Procedural fluency is the ability to perform mathematical procedures accurately, efficiently, and flexibly (NCTM, 2023). It is a fundamental skill that is essential for success in mathematics. Students who are procedurally fluent are able to solve problems quickly and easily, and they are less likely to make mistakes. Much has been written about the importance of strengthening mathematics skills of younger students, in fact, the Bill and Melinda Gates Foundation has made a 10 year commitment to strengthen mathematics instruction in America.
There are many reasons why procedural fluency is important. First, it allows students to focus on understanding the concepts behind the procedures. When students are not struggling to remember how to do something, they can focus on why they are doing it. This deeper understanding leads to better problem-solving skills and a more positive attitude towards mathematics.
Second, procedural fluency is essential for success in higher-level mathematics. Many of the concepts that students learn in algebra, geometry, and calculus require a strong foundation in basic arithmetic. Students who are not procedurally fluent will struggle to keep up with the pace of more advanced courses.
Third, procedural fluency is important for everyday life. We use math every day, from balancing our checkbooks to calculating the tip at a restaurant. Students who are procedurally fluent will be better prepared to handle the mathematical challenges they face in their daily lives.
Developing Procedural Fluency
So how can we help students develop procedural fluency? The NCTM has identified several approaches necessary to improve student learning:
- Explicit instruction. Students need to be taught how to perform procedures correctly. This includes providing clear explanations, modeling the procedures, and giving students opportunities to practice.
- Multiple strategies. There are often multiple ways to solve a math problem. Teaching students multiple strategies can help them develop a deeper understanding of the concepts and make them more flexible problem solvers.
Automaticity. Students need to practice procedures until they become automatic. This means that they can perform them without having to think about it.
- Assessment. It is important to assess procedural fluency regularly. This can help identify students who are struggling and provide them with the support they need.
Procedural fluency is a critical skill for all students. By providing explicit instruction, using multiple strategies, promoting automaticity, and assessing regularly, we can help students develop the procedural fluency they need to succeed in mathematics.
The Bill and Melinda Gates Foundation goes so far as to identify additional approaches that show value, including:
- Using manipulatives. Manipulatives can help students visualize concepts and make them more concrete.
Playing games. Games can provide a fun and engaging way to practice math skills.
- Incorporating technology. There are a number of educational apps and websites that can help students practice math skills.
- Encouraging students to explain their thinking. This can help them identify areas where they need more practice.
- Making math relevant to students’ lives. Show them how math is used in the real world.
Our Procedural Fluency Model
At CTL, we take the premise that all students deserve the opportunity to develop strong procedural fluency. We have been working in this arena for over a decade and our comprehensive framework takes advantage of both sets of practices and includes:
- Explicit strategy instruction: Strategies for developing flexible approaches to basic facts have been documented and we build classroom experiences that help students work through foundational strategies and then progress through derived fact strategies that lay the groundwork for flexible computations skills. .
- Game-based practice: Students practice applying their strategies through games and other engaging activities that provide concrete context. This helps them develop fluency in a fun and motivating environment, while reducing mathematical anxiety, especially for high-poverty students.
- Formative assessment: Teachers regularly assess students’ progress to identify areas where they need additional support through simple question and answer routines. This lets teachers know what students know and how they are finding their answers further allowing for targeted instruction and differentiation.
We need to work together to improve outcomes for all students. Find out more about our model and the work we are doing for students today!