First language acquisition of number words and its relation with the acquisition of indefinite articles and plural marking

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Research MA Linguistics

First language acquisition of number words

and its relation with the acquisition of

indefinite articles and plural marking

Student: Irene Mistro

Supervisors: dr. Petra Sleeman prof. dr. Aafke Hulk

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Abstract

The present study examined the acquisition and use of “one”, “two” and plural marking in L1 speakers of Italian, French, English and Dutch. I wanted to see if children use “one” before starting to use “two” and if there are crosslinguistic differences considering that in the Romance languages the indefinite article corresponds to the number “one”. With respect to the use of “two” it is said to be a lexical marker for plurality, is it actually the case or do children start using plural morphosyntax before the number word? Through the analysis of children speech retrieved from the CHILDES database I could observe that children use number words before acquiring their meaning but even in the use they start with “one” before “two” as numerals’ acquisition claims. Children also start using plural morphology before they start using “two” thus suggesting that plural marking might help in the acquisition of number words and not that number words, e.g. “two”, are lexical markers for plurality as postulated in previous studies.

Keywords: one, two, indefinite articles, plural marker, singular/plural distinction

1. Introduction and Hypotheses

When learning number words children have to learn that words refer to numerosities: to a quantity x that is expressed through a word. As argued by Spelke (2011) children have a core system of numbers, i.e. an innate understanding of numbers, what they have to achieve when learning a language is how to map the numerical concepts into number words. Among the number words “one” is the only word that refers to a single item and not to a plurality of items, in the same way “a”, as a determiner, refers to a single item. Both determiners and number words’ meanings are related to quantities and their syntactic characteristics are similar: number words can be used as determiners or as adjectives, both are considered by children as modifiers (Wynn, 1992). Around the age of 2 children start using determiners and seem to have a “strong representation of the “determiner” category” (Kemp et al., 2005) and studies on the topic have argued that the indefinite article is usually the most used determiner.

In the present study I am interested in the relation between the acquisition of determiners, more specifically the indefinite article, and cardinality and in the relation between plural morphosyntax and cardinality in children’s acquisition. My first two hypotheses aim at studying indefinite articles and cardinality: “one” and “a/an” both refer to single items. My assumption is that children would use “one” and “a/an” before using “two”, “three” and other number words. The reason behind this assumption is that children learn the meaning of number words gradually, usually building up from “one” to “two” and so on, developing a counting system (Wynn, 1992) or counting principle (Schaeffer et al, 1974). Moreover the fact that “one” has a special status among number words being the only one that refers to singularity, should be reflected also in the child’s learning process. Therefore my first hypothesis is that children would start using “one” and “a” before they start using “two” and/or other number words. The

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second hypothesis is that, from a crosslinguistic perspective, we can assume there will be differences in the learning of the number word “one” and the indefinite article “a/an” in English and Dutch with respect to French and Italian. The Germanic languages in the study have in fact a difference in the way they express the number word and the indefinite article while in the Romance languages investigated the word for “one”: “un/uno” carries both cardinality and indefiniteness “features”. Dryer (2005) classifies Dutch and English as languages that have an indefinite article distinct from “one” while French and Italian are classified as having the indefinite article to be the same as “one”. My second hypothesis is then thought as a crosslinguistic analysis of when “one” and “a” start to be used in comparison with the (other) number words. Assuming the first hypothesis to be true we would expect English and Dutch speaking children to start using “one” and “a/an” earlier than French and Italian speaking children since the first two languages are more transparent in their distinction between cardinality and indefiniteness. According to Coene (2006), who analysed the acquisition of indefinite articles in, a.o. French and Italian, the DP is learned gradually by children given its status of functional category. According to Coene’s (2006) analysis the functional structure of the NP has two features that need to be learned: number and person. While learning these features the child will start learning bare nouns, quantifiers and indefinite articles with a non-specific reading first. Indefinite articles with a non-specific reading follow and at last definite articles are learned. Coene’s analysis explains how children acquire indefinite articles and why indefinite articles are acquired before definite ones. More generally the idea is that NumberP is acquired before DP.

The second part of the study refers to the relation between number words and plural morphosyntax. As Wynn (1992) points out “the syntax of the number words tells children that they refer to properties of sets of entities, not of individual entities”. Moreover by the time children know the cardinal meaning of the word “two” they “have already determined” (Wynn, 1992), or they nevertheless should be able to start determining, that each of the number words refers to a specific quantity, a “unique numerosity” in Wynn’s words. Before children are actually able to determine the specific quantity of “two” or any other of the number words for that matters, it takes time. According to Sarnecka et al. (2007) children acquire the meaning of “two” as denoting specifically two elements by the age of 3, while it happens just a bit later than 3 according to Spelke (2011), but already around 24 months children can distinguish between “one” and “more than one” (Barner et al., 2007). This means that children start using number words before they attribute them their specific, quantity related meaning. My hypothesis (the third) is that children use number words, more specifically “two”, as suggested by Kilani-Schoch (1998) for French and Clark and Nikitina (2009) for English to help them express plurality. This is because they already understand that number words refer to “more than one” but since they don’t have a specific quantity mapped to number reference they would use number words, together with words like “some” and “more”, to help them indicate plurality. The topic is source for controversy and requires further studying since there are different positions on children’s use of “two”. If on the one hand we have studies that argue that “two” is used as a lexical marker for plurality (Kilani-Schoch,1998 and Clark and Nikitina, 2009) on the other hand researchers have argued that it is actually not the case (Sarnecka et al., 2007). The results of the present study should be particularly of help to shed light on the issue. My fourth and last hypothesis is that there should be crosslinguistic differences in the speed of

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acquisition of morphological number marking among the languages under analysis since they all mark plurality in a different way. My hypothesis is that plural marking is acquired first in Italian since plurality is marked on the noun and, when present, on the determiner and adjectives, whereas in French it is mostly marked on the determiner. In Dutch plurality is marked mainly on the noun and in English only on the noun.

