Students Need Procedural Fluency in Mathematics
Reston, Va., August 11, 2014-Procedural fluency is a critical component of mathematical proficiency; but it is much more than memorizing facts or processes, or being able to use only one approach in a given situation, according to a new position statement issued by the National Council of Teachers of Mathematics (NCTM). Procedural fluency is the ability to apply processes, techniques, and strategies accurately, efficiently, and flexibly; to transfer these methods to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or approach is more appropriate to apply than another.
"Business and political leaders are asking schools to ensure that students leave high school 'college and career ready,' possessing 21 st century competencies that will prepare them for adult roles as citizens, employees, managers, parents, volunteers, and entrepreneurs. Using mathematics effectively to solve real-world problems is a critical component of those competencies, and, consequently, is a strong emphasis in the Common Core State Standards for Mathematics and other high-quality standards" said NCTM President Diane Briars. "Developing procedural fluency is a critical part of instruction to ensure that students are adequately prepared for their futures."
Procedural fluency builds on a foundation of conceptual understanding, strategic reasoning, and problem solving. To develop procedural fluency, students need experience in integrating concepts and processes and building on familiar methods as they create their own informal strategies and procedures. They need opportunities to justify both informal strategies and commonly used techniques mathematically, to support and justify their choices of appropriate processes, and to strengthen their understanding and skill through distributed practice.
According to NCTM's position statement, procedural fluency supports students' analysis of their own and others' calculation and algebraic methods, such as written processes and mental methods for the four arithmetic operations, different ways of solving equations, as well as their own and others' use of tools like calculators, computers, and manipulative materials. It extends students' computational fluency and applies in all strands of mathematics.
Furthermore, effective teaching practices provide experiences that help students to connect problem-solving processes with the underlying concepts and provide students with opportunities to rehearse or practice strategies and to justify the steps in their reasoning and solutions. Practice is essential for building fluency; however it should be brief, engaging, purposeful, and distributed.
Read the complete position statement .
The National Council of Teachers of Mathematics is the public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. It is the world's largest organization dedicated to improving mathematics education in prekindergarten through grade 12. The Council's Principles and Standards for School Mathematics includes guidelines for excellence in mathematics education and issues a call for all students to engage in more challenging mathematics. Its Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics identifies the most important mathematical topics for each grade level. Focus in High School Mathematics: Reasoning and Sense Making advocates practical changes to the high school mathematics curriculum to refocus learning on reasoning and sense making. Principles to Actions: Ensuring Mathematical Success for All describes the policies and actions required for a high-quality mathematics education for all students. NCTM is dedicated to ongoing dialogue and constructive discussion with all stakeholders about what is best for our nation's students.
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