Finding one's meaning: a test of the relation between quantifiers and integers in language development

We explored children’s early interpretation of numerals and linguistic number marking, in order to test the hypothesis (e.g., Carey (2004). Bootstrapping and the origin of concepts. Daedalus, 59-68) that children’s initial distinction between one and other numerals (i.e., two, three, etc.) is bootstrapped from a prior distinction between singular and plural nouns. Previous studies have presented evidence that in languages without singular-plural morphology, like Japanese and Chinese, children acquire the meaning of the word one later than in singular-plural languages like English and Russian. In two experiments, we sought to corroborate this relation between grammatical number and integer acquisition within English. We found a significant correlation between children’s comprehension of numerals and a large set of natural language quantifiers and determiners, even when controlling for effects due to age. However, we also found that 2-year-old children, who are just acquiring singular-plural morphology and the word one, fail to assign an exact interpretation to singular noun phrases (e.g., a banana), despite interpreting one as exact. For example, in a Truth-Value Judgment task, most children judged that a banana was consistent with a set of two objects, despite rejecting sets of two for the numeral one. Also, children who gave exactly one object for singular nouns did not have a better comprehension of numerals relative to children who did not give exactly one. Thus, we conclude that the correlation between quantifier comprehension and numeral comprehension in children of this age is not attributable to the singular-plural distinction facilitating the acquisition of the word one. We argue that quantifiers play a more general role in highlighting the semantic function of numerals, and that children distinguish between numerals and other quantifiers from the beginning, assigning exact interpretations only to numerals.     

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.     

How to learn the natural numbers: inductive inference and the acquisition of number concepts

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51-B60.] argue that such an inductive inference is consistent with a representational system that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles.     

Find the picture of eight turtles: a link between children's counting and their knowledge of number word semantics

An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity—with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting.     

Grammatical language impairment and the specificity of cognitive domains: relations between auditory and language abilities

Grammatical-specific language impairment (G-SLI) in children, arguably, provides evidence for the existence of a specialised grammatical sub-system in the brain, necessary for normal language development. Some researchers challenge this, claiming that domain-general, low-level auditory deficits, particular to rapid processing, cause phonological deficits and thereby SLI. We investigate this possibility by testing the auditory discrimination abilities of G-SLI children for speech and non-speech sounds, at varying presentation rates, and controlling for the effects of age and language on performance. For non-speech formant transitions, 69% of the G-SLI children showed normal auditory processing, whereas for the same acoustic information in speech, only 31% did so. For rapidly presented tones, 46% of the G-SLI children performed normally. Auditory performance with speech and non-speech sounds differentiated the G-SLI children from their age-matched controls, whereas speed of processing did not. The G-SLI children evinced no relationship between their auditory and phonological/grammatical abilities. We found no consistent evidence that a deficit in processing rapid acoustic information causes or maintains G-SLI. The findings, from at least those G-SLI children who do not exhibit any auditory deficits, provide further evidence supporting the existence of a primary domain-specific deficit underlying G-SLI.     

Why is number word learning hard? Evidence from bilingual learners

Young children typically take between 18 months and 2 years to learn the meanings of number words. In the present study, we investigated this developmental trajectory in bilingual preschoolers to examine the relative contributions of two factors in number word learning: (1) the construction of numerical concepts, and (2) the mapping of language specific words onto these concepts. We found that children learn the meanings of small number words (i.e., one, two, and three) independently in each language, indicating that observed delays in learning these words are attributable to difficulties in mapping words to concepts. In contrast, children generally learned to accurately count larger sets (i.e., five or greater) simultaneously in their two languages, suggesting that the difficulty in learning to count is not tied to a specific language. We also replicated previous studies that found that children learn the counting procedure before they learn its logic – i.e., that for any natural number, n, the successor of n in the count list denotes the cardinality n + 1. Consistent with past studies, we found that children’s knowledge of successors is first acquired incrementally. In bilinguals, we found that this knowledge exhibits item-specific transfer between languages, suggesting that the logic of the positive integers may not be stored in a language-specific format. We conclude that delays in learning the meanings of small number words are mainly due to language-specific processes of mapping words to concepts, whereas the logic and procedures of counting appear to be learned in a format that is independent of a particular language and thus transfers rapidly from one language to the other in development.     

Re-visiting the competence/performance debate in the acquisition of the counting principles

Advocates of the "continuity hypothesis" have argued that innate non-verbal counting principles guide the acquisition of the verbal count list (Gelman & Galistel, 1978). Some studies have supported this hypothesis, but others have suggested that the counting principles must be constructed anew by each child. Defenders of the continuity hypothesis have argued that the studies that failed to support it obscured children's understanding of counting by making excessive demands on their fragile counting skills. We evaluated this claim by testing two-, three-, and four-year-olds both on "easy" tasks that have supported continuity and "hard" tasks that have argued against it. A few noteworthy exceptions notwithstanding, children who failed to show that they understood counting on the hard tasks also failed on the easy tasks. Therefore, our results are consistent with a growing body of evidence that shows that the count list as a representation of the positive integers transcends pre-verbal representations of number.     

