Numerical Discrimination and the Constraints of Working Memory in Infancy

Abstract

We examined numerical discrimination in 12-, 18-, and 24-month-old infants (N=156) using looking-time methodology and continuous eye-tracking. Infants discriminated 2 vs. 3 items at 12 months but required 3:1 ratio for larger quantities. Violation-of-expectation paradigms revealed capacity limitations consistent with subitizing range constraints. Visual working memory capacity predicted individual differences in discrimination performance.

Introduction

The development of numerical cognition in infancy has been extensively documented through looking-time and preferential-looking paradigms (Wynn, 1992; Xu & Spelke, 2000). However, the precise role of working memory limitations in constraining early numerical representations remains poorly understood. Current models posit that infants possess both an approximate number system (ANS) for large quantities and a precise object-tracking system (OTS) for small set sizes, but the neural and cognitive mechanisms determining the boundary between these systems have not been empirically characterized in a developmental sample.

We hypothesized that working memory constraints impose a hard limit on precise numerical discrimination in infancy, and that this limit progressively expands during the second and third years of life. Specifically, we predicted that infants would show precise discrimination for quantities within the subitizing range (1–3 items) but rely on approximate magnitude estimation for larger sets. Furthermore, we expected individual differences in working memory capacity—indexed via assessment of object tracking—to predict numerical discrimination performance, providing evidence for a shared representational bottleneck.

Method

Participants

We recruited 156 infants (M age = 18.4 months; range 12–26 months; 47% female) from the Greater Montreal metropolitan area. Participants were stratified by age into three groups: 12-month-olds (n=52), 18-month-olds (n=54), and 24-month-olds (n=50). All participants were full-term, with no reported hearing or vision impairments. Informed consent was obtained from parents or guardians. Three additional infants were tested but excluded due to excessive fussiness or drowsiness, consistent with our a priori exclusion criteria.

Procedure

Each infant participated in two sessions separated by one week. In Session 1, we administered the Object Tracking Task (OTT; Pylyshyn & Storm, 1988) modified for infants, in which 1–4 target objects among 1–8 total objects moved on a screen, and the infant's gaze was recorded via high-speed eye tracker (SMI Red-m, 60 Hz sampling rate). Trials lasted 8 seconds; we scored the proportion of time the infant's gaze was directed toward target regions, with chance = 0.125 for 4 targets. This provided an index of working memory capacity.

In Session 2, conducted one week later, infants viewed pairs of visual arrays in alternating conditions. In the Equality condition, they saw 2 versus 2, then 3 versus 3 items (habituation); in the Inequality condition, they saw 2 versus 3, then 3 versus 4 items, or 6 versus 9 items (large set, 1.5:1 ratio). Each trial lasted 10 seconds; we recorded total looking time to each array and computed violation-of-expectation scores (difference in looking time between expected and unexpected outcomes). Stimulus locations and order were counterbalanced.

Results

A 3 (age group) × 2 (array comparison) repeated-measures ANOVA on looking time (in seconds) revealed significant main effects of both age group, F(2, 150) = 4.62, p = .011, partial η² = .058, and array comparison, F(1, 150) = 22.41, p < .001, partial η² = .130. The interaction was significant, F(2, 150) = 5.89, p = .003, partial η² = .073.

Twelve-month-olds showed significant discrimination for 2 versus 3 (M difference = 2.1 sec, 95% CI [0.8, 3.4], t(51) = 3.24, p = .002, d = 0.91), but not for 3 versus 4 (M difference = 0.6 sec, t(51) = 0.84, p = .40) or 6 versus 9 (M difference = 0.4 sec, t(51) = 0.62, p = .54). By 24 months, infants showed discrimination for 2 versus 3 (d = 1.03, p < .001), 3 versus 4 (d = 0.72, p = .001), and 6 versus 9 (d = 0.53, p = .048). Critically, individual differences in OTT performance (proportion of time fixating targets) predicted numerical discrimination ability: a mixed-model regression controlling for age showed that each 10% increase in OTT accuracy was associated with a 0.5-second increase in looking-time violation-of-expectation (β = 0.50, SE = 0.18, t = 2.78, p = .006).

Discussion

These findings provide developmental evidence that working memory constraints delimit the precision of infants' numerical representations. The subitizing-like pattern observed at 12 months—precise discrimination only for very small quantities—aligns with known working memory capacity limits in older populations. The expansion of precise discrimination by 24 months, coupled with individual differences correlating with object-tracking ability, suggests that maturation of prefrontal and parietal working memory networks supports the emergence of more flexible numerical competence.

Future longitudinal designs tracking individual infants across longer time periods would clarify whether working memory capacity is a primary determinant of numerical development or merely a correlate. The role of language in breaking free from working memory constraints—notably, the acquisition of number words—also warrants investigation in bilingual and trilingual samples. These findings have implications for early identification of atypical numerical development and for designing numeracy interventions in early childhood education.

References

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