What’s the smartest way to help kids master math? A groundbreaking new report says it’s not about picking sides in the age-old battle between memorizing multiplication tables and exploring math concepts. Instead, the most effective approach blends both—timed practice and deep discussion—creating a powerful cycle of learning.
Published in Psychological Science in the Public Interest, the report—What the Science of Learning Teaches Us About Arithmetic Fluency—draws on years of developmental cognitive research to redefine what arithmetic fluency really means and how to teach it better.
“We want to be clear: Educators don’t have to choose between timed practice and rich classroom discussions,” said lead author Nicole McNeil from the University of Notre Dame. “It’s the pairing of both that strengthens memory and understanding.”
The authors—McNeil, Nancy Jordan (University of Delaware), Alexandria Viegut (University of Wisconsin–Eau Claire), and Daniel Ansari (Western University)—explain that arithmetic fluency is more than just quick recall of facts like 6 × 8 = 48. It also involves recognizing patterns and using number relationships to solve problems. And it starts early—right from a child’s preschool years.
Just as phonics is key to reading, early number sense forms the foundation for math. The report recommends activities like counting cereal bits or arranging blocks to strengthen these skills. From there, kids progress through stages—from intuitive “I just know” thinking to articulating strategies like “start with the bigger number,” and eventually reaching automatic recall through structured practice.
The report offers a practical teaching roadmap:
- Spot early gaps in number understanding
- Teach thinking strategies (like using 10 as a reference)
- Use retrieval practice—but only when kids are already accurate
- Include timed drills sparingly, after fluency begins to form
- Always circle back to discussion and justification
Importantly, the authors emphasize that this isn’t a rigid checklist. Rather, it’s a dynamic cycle—moving back and forth between reasoning and retrieval to help children think fast and think deeply.
Why does it matter? Because math fluency doesn’t just help with test scores. Studies link it to success in algebra, problem solving, and even long-term academic and income outcomes.
An accompanying commentary by developmental psychologist Melissa Libertus adds depth, pointing to the potential of digital tools and the impact of parents’ math anxiety.
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