Preschoolers' Magnitude Comparisons are Mediated by a Preverbal Analog Mechanism

Abstract

We report a study of 3- to 5-year-olds who performed a magnitude-comparison task. Stimuli were a series of pairs of arrays that sometimes differed in numerosity, and the children were asked to point to the more numerous array in each pair. The proportion of accurate responses was above chance for all age groups. However, error patterns were consistent with analog models of magnitude representation. Errors varied systematically with the ratio of stimulus pairs. Items with a 2:3 ratio were harder than items with a 1:2 ratio. Performance on posttests of verbal counting ability was variable, but did not predict performance on the numerical discrimination task. We argue that neither verbal counting nor nonnumerical perceptual strategies can explain these results. This study supports the hypothesis that adults and children share preverbal, analog representations of magnitude.

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

“…Elephant Game). The results provide strong support for the hypothesis that verbal counting and nonverbal quantitative reasoning are related in children, and help bring clarity to a conflicted body of findings about the relationship between these skills during development (e.g., Huntley-Fenner & Cannon, 2000;Mix, 1999aMix, , 1999bRousselle, Palmers, & Noël, 2004). Just like adults whose language lacks an integer list (Flaherty & Senghas, 2011;Frank et al, 2008;Spaepen, Coppola, Spelke, Carey, & Goldin-Meadow, 2011), children who do not yet understand cardinality exhibit relatively coarse representations of numerical quantity when the quantity to be represented is greater than four-beyond the limit of the parallel individuation system.…”

“…Importantly, many of the studies on number language and concepts do not provide convincing evidence regarding the relationship between acquiring the cardinal principle and representing large sets in typical development, because the methods used do not evaluate both of these abilities simultaneously (Brannon & Van de Walle, 2001;Huntley-Fenner & Cannon, 2000;Mix, 1999aMix, , 1999bMix, , 2008aMix, , 2008bMix, Huttenlocher, & Levine, 1996;Negen & Sarnecka, 2010). To test the hypothesis that acquiring a count list allows us to represent and track large exact quantities, two criteria need to be met: First, it is necessary to compare preschoolers who have not yet acquired the cardinal principle (i.e., SS-knowers) to those who have (i.e., CP-knowers).…”

The construction of large number representations in adults

“…A preverbal counting system could not have produced the patterns of RT we observed in Experiment 4; the fact that RT did not increase with set size shows that these sets were enumerated by a noniterative process. Recent studies suggest that when young children estimate the numerosities of briefly presented groups of objects, they too produce patterns of performance consistent with the operation of non-iterative enumeration processes (Huntley-Fenner, 2001;Huntley-Fenner & Cannon, 2000).…”

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…As some researchers assume, this implies that infants can already differentiate between discrete quantities (see Antell & Keating, 1983;Bijeljac-Babic, Bertoncini, & Mehler, 1993;Huntley-Fenner & Cannon, 2000;Starkey & Cooper, 1980;Wynn, 1992; for large numerosities: Xu, Spelke, & Goddard, 2005). Others believe that infants only differentiate between the spatial extent of quantities but not between discrete amounts (see Clearfield & Mix, 1999Feigenson, Carey, & Spelke, 2002;Mix, Huttenlocher, & Levine, 1996Rousselle, Palmers, & Noël, 2004;Simon, Hespos, & Rochat, 1995; for small numerosities: Xu, Spelke, & Goddard, 2005).…”