Table 1 – Plural marking across languages

English Plurality marker on the Noun: N+-s Plurality marker on the Article: no

Dutch Plurality marker on the Noun: N+-en or –s Plurality marker on the article:

Sing. Common > de Pl. Common/Neuter> de Neuter> het

French Plurality marker on the Noun: not in speech, except for rare cases such as

cheval(sing)/chevaux (pl) ‘horse’

Plurality marker on the Article Sing. M> le/l’ Pl. M/F les F> la/l’

Italian Plurality marker on the Noun: fem. nouns take a feminine ending: casa-case masc. nouns take a masc. ending: libro-libri Plurality marker on the Article:

Sing. M> il/lo/l’ Pl. M> i/gli F> la/l’ F> le

Hypotheses three and four can be motivated as follows. Studies on the topic (Barner et al., 2007 and 2011, and Clark and Nikitina, 2009) mostly take into consideration children acquiring English but studies have been conducted on Romance languages, too. Kilani-Schoch (1998) describes the acquisition of number in a French speaking child from age 1;06.24 to age 3;00.8. The author has subdivided the acquisition of number in 7 periods. In the first period the child starts “to indicate plurality by referring to two or more objects” (Kilani-Schoch, 1998, 28):

(1) Sophie 1;07.15 SOP: a papo [: bateau] FILL boat DID: un bateau oui a boat yes SOP: deux two

DID: deux bateaux

two boats (Kilani-Schoch, 1998, 29) A first plural noun “chevaux” appears later on, at the age of 1;09.13. Given previous studies on the topic we can therefore assume that children will use “two” as a plural marker for a short period of time before being able to productively use plural morphology. My aim is to test for the actual presence of a number word as a plural marker in English, Dutch, French and Italian

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and for the possible differences among these languages. I expect crosslinguistic differences given that all of the languages in the sample mark plurality in a different way (see Table 1). The next sections will present previous studies on the topics of interest for the research. Sections 5 and 6 will explain the research I conducted and its results. A discussion of said results will follow.

2. Acquisition of number words and their meaning

Infants have knowledge of numbers before they start speaking and before they associate a numerical quantity to a precise number word. Infants and animals share a similar representation of numbers where small numbers are represented with a higher degree of accuracy than bigger numbers, circa above 3, (Dehaene, 2001). According to Dehaene (2001) knowledge of numerical quantities resides in a specific area of our brain, the interparietal cortex of both hemispheres. The hypothesis is sustained by the fact that lesions on the area give rise to deficits in the processing of numbers and brain imaging shows activation of this area of the brain when number processing is required (see Dehaene and literature in the article for further reference). “The Number Sense” (TNS), as the author calls it, is nevertheless the product of not just one area of our brain, the interparietal cortex, but that of the conjoint work of three areas. The three areas are responsible for our processing of numbers, which requires an “analogical representation of numbers”, a linguistic representation and a visual one (Dehaene, 2001, 25-26). The model relies on the fact that processing of numbers is due to the interaction of these three different “formats”, their continuous communication is what allows children to learn how to use numbers and calculate as adults. According to the author the model also explains why the achievement of a mathematical knowledge takes time: the three elements are not perfectly integrated right away and while they get to the necessary integration the child learns how to process and compute numbers. The idea of a “core knowledge” of geometry and numbers that supports abstract numerical concepts is also found in, a.o., Spelke (2011) and Izard et al. (2009) Studies to prove humans’ “core knowledge” of numbers have been conducted on infants, from new-borns to preschool children, and adults. They show that both children and adults, present an “approximate number system” (ANS), which includes the ability to discriminate small and big sets and to compare and sum numerical quantities. New-borns habituated to a sequence of items and/or sounds react to the changes in the sequence. Researchers have been able to establish that infants can distinguish small from big sets when the difference between sets, that are usually not over 10 items, is a number higher than four (Cordes and Brannon (2009) tested 7 months old infants). Izard et al. (2009) also argue that infants have a knowledge of numerical quantities even when they are abstract, e.g. when the numerical quantities compared in the test belong to different formats and modalities, like auditory, tactile, or visual stimuli presented non-simultaneously. In their study children were habituated first to an auditory stimulus and after the familiarization they were tested with a visual array of either the same quantity of items of the auditory stimulus or a different one. Infants’ reaction to the test is further evidence in favour of a core knowledge of numbers. Whether we use Spelke’s ANS or Dehaene’s TNS it is a matter of terminology, but in both cases the authors argue that there is an innate knowledge of “numbers” between non-humans and humans. This innate knowledge is approximate, i.e. it

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does not give us a precise and exact knowledge but an imperfect one that allows us to distinguish big quantities from small ones and to understand when a quantity is added or subtracted from a previous set. A fundamental question then arises: how are numbers (and number words) learned to achieve the exact number knowledge?

