Preschool children use space, rather than counting, to infer the numerical magnitude of digits: Evidence for a spatial mapping principle

Abstract

A milestone in numerical development is the acquisition of counting principles which allow children to exactly determine the numerosity of a given set. Moreover, a canonical left-to-right spatial layout for representing numbers also emerges during preschool. These foundational aspects of numerical competence have been extensively studied, but there is sparse knowledge about the interplay between the acquisition of the cardinality principle and spatial mapping of numbers in early numerical development. The present study investigated how these skills concurrently develop before formal schooling. Preschool children were classified according to their performance in Give-a-Number and Number-to-position tasks. Experiment 1 revealed three qualitatively different groups: (i) children who did not master the cardinality principle and lacked any consistent spatial mapping for digits, (ii) children who mastered the cardinality principle and yet failed in spatial mapping, and (iii) children who mastered the cardinality principle and displayed consistent spatial mapping. This suggests that mastery of the cardinality principle does not entail the emergence of spatial mapping. Experiment 2 confirmed the presence of these three developmental stages and investigated their relation with a digit comparison task. Crucially, only children who displayed a consistent spatial mapping of numbers showed the ability to compare digits by numerical magnitude. A congruent (i.e., numerically ordered) positioning of numbers onto a visual line as well as the concept that moving rightwards (in Western cultures) conveys an increase in numerical magnitude mark the mastery of a spatial mapping principle. Children seem to rely on this spatial organization to achieve a full understanding of the magnitude relations between digits.

Making Sense of Number Words and Arabic Digits: Does Order Count More?

“…In a recent study, CP-knowers were classified as mappers and non-mappers based on their ability to spatially map numbers on the visual number line from 1 to 10 (i.e., number line task; Sella, Berteletti, Lucangeli, & Zorzi, 2017). CP-mappers linearly placed digits along the line whereas CP-non-mappers mainly placed digits in a non-numerical manner (e.g., all the digits in the middle of the line).…”

“…Here, we provide further evidence on the development of exact symbolic numerical representation in young children. The fact that not all CP-knowers can compare the numerical magnitude of numbers suggests that, despite the mastering of the cardinality principle in the GaN task, CP-knowers still lack the knowledge of the exact numerical magnitude represented by symbolic numbers (Davidson, Eng, & Barner, 2012;Le Corre, 2014;Sella et al, 2017). In this light, the GaN task is suboptimal to assess an exact symbolic numerical knowledge, which, instead, can be assessed using a number comparison task.…”

Spatial Skills, Reasoning, and Mathematics

“…Humans are predisposed to associate spatial magnitude (such as line length or area) with numerical magnitude, even in the absence of formal schooling (de Hevia & Spelke, 2010;Dehaene, Bossini, & Giraux, 1993;Dehaene, Izard, Spelke, & Pica, 2008;Lourenco & Longo, 2010;Pinel, Piazza, Le Bihan, & Dehaene, 2004;Zorzi, Priftis, & Umiltà, 2002). Children in Western societies begin to map symbolic numbers (Arabic numerals) to space in a left-to-right orientation as early as preschool and kindergarten (Ebersbach, 2015;Sella, Berteletti, Lucangeli, & Zorzi, 2017). Theoretical accounts describe children's number line representations as initially logarithmic, in which they allocate more space to smaller numbers and less space to larger numbers (Opfer & Siegler, 2007;Opfer, Siegler, & Young, 2011;Siegler & Opfer, 2003).…”

Playing Reading, Using Hands: Which Activities are Linked to Number-Space Processing in Preschool Children?

“…One valid but thus far unresolved question is whether such ordinal spatial mapping is nevertheless enhanced by acquisition of the cardinal counting principle, i.e. knowing that the last spoken numeral represents the numerosity of a counted set (Le Corre & Carey, 2007;Wynn, 1992; for discussion on the relation between this principle and the ability to order numerals along physical line see Sella, Berteletti, Lucangeli, & Zorzi, 2017).…”