Mastering the Math Moves: Rethinking Fluency
When we think about procedural fluency in math, it’s easy to default to speed drills, flashcards, and the dreaded timer. But let’s be real: procedural fluency isn’t about racing the clock—it’s about helping students develop efficiency, accuracy, and flexibility in their math thinking. It’s one of the five strands of mathematical proficiency, and when done right, it gives students the mental bandwidth to think deeply instead of just crunching numbers.
Fluency doesn’t have to be boring—and it definitely shouldn’t be. With the right approach, students can master essential skills through experiences that are actually engaging. (Yes, they might even have fun practicing math.)
What Is Procedural Fluency (and Why Should We Care)?
According to the National Research Council (2001), procedural fluency is “carrying out procedures flexibly, accurately, efficiently, and appropriately.” In other words, this isn’t about rote memorization—it’s about giving students a toolbox of strategies they can use to solve problems in ways that make sense to them.
When students lack fluency with basic facts, they’re more likely to get bogged down in multi-step problems and lose the thread of the larger concept. As Morano, Randolph, Markelz, and Church (that’s me!) explain in their 2020 article, “students who lack fact fluency can experience high cognitive load and frustration when learning more complex material,” making it harder to focus on conceptual understanding or strategy use.
Let’s break it down: if a student has to pause and count on their fingers during every multiplication step while adding fractions, they’re not learning about fraction addition—they’re just trying to survive the problem.
Strategy + Mastery = Fluency That Sticks
So how do we actually help students build real fluency? The research points to a two-pronged approach: combine explicit strategy instruction with meaningful, mastery-based practice.
Strategy instruction helps students derive unknown facts using patterns, relationships, and number sense. For example: “If I know 5 × 5, then 6 × 5 is just one more group of 5.” That kind of reasoning builds connections and strengthens understanding.
Then comes the mastery work—structured, repeated practice with feedback that helps students build speed and accuracy. This is what frees up cognitive resources so they can focus on higher-level thinking. And my favorite kind of mastery practice? Games! There is neuroscience that backs up game-based learning, not to mention they’re just fun.
And here’s the kicker: when students get both, they do better across the board. Research shows this approach not only boosts retrieval speed, but also improves students’ ability to apply facts in multi-digit computations and mental math (Woodward, 2006; Ok & Bryant, 2016). It's not a tug-of-war between speed and understanding—it's about building both, in sync.
What This Looks Like in Practice
In action, this dual approach means:
Strategy Instruction: Students are explicitly taught efficient, research-backed strategies to derive facts. Think helping facts, doubles, near-doubles, and using properties like the distributive property. These aren’t just tricks—they’re conceptual tools that deepen number sense and make math make sense.
Engaging Mastery Practice: After learning a strategy, students need repeated, responsive practice that helps them internalize the facts. But forget the flashcards. Think activities that are adaptive, interactive, and genuinely enjoyable—offering feedback, challenge, and just the right amount of support to keep students in the zone of productive effort (not frustration or boredom). Some of my favorite games include: Salute, Oh No 99, and Contig.
This blended approach—clear strategies + responsive practice—is aligned with recommendations from the Institute of Education Sciences (Gersten et al., 2009) and echoes what works in effective classroom instruction (Morano et al., 2020).
A Few Final Thoughts (and a Pep Talk)
Procedural fluency is so much more than a memory contest. It’s about giving students access to higher-level math, to deeper understanding, and to the confidence that they can do it.
Fluency is not a finish line to cross. It’s a foundation to stand on.
When we intentionally design instruction that balances strategy and practice, we’re not just preparing students for the next math lesson—we’re equipping them for the long game: confidence, competence, and mathematical agency.
Let’s build fluency that fuels thinking, not just performance.
References
Morano, S., Randolph, K., Markelz, A., & Church, N. (2020). Combining explicit strategy instruction and mastery practice to build arithmetic fact fluency. TEACHING Exceptional Children. https://doi.org/10.1177/0040059920906455
Ok, M. W., & Bryant, D. P. (2016). Effects of a strategic intervention with iPad practice on the multiplication fact performance of fifth-grade students with learning disabilities. Learning Disability Quarterly, 39(3), 146–158. https://doi.org/10.1177/0731948715598285
Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29(4), 269–289. https://doi.org/10.2307/30035554
National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press. https://doi.org/10.17226/9822
Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: Institute of Education Sciences. https://ies.ed.gov/ncee/WWC/PracticeGuide/26
