Why Fluency is Critical in K-5 Math Classrooms

And How to Promote Fluency in Math Instruction

By Dr. Lanette Trowery, Sr. Director of Learning at McGraw Hill School and Margaret Bowman, Academic Designer at McGraw Hill School

What is fluency in math?

While there is some theoretical debate in defining what fluency means and how it can be measured, Biancarosa and Shanley (2016) state that it should be treated as “a holistic description of a skilled performance” (p. 14). In other words, it is not one specific skill, nor is it simply about speed. Baroody (2011, as cited in Clarke, Nelson, & Shanley, 2016) defined fluency as the quick, accurate recall of facts and procedures, and the ability to use them efficiently (p. 71).

The repeated themes in fluency research relate to accuracy and speed (Rhymer, Dittmer, Skinner, & Jackson, 2000) as well as efficiency. Efficiency and speed are somewhat related in that, as students develop and use more efficient strategies to solve problems, they are likely to increase their speed.

Fluency, not to be confused with automaticity, involves the application of automatic computation. For example, multi-digit addition or long division requires the application of memorized computations while fluently carrying out the procedure (Hasselbring & Bausch, 2017). This means that although automatic recall of math facts is important, students must also be able to quickly and accurately conduct procedures to be fluent in more complex mathematical computations. In this way, fluency also takes into account the relationships among conceptual understanding, procedural knowledge, and basic fact recall (Clarke, Nelson, & Shanley, 2016).

Why is fluency important in math?

Research in the elementary grades has shown many key benefits of fluency, including:

Proficiency. One such benefit is that fluency supports mathematical proficiency (Clarke, Nelson, & Shanley, 2016). “When students are fluent in computation, they are more likely to develop the number sense that underlies more complex mathematics problem solving” (Gersten & Chard, 1999, as cited in Carr, Taasoobshirazi, Stroud, & Royer, 2011).

Higher-Order Thinking. Fluency also frees up working memory that can be used for higher-order activities (Carr et al., 2011; Clarke, Nelson, & Shanley, 2016; Hasselbring & Bausch, 2017; Ramos-Christian, Schleser, & Varn, 2008). When the load on working memory is reduced, students have a greater capacity to think about and solve more complex problems and tasks.

🧠 For more on the science behind working memory and the brain, check out this animation on the cognitive load theory:

Achievement. By supporting proficiency and creating the means for students to conduct higher-order tasks, fluency has been shown to predict greater mathematics achievement (Carr et al., 2011). According to Greene, Tiernan, and Holloway (2018), students who have greater fluency are better able to retain and maintain what they have learned, focus on a task even when distractions arise, and apply their learning to new contexts. Inversely, students who lack fluency have been shown to have persisting mathematical difficulties.

How can teachers promote fluency in math education?

Practice, practice, practice. Practice is key. High levels of performance can be attributed to deliberate practice, which differs from drill and practice exercises. Deliberate practice involves activities that are designed to improve performance, have set objectives just above one’s current level of competence, provide feedback, and involve repetition. A teacher or coach should guide students in correctly learning and practicing a skill (Hasselbring & Bausch, 2017, p. 58). Effective practice strategies include incremental rehearsal, such as flashcards-based activities; practice sessions with modeling; and self-management strategies, such as cover, copy, and compare (Clarke, Nelson, & Shanley, 2016).

Feedback. Providing immediate feedback (rather than after students have completed an entire practice session) prevents students from practicing incorrect responses (Berrett & Carter, 2018; Rhymer et al., 2000). Upon receiving feedback, students are able to take corrective measures, and then continue practicing with this improved understanding. Peer-tutoring has also been shown to improve fluency by individualizing support based on students’ specific needs while also providing feedback and maintaining engagement in the task (Greene et al., 2018). Students who engage in peer mentoring benefit by being both the mentee and the mentor. Peer mentors can also help students find efficient strategies for more quickly solving problems. Teachers should then help students to connect their own strategies and methods to more efficient procedures (NCTM, 2014).

Education Technology. Computer-based interventions have been shown to improve fluency (Carr et al., 2011). Research demonstrates that computer-assisted instruction (CAI), when used appropriately, can function as an effective supplementary tool “by providing opportunities for added practice and by differentiating the educational experience of each child. Other advantages of incorporating CAI in the classroom include immediate feedback, automated progress monitoring and adaptive instruction, increased engagement, and high accessibility” (Berrett & Carter, 2018, p. 226).

