Is being fast with math facts the same as being fluent? Not quite. A new scientific review challenges the idea that speed alone defines math fluency, arguing that children build stronger and more lasting math skills through a combination of conceptual understanding, smart practice, and thoughtful reflection.

Published in Psychological Science in the Public Interest, the report draws on decades of cognitive and developmental science to propose a new, evidence-based model of math instruction—one that helps children become not just quicker, but deeper thinkers in math.

“We want to be clear: Educators don’t have to choose between timed practice and rich classroom discussions,” said lead author Nicole McNeil. “A carefully structured approach—pairing brief, timed sessions that strengthen facts in memory with purposeful reasoning and discussion activities that weave those facts into an integrated knowledge network—gives students the fluency they need to succeed.”

The authors of the study reviewed research ranging from neuroimaging to longitudinal classroom studies. Their conclusion: fluency should be redefined as accurate, flexible, and efficient use of math facts and strategies, not just memorized speed.

Fluency begins early in development. Children develop number sense—understanding quantities, relations, and simple operations—long before they can explain their thinking. For example, a child might know that combining five and three blocks makes eight, even if they can’t yet describe the process.

The review shows that children move through phases of implicit and explicit understanding. They start with intuitive strategies, then learn to explain and justify their reasoning, and eventually—through well-designed practice—retrieve that knowledge automatically with little effort. This re-proceduralization is key to solving more complex math problems down the line.

Most important, the authors emphasize that these shifts need to be nurtured in both directions: from intuition to explanation, and from explanation to automaticity.

The authors outline several instructional practices that help children develop fluency effectively:

• Monitor early progress to catch gaps in a child’s basic number understanding.
• Use explicit instruction to teach strategic thinking, such as using 10 as a reference point for calculations.
• Provide well-structured retrieval practice to reinforce combinations and results (e.g., 6 + 7 = 13).
• Incorporate timed practice only after children have already shown they’re accurate with the material.
• Create space for discussion and reflection, where children explain their reasoning and engage with math ideas aloud.

Together, these practices form a cycle: conceptual understanding → targeted practice → reflection, which helps children make sense of numbers and use them flexibly—not just recite them fast.

The review underscores the importance of fluency for broader learning. Students who build strong arithmetic fluency in early grades are better prepared to tackle algebra, word problems, and fractions later on. The benefits extend well beyond the classroom—studies show a connection between early math fluency and higher educational achievement, career success, and income in adulthood.

True fluency in any subject isn’t about speed, flashcards, drills alone. It’s about thinking flexibly, building understanding, and practicing with purpose. When kids get the right balance of structure, speed, and sense-making, they’re not just doing math faster—they’re thinking better for their general development.

N McNeil et al. What the Science of Learning Teaches Us About Arithmetic Fluency. Psychological Science in the Public Interest (2025). https://doi.org/10.1177/15291006241287726