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As adult humans, we can reason about quantity in at least two distinct ways: the first, through our intuitive but imprecise perception of quantity (e.g., when quickly deciding which route home is faster) and, the second, through slowly learned precise number representations (e.g., when counting how many items are in our shopping basket or using a ruler to measure exact length). By age 5, children form an interface between these two systems, allowing them to quickly translate their intuitive perceptual representations to number words and vice-versa (Le Corre & Carey, 2007; Odic, Le Corre, & Halberda, 2015). For example, when shown a display of dots (too quickly to count) children older than 5 can nevertheless convert their perceptual representation of number into an exact number word.
Here, we explore how the interface between language and intuitive quantity representations is acquired for perceptual domains beyond number: length and area. Children (N = 90) between the ages of 5 and 12 completed two tasks. In the discrimination task (Figure 1), they were shown displays of blue and yellow stimuli and asked to determine which side was more numerous in number (i.e., judging whether there are more blue or yellow dots), length (i.e., judging which line is longer), and area (i.e., judging which blob is bigger). This task allowed us to measure individual and developmental differences in children’s perception of quantity. Subsequently, children completed an estimation task in which they had to judge how many items there were. Here, children were given novel units, each corresponding to a particular dimension (Figure 1; toma for number, blicket for length, and modi for area). We then displayed arrays of dots, a single line, or a single blob on the screen, and asked children to estimate how many of the particular unit could fit inside the shown stimulus (e.g., “How many blickets are there here?”). We indexed the quality of children’s estimation performance by computing linear slopes and variability of their estimates.
Consistent with previous work (Odic, 2018; Odic, Libertus, Feigenson, & Halberda, 2013), we found that individual and developmental differences in children’s number perception did not correlate with their perception of length or area. In contrast to this, however, we found that estimation performance was strongly correlated across the three domains: both linear slopes and variability for number estimates correlated with length estimates (rho-slopes = .26, p = .01; rho-variability = .32, p = .002), and area estimates (rho-slopes = .33, p = .001; rho-variability = .35, p < .001), which in turn correlated with each other (rho-slopes = .46, p < .001; rho-variability = .49, p < .001). A principal component analysis also revealed that estimation performance constituted a single factor. Taken together, these results suggest that while the perceptual representations of number, length, and area are distinct, the interface that children form between language and these representations is not. We discuss these results in the broader context of children’s developing sense of quantity and the relationship between language and thought.