Cross‐magnitude interactions across development: Longitudinal evidence for a general magnitude system

Abstract

There is general agreement that humans represent numerical, spatial, and temporal magnitudes from early in development. However, there is disagreement about whether different magnitudes converge within a general magnitude system and whether this system supports behavioral demonstrations of cross-magnitude interactions at different developmental time points. Using a longitudinal design, we found a relation between children's cross-magnitude interactions assessed at two developmental time points with different behavioral measures. More specifically, stronger cross-magnitude interactions in infancy (M = 9.3 months) predicted a stronger cross-magnitude congruity effect at preschool age (M = 44.2 months), even when controlling for performance on measures of inhibitory control, analogical reasoning, and verbal competence at preschool age. The results suggest a common mechanism for cross-magnitude interactions at different points in development as well as stability of the underlying individual differences. We argue that this mechanism reflects a nonverbal general magnitude system that is operational early in life and that displays continuity from infancy to preschool age.

Development of a Possible General Magnitude System for Number and Space

“…Contrasting findings might be due to age differences, since children in Odic et al (2013) study were much younger (3–6 years) compared to the present study (8–13 years). However, it has to be mentioned that reported findings in younger children are mixed and for instance Lourenco and Aulet (2018) reported in a recent study cross-magnitude interactions in infancy and at 3.7 years of age.…”

A theory of perceptual number encoding.

“…It is well known that nonnumerical magnitudes, such as the physical sizes of individual objects, the total surface area occupied, and their density within a container, affect number judgments in predictable ways. For example, on a magnitude comparison task, in which participants judge which of two arrays is numerically larger, there are robust congruity effects, such that participants’ judgments of number depend on the relation between number and co-occurring nonnumerical magnitudes (Hurewitz et al, 2006; Lourenco & Aulet, 2019; Miller & Baker, 1968; Nys & Content, 2012; Sophian & Chu, 2008). Participants are typically slower at judging which display is larger in number when the cumulative area is incongruent with this decision (i.e., smaller, not larger).…”

Numerosity and cumulative surface area are perceived holistically as integral dimensions.

“…An alternative to the dominant view argues for the existence of representational overlap between numerical and nonnumerical dimensions. Often, however, even proponents of this position posit magnitude dimensions that are initially independent and only later integrated within a general magnitude system (Lourenco & Aulet, 2019; Walsh, 2003), perhaps via Bayesian cue combination (Martin, Wiener, & van Wassenhove, 2017; Petzschner, Glasauer, & Stephan, 2015). A more provocative, although less frequently discussed, proposal is that the proposed overlap may be primary and perceptual in nature, such that number and nonnumerical magnitudes are perceived in a holistic manner.…”