Children's Understanding of the Natural Numbers’ Structure

Jennifer Asmuth*, Emily M. Morson, Lance J. Rips

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi,; Siegler & Opfer,). However, several investigators have questioned this argument (e.g., Barth & Paladino,; Cantlon, Cordes, Libertus, & Brannon,; Cohen & Blanc-Goldhammer,). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as “5” or “80”). In Experiments 1 and 2, when 5- and 6-year-olds choose between number lines in a forced-choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1–100 are arranged. The bead placement of 4- and 5-year-olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number-line task may depend on strategies specific to the task.

Original languageEnglish (US)
Pages (from-to)1945-1973
Number of pages29
JournalCognitive Science
Issue number6
StatePublished - Aug 2018


  • Natural numbers
  • Number concepts
  • Number development
  • Number line
  • Numerical cognition

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Cognitive Neuroscience
  • Artificial Intelligence


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