Free versus anchored numerical estimation: A unified approach

Cognition
John E OpferDan Kim

Abstract

Children's number-line estimation has produced a lively debate about representational change, supported by apparently incompatible data regarding descriptive adequacy of logarithmic (Opfer, Siegler, & Young, 2011) and cyclic power models (Slusser, Santiago, & Barth, 2013). To test whether methodological differences might explain discrepant findings, we created a fully crossed 2×2 design and assigned 96 children to one of four cells. In the design, we crossed anchoring (free, anchored) and sampling (over-, even-), which were candidate factors to explain discrepant findings. In three conditions (free/over-sampling, free/even-sampling, and anchored/over-sampling), the majority of children provided estimates better fit by the logarithmic than cyclic power function. In the last condition (anchored/even-sampling), the reverse was found. Results suggest that logarithmically-compressed numerical estimates do not depend on sampling, that the fit of cyclic power functions to children's estimates is likely an effect of anchors, and that a mixed log/linear model provides a useful model for both free and anchored numerical estimation.

References

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May 14, 2003·Psychological Science·Robert S Siegler, John E Opfer
Apr 2, 2004·Child Development·Robert S Siegler, Julie L Booth
Jan 20, 2006·Developmental Psychology·Julie L Booth, Robert S Siegler
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Citations

Feb 3, 2016·Frontiers in Psychology·Clarissa A Thompson, John E Opfer
Apr 15, 2016·Developmental Science·Robert S Siegler
Mar 24, 2018·Developmental Science·Maxine LaiHilary Barth
Oct 28, 2019·Child Development·Lei YuanLinda B Smith
Feb 23, 2019·Frontiers in Psychology·Daniele DidinoAndré Knops
Feb 24, 2017·Developmental Science·David W Braithwaite, Robert S Siegler
Oct 31, 2018·Cognitive Science·Dale J CohenPhilip T Quinlan
Apr 4, 2017·Cognitive Research: Principles and Implications·Ilyse ResnickThomas F Shipley
Oct 4, 2018·Frontiers in Psychology·Jaccoline E Van 't NoordendeEvelyn H Kroesbergen
Feb 20, 2019·Frontiers in Psychology·John OpferFrancesca Marciani
Apr 24, 2021·Frontiers in Psychology·Erin N Graham, Christopher A Was
Aug 3, 2021·Acta Psychologica·Regina Miriam Reinert, Korbinian Moeller
Aug 26, 2021·PloS One·John E OpferRobert S Siegler

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