Various studies attempted to answer this question from the perspective of cognitive psychology and linguistics. Children start using number words before knowing the exact numerical quantity they refer to. Although there are discrepancies in the literature on when children have acquired the precise numerical reference to each number word we know that they start using words like “one” or “five” before knowing their actual meaning. It seems that children learn to recite number words’ lists separately from learning to use “one”, “two” and “three” as quantifiers. Afterwards they learn to associate the exact numerical meaning progressively to “one”, “two” and “three”. Afterwards they master the counting principle, i.e. they understand that number words refer to a number that grows one unit higher every time (x, x+1 …). (Sarnecka et al., 2007). Children’s mapping of a numerical quantity to a number word takes time. According to Wynn (1992) before knowing the cardinal meaning of each number word children know that they refer to numerosities. Children start using the number words for “one” before the number word for “two”, and “two” before “three” and so on; this is most likely due to the input they receive (Wynn, 1992 and Sarnecka et al., 2007). In the same way they gradually link the number words to their cardinal meaning and become one-knowers by the age of 2 ½ (Sarnecka et al, 2007) to 3 (Spelke, 2011). Then they progressively become two-knowers and three-knowers. When learning number words children have to find a way to make the three “formats” described by Dehaene (2001) (but also found in Spelke, 2011) work together. It is a linguistic, visual and analogical enterprise. Acquisition of number words and their meaning is the result of the acquisition of skills. Skills that integrate and build one on the other. Schaeffer et al. (1974) tested for the acquisition of counting skills in children. The main ones are, in growing complexity: the cardinality rule, the counting procedure and the knowledge that x+1 is greater than x. The cardinality rule is the restatement of the last counted number in a count, independently of the correctness of the count itself. When asked, children would count numbers out loud and repeat the last number word out loud, i.e. the number word they think refers to the quantity they are presented with. One refers to counting procedure when talking of the coordination between counting and the objects counted and the order of the number words during counting. Knowledge that x+1 is greater than x is also a skill that is acquired over time. Bigger differences between sets of items are recognised better than smaller ones and acknowledging the difference between x and x+1 implies a better skill in tracking quantities and a certain ability in mapping number words to their cardinal meaning. To understand how the development of these skills works Schaeffer et al. tested children aged 2 to 6 and designed six different tests. Tests required children to, e.g. count drum’s taps, recognise small and big quantities, give a required number of elements and choose quantities of items. In this study children were divided into groups according to the “developmental stage” they were in. The stages represent how well the children could count arrays of 5 to 7 items, with respect to the cardinality rule, and how well they could distinguish sets of items such as x and x+1 or x and

x+4.

Stage I children had an average age of 3;08, they had an age range from 2;00 to 5;00. Children in this group would not count aloud signalling an inability to apply the counting procedures

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and subsequently the cardinality rule. They were able to recognise small sets of objects (1 to 4) as belonging to a numerical pattern like distinguishing 1- and 2-objects’ sets, or sets of 2 and 3 objects. Stage I children are on average older than stage II children due to the fact that some of them were 5 years old, this means one, or more, of the children were slower than the others in the acquisition of number words and set the average at an higher age point than stage II children. No explanations are given by the authors with respect to this issue. Stage II children have an age comprised between 2;09 and 4;06, average age of 3;05, they show acquisition of the counting procedure since they can count correctly up to 7 but they are not able to apply the cardinality rule. They still have difficulties to recognise numerosities higher than 5 when asked to apply the “x+1 is greater than x” skill but they have no problems applying it to smaller quantities (1- 4). Stage III children applied the cardinality rule correctly 99% of the times which also means they had no problems using counting procedures, they performed better than stage II children with respect to the x+1 skill but still had difficulties with numbers bigger than 5. Their average age is 4;02, with an age range between 3;03 and 5;03. Stage IV children, average age 5;06, have no problems with the counting procedure and the cardinality rule and they can recognise the difference between x and x+1, with a correct performance 92% of the times. Schaeffer et al.’s study shows how the counting skills and the learning of numbers is made of different abilities integrating one another over time but it also shows that children use number words before associating them to their precise meaning, before acquiring the cardinality rule. Wynn (1992) tries to understand how children map the numerical concept to the number word. She argues that children have acquired the meaning of number words when they acquire the cardinal-word principle, what Schaeffer calls the cardinality rule. Once again the acquisition process is the product of skills’ acquisition and their integration and cooperation. Wynn tested 20 children on a longitudinal study over a period of 7months for 14 of them, age range between 2;06 and 4;02, and of 2 months for the remaining 6, who had an age range of 2;07 to 3;03. Children were tested with the “give a Number” test to determine of up to which number words they knew the actual cardinal value. Children were asked to bring the investigator a number of items, starting with one item and using higher numbers according to the child’s ability. Given the results of this test children were divided in four groups on the basis of their knowledge level. Group 1 children gave only one item correctly, group 2 gave two, group 3 gave three and group 4 gave four or more items correctly (Wynn doesn’t specify the age ranges of the groups, probably due to the longitudinal nature of the study). The other tests were a “how many” test, to assess the knowledge of the cardinal-word principle, a control test and a test to establish the knowledge of precise numerosities. Wynn’s study indicates that children know that number words refer to numerosities even from an early age (already at 2;06), before mapping the number word to its cardinal meaning. An alternative explanation is that children might consider any number word different than “one” as a reference to plurality. The results of the study confirm that children first learn “one, “two” and “three” and learn higher numbers acquiring the cardinal-word principle. Moreover in the 7 months of testing only one child went from group 1 to group 4 confirming that it takes a long amount of time to acquire the meaning of number words. Wynn estimates it takes over one year, but there are also great individual differences. According to the author, possible explanations of why it takes such a long time span to learn the meaning of number words are to be found in the syntactic properties of number words that are similar to those of determiners. Children start recognising determiners around 2

