title: Free versus anchored numerical estimation: A unified approach.
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.
authors.affiliation: The Ohio State University, 245 Psychology Building, Columbus, OH 43210, USA. Electronic address: opfer.7@osu.edu.
authors.forename: John E
authors.initials: JE
authors.lastname: Opfer
authors.affiliation: University of Oklahoma, Dale Hall Tower, Norman, OK 73019, USA(2). Electronic address: cthomp77@kent.edu.
authors.forename: Clarissa A
authors.initials: CA
authors.lastname: Thompson
authors.affiliation: The Ohio State University, 245 Psychology Building, Columbus, OH 43210, USA.
authors.forename: Dan
authors.initials: D
authors.lastname: Kim
mesh_terms: D002648:Child; D003071:Cognition; D003210:Concept Formation; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D008960:Models, Psychological
keywords: Cognitive development; Estimation; Learning; Numerical cognition