Numerosity and number signs in deaf Nicaraguan adults

Abstract

What abilities are entailed in being numerate? Certainly, one is the ability to hold the exact quantity of a set in mind, even as it changes, and even after its members can no longer be perceived. Is counting language necessary to track and reproduce exact quantities? Previous work with speakers of languages that lack number words involved participants only from non-numerate cultures. Deaf Nicaraguan adults all live in a richly numerate culture, but vary in counting ability, allowing us to experimentally differentiate the contribution of these two factors. Thirty deaf and 10 hearing participants performed 11 one-to-one matching and counting tasks. Results suggest that immersion in a numerate culture is not enough to make one fully numerate. A memorized sequence of number symbols is required, though even an unconventional, iconic system is sufficient. Additionally, we find that within a numerate culture, the ability to track precise quantities can be acquired in adulthood.

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

“…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. On small-number trials with set sizes of one, two, and three, SS-knowers performed no differently from CP-knowers, consistent with evidence for a primitive, language-independent cognitive system for representing small exact quantities (Agrillo, Piffer, Bisazza, & Butterworth, 2012;Feigenson, Carey, & Hauser, 2002;Starr, Libertus, & Brannon, 2013).…”

“…We provide developmental evidence for the cross-cultural finding that knowledge of a meaningful count list is related to more precise non-verbal representation of large numbers (Flaherty & Senghas, 2011;Frank et al, 2008;Gordon, 2004;Spaepen et al, 2011).…”

“…This pattern of results has also been found in another population. Flaherty and Senghas (2011) showed that older deaf signers in Nicaragua who lacked a stable count list also faced difficulties re-creating exact set sizes larger than six, but they were capable of re-creating small sets. Collectively, these studies show that speakers of languages that do not have a verbal count list have difficulty representing and tracking large but not small quantities, suggesting that the acquisition of verbal number is central to solving nonverbal numerical problems that require the representation of large exact quantities.…”

Sounding the depths at the confluence of numerosity and language

“…Such results suggest quite strongly that the mere differentiation of exact quantities greater than three (and an understanding of the successor principle), in addition to the manipulation and storage of such quantities (Frank et al 2008), relies on the conceptual tool of numeric language. As noted in C. Everett (2013aEverett ( , 2013c, these results are broadly consistent with results obtained among Nicaraguan home signers that do not have exact terms for cardinal sets either (Spaepen et al 2011;Flaherty and Senghas 2011), and are also consistent with subtraction-based tasks carried out amongst the Mundurukú (Pica et al 2004). Figure 2 depicts a trial of the basic one-to-one recognition task, in which Pirahã were tasked with recognizing mere correspondences between quantities by matching a stimuli array with their own array.…”

Toward exact number: Young children use one-to-one correspondence to measure set identity but not numerical equality

“…In Piaget’s experiments, moreover, children use one-to-one correspondence to construct sets of the same number (Gréco & Morf, 1962; Piaget, 1965). Finally, set-reproduction tasks have been used to assess knowledge of exact quantities in populations of children and adults without access to exact numerical symbols (Butterworth, Reeve, Reynolds, & Lloyd, 2008; Everett & Madora, 2012; Flaherty & Senghas, 2011; Frank et al, 2008; Gordon, 2004; Spaepen, Coppola, Spelke, Carey, & Goldin-Meadow, 2011). …”