Scientists discover a better way for kids to learn math

Children’s first encounters with math usually happen at the breakfast table or on the playground, not in a classroom. Developmental scientists have long known that these everyday experiences – like counting blocks or footsteps to the front door – nurture an intuitive sense of quantity.

According to a comprehensive report, a strong “number sense” builds arithmetic fluency, which later supports success in algebra, geometry, and adult earnings.

Yet the route from cereal-box counting to fluent calculation has been hotly debated: Should teachers focus on memorizing multiplication tables, or on fostering deeper conceptual reasoning? The new review concludes that the debate sets up a false choice.

New framework for learning math

Drawing on behavioral experiments, longitudinal research, neuroimaging data, and classroom design studies, the researchers propose a three-stage cycle in which facts and concepts reinforce one another.

They believe fluency starts with understanding, improves with timed practice, and deepens through reflection and discussion.

“We want to be clear: Educators don’t have to choose between timed practice and rich classroom discussions,” said study lead author Nicole McNeil of the University of Notre Dame.

“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.”

Brain shifts with practice

The researchers frame math learning as a dynamic movement between two knowledge states. Young children start with implicit insights: they can combine two sets of crackers and anticipate a larger pile without articulating why.

Over time, guided instruction turns these hunches into explicit strategies, such as “counting on from the bigger number” or recognizing that addition is commutative.

With continued, targeted practice – ideally in short, carefully timed bursts – these explicit strategies become automatic, freeing up mental resources for higher-level problem solving.

Neuroimaging studies cited in the report reveal that as this process unfolds, brain activation patterns begin to shift. Brain activity shifts from effortful reasoning to rapid recall, reflecting the child’s move from counting slowly to instant retrieval.

No more math wars

Because fluency develops through intertwined conceptual and procedural growth, the authors argue, classroom instruction should regularly cycle between the two.

Early progress monitoring is recommended to spot gaps in mental number representations. Explicit teaching of thinking strategies, such as making tens, can help address those gaps.

The research team also suggests using retrieval exercises designed to be brief enough to encourage speed only after accuracy has been achieved.

Each timed practice session should end with group discussion where students explain methods and link facts to broader ideas. This “explain–practice–explain” rhythm avoids the pitfalls of rote memorization while ensuring that knowledge can be deployed automatically when needed, noted the researchers.

Math skills shape futures

The paper’s authors and an accompanying commentary by Melissa E. Libertus of the University of Pittsburgh highlight the practical stakes.

Students who leave elementary school fluent in arithmetic adapt more readily to algebraic symbolism, grasp fraction magnitudes more accurately, and solve multi-step word problems more efficiently.

Longitudinal data link early math skills to later academic attainment and even adult income. The experts argue that arithmetic fluency is essential in today’s data-driven world – just as important as reading.

Training teachers with research

Despite the strong evidence base, many teacher-preparation programs devote limited time to the cognitive science of math learning. The researchers call for more explicit coursework that helps future educators evaluate instructional materials through the lens of learning research.

Digital tutoring systems and adaptive practice apps can help – but only when educators integrate them into conceptual discussions and reflective reasoning.

Future research should explore how parents’ math anxiety affects children and how digital tools can personalize practice while preserving depth.

A new classroom model

The report arrives at a moment when timed tests and “math wars” rhetoric still spark controversy. Speed and understanding aren’t opposing goals – they build on each other in a well-designed learning process.

By letting children’s initial intuitions surface, honing them through targeted practice, and weaving them back into rich conceptual networks, educators can cultivate the kind of fluency that supports future math learning. This fluency also aids in real-world problem solving.

The science of learning, the authors argue, shows that arithmetic proficiency is built not on memorization alone and not on exploration alone, but on a deliberate interplay of the two. This is proof that, in mathematics as in many areas of education, balance and evidence go hand in hand.

Nancy Jordan of the University of Delaware, Alexandria Viegut of the University of Wisconsin–Eau Claire, and Daniel Ansari of Western University are co-authors of the study.

The research is published in the journal Psychological Science in the Public Interest.

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