Besides content-area knowledge, the Common Core math standards include a list of eight skills that math teachers should integrate across the curriculum.

What does teaching math look like under the Common Core standards? Lots of classroom interaction and more inquiry-based approaches to learning, according to experts who are helping schools integrate the standards into instruction.

As schools prepare for Common Core assessments beginning in the 2014-15 school year, curriculum directors are working with math teachers to make sure their practices encompass the standards’ core concepts.

The standards build on knowledge and skills from prior grade levels as they deal with increasingly complex topics such as fractions and negative numbers. They stress conceptual understanding to ensure that students truly absorb what they are learning, instead of merely memorizing for a test, then forgetting much of what they learn.

Besides content-area knowledge, the Common Core math standards include a list of eight skills—called the Standards for Mathematical Practice—that math teachers should integrate across the curriculum. These skills are:

  • 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 K-5 math standards aim to give students a “solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals—which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications.”

Middle school math standards help prepare students for higher-level math in high school, and high school math focuses on mathematical modeling and using math to analyze situations, understand them, and inform decision-making.

The standards are written so that multiple math domains work together at the same time—and educators aren’t teaching algebra in isolation of statistics, for instance.

What does this mean for schools? EngageNY, a site maintained by the New York State Department of Education, outlines six “instructional shifts” that are necessary for implementing the Common Core math standards: