Young children's understanding of “more” and discrimination of number and surface area.

Abstract

The psychology supporting the use of quantifier words (e.g., “some,” “most,” “more”) is of interest to both scientists studying quantity representation (e.g., number, area) and to scientists and linguists studying the syntax and semantics of these terms. Understanding quantifiers requires both a mastery of the linguistic representations and a connection with cognitive representations of quantity. Some words (e.g., “many”) refer to only a single dimension, whereas others, like the comparative “more,” refer to comparison by numeric (“more dots”) or nonnumeric dimensions (“more goo”). In the present work, we ask 2 questions. First, when do children begin to understand the word “more” as used to compare nonnumeric substances and collections of discrete objects? Second, what is the underlying psychophysical character of the cognitive representations children utilize to verify such sentences? We find that children can understand and verify sentences including “more goo” and “more dots” at around 3.3 years—younger than some previous studies have suggested—and that children employ the Approximate Number System and an Approximate Area System in verification. These systems share a common underlying format (i.e., Gaussian representations with scalar variability). The similarity in the age of onset we find for understanding “more” in number and area contexts, along with the similar psychophysical character we demonstrate for these underlying cognitive representations, suggests that children may learn “more” as a domain-neutral comparative term.

Children’s mappings between number words and the approximate number system

“…Across multiple literatures, there is evidence for many other contents that rely on continuous representations similar to the ANS; these include representations of approximate area (Brannon, Lutz, & Cordes, 2006;Odic, Libertus, et al, 2013;Odic, Pietroski, Hunter, Lidz, & Halberda, 2013), length (Droit-Volet et al, 2008), time (Droit-Volet et al, 2008;Meck & Church, 1983;Walsh, 2003), speed (Möhring, Libertus, & Bertin, 2012), and many more (Cantlon et al, 2009;Dehaene & Brannon, 2011;Feigenson, 2007). Each of these is available prelinguistically and humans in many cultures eventually master an ability to map from these representations into discrete values and vice versa (e.g., ''the speed limit is 130 km/h'', ''these crayons are various shades of red'').…”

Processing of Numerical and Proportional Quantifiers

“…The patient showed preserved understanding of quantifiers (many, a few) but severe impairments in understanding non-quantifier words of similar frequency, signifying that quantifier terms might originate in the numerical system rather than in the language system. Alternatively, quantifier comprehension is studied in terms of cardinality comparison, governed by the ANS (Halberda et al, 2008a;Heim et al, 2012;Lidz et al, 2011;Odic et al, 2013;Pietroski et al, 2009). In two behavioral studies, researchers asked adults to evaluate visual displays containing yellow and blue circles flashed for 200 ms with respect to the question "Are most of the circles yellow?".…”

“…The mapping of quantifiers onto numerical scales has been proposed in logic, formal semantics, syllogistic reasoning as well as linguistic comprehension and processing (Bass, Cascio, & O'Connor, 1974;Clark, 1969;Geurts, 2003;Holyoak & Glass, 1978;Sanford, Moxey, & Paterson, 1994). 1 However, the direct link between magnitude knowledge and quantifier comprehension was established in cognitive neuroscience more recently (Halberda, Taing, & Lidz, 2008a;Heim et al, 2012;Lidz, Pietroski, Halberda, & Hunter, 2011;McMillan, Clark, Moore, Devita, & Grossman, 2005;McMillan, Clark, Moore, & Grossman, 2006;Odic, Pietroski, Hunter, Lidz, & Halberda, 2013;Pietroski, Lidz, Hunter, & Halberda, 2009;Szymanik & Zajenkowski, 2010;Troiani et al, 2009;Zajenkowski, Styla, & Szymanik, 2011;Zajenkowski, Szymanik, & Garraffa, 2014). Moreover, the exact role of numerical processing in interpreting quantifiers, namely, in estimation and comparison, is gradually emerging (Halberda et al, 2008a;Heim et al, 2012;Lidz et al, 2011;Odic et al, 2013;Pietroski et al, 2009;Zajenkowski et al, 2014).…”

The effect of stimulus variability on children's judgements of quantity

“…Lourenco and Longo (2010) provided direct evidence for the presence of shared representations for space, number, and time in preverbal infants, who were able to transfer associative learning across magnitude dimensions. More recently, 3-year-olds have been shown to learn the meaning of the word ''more'' in context of both approximating number and approximating area, suggesting an underlying similarity between these 2 dimensions (Odic, Pietroski, Hunter, Lidz, & Halberda, 2013). In a related study, Odic, Libertus, Feigenson, and Halberda (2012) tested forty 3-to 6-year-old children and adults in both a number and an area discrimination task in which participants selected the greater of 2 quantities across a range of ratios.…”