The teaching practices delineated in Principles to Actions (NCTM 2014, 42) call on us to “build procedural fluency from conceptual understanding.” But the question teachers face is what constitutes this “foundation of conceptual understanding” that enables students to “become skillful in using procedures flexibly as they solve contextual and mathematical problems?”
We believe that teachers must embrace nine pivotal understandings to support the development of numerical fluency in all students.
These nine pivotal ideas provide a cognitive foundation upon which children become numerically fluent. It should be clear at this point that these understandings cannot be taught in only a lesson or two. Rather, they must be integrated into ongoing activities and conversations and infused throughout instruction.
Patsy Kanter is an author, teacher, and international math consultant. She worked as the Lower School Math Coordinator and Assistant Principal at Isidore Newman School in New Orleans, Louisiana, for 13 years. Patsy is the co-author of Every Day Counts: Calendar Math and a consulting author for Math in Focus.
Follow Patsy on Twitter @patsykanter
Steve Leinwand is the author of the bestselling Heinemann title Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement.He is Principal Research Analyst at the American Institutes for Research in Washington, D.C., where he supports a range of mathematics education initiatives and research. Steve served as Mathematics Supervisor in the Connecticut Department of Education for twenty-two years and is a former president of the National Council of Supervisors of Mathematics.