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Ch 4: Build Procedural Fluency from Conceptual Understanding


A conceptual understanding of math is essential for students to be successful in math classes throughout their life. To me, conceptual understanding is the basics of math (addition, subtraction, multiplication, division, equalities, etc), why these concepts work, how they work together, and then being able to remember and draw from these concepts in more complex problems. In order for students to gather conceptual understanding, they need to be willing and ready to learn and they also need to believe in themselves and their intelligence. The teacher's role is to be the expert but to guide students toward these understandings and not simply state them like facts, or else students will memorize them and not understand why these concepts work and why they are important in the future. 

Procedural fluency is the ability to use equations, representations, manipulatives, etc to solve a simple problem. The word simple is relative to the child’s grade level and also their academic level. For example, we would expect a 4th-grade student to be able to use procedural fluency to solve 5 + 5 but we wouldn't expect the same 4th-grade student to be able to solve a system of equations. For students, it is their willingness to learn these procedures well enough that they can perform them quickly and accurately without help. To get to this level, students will need to be active learners and participate in learning activities. The teacher’s job is to help students learn these procedures and then support them in being able to follow them fluently. Homework helps students develop this procedural fluency by allowing students to further practice these procedures at home until they become second nature to the students and they don't need assistance or reference to their notes.

To tie the two together, students cant develop procedural fluency without a conceptual understanding. For example, high school students will not be able to become fluent in solving a system of equations if they don't have the conceptual understanding that the two equations are lines and they are trying to find the coordinates where they cross.  This teaching strategy reminds me of the CCSM standard look for and make use of structure. When students have a conceptual understanding of topics and later procedural fluency of more complex topics, students will develop a sense of patterns that occur which will further help their procedural fluency. In order for teachers to promote this teaching practice, they need to ensure students fully understand the concepts before teaching how to use those concepts in more complex situations and procedures to set students up for success. They also need to give students plenty of practice with the procedures or else they won't be able to become fluent.

Huinker, D., & Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices, K – Grade 5. Reston, VA: NCTM


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