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and a half years of age and they are sensitive to their syntax and their singularity/plurality characteristics. Knowledge and understanding of determiners can help in numbers’ acquisition. Studies have also been conducted on the relation of singularity/plurality marking and number acquisition. Sarnecka et al (2007) tested Russian, English and Japanese speaking children to see if the plurality marking affects children’s performance in the acquisition of number words. Their results suggest that in languages like Japanese, where there is no singular/plural morphology distinction, number words are learned later than in English and Russian, where there is a distinction between singular and plural. Wynn’s (1992) conclusion, together also with Kilani-Schoch (1998) and Clark and Nikitina (2009), seems to be in contrast with Sarnecka et al’s (2007) one. The formers argue that number words help in learning plural/singular morphosyntax while the latter argues that it is plural/singular distinction that helps learning number words. Part of the present’s study work on “two” and plural morphosyntax will try to find a solution to the issue.

Summing up we have seen that research on the topic indicates that children start distinguishing numerosities early: already around 24 months of age they distinguish between “one” and “more than one” (Barner et al., 2007) but the acquisition of number words and their meaning is a challenging process that takes over almost one year to be completed. As we have seen researchers seem to agree on the fact that it is an acquisition of skills that build one on the other and cooperate together. Another element that different studies have in common is the fact that “number acquisition” is not learned in isolation but determiners and singularity/plurality marking have a role in this process.

3. Acquisition of determiners and indefinite articles

The acquisition of determiners raises important questions on children’s acquisition of syntax and of functional categories, which implies an understanding of the grammatical and syntactic structure more similar to the adult one. Different theories of language acquisition have tried to explain how children learn functional categories. Two main models have been proposed: a full competence or continuity model and a maturation hypothesis. The first model assumes that the full syntactic structure of the grammar is available to the child in the same way it is available to the adult. The maturation hypothesis argues that children’s grammar develops gradually over time. The maturation is due to different acquisitional stages which also coincide with the child’s neurological maturation (a.o. Coene, 2006, Bohnacker, 1997, Pine and Lieven, 1997). It has been discussed that children already at the age of 2 or 3 have some knowledge of grammar. With respect to the determiner’s category children show sensitivity to the way determiners combine with the other words in the sentence already at an early age. This is further proved by the fact that several studies on the acquisition of determiners show that children are better with tasks assessing determiners than with appropriate use of determiners. Thus showing a higher understanding of the determiner’s category opposed to a lower level of productivity (Kemp, 2005). It has been established that children learn the determiner category gradually, of particular interest for the present research is the way articles are processed and learned, more specifically indefinite articles. Learning articles children seem to go through three steps. At first they use bare nouns without any determiner. In a later stage they start using what have

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been described as “place holders” or “fillers”, i.e. a syllable or schwa sound that usually appears before the noun in place of the article. In languages like Dutch and especially English the schwa sound of the filler can be homophonous to the actual indefinite article. Afterwards children start using articles and, more in general, determiners. This means that they can both use them correctly with respect to gender and number, but also with respect to specific and non-specific reference. It also means that they can select the appropriate determiner with respect to the context and the interlocutor’s knowledge (a.o. Rozendaal, 2008). In the period during which children use fillers, articles also appear in their speech, but said articles are to be considered as “impostors” since the child has not yet connected the article to its grammatical role (Bohnacker, 1997). According to Pine and Lieven (1997) this gradual learning process is the result of a sensitivity to the distributional properties of determiners and nouns. Determiners seem to appear first in specific and pre-imposed frames, like in constructions such as “in the X” or “that’s a(n) X”. Gradually the possible “frames” in which determiners can appear broadens and children expand their knowledge up to the point where they would actually build an adult-like determiner category.

My interest in the present study revolves around the acquisition of the indefinite article given its correlation with the number “one”. In their study Kemp et al. (2005) tested 2, 3 and 4 years olds for a total of 60 English speaking children. The aim of the study was to observe the participants’ spontaneous production of determiner + noun combinations. Two years olds resulted to prefer the use of “a” over “the” and to be less creative in their use of determiners, this is due to the fact that their knowledge of the determiner category is limited and this reflects on their use of the language. Their findings are in line with Maratsos (1976) study where he tested English children’s distinction of the definite and indefinite articles in 3 and 4 years olds. The 3 years old children had a tendency to overuse “a” over “the”. With respect to the acquisition of articles, in particular indefinite articles in Romance languages, a more syntax-oriented analysis explaining the gradual learning of articles is found in Coene (2006). She argues that while syntax is a constant, linguistic development is the product of acquisition and connection of lexicon and of abstract features to morphological markers. Articles are then a connection of the lexical items to the features of number and person, where /± person/ is a subset of number. A very important passage in her study is that the number feature explains why the grammaticalized NumP is reinterpreted as an indefinite article. Thus explaining why indefinite article and number “one” coincide. The person features are responsible for the projection of D and entail uniqueness, therefore definite articles relate to such feature. In fact the features /+number/ and /+person/ together characterize definite articles, while indefinite articles are expressed by the /-number/ feature when they entail a non-specific reading1_{and by} /+ number, - person/ when the reading is specific. The acquisition of the features explains the order in the acquisition of the indefinite articles. At the earliest ages of acquisition the child still has not recognized and “valued” the features; this explains the omission of articles and the use of bare nouns. The intermediate stage, the one where the child uses fillers, is seen as a stage where the child is aware of the necessity of a grammatical element but still has not identified the determiner as such. Finally the child gradually acquires, or “valuate”, first the /± number/

