Numerical Estimation Under Supervision

Children's number-line estimation has produced a lively debate about representational change, supported by apparently incompatible data regarding the descriptive adequacy of logarithmic (Opfer et al., 2011) and power models (Slusser et al., 2013). To test whether methodological differences might explain discrepant findings, we created a fully crossed 2x2 design and assigned 96 children to one of four cells. In the design, we crossed sampling (over-, even-) and supervision (with feedback, without feedback), which were candidate factors to explain discrepant findings. In three conditions (over-sampling/unsupervised-83%, evensampling/unsupervised-67%, and over-sampling/supervised58%), the majority of children provided estimates better fit by the logarithmic than by the power function. In the last condition (even-sampling/supervised-30%), the reverse was found. Overall, a reliable association (p < .0001) was found between proportion best fit by the power function and supervision. Results suggest that the fit of the power function to children's estimates is likely an artifact of supervision.