Cross-cultural studies suggest that access to a conventional language containing words that can be used for counting is essential to develop representations of large exact numbers. However, cultures that lack a conventional counting system typically differ from cultures that have such systems, not only in language but also in many other ways. As a result, it is difficult to isolate the effects of language on the development of number representations. Here we examine the numerical abilities of individuals who lack conventional language for number (deaf individuals who do not have access to a usable model for language, spoken or signed) but who live in a numerate culture (Nicaragua) and thus have access to other aspects of culture that might foster the development of number. These deaf individuals develop their own gestures, called homesigns, to communicate. We show that homesigners use gestures to communicate about number. However, they do not consistently extend the correct number of fingers when communicating about sets greater than three, nor do they always correctly match the number of items in one set to a target set when that target set is greater than three. Thus, even when integrated into a numerate society, individuals who lack input from a conventional language do not spontaneously develop representations of large exact numerosities.numerical cognition | language and thought | deafness | gestural communication

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All natural languages have formal devices for communicating about number, be they lexical (e.g., two, many) or grammatical (e.g., plural markings on nouns and/or verbs). Here we ask whether linguistic devices for number arise in communication systems that have not been handed down from generation to generation. We examined deaf individuals who had not been exposed to a usable model of conventional language (signed or spoken), but had nevertheless developed their own gestures, called homesigns, to communicate. Study 1 examined four adult homesigners and a hearing communication partner for each homesigner. The adult homesigners produced two main types of number gestures: gestures that enumerated sets (cardinal number marking), and gestures that signaled one vs. more than one (non-cardinal number marking). Both types of gestures resembled, in form and function, number signs in established sign languages and, as such, were fully integrated into each homesigner's gesture system and, in this sense, linguistic. The number gestures produced by the homesigners’ hearing communication partners displayed some, but not all, of the homesigners’ linguistic patterns. To better understand the origins of the patterns displayed by the adult homesigners, Study 2 examined a child homesigner and his hearing mother, and found that the child's number gestures displayed all of the properties found in the adult homesigners’ gestures, but his mother's gestures did not. The findings suggest that number gestures and their linguistic use can appear relatively early in homesign development, and that hearing communication partners are not likely to be the source of homesigners’ linguistic expressions of non-cardinal number. Linguistic devices for number thus appear to be so fundamental to language that they can arise in the absence of conventional linguistic input.

Learning the cardinal principle (the last word reached when counting a set represents the size of the whole set) is a major milestone in early mathematics. But researchers disagree about the relationship between cardinal principle knowledge and other concepts, including how counting implements the successor function (for each number word N representing a cardinal value, the next word in the count list represents the cardinal value N + 1) and exact ordering (cardinal values can be ordered such that each is one more than the value before it and one less than the value after it). No studies have investigated acquisition of the successor principle and exact ordering over time, and in relation to cardinal principle knowledge. An open question thus remains: Is the cardinal principle a "gatekeeper" concept children must acquire before learning about succession and exact ordering, or can these concepts develop separately? Preschoolers (N = 127) who knew the cardinal principle (CP-knowers) or who knew the cardinal meanings of number words up to "three" or "four" (3-4-knowers) completed succession and exact ordering tasks at pretest and posttest. In between, children completed one of two trainings: counting only versus counting, cardinal labeling, and comparison. CP-knowers started out better than 3-4-knowers on succession and exact ordering. Controlling for this disparity, we found that CP-knowers improved over time on succession and exact ordering; 3-4-knowers did not. Improvement did not differ between the two training conditions. We conclude that children can learn the cardinal principle without understanding succession or exact ordering and hypothesize that children must understand the cardinal principle before learning these concepts.