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Is 27 a Big Number? Correlational and Causal Connections Among Numerical Categorization, Number Line Estimation, and Numerical Magnitude Comparison


  • Thanks to the children, teachers, and principals of the Fox Chapel Area School District; to Richard Scheines for help with the path analysis, to Nicole R. Hallinen for assistance coding the data; and to the Department of Education (Grant R305H020060 and Graduate Training Grant R305B040063) and National Institutes of Health (Grant HD 19011) who supported this research.

concerning this article should be addressed to Elida V. Laski or Robert S. Siegler, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213. Electronic mail may be sent to or


This study examined the generality of the logarithmic to linear transition in children’s representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5–8 years) suggested parallel transitions from kindergarten to second grade in the representations used to perform number line estimation, numerical categorization, and numerical magnitude comparison tasks. Individual differences within each grade in proficiency for the three tasks were strongly related. Experiment 2 (27 girls and 13 boys, ages 5–6 years) replicated results from Experiment 1 and demonstrated a causal role of changes in categorization in eliciting changes in number line estimation. Reasons were proposed for the parallel developmental changes across tasks, the consistent individual differences, and the relation between improved categorization of numbers and increasingly linear representations.