1_{Bare nouns, quantifiers and indefinite articles with a non-specific reading are all expressed by the /-number/}

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feature and then the /± person/ feature. This explains the emergence for indefinite articles before definite articles (Coene, 2006). Coene’s analysis explains the acquisition of definite and indefinite articles in Romance languages, but her analysis can be expanded at least to the languages taken into consideration in the present study, in fact works on English speaking children also agree that indefinite articles are acquired first. As for Dutch, and a crosslinguistic comparison of acquisition of reference, and therefore articles, in Dutch, English and French Rozendaal’s study (2008) could help shed some light on the topic. She uses CHILDES transcripts of children between 2;00 and 3;03 years of age to study reference and also gives an analysis of pragmatic functions and the input the children receive. She observes that all children (three for English, three for Dutch and four for French) have already started to use most of the different determiner’ types productively by age 2;06. Nevertheless there are differences in the use of determiners in obligatory contexts, which is also reflected in the children’s speed of acquisition. French children receive higher inputs since determiners are used obligatorily in a higher number of contexts. Therefore French children are faster in the acquisition of determiners than Dutch and English children. For the present study, since Italian has an higher use of determiners, similar to the case of French, I expect French and Italian children to behave similarly and have similar acquisitional speed.

4. Acquisition of plural marking

The acquisition of number words is linked on the one hand to the indefinite articles, given their relation to the numeral “one”, and on the other hand to the acquisition of plural marking. According to Sarnecka et al. (2007) English and Russian speaking children would learn number words faster than Japanese children because in the first two languages there is a strong distinction of singular vs. plural morphology but not in the last one. Other studies argue that children use number words, in particular “two” as a (lexical) plural marker in French (Kilani- Schoch, 1998) and in English, where, when the plurals emerge, lexical marking is preferred over morphological marking (Wood et al. 2009). Therefore plurality is indicated by the number word produced along with the plural suffix on the noun it refers to (Clark and Nikitina, 2009). I hope to untangle the issue with the present study but first, in order to understand if it is plural morphology that influences number words acquisition or vice-versa, it is important to understand how children acquire plural morphology to begin with. The first acquisitional step for the child is the distinction between “one” and “more than one”. Studies on English speaking children show that they start distinguishing small sets of items at an early age. At 18 months they can distinguish 1 vs. 3 but are unable to distinguish 1 vs. 4, this means that they can represent sets as being composed of one, two or three items but they cannot represent four as a “more than one” numerosity, therefore a singular/plural distinction is not yet in place (Barner et al., 2007). For their study on the acquisition of singular/ plural morphosyntax Barner et al. (2007) asked for parental reports about children’s use of plural morphosyntax. Children start using plural morphosyntax around 22 months of age. By this time they also start distinguishing 1 vs. 4, and children who had already started using plural morphology were more successful at distinguishing 1 vs. 4 than those who didn’t. At this age point children do not distinguish 2 vs. 4. If children can distinguish 1 vs. 2, 1 vs. 3, and 1vs. 4, it would be expected that they can

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discriminate 2 vs. 4 since it is assumed that singular/plural distinction is then in place. On this issue Barner et al.’s (2007) conclusion confirms that at 24 months of age the singular/plural distinction is in place, despite difficulties in discriminating 2 vs. 4. Their results are consistent with other studies on the acquisition of singular/plural morphosyntax that found that by 24 months children are sensitive to number marking in the sentence while they aren’t at 20 months (Wood et al., 2009). Kouider et al. (2006) also tried to assess when children start mapping the singular/ plural morphology. They tested children both for plural sentences and nouns, i.e. differences in the interpretation of sentences of the type “There is a blicket” vs. “There are some blickets” and “Look at the blicket!” vs. “Look at the blickets”. Participants at 20 months of age failed to perceive singular plural distinctions. At 24 months children are sensitive to plural marking in the sentence but are not able to rely solely on the plural morphology, while at 36 months children can rely on plural morphology alone. Their study hints to the fact that distinctions such as is/are, or a/some are learned before the plural suffix starts playing a relevant role in the singular/ plural distinction. Studies on acquisition of plural morphosyntax all agree, at least as far as English is concerned, that children learn morphology gradually, being able to understand marking in the sentence and more transparent forms (e.g. some, two, etc.) at first while they acquire the plural suffix –s later on (a.o. Clark and Nikitina, 2009; Wood et al., 2009, and Kouider et al., 2006). Particularly interesting is Clark and Nikitina’s study, they used both natural speech transcriptions and specific tests to see how children convey plurality before they master the plural morphology. Children in their transcriptions showed a preference for the use of “two” as a lexical “helping” element when trying to convey plurality, while the tests showed that children rely on different strategies to convey plurality, even reduplication of the singular noun being one of them. The authors nevertheless admit that there is not a uniform way for children to acquire the “one” and “more than one” distinction and there is a lack of studies taking the individual differences into account. The studies discussed examine English but languages have different ways of expressing number, and different categories are grammaticalized in different ways (Stephany, 1998). With respect to French the acquisition of plural morphology is influenced by the development of the entire noun phrase. Nevertheless there are indications that lexical forms are used at first to express plurality. A study of one single child over a period that goes from 1;06 to 3;00 years of age has shown the gradual acquisition of the French plural morphology. French plurality is expressed on determiners, pronouns, the verbal inflection, some adjectives and a few (less than 50) nouns (Kilani-Schoch, 1998). The child in the study started indicating plurality through the use of “two” between the age of 1;06 and 1;09, while the use of plural nouns and forms like cheval/chevaux (horse/horses) is reported after 2;03. In the following stages the child started using plural morphology and rarely omitted plurals in obligatory contexts between 2;05 and 2;07. An overregularization of plural forms, e.g. use of chevals in place of chevaux is attested after 2;10. The author states that such overregularization is evidence of an actual “morphological processing” of plurality by the child (Kilani-Schoch, 1998). French speaking children seem to fully acquire plural morphology in a gradual piecemeal fashion, like the English children, but if we assume that overregularization is an indication of the actual processing of plurality then this seems to appear at a rather late stage, due to the plural marking of the French NP.

