How 15 Hundred Is Like 15 Cherries: Effect of Progressive Alignment on Representational Changes in Numerical Cognition

TLDR

The study examines how understanding of the decimal system evolves with age and experience, hypothesizing that highlighting commonalities between small and large numerical scales will encourage children to generalize linear representations to larger scales. Experiment 1 had second, third, sixth graders and adults estimate number lines across 0–1,000, 0–10,000, and 0–100,000 scales, while Experiment 2 assigned second graders to groups that varied in how they highlighted commonalities between small and large scales. Results showed that linear estimate accuracy rose with age but fell with scale size, and only children exposed to progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, indicating that analogies between numeric scales promote broad generalization.

Abstract

How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0–1,000, 0–10,000, and 0–100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15:100::1500:10000) might prompt children to generalize their linear representations to ever‐larger scales. Experiment 2 assigned second graders ( N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations.