An association between understanding cardinality and analog magnitude representations in preschoolers

Relationships between approximate number system acuity and early symbolic number abilities

“…Of the 79 children tested, 5 were pre-knowers, 12 had a highest response of ''one'', 19 had a highest response of ''two'', 5 reached ''three'', 12 reached ''four'', 12 reached ''five'', and 14 reached ''seven'' (see Table 3). Note that, although earlier studies considered that children who succeed with four items have grasped the counting principle of cardinality (e.g., [21]), some of our participants were able to produce correct responses for four items but not for five, and some others succeeded for five items but not seven (for similar results, see [49]). …”

“…This means that, when accuracy is below chance level for a specific ratio, no better performance is expected for smaller ratios. Therefore, our participants first performed trials corresponding to three large ratios (1:2, 2:3, 3:4), exactly as in previous studies on young children [40,49]. Then, they were presented with the next finer ratios (4:5, 5:6, 6:7, 7:8), one per block according to the span procedure, until accuracy fell below 75% (6 out of 8 correct responses) within a block.…”

“…However, several other studies found a link between performance in comparing numerosities and cardinality proficiency. Preschool children aged 2-5 who possessed some understanding of the cardinality principle showed higher precision in discriminating two sets of visual objects varying along different ratios than children who had no or only little cardinality knowledge [3,40,49]. Beyond numerosity comparison, the counting level may also influence verbal estimation of large numerosities in older children.…”

Conceptual correlates of counting: Children’s spontaneous matching and tracking of large sets reflects their knowledge of the cardinal principle

“…One explanation is that CP-knowers have better numerical acuity (e.g., Chu & Geary, 2015;Shusterman et al, 2016;Wagner & Johnson, 2011), which may help them more accurately encode and reason about the larger set sizes in the non-verbal tasks. This explanation accords with the data in some ways.…”

“…Most of the studies in this area do not focus on how counting ability and the acquisition of the cardinal principle relates to the development of nonverbal numerical representations. Several recent studies explicitly test for and find a relationship between cardinality and ANS acuity (Chu & Geary, 2015;Shusterman, Slusser, Halberda, & Odic, 2016;Wagner & Johnson, 2011), indicating a qualitative change in magnitude representations when children acquire cardinality. These studies used a dot comparison task in which participants were shown two sets of dots and asked to select the more numerous set (e.g., "Point to the side with more dots").…”