Studies on the acquisition of Italian morphosyntax showed that free morphemes are learned later than bound morphemes (Caprin and Guasti, 2009 and reference therein). Caprin and

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Guasti’s work (2009) does not focus on the acquisition of singular/plural morphosyntax but on acquisition of Italian morphosyntax more in general, studying use of verbal inflections and auxiliaries, articles and pronouns in 59 children aged between 22 to 35 months. Nevertheless their findings are still relevant to the present study especially for what concerns acquisition of articles, which children start using around 18 to 22 months of age. They observed that, while omissions of articles are present, Italian children seldom make gender and/or number agreement mistakes, thus indicating that they have an adult-like understanding and use of singular/plural marking within the NP already at an early age. Given this background knowledge on the topics that interest the present research the reader can now understand how these three topic: acquisition of number words, “one”/ indefinite articles, and plural morphology, develop in a parallel fashion and acquisition of one is linked to the acquisition of the others.

5. Methodology

The research aims to study how number words, plurality marking and indefinite articles interact in children’s first language acquisition. The data collected through CHILDES (MacWhinney, 2000) are examples of spontaneous speech and interactions between children and their interlocutors, usually members of the family. The transcripts of these spontaneous interactions allowed me to see if and when children speaking French, Italian, Dutch and English start using number words, especially “one” and “two”, indefinite articles and plural nouns, and how they use them. The CHILDES’ material used and the language acquisition development studied in the selected transcriptions lead to answers to my research questions and hypotheses that I will hereinafter discuss.

5.1 Subjects and age points

Given the crosslinguistic nature of the study three children were selected for every one of the languages of interest for the research. All children are between the age of 1;08 and 2;06, with the exception of Martina, an Italian child whose closest transcript for the 2;06 age point was available at age 2;07. The age points were selected according to previous studies on number words and acquisition. As previously argued, according to previous research, a series of age points have turned out to be relevant in the acquisition of numerals, determiners and plural morphology. In order to learn both plural morphology and number words children need to know the distinction between “one” and “more than one”. Said distinction is in place at 24 months of age (a.o. Barner et al., 2007) while the first plural nouns seem to appear around 20 to 24 months of age for the English speaking children (Wood et al., 2009) and between 1;06 and 2;04 in the French child in Kilani-Schoch study (1998). Rozendaal’s (2008) study on reference shows that by 2;06 years of age speakers of all three languages: English, Dutch, and French, are using a variety of determiner’s types productively. Moreover studies on number words, their meaning and acquisition, agree that children around 2;06 to 3 years of age learn the meaning of the number word “one” as a specific quantity. Children around this age are usually “one-knowers” (a.o. Spelke, 2011; Sarnecka et al., 2007) therefore they can also start contrasting “one” and “more than one” in a more precise manner. With these premises it seems that the period that

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goes from 1;08 (20 months) to 2;06 years of age is of crucial importance in the acquisition of number-related morphosyntax and lexicon. Therefore I decided to set the first age point for the present study at 1;08 and the last age point at 2;06, which allows me to have a longitudinal study. Given these age criterion children were selected primarily on the availability of the transcripts for the age points of interest.

Italian

Italian children were selected following the criteria of age and availability of transcripts. The children are two girls, Martina and Diana from the Calambrone corpus (Cipriani et al., 1989) and one boy, Marco, from the Tonelli corpus (Tonelli et al., 1998). The Italian children have higher MLUs than the other children nevertheless their use of number words, indefinite articles and plural allowed for a comparison with the other languages’ speakers since they do not have particularly higher entrances. As for the age point selected, when no transcriptions were available for the age point of interest the closest one was chosen, either a few days earlier or a few days past the target month. For Martina the closest ones to the target point were selected at age 2;01 for 2;00, 2;03 for 2;02 and 2;07 for 2;06, all within a maximum of 12 weeks range from the previous age point. Given the limited amount of Italian children’s transcripts available in CHILDES for the age range of the study I decided not to use other children’s transcripts since all of them presented similar issues with respect to the coincidence of the available transcripts to the age points of interest.

