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Free versus anchored numerical estimation: A unified approach
John E Opfer1, Clarissa A Thompson2, Dan Kim1
1The Ohio State University, 245 Psychology Building, Columbus, OH 43210, USA.
Cognition
|January 17, 2016
Summary
Children's number estimation is better explained by logarithmic models, especially without anchors. Anchors can cause estimates to appear better fit by cyclic power functions, suggesting a mixed model is most accurate.
Area of Science:
- Cognitive Psychology
- Developmental Psychology
- Mathematics Education
Background:
- Children's number-line estimation is debated, with conflicting data supporting logarithmic and cyclic power models.
- Methodological differences in studies may explain these discrepant findings on numerical representation.
- Previous research has not fully explored the impact of anchoring and sampling on estimation models.
Purpose of the Study:
- To investigate whether methodological factors, specifically anchoring and sampling, influence the descriptive adequacy of logarithmic versus cyclic power models of children's number-line estimation.
- To determine the conditions under which logarithmic and cyclic power functions best describe children's numerical estimates.
- To propose a more comprehensive model for children's number estimation.
Main Methods:
- A 2x2 between-subjects design was employed, crossing anchoring (free vs. anchored) and sampling (over-sampling vs. even-sampling).
- Ninety-six children participated and were assigned to one of the four experimental conditions.
- Estimation data from each condition were analyzed to determine the best fit for logarithmic and cyclic power functions.
Main Results:
- In three conditions (free/over-sampling, free/even-sampling, anchored/over-sampling), estimates were predominantly better fit by a logarithmic function.
- In the anchored/even-sampling condition, estimates were better fit by a cyclic power function, indicating an effect of anchors.
- Logarithmically-compressed numerical estimates were found to be independent of sampling methods.
Conclusions:
- The fit of cyclic power functions to children's estimates appears to be an artifact of anchoring procedures.
- Logarithmic compression is a robust feature of numerical estimation, unaffected by sampling strategies.
- A mixed log/linear model is proposed as a versatile framework for understanding both free and anchored numerical estimation in children.
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