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How 15 Hundred Is Like 15 Cherries: Effect of Progressive Alignment on Representational Changes in Numerical Cognition
Author(s) -
Thompson Clarissa A.,
Opfer John E.
Publication year - 2010
Publication title -
child development
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.103
H-Index - 257
eISSN - 1467-8624
pISSN - 0009-3920
DOI - 10.1111/j.1467-8624.2010.01509.x
Subject(s) - psychology , generalization , cognition , scale (ratio) , developmental psychology , numerical cognition , age groups , cognitive development , mathematics , cognitive psychology , statistics , demography , mathematical analysis , geography , cartography , neuroscience , sociology
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.