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The Beginnings of Number: From Subitizing to the Cardinality Principle

By Leon MoriguchiPublished May 13, 2026Updated May 18, 20266 min read日本語版あり
Audience
Parents of children aged 1–5; those interested in early childhood education

TL;DR

  • ·Two distinct numerical systems — subitizing for small quantities and the approximate number system for larger ones — are present from infancy and form the substrate onto which verbal counting is later mapped
  • ·Reciting "one, two, three" is not the same as counting; the cardinality principle (understanding that the last number said represents the whole group) typically consolidates between ages 3.5 and 4, with wide individual variation
  • ·Everyday encounters with quantity — sharing food, matching cups to spoons, comparing piles — provide more durable mathematical scaffolding than flashcards or drills

Contents

  1. Lead
  2. At Five Months: "1 + 1 = 1 Looks Wrong"
  3. Two Core Systems
  4. What "Understanding Numbers" Actually Requires
  5. What Parents Can Actually Observe
  6. Summary
  7. References

Lead

"She's three and still can't count" is usually not a cause for concern — and the reason is more interesting than it might sound. Hearing "one, two, three" come out of a child's mouth does not necessarily mean that child is counting, and conversely, a child who never says those words aloud may be quietly building a genuine understanding of quantity.

Number concept development runs considerably deeper than the surface skill of reciting a sequence. It begins in infancy with an intuitive grasp of amount, works its way through the gradual acquisition of counting principles across ages three and four, and arrives — in a moment researchers have spent decades trying to characterize — at the understanding that the last number you say when counting a group represents the whole group. This article lays out what the evidence currently shows about how that journey unfolds.

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