The Common Core Standards for Mathematical Content are a balance of procedure and understanding. Mathematical understanding and procedural skills are equally important and assessable. Students will no longer to be able to rely simply on the inputà formulaà output procedural process common in math lessons. Instead, the Mathematical Content Standards will set an expectation of understanding and procedure, providing students with a flexible base from which to work.
Organized into grade-specific mathematical standards, the Standards for Mathematical Content consist of three key parts.
Domains: Large groups of related mathematical standards. Standards from different domains are often closely related.
Standards: Define what students should understand and be able to do.
Clusters: Groups of related mathematical standards.
You’ll notice the Common Core Standards for Mathematical Content do not dictate curriculum, learning pathways or teaching methods. Ideally, each mathematical standard would read “students who already know X should next come to learn Y.” Unfortunately, existing education research cannot yet specify these learning pathways. Instead, the Mathematical Content standards leave the door open for research on learning progressions to inform and improve to design of mathematical standards to a much greater extent than is possible today.
To read extended definitions of the Common Core Standards of Mathematical Practice and a full list of the Common Core Standards for Mathematical Content, you can visit the Common Core State Standards for Mathematics.
More About the Common Core State Standards:
The Common Core State Standards: English Language Arts»
The Common Core State Standards: An Overview»
The Common Core State Standards: New Approach to Student Assessment»