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AbstractSymbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test competing theories of early number learning by measuring event‐related brain potentials during a novel number word‐quantity comparison task in 3–4‐year‐old preschool children (N = 128). We find several qualitative differences in neural processing of number by conceptual stage of development. Specifically, we find differences in early attention‐related parietal electrophysiology (N1), suggesting that less conceptually advanced children process arrays as individual objects and more advanced children distribute attention over the entire set. Subsequently, we find that only more conceptually advanced children show later‐going frontal (N2) sensitivity to the numerical‐distance relationship between the number word and visual quantity. The nature of this response suggested that exact rather than approximate numerical meanings were being associated with number words over frontal sites. No evidence of numerical distance effects was observed over posterior scalp sites. Together these results suggest that children may engage parallel individuation of objects to learn the meanings of the first few number words, but, ultimately, create new exact cardinal value representations for number words that cannot be defined in terms of core, nonverbal number systems. More broadly, these results document an interaction between attentional and general cognitive mechanisms in cognitive development.Research Highlights
Conceptual development in numeracy is associated with a shift in attention from objects to sets.
Children acquire meanings of the first few number words through associations with parallel attentional individuation of objects.
Understanding of cardinality is associated with attentional processing of sets rather than individuals.
Brain signatures suggest children attribute exact rather than approximate numerical meanings to the first few number words.
Number‐quantity relationship processing for the first few number words is evident in frontal but not parietal scalp electrophysiology of young children.

AbstractA wealth of studies have investigated numerical abilities in infants and in children aged 3 or above, but research on pre‐counting toddlers is sparse. Here we devised a novel version of an imitation task that was previously used to assess spontaneous focusing on numerosity (i.e. the predisposition to grasp numerical properties of the environment) to assess whether pre‐counters would spontaneously deploy sequential (item‐by‐item) enumeration and whether this ability would rely on the object tracking system (OTS) or on the approximate number system (ANS). Two‐and‐a‐half‐year‐olds watched the experimenter performing one‐by‐one insertion of 'food tokens' into an opaque animal puppet and then were asked to imitate the puppet‐feeding behavior. The number of tokens varied between 1 and 6 and each numerosity was presented many times to obtain a distribution of responses during imitation. Many children demonstrated attention to the numerosity of the food tokens despite the lack of any explicit cueing to the number dimension. Most notably, the response distributions centered on the target numerosities and showed the classic variability signature that is attributed to the ANS. These results are consistent with previous studies on sequential enumeration in non‐human primates and suggest that pre‐counting children are capable of sequentially updating the numerosity of non‐visible sets through additive operations and hold it in memory for reproducing the observed behavior.

AbstractTwo non‐verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here we used an individual differences approach to test for a relationship between the spontaneously evoked brain signatures (using event‐related potentials) of PI and the ANS and initial development of symbolic number concepts in preschool children as displayed by counting. We observed that individual differences in the neural signatures of the PI system, but not the ANS, explained a unique portion of variance in counting proficiency after extensively controlling for general cognitive factors. These results suggest that differences in early attentional processing of objects between children are related to higher‐level symbolic number concept development.