Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison.

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.