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Number Sense Before Arithmetic: What Actually Prepares Young Children for Math

By Leon MoriguchiPublished May 13, 2026Updated May 18, 20266 min read日本語版あり
Audience
Parents of children ages 3–6

TL;DR

  • ·Math skills at school entry are the strongest predictors of later academic outcomes across multiple longitudinal datasets — stronger than reading skills, attention, or socio-emotional behavior at kindergarten entry
  • ·Number sense (intuitive understanding of quantity, comparison, and number structure) predicts later math achievement better than calculation accuracy; procedural knowledge and conceptual knowledge draw on independent cognitive resources and practicing one does not substitute for the other
  • ·The developmental sequence from subitizing to counting to cardinality to operations is not one instruction can meaningfully short-circuit — drilling calculation before cardinality is stable produces procedure without understanding

Contents

  1. Lead
  2. Four stages in number development
  3. 1. Subitizing
  4. 2. Counting
  5. 3. Cardinality
  6. 4. Number operations (addition and subtraction)
  7. What longitudinal research shows about preschool number sense
  8. Sarama and Clements: learning trajectories
  9. The problem with drilling ahead of readiness
  10. What parents can do today
  11. Summary
  12. References

Lead

The impulse to introduce addition before kindergarten, or to have a child practice writing numerals, is understandable. "Earlier means more prepared" is an intuitive heuristic. But developmental research returns a consistent finding: there is a set of precursor skills that need to be in place before formal arithmetic makes conceptual sense, and drilling on calculation before those foundations are solid tends not to translate into lasting mathematical ability.

How does numerical understanding actually develop? What does the longitudinal evidence say about what genuinely prepares children for school mathematics? This article draws on Sarama and Clements's learning trajectories framework and related longitudinal research to map the development from infancy through the preschool years.

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