Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. Procedural fluency is more than memorizing facts or procedures, and it is more than understanding and being able to use one procedure for a given situation. Procedural fluency builds on a foundation of conceptual understanding, strategic reasoning, and problem solving (NGA Center & CCSSO, 2010; NCTM, 2000, 2014). Research suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999). Therefore, the development of students’ conceptual understanding of procedures should precede and coincide with instruction on procedures. Although conceptual knowledge is an essential foundation, procedural knowledge is important in its own right. All students need to have a deep and flexible knowledge of a variety of procedures, along with an ability to make critical judgments about which procedures or strategies are appropriate for use in particular situations (NRC, 2001, 2005, 2012; Star, 2005).
Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3–19.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010).Common core state standards for mathematics. Common core state standards (college- and career-readiness standards and K–12 standards in English language arts and math). Washington, DC: Author. http://www.corestandards.org.
National Research Council (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
National Research Council. (2005). How students learn: History, mathematics, and science in the classroom. Washington, DC: National Academies Press.
National Research Council. (2012). Education for life and work: Developing transferable knowledge and skills for the 21st century. Washington, DC: National Academies Press.
Star, J. R. (2005). Reconceptualizing conceptual knowledge. Journal for Research in Mathematics Education, 36(5), 404–411.