Skip to main content

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


Comments

Post a Comment

Popular posts from this blog

Manipulatives

  Using manipulatives in elementary mathematics is extremely important for students to gain a conceptual understanding of a variety of mathematical topics. It can be difficult for teachers to determine if students can transfer their understanding from manipulatives to other situations but this is why teachers need to plan time to have students learn the concepts with the manipulatives and then give the students time to solve the problems and only use manipulatives to check their work before finally removing the manipulatives and assessing the student’s knowledge because they won’t usually have these manipulatives in higher grades and outside of the classroom. In order to assess this growth and understanding, teacher observation and questioning are crucial. Teachers need to walk around the classroom or pull individual students or small groups and have students demonstrate their thinking with and without manipulatives. Manipulatives are also great because they help students improve t...
Post a Comment
Read more

Grade Level Curriculum Reflection

     Through this year-long curriculum, I learned how important it is for teachers to plan ahead. There are so many standards that need to be covered throughout the year and the standards all vary in the length of time it will take to teach and for the students to master. Teachers need to plan for this and read through all the standards at the beginning of the year to make sure they have time to get to everything. I have been in math classes before (more in middle school) that seem to be so rushed at the end of the year which could have been due to the teacher’s lack of a year-long curriculum plan. Obviously, other things could have come up or lessons took longer than my teacher thought, but it still reminds me of the importance of having a plan because I know how stressed I was when I had to learn concepts too quickly and didn't have time to master them before the tests. I also learned how important it is to review standards from the previous grade because they tie in so...
Post a Comment
Read more