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:

**Focus**: Teachers must narrow the scope of how time and energy is spent in math classes to focus more deeply on the concepts that are given priority in the standards.**Coherence**: Principals and teachers must carefully connect the learning within and across grades, so that students can build new understanding onto foundations built in previous years.**Fluency**: Students are expected to have speed and accuracy with simple calculations; teachers must structure class and/or homework time for students to memorize core functions through repetition.**Deep Understanding**: Students must deeply understand and operate easily within a math concept before moving on. They must learn more than the trick to get the answer right: They must learn the math behind the problem.**Application**: Students are expected to use math and choose the appropriate concept for application, even when they are not prompted to do so.**Dual Intensity**: Students are practicing and understanding. There is more than a balance between these two things in the classroom—both are occurring with intensity.

Inside Mathematics, a website that grew out of an initiative from the Noyce Foundation, includes a number of videos showing exemplary math lessons that address the eight practice standards. It’s clear from watching the videos that math classes—if they weren’t this way before—are about to get a lot more boisterous, as math instruction becomes an interactive process that challenges students to solve problems and discuss their reasoning through a deeper level of discourse.

In one series of videos, teacher Fran Dickinson leads fifth and sixth graders at San Carlos Charter School through a lesson in numerical patterning. As students suggest input numbers, Dickenson generates an output value, and students are asked to define the function. They also discuss whether the number zero is a possible input value. After the students work on this task in small groups, Dickenson leads a discussion with the entire class—addressing the standards on reasoning abstractly, constructing viable arguments, and critiquing others.

The North Carolina Department of Public Instruction has started a wiki to help educators adjust to the Common Core math standards, said Maria Pitre-Martin, director of the state’s K-12 Curriculum and Instruction division.

“Change is difficult,” Pitre-Martin acknowledged. “We’re in the first year of teaching [with] the Common Core, so our teachers did feel kind of overwhelmed by the magnitude of the changes.” But as educators wrap up their first year of implementing the standards, “we feel they are going to be in a better place,” she said.

Oregon’s Salem-Keizer Public Schools has been working to foster a deeper understanding of math for several years, said Lesli Ficker, an elementary math specialist in the district’s curriculum department—so it was ahead of the curve when it came time to implement the Common Core.

Initially, the district’s curriculum leaders were wary of implementing yet another set of standards, but “after we lived with it a little bit, it became an opportunity, because everybody is going to feel the urgency,” Ficker said.

She added: “Our [best] practices haven’t changed. If you’ve been integrating good instructional practices and inquiry-based strategies, you’re going to be OK.”

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