The progressive 6-year-old conserver: Numerical saliency and sensitivity as core mechanisms of numerical abstraction in a Piaget-like estimation task

Abstract

In Piaget’s theory of number development, children do not possess a true concept of number until they are able to reason on numerical quantity regardless of changes in other nonnumerical magnitudes, such as length. Recent studies have echoed this result by arguing that abstracting number from nonnumerical dimensions of magnitude is a developmental milestone and a strong predictor of mathematics achievement. However, the mechanisms supporting such abstraction remain largely underspecified. We aimed to study how identification of the numerical equivalence in a Piaget-like estimation task by 6-year-old children is affected by (a) the degree of interference between number and nonnumerical magnitudes and (b) children’s spontaneous orientation to numerosity. Six-year-old children first performed a card sorting task assessing their spontaneous orientation towards numerosity, spacing, or item size in a set of dots. Then, they completed a Piaget-like same/different numerical estimation task using two rows of dots in which the length ratio between the two rows varied systematically. Children were less likely to accept the numerical equivalence in the Piaget-like estimation task (a) as the difference in spacing between the dots increased and (b) as the children were more spontaneously oriented towards spacing over number in the card sorting task. Our results suggest that abstracting number depends on its saliency, which varies both as a function of the context (i.e., length ratio between the two rows) and of individual differences in children’s sensitivity to the numerical aspects of their environment. These factors could be at the root of the observed development of performance in the seminal number-conservation task, which appears as a progressive abstraction of number rather than a conceptual shift, as Piaget hypothesized.