What cognitive system(s) initially provide the numerical content that defines the cardinal number words for young children? Le Corre and Carey (2007) argued that the answer cannot be the analogue magnitude system. Here we reexamine the most powerful of their arguments, which concerned the system’s signature scalar variability (the standard deviation of answers grows linearly with the mean). Using adult data, we explore a nuance of this signature: that while it is certainly true of the continuous, underlying activation in the brain, it may not always be true of the number-word responses that people produce. With this in mind, we re-examine the aforementioned variability argument; contrary to Le Corre and Carey, we conclude that young children’s estimates of small set sizes (up to and including their number-knower-level) do show scalar variability. 

Although everyone perceives approximate numerosities, some people make more accurate estimates than others. The accuracy of this estimation is called approximate number system (ANS) acuity. Recently, several studies have reported that individual differences in young children's ANS acuity are correlated with their knowledge of exact numbers such as the word 'six' (Mussolin et al., 2012, Trends Neurosci. Educ., 1, 21; Shusterman et al., 2011, Connecting early number word knowledge and approximate number system acuity; Wagner & Johnson, 2011, Cognition, 119, 10; see also Abreu-Mendoza et al., 2013, Front. Psychol., 4, 1). This study argues that this correlation should not be trusted. It seems to be an artefact of the procedure used to assess ANS acuity in children. The correlation arises because (1) some experimental designs inadvertently allow children to answer correctly based on the size (rather than the number) of dots in the display and/or (2) young children with little exact-number knowledge may not understand the phrase 'more dots' to mean numerically more. When the task is modified to make sure that children respond on the basis of numerosity, the correlation between ANS acuity and exact-number knowledge in normally developing children disappears.

Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g. Bialystok, 2001; Hilchey & Klein, 2011). Other studies have looked for such an advantage but found none (e.g. Morton & Harper, 2007; Paap & Greenberg, 2013). The present study compared monolingual and bilingual children’s performance on a numerical discrimination task, which required children to ignore area and attend to number. Ninety-two children, ages 3 to 6 years, were asked which of two arrays of dots had ‘more dots’. Half of the trials were congruent, where the numerically greater array was also larger in total area, and half were incongruent, where the numerically greater array was smaller in total area. All children performed better on congruent than on incongruent trials. Older children were more successful than younger children at ignoring area in favor of number. Bilingual children did not perform differently from monolingual children either in number discrimination itself (i.e. identifying which array had more dots) or at selectively attending to number. The present study thus finds no evidence of a bilingual advantage on this task for children of this age.