Table 2 – Italian age points

Age point Marco Diana Martina

1; 08 1; 08. 03 1; 08. 05 1; 08. 02 1; 10 1, 10. 12 1; 10. 07 1; 10. 29 2; 00 2; 00. 00 2, 00. 02 2; 01. 12 2; 02 2; 01. 27 2; 01. 25 2; 03. 01 2; 04 2; 03. 29 2; 05. 01 2; 04. 13 2; 06 2; 05. 24 2; 06. 13 2; 07. 12 French

The French children were selected among a group of children previously selected for Hulk and Sleeman’s study (in preparation) on the acquisition of nominal ellipsis and reference, for the age points at 1;08, 2;00 and 2;04 the same transcripts were used in both studies. They were chosen considering similar MLU and availability of age points. The French children are two girls, Anais and Marie, and a boy, Nathan, all from the Lyon corpus (Demuth and Tremblay, 2008).

Table 3 – French age points

Age point Anais Marie Nathan

1; 08 1; 08. 11 1; 08. 20 1; 08. 16 1; 10 1; 10. 23 1; 10. 12 1; 10. 00 2; 00 2; 00. 16 2; 00. 09 2; 00. 16 2; 02 2; 02. 26 2; 02. 19 2; 02. 11 2; 04 2; 04. 21 2; 05. 02 2; 04. 10 2; 06 2; 06. 22 2; 06. 15 2; 06. 01

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English

English speaking children are all speakers of the Northern American English variety. They all have transcripts available for all the age points I am interested in in the study. From the Davis corpus (Dolata et al., 2008) I selected Cameron and Charlotte and from the Sachs corpus (Sachs, 1983) I used Naomi’s transcripts. Cameron’s first transcript available for the 2;02 age point was at age 2;03 and 5 days, which is only a few days after the target age point and was therefore still considered a suitable option.

Table 4 – English age points

Age point Cameron Charlotte Naomi

1; 08 1; 08. 00 1; 08. 00 1; 08. - 1; 10 1; 10. 07 1; 10. 11 1; 10. 23 2; 00 2; 00. 21 2; 00. 13 2; 00. 18 2; 02 2; 03. 05 2; 02. 13 2; 02. 25 2; 04 2; 04. 22 2; 04. 07 2; 04. 16 2; 06 2; 06. 17 2; 06. 12 2; 06. 05 Dutch

As it is the case for the French children, also the Dutch children were selected among those used in Hulk and Sleeman’s study (in preparation). The Dutch children are Daan and Matthijs, from the Groningen corpus (Bol, 1995) and Sarah, from the Van Kampen corpus (van Kampen, 1994). While for Daan and Sarah there were transcripts available for all the age points, Matthijs’ first age point available is at 1;10, there are no data for this child at age 1;08. As for the French children the same Dutch speakers’ transcripts were used for the present study and Hulk and Sleeman’s study at 1;08, 2;00 and 2;04.

Table 5 – Dutch age points

Age point Daan Sarah Matthijs

1; 08 1; 08. 21 1; 08. 28 - 1; 10 1; 10. 16 1; 10. 13 1; 10. 13 2; 00 2; 00. 04 2; 00. 17 2; 00. 09 2; 02 2; 02. 16 2; 02. 20 2; 02. 20 2; 04 2; 04. 28 2; 04. 24 2; 04. 24 2; 06 2; 06. 11 2; 06. 19 2; 06. 19 5.2 Data Selection

The selected files were downloaded from the CHILDES (MacWhinney, 2000) transcripts’ and analysed through the CLAN’s programme (MacWhinney, 2000). An analysis of the MLU was carried out to have a general understanding of children’s proficiency. As can be seen in Table 6, the Italian children, especially Diana and to some extents Marco, have particularly high MLUs compared to the other children. As previously stated, despite their higher number of MLUs their use of number words and plurals was not higher than the other children, therefore I could still compare them with the others.

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Table 6 – MLU of all the children per Language

Once the children and the transcripts were selected I analysed them with the CLAN programme for frequency and the presence and use of indefinite articles, number words, in particular “one” and “two” and plural nouns.

5.3 Use of “one” and the indefinite article

I first collected, through the frequency, if and how many times “one” and/or the indefinite articles were used throughout the different age points of every child. I subsequently selected every entrance of “one” and the indefinite articles, when they were not the same word, and analysed their use. I divided the different kind of uses of “one”/indefinite article in four different groups: when used in a counting sequence, used as reference, used in isolation and ambiguous cases. Since the frequency tool in CLAN does not count for repetitions within the same line I also counted the number of entrances per age point including the repetitions. “One” was considered as part of a counting sequence when uttered in a sequence of number words. The number words did not have to be uttered in the correct counting order, since we don’t expect children within this age range to fully and precisely know the correct order of a counting sequence (2).

(2) CHI: one two three. Cameron (1;10) CHI: I count one two three four five six.

CHI: seven eight nine.

Reference includes “one” used as a determiner (3.a) and as a pronoun, therefore cases like those of noun ellipsis were considered as reference (3.d). I further divided reference as correct and incorrect reference. The indefinite article (which is singular) followed by a plural noun was considered as incorrect reference. As it is shown in example (3.b) un is the masculine indefinite article and it is followed by cani (dogs), where - i marks the plural. In cases like this the child might have been influenced by the context, or might have chosen a plural marker in place of the singular or he does not know the correct morphology for number. I considered as correct reference examples like those in (3.c) because, since the lack of agreement is in the gender with a masculine noun followed by a feminine noun, the error has no impact in the number morphology.

