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Common Core's Focus on Concepts Is Key to Improving Math Education, Report Says

The Common Core State Standards' emphasis on conceptual understanding in math will improve students' problem-solving skills and ultimately help prepare them for jobs of the future, argues a new report by the Center for American Progress, a Washington-based think tank.

Math instruction in the United States has traditionally focused on algorithms and proceduresexplain Catherine Brown and Max Marchitello, the authors of the report. Under the common core, students spend more time learning the underlying math concepts and how to apply them. "As a result, students become stronger critical thinkers and problem solvers and will be better prepared for the rigorousness of today's job market," they write.

CCSS procedural vs conceptual.JPGWhile much of the writing about the common core remains at the the 30,000-foot, theoretical level, this report, for the most part, is focused on specifics: It drills down into individual standards and gives examples for how the skills are taught differently under the common core vs. previous state standards. 

For instance, it shows an addition problem done two ways. First, with the traditional, vertical algorithm:

CCSS algorithm addition.JPG

And then a more conceptual way of teaching addition, which focuses on understanding place value and having good number sense:

CCSS conceptual add.JPGThe report rightly points out that students do still learn the traditional algorithm under the common core. (It shows up in 4th grade.) They're just introduced to the concepts first (beginning in 1st grade). "Learning the conceptual approach to math is just as important as learning to add with paper and pencil before using a calculator," the authors write.


It's worth noting though, as I've written before, that the common core is not actually a very prescriptive document. In fact, Jason Zimba, one of the lead writers of the math standards, has argued that teachers can introduce the algorithm right away in 1st grade along with the addition and subtraction concepts, and still be consistent with the standards. (He's even drawn out a table for how to do that.) But in truth, that's not how most math teachers will interpret the standards. 

The Center for American Progress report also explains that in the common core, concepts build on each other year after year—1st grade students, for instance, are exposed to foundational concepts in fractions and geometry. The long, slow rollout of important mathematical ideas helps prevent misunderstandings when students get to more complicated problems, it says.

"At a time when calculators and computers are ubiquitous, workers need to move beyond the surface to understand underlying concepts, be deep thinkers and problem solvers, and apply their skills to new situations," the authors write.

The Center for American Progress has long been supportive of the common-core standards. The report concludes with recommendations for ensuring conceptual math is taught well, such as providing ongoing professional development, training parents in the new methods, and incorporating conceptual math into teacher-preparation programs.

Images: From the Center for American Progress report, "Math Matters: How the Common Core Will Help the United States Bring Up Its Grade on Mathematics Education."

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