The semantics and acquisition of number words: integrating linguistic and developmental perspectives

This article brings together two independent lines of research on numerally quantified expressions, e.g. two girls. One stems from work in linguistic theory and asks what truth conditional contributions such expressions make to the utterances in which they are used--in other words, what do numerals mean? The other comes from the study of language development and asks when and how children learn the meaning of such expressions. My goal is to show that when integrated, these two perspectives can both constrain and enrich each other in ways hitherto not considered. Specifically, work in linguistic theory suggests that in addition to their 'exactly n' interpretation, numerally quantified NPs such as two hoops can also receive an 'at least n' and an 'at most n' interpretation, e.g. you need to put two hoops on the pole to win (i.e. at least two hoops) and you can miss two shots and still win (i.e. at most two shots). I demonstrate here through the results of three sets of experiments that by the age of 5 children have implicit knowledge of the fact that expressions like two N can be interpreted as 'at least two N' and 'at most two N' while they do not yet know the meaning of corresponding expressions such as at least/most two N which convey these senses explicitly. I show that these results have important implications for theories of the semantics of numerals and that they raise new questions for developmental accounts of the number vocabulary.     

The role of prior experience in language acquisition

Learners exposed to an artificial language recognize its abstract structural regularities when instantiated in a novel vocabulary (e.g., Gómez, Gerken, & Schvaneveldt, 2000; Tunney & Altmann, 2001). We asked whether such sensitivity accelerates subsequent learning, and enables acquisition of more complex structure. In Experiment 1, pre-exposure to a category-induction language of the form aX bY sped subsequent learning when the language is instantiated in a different vocabulary. In Experiment 2, while naíve learners did not acquire an acX bcY language, in which aX and bY co-occurrence regularities were separated by a c-element, prior experience with an aX bY language provided some benefit. In Experiment 3 we replicated this finding with a 24-hour delay between learning phases, and controlled for prior experience with the aX bY language's prosodic and phonological characteristics. These findings suggest that learners, and the structure they can acquire, change as a function of experience.     

The phonological-distributional coherence hypothesis: cross-linguistic evidence in language acquisition

Several phonological and prosodic properties of words have been shown to relate to differences between grammatical categories. Distributional information about grammatical categories is also a rich source in the child's language environment. In this paper we hypothesise that such cues operate in tandem for developing the child's knowledge about grammatical categories. We term this the Phonological-Distributional Coherence Hypothesis (PDCH). We tested the PDCH by analysing phonological and distributional information in distinguishing open from closed class words and nouns from verbs in four languages: English, Dutch, French, and Japanese. We found an interaction between phonological and distributional cues for all four languages indicating that when distributional cues were less reliable, phonological cues were stronger. This provides converging evidence that language is structured such that language learning benefits from the integration of information about category from contextual and sound-based sources, and that the child's language environment is less impoverished than we might suspect.     

The relation between language and cognition in 3- to 9-year-olds: the acquisition of grammatical gender in French

The French language has a grammatical gender system in which all nouns are assigned either a masculine or a feminine gender. Nouns provide two types of gender cues that can potentially guide gender attribution: morphophonological cues carried by endings and semantic cues (natural gender). The first goal of this study was to describe the acquisition of the probabilistic system based on phonological oppositions on word endings by French-speaking children. The second goal was to explore the extent to which this system affects categorization. In the study, 3- to 9-year-olds assigned gender categorization to invented nouns whose endings were typically masculine, typically feminine, or neutral. Two response conditions were used. In the determiner condition, children indicated the gender class by orally providing the determiner un or une marked for gender. In the picture condition, responses were given by pointing to the picture of a Martian-like female or male person that would be best called by each spoken pseudoword. Results indicated that as young as 3 years, children associated the determiner corresponding to the ending bias at greater than chance levels. Ending-consistent performance increased from 3 to 9 years of age. Moreover, from 4 years of age onward, sensitivity to endings affected categorization. Starting at that age, pictures were selected according to endings at greater than chance levels. This effect also increased with age. The discussion deals with the mechanisms of language acquisition and the relation between language and cognition.     

Linguistic self-correction in the absence of feedback: a new approach to the logical problem of language acquisition

In a series of studies children show increasing mastery of irregular plural forms (such as mice) simply by producing erroneous over-regularized versions of them (such as mouses). We explain this phenomenon in terms of successive approximation in imitation: Children over-regularize early in acquisition because the representations of frequent, regular plural forms develop more quickly, such that at the earliest stages of production they interfere with children's attempts to imitatively reproduce irregular forms they have heard in the input. As the strength of the representations that determine children's productions settle asymptotically, the early advantage for the frequent regular forms is negated, and children's attempts to imitate the irregular forms they have observed become more likely to succeed (a process that produces the classic U-shape in children's acquisition of plural inflection). These data show that children can acquire correct linguistic behavior without feedback in a situation where, as a result of philosophical and linguistic analyses, it has often been argued that it is logically impossible for them to do so.     

Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

Previous studies showed that children learning a language with an obligatory singular/plural distinction (Russian and English) learn the meaning of the number word for one earlier than children learning Japanese, a language without obligatory number morphology (Barner, Libenson, Cheung, & Takasaki, 2009; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007). This can be explained by differences in number morphology, but it can also be explained by many other differences between the languages and the environments of the children who were compared. The present study tests the hypothesis that the morphological singular/plural distinction supports the early acquisition of the meaning of the number word for one by comparing young English learners to age and SES matched young Mandarin Chinese learners. Mandarin does not have obligatory number morphology but is more similar to English than Japanese in many crucial respects. Corpus analyses show that, compared to English learners, Mandarin learners hear number words more frequently, are more likely to hear number words followed by a noun, and are more likely to hear number words in contexts where they denote a cardinal value. Two tasks show that, despite these advantages, Mandarin learners learn the meaning of the number word for one three to six months later than do English learners. These results provide the strongest evidence to date that prior knowledge of the numerical meaning of the distinction between singular and plural supports the acquisition of the meaning of the number word for one.     

Tracking irregular morphophonological dependencies in natural language: evidence from the acquisition of subject-verb agreement in French

This study examines French-learning infants’ sensitivity to grammatical non-adjacent dependencies involving subject-verb agreement (e.g., le/les garçons lit/lisent ‘the boy(s) read(s)’) where number is audible on both the determiner of the subject DP and the agreeing verb, and the dependency is spanning across two syntactic phrases. A further particularity of this subsystem of French subject-verb agreement is that number marking on the verb is phonologically highly irregular. Despite the challenge, the HPP results for 24- and 18-month-olds demonstrate knowledge of both number dependencies: between the singular determiner le and the non-adjacent singular verbal forms and between the plural determiner les and the non-adjacent plural verbal forms. A control experiment suggests that the infants are responding to known verb forms, not phonological regularities. Given the paucity of such forms in the adult input documented through a corpus study, these results are interpreted as evidence that 18-month-olds have the ability to extract complex patterns across a range of morphophonologically inconsistent and infrequent items in natural language.     

Cumulative and non-cumulative semantic interference in object naming: Evidence from blocked and continuous manipulations of semantic context

Experiments involving blocked and continuous manipulations of the semantic naming context demonstrate that, when speakers name several taxonomically related objects in close succession, they display persistent interference effects. A review of studies using the blocked paradigm shows that, unlike the continuous paradigm, it typically does not induce cumulative interference effects in healthy speakers. This contrasts with the simulation results obtained from a model of semantic context effects recently put forward by Oppenheim and colleagues [Oppenheim, G. M., Dell, G. S., & Schwartz, M. F. (2010). The dark side of incremental learning: A model of cumulative semantic interference during lexical access in speech production. Cognition, 114, 227--262], which generates cumulative effects in both paradigms. We propose that the effects are non-cumulative in the blocked paradigm, because it allows participants to bias top-down the levels of activation of lexical-semantic representations, thereby curtailing the accumulating interference. Indeed, prior research has shown that the interference effects in the blocked paradigm are exacerbated when participants carry out a concurrent digit-retention task, loading on working memory and reducing their capacity to exert a top-down bias. In Experiment 1, combining the continuous paradigm with a digit-retention task, we demonstrate that this does not exacerbate cumulative context effects, corroborating the selective role of working memory and the associated top-down biasing mechanism in the blocked paradigm. A review of neuropsychological and neuroimaging studies demonstrates that left inferior frontal regions may play a critical role in controlling semantic interference top-down. We discuss the implications of these findings for language production research and for models of lexical-semantic encoding.     

The role of language in mathematical development: evidence from children with specific language impairments

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.     

Semantic access in number processing investigated with Japanese Kanji and Kana numerals

In number processing, semantic representations are efficiently activated. These representations frequently affect task performance, as demonstrated by semantic effects such as the distance effect (longer reaction times to closer numerical pairs in comparison tasks). The objective of this study was to investigate whether efficient semantic access is a distinctive feature of number processing using the Japanese language. Japanese was chosen to investigate possible effects of ideographic processing and word frequency: Kanji numerals in Japanese are ideograms and are used frequently, while Kana numerals are phonograms and are used infrequently. The results confirmed a distance effect in the numerical and physical matching tasks with both Arabic and Kanji numerals regardless of notation or task (Experiment 1). However, the effect was not observed with the Kana pairs (Experiment 2), thereby suggesting that semantic access is not always efficient in number processing. The results can be explained coherently within a general framework of word recognition by assuming that both the type of character and the word frequency play a critical role in determining the efficiency of semantic access.