Six does not just mean a lot: preschoolers see number words as specific

Abstract

This paper examines what children believe about unmapped number words - those number words whose exact meanings children have not yet learned. In Study 1, 31 children (ages 2-10 to 4-2) judged that the application of five and six changes when numerosity changes, although they did not know that equal sets must have the same number word. In Study 2, 15 children (ages 2-5 to 3-6) judged that six plus more is no longer six, but that a lot plus more is still a lot. Findings support the hypothesis that children treat number words as referring to specific, unique numerosities even before they know exactly which numerosity each word refers to.

Inference and exact numerical representation in early language development

“…This suggests that children make inferences about unknown numeral meanings based on known meanings. Relevant to our later discussion, Condry and Spelke also provide evidence that although children think unknown numerals contrast in meaning (with known numerals and with each other), they do not think that these meanings are exact (see Sarnecka & Gelman, 2004, for evidence that children assume that unknown numbers contrast in meaning). Specifically, children in their study failed to recognize that a given numeral -e.g., eight -no longer applies to a set if an object is removed, or if the set is either doubled or halved (though see Sarnecka & Gelman, 2003, for conflicting results).…”

Bootstrapping in a language of thought: A formal model of numerical concept learning

“…They did not show this patten for nonsense word such as "Can you show me blicket balloons?" Similarly, children map number words to specific cardinalities, even if they do not know which cardinalities (Sarnecka & Gelman, 2004;Lipton & Spelke, 2006). Bloom and Wynn (1997) suggest that perhaps this can be accounted for by a learning mechanism that uses syntactic cues to determine that number words are a class with a certain semantics.…”

Learning to represent exact numbers

“…Of course, different children reach this milestone at different times, but in a sample of cardinal principle sometime between 34 and 51 months old. That is, any time from a couple of months before their third birthday to a couple of months after their fourth birthday (Negen & Sarnecka, 2012;Sarnecka & Carey, 2008;Sarnecka & Gelman, 2004;Sarnecka et al, 2007;Sarnecka & Lee, 2009;Slusser et al, 2013;Slusser & Sarnecka, 2011). Children from lowerincome backgrounds come to understand cardinality significantly later, at age 4 or older (Fluck & Henderson, 1996;Jordan & Levine, 2009).…”

“…Studies using the Give-N task have shown that children's performance moves through a predictable series of levels, called number-knower levels (e.g., Condry & Spelke, 2008;Le Corre & Carey, 2007;Le Corre et al, 2006;Negen & Sarnecka, 2012;Sarnecka & Gelman, 2004;Sarnecka & Lee, 2009Slusser, Ditta, & Sarnecka, 2013;Slusser & Sarnecka, 2011;Wynn, 1990Wynn, , 1992b. These number-knower levels are found in children acquiring number systems not only in English, but also in Arabic, Japanese, Mandarin Chinese, Russian, Slovenian, and even among the Tsimane', a farming and foraging society in rural Bolivia (Almoammer et al, 2013;Barner, Libenson, Cheung, & Takasaki, 2009;Li, Le Corre, Shui, Jia, & Carey, 2003;Piantadosi, Jara-Ettinger, & Gibson, 2014;Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007).…”

“…To find out when (i.e., at what number-knower level) children understand this, Susan Gelman and I tested 54 children on a task called the Transform-Sets task (Sarnecka & Gelman, 2004). In this task, children were shown a set of five or six objects labeled with a number word (e.g.…”