Four- to six-year-olds’ ratio reasoning-from 2D to 3D quantities

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Recent research has suggested that young children may have primitive knowledge of ratio and proportions. However, it is unclear how precisely young children represent ratio magnitudes and how well they apply their ratio knowledge across different contexts. The current study examined 4- to 6-year-olds’ reasoning of ratio magnitudes. In the baseline task, children judged ratio relations between 2 D lengths. In the 3 D depth task, children judged ratio relations of two pictorial depths. In the 3 D cube task, children judged ratio relations of the volumes of two pictorially presented cubes. Linear regression models of estimated ratios on expected ratios were significant across all three tasks for all children groups. Children demonstrated a remarkable ability in understanding and expressing ratio magnitudes. However, relative to the baseline condition, the 3 D depth and cube tasks were associated with smaller explained variance and, hence, more noise. Children, particularly 4-year-olds, were unable to distinguish ratios of slightly different magnitudes in the 3 D cube task. Our study reveals both the potential and the limits of young children’s ratio reasoning abilities.

Original languageEnglish
Pages (from-to)212-238
Number of pages27
JournalThinking and Reasoning
Issue number2
StatePublished - 2021


  • Ratio reasoning
  • cube
  • depth
  • linear
  • scale
  • volume


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