Should we let children practice tables and sums endlessly, or is it all about “comprehension of arithmetic”? For years, these two camps have seemed to be on opposite sides, leading to heated discussions in some places. However, in a large-scale new overview by McNeil and colleagues (2025), which I found via Dan Willingham, the researchers aim to provide clarity. And the good news, according to them, is that we don’t have to make a choice. Automating and learning strategies don’t have to be opposites; they can reinforce each other.

Children who can recall arithmetic facts fluently from memory do better in complex math tasks because they can keep their working memory free for thinking and reasoning. Something I have also been explaining for years, literally. At the same time, it turns out that children benefit more from practice if they already understand what numbers are about. Fluency, therefore, arises from the interaction between insight and repetition. Not ‘cramming or understanding’, but ‘cramming with understanding’

So what really works, according to McNeil and colleagues?

• First insight: Understanding what addition means, being able to group numbers, and seeing connections between operations.

• Then practice: For example, practice with 6 + 7 = 13, but only when the child understands why it is correct.

• And yes, time pressure too – but only if the child is already accurate. Then, a short practice with a timer helps to develop fluency, without unnecessary stress.

There are clear pitfalls. Testing speed too early can cause frustration and even fear of failure, especially in young children. But waiting too long to practice ensures that strategies do not become ingrained. What counts is timing and approach: retrieval practice, spaced practice and reflection on strategy have proven effective.

And why should you care? Because the effects of math skills extend far beyond the classroom. McNeil and colleagues say that research shows that children who excel in math perform better in math, science, and life. In fact, early math skills predict future socioeconomic status in adulthood, independent of IQ or language skills.

Children who can calculate quickly and accurately have more space to think about fractions, equations or reasoning with variables. They don’t have to get stuck counting on their fingers. This not only makes math more fun, but also more logical, clearer and less stressful.

McNeil and her team make concrete recommendations:

• Invest in number sense and understanding of number relationships (even in kindergarten)

• Combine this with explicit instruction and exercises that are cleverly structured

• Only use time limits when the child is ready

• Allow time to compare and discuss different solution strategies

So the next time someone says “cramming sums is old-fashioned” or “playful learning is the only right way”, you know better: really learning math is building, understanding, practising and deepening – and maybe even in that order.

Abstract of the article about this framework :

High-quality mathematics education not only improves life outcomes for individuals but also drives innovation and progress across society. But what exactly constitutes high-quality mathematics education? In this article, we contribute to this discussion by focusing on arithmetic fluency. The debate about how best to teach arithmetic has been long and fierce. Should we emphasize memorization techniques such as flashcards and timed drills or promote “thinking strategies” via play and authentic problem solving? Too often, recommendations for a “balanced” approach lack the depth and specificity needed to effectively guide educators or inform public understanding. Here, we draw on developmental cognitive science, particularly Sfard’s process–object duality and Karmiloff-Smith’s implicit–explicit knowledge continuum, to present memorization and thinking strategies not as opposing methods but as complementary forces. This framework enables us to offer specific recommendations for fostering arithmetic fluency based on the science of learning. We define arithmetic fluency, provide evidence on its importance, describe the cognitive structures and processes supporting it, and share evidence-based guidance for promoting it. Our recommendations include progress monitoring for early numeracy, providing explicit instruction to teach important strategies and concepts, implementing well-structured retrieval practice, introducing time-limited practice only after students demonstrate accuracy, and allocating sufficient time for discussion and cognitive reflection. By blending theory, evidence, and practical advice, we equip educators and policymakers with the knowledge needed to ensure all children have access to the opportunities needed to achieve arithmetic fluency.