What are some actionable, everyday instructional practices for fluency in math?

• Regularly incorporate short activities that are designed to help students activate their prior knowledge to practice skills that will be needed for the new mathematical content. Be sure to select activities that include problems that aid in increasing students’ computational accuracy and speed.
• End lessons with practice problems that involve computations and provide immediate feedback.
• Use technology (gamified programs are even better!) that allow students to practice speed and accuracy.
• Combine opportunities for fluency building with opportunities for mathematical discourse and metacognition by allowing students to recall prior learning and discuss their thinking around solving problems efficiently.
• When possible, consider adopting a spiral review or spaced practice model to ensure students are afforded multiple opportunities to recall and practice consistently over time.

🧠 The animation below breaks down why spaced practice aligns to how the brain works, and how to implement it in the classroom:

For more on the importance of math fact fluency, and how math fact fluency is practiced through specific instructional elements in Reveal Math K-5, see the full Reveal Math K-5 Research Foundations.

About the Authors

Lanette Trowery, Ph.D. is the Senior Director of the McGraw Hill Learning Research and Strategy Team.

Lanette was in public education for more than 25 years, working as a university professor, site-based mathematics coach, elementary and middle school teacher, mathematics consultant, and a professional learning consultant, before coming to McGraw Hill in 2014. She earned her Master’s and Doctorate from the University of Pennsylvania.

Lanette’s team, Learning Research and Strategy, serves as the center of excellence for teaching and learning best practices. Her team conducts market, effectiveness, and efficacy research into products to provide insights and recommendations to product development. They collaborate across internal teams, external experts, and customers to establish guiding principles and frameworks to move from theory to practice.

Margaret Bowman is an Academic Designer in the Mathematics Department at McGraw Hill.

Margaret earned her Bachelor of Science in Education from Ashland University with a teaching license in Middle Grades Education, and her Master of Education from Tiffin University. She was a middle school Math and Language Arts teacher for six years before joining the middle school team at McGraw Hill in 2012, writing and designing print and digital curriculum.

Margaret is also a Research Associate in the Research Laboratory for Digital Learning at The Ohio State University. She is nearing completion of a PhD in Educational Studies with an emphasis in Learning Technologies. Her past research and journal publications have focused on teachers’ value for using technology in the classroom and technology’s impact on student learning. Her current research examines how students’ use of technology can improve the value they have for mathematics and their expectations that they can succeed.

References

Berrett, A. & Carter, N. (2018). Imagine math facts improves multiplication fact fluency in third-grade students. Journal of Behavioral Education, 27(2), 223–239.

Biancarosa, G. & Shanley, L. (2016). What is fluency? In Cummings, K., & Petscher, Y. (Eds.), The fluency construct: Curriculum-based measurement concepts and applications (1st ed., pp. 67–89). New York, NY: Springer.

Carr, M., Taasoobshirazi, G., Stroud, R., & Royer, J. (2011). Combined fluency and cognitive strategies instruction improves mathematics achievement in early elementary school. Contemporary Educational Psychology, 36(4), 323–333.

Clarke, B., Nelson, N., & Shanley, L. (2016). Mathematics fluency — More than the weekly timed test. In Cummings, K. & Petscher, Y. (Eds.), The fluency construct: Curriculum- based measurement concepts and applications (1st ed., pp. 67–89). New York, NY: Springer.

Greene, I., Tiernan, A., & Holloway, J. (2018). Cross-age peer tutoring and fluency-based instruction to achieve fluency with mathematics computation skills: A randomized controlled trial. Journal of Behavioral Education, 27(2), 145–171.

Hasselbring, T. & Bausch, M. (2017). Building foundational skills in learners. In Cibulka, J., & Cooper, B. (Eds.), Technology in school classrooms: How it can transform teaching and student learning today. Lanham: Rowman & Littlefield.

Ramos-Christian, V., Schleser, R., & Varn, M. (2008). Math fluency: Accuracy versus speed in preoperational and concrete operational first and second grade children. Early Childhood Education Journal, 35(6), 543–549.

Rhymer, K. N., Dittmer, K. I., Skinner, C. H., & Jackson, B. (2000). Effectiveness of a multi-component treatment for improving mathematics fluency. School Psychology Quarterly, 15(1), 40–51.