Emergent Morphology in Child Homesign: Evidence from Number Language.

Human languages, signed and spoken, can be characterized by the structural patterns they use to associate communicative forms with meanings. One such pattern is paradigmatic morphology, where complex words are built from the systematic use and re-use of sub-lexical units. Here, we provide evidence of emergent paradigmatic morphology akin to number inflection in a communication system developed without input from a conventional language, homesign. We study the communication systems of four deaf child homesigners (mean age 8;02). Although these idiosyncratic systems vary from one another, we nevertheless find that all four children use handshape and movement devices productively to express cardinal and non-cardinal number information, and that their number expressions are consistent in both form and meaning. Our study shows, for the first time, that all four homesigners not only incorporate number devices into representational devices used as predicates , but also into gestures functioning as nominals, including deictic gestures. In other words, the homesigners express number by systematically combining and re-combining additive markers for number (qua inflectional morphemes) with representational and deictic gestures (qua bases). The creation of new, complex forms with predictable meanings across gesture types and linguistic functions constitutes evidence for an inflectional morphological paradigm in homesign and expands our understanding of the structural patterns of language that are, and are not, dependent on linguistic input.

Number gestures predict learning of number words.

When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture-speech "mismatches" on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture-speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word "three" and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number-word instruction. We used the Give-a-Number task to measure number knowledge in 47 children (Mage  = 4.1 years, SD = 0.58), and used the What's on this Card task to assess whether children produced gesture-speech mismatches above their knower level. Children who were early in their number learning trajectories ("one-knowers" and "two-knowers") were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture-speech mismatches at pretest. The findings suggest that numerical gesture-speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number-learning.

Meaning before order: Cardinal principle knowledge predicts improvement in understanding the successor principle and exact ordering.

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.

Gesture as a window onto children's number knowledge.

Before learning the cardinal principle (knowing that the last word reached when counting a set represents the size of the whole set), children do not use number words accurately to label most set sizes. However, it remains unclear whether this difficulty reflects a general inability to conceptualize and communicate about number, or a specific problem with number words. We hypothesized that children's gestures might reflect knowledge of number concepts that they cannot yet express in speech, particularly for numbers they do not use accurately in speech (numbers above their knower-level). Number gestures are iconic in the sense that they are item-based (i.e., each finger maps onto one item in a set) and therefore may be easier to map onto sets of objects than number words, whose forms do not map transparently onto the number of items in a set and, in this sense, are arbitrary. In addition, learners in transition with respect to a concept often produce gestures that convey different information than the accompanying speech. We examined the number words and gestures 3- to 5-year-olds used to label small set sizes exactly (1-4) and larger set sizes approximately (5-10). Children who had not yet learned the cardinal principle were more than twice as accurate when labeling sets of 2 and 3 items with gestures than with words, particularly if the values were above their knower-level. They were also better at approximating set sizes 5-10 with gestures than with words. Further, gesture was more accurate when it differed from the accompanying speech (i.e., a gesture-speech mismatch). These results show that children convey numerical information in gesture that they cannot yet convey in speech, and raise the possibility that number gestures play a functional role in children's development of number concepts.

Approximate number word knowledge before the cardinal principle.

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge.

Generating a lexicon without a language model: Do words for number count?

Homesigns are communication systems created by deaf individuals without access to conventional linguistic input. To investigate how homesign gestures for number function in short-term memory compared to homesign gestures for objects, actions, or attributes, we conducted memory span tasks with adult homesigners in Nicaragua, and with comparison groups of unschooled hearing Spanish speakers and deaf Nicaraguan Sign Language signers. There was no difference between groups in recall of gestures or words for objects, actions or attributes; homesign gestures therefore can function as word units in short-term memory. However, homesigners showed poorer recall of numbers than the other groups. Unlike the other groups, increasing the numerical value of the to-be-remembered quantities negatively affected recall in homesigners, but not controls. When developed without linguistic input, gestures for number do not seem to function as summaries of the cardinal values of the sets (four), but rather as indexes of items within a set (one-one-one-one).

Communicating about quantity without a language model: number devices in homesign grammar.

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.

Number without a language model.

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.

Will any doll do? 12-month-olds' reasoning about goal objects.

Infants as young as 5 months of age view familiar actions such as reaching as goal-directed (Woodward, 1998), but how do they construe the goal of an actor's reach? Six experiments investigated whether 12-month-old infants represent reaching actions as directed to a particular individual object, to a narrowly defined object category (e.g., an orange dump truck), or to a more broadly defined object category (e.g., any truck, vehicle, artifact, or inanimate object). The experiments provide evidence that infants are predisposed to represent reaching actions as directed to categories of objects at least as broad as the basic level, both when the objects represent artifacts (trucks) and when they represent people (dolls). Infants do not use either narrower category information or spatiotemporal information to specify goal objects. Because spatiotemporal information is central to infants' representations of inanimate object motions and interactions, the findings are discussed in relation to the development of object knowledge and action representations.