(3) a. CHI: fai una palla grande! Marco (2;00) make/draw aFEM big ballFEM!

b. CHI: un cani, cani.

mlu ITALIAN FRENCH ENGLISH DUTCH

MARCO DIANA MARTINA ANAIS MARIE NATHAN CAMERON CHARLOTTE NAOMI DAAN SARAH MATTHIJS 1.08 2.142 3.016 1.895 1.251 1.891 1.188 2.006 1.052 1.211 1.088 1.080 / 1.10 2.527 3.690 1.654 1.209 1.694 1.108 2.632 1.185 1.565 1.090 1.173 1.460 2.00 2.612 4.330 1.859 1.603 1.887 1.376 2.686 1.429 2.043 1.404 1.677 1.418 2.02 3.171 5.884 2.565 1.565 2.077 1.189 2.161 1.710 2.532 1.665 2.147 1.763 2.04 4.450 6.086 2.686 1.501 2.745 1.676 2.985 1.910 2.319 2.193 2.460 1.940 2.06 3.987 6.732 2.511 2.569 3.319 1.641 2.515 2.525 2.935 2.385 2.744 2.849

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aSING dogsPL, dogsPL Marco (1;08) MOT: no questo è un cavallo.

no this is a horse

c. CHI: dagli un medicina! Diana (2;04) give+him aMASCH SING medicineFEM SING

d. CHI: color this one. Cameron (1;08)

The selected word was considered as uttered in isolation when it was not followed by a noun it referred to or by (other) number words and was the only word in the utterance (4), as such it could be an instance of noun ellipsis or an attempt of the child at counting.

(4) MAR: uno. Marco (1;10) one

The entrances were considered ambiguous when the context was not clear or they were not part of any of the other groups. Entrances such as “one yyy” or “one xxx” were considered ambiguous. Based on the context some of the entrances of the type “xxx/yyy one” (or “xxx/yyy two”) were considered as cases in which the number word was uttered in isolation.

5.4 Use of “two”

To have an accurate analysis of when and how children use “two” I applied the same method used for “one” and divided the various entrances of “two” into the same groups seen above. “Two” was considered as part of a counting sequence when uttered with one or more other number words, not necessarily in the correct order (2). As for the reference, “two” was considered as such when used as a quantifier/adjective followed by a noun or when used as a pronoun (5).

(5) CHI: je te donne deux euros. Marie (2; 06) I give you two euros

MOT: ah tu m(e) les donnes? ah you give them to me?

Gender distinctions do not present an issue in the use of “two” with an NP and instances of incorrect reference were considered those which presented problems of number agreement (6). For examples like the one in (6), which is also the only example of incorrect number agreement after “two”, I relied on the transcript (MOT) since the plural morphology on the noun is not made explicit in the phonology, and one can assume from the apparent correction made by the mother that the child referred to a singular noun after using “two”.

(6) CHI: deux papa. Anais, (2; 02) two dad

MOT: deux papas? two dads?

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Nevertheless in French it is only possible to make this distinction appropriately with the few (less than 50) nouns that are marked differently on the plural than on the singular.

Once again “two” was considered as uttered in isolation when it wasn’t followed by anything else in the same utterance.

A few entrances of “two” were considered ambiguous when they were not considered as belonging to any of the above categories (7).

(7) CHI: xxx yyy deux yyy, yyy pas yyy yyy pin+pon. Marie (1; 10) xxx yyy two yyy, yyy not yyy yyy pin+pon (pompiers =firefighter(?)) MOT: ah, y+a deux pin+pon là

ah, there are two firefighters there

5.5 Use of plurals

As far as the use of plural nouns and plural morphology is concerned I decided to look if plural nouns, therefore use of plural morphology, were present or absent in the speech production. In contrast to what was previously seen for “one” and “two” I was not interested in the quantity of the production of plurals but only in the presence or absence of plural nouns in the spontaneous speech. To analyse if and when children used plural nouns I first went through the frequency output of every selected transcript and looked for the presence of plural nouns, i.e. nouns carrying a plural suffix, other indications were, especially for the Romance languages, plural articles and plural adjectives. Once the presence of plural nouns at a selected age point was established I looked into the use of the plural nouns. In case the plural noun was present I looked for a “minimal pair” in the same transcript, i.e. if at the same age point the child uses the same noun both in singular and plural. Thus showing an (initial) understanding of the different morphology and therefore of the different meaning conveyed by the use of plural marking. Since my interest is in how children use plural nouns I selected the plural nouns in the transcripts and looked for plural nouns used with number words, in agreement with adjectives and/or determiners and used with “helping words” such as “many”, “a lot of” or “all”. The use of number words with plurals is relevant in the present study since I am interested in understanding if the use of number words, especially “two”, helps children learn plural morphology. Therefore instances such as that in (8) are particularly relevant to understand the development of plural morphology.

(8) CHI: I got two bears. Charlotte (2; 04)

I also looked for plural nouns used in number agreement with determiners and/or adjectives, this is especially relevant in Italian, and in part in French, to see how proficient the child is in the use of the plural morphology since the entire NP has to agree in number with the noun. Nevertheless number agreement can be found in English and Dutch too, still taking into consideration that the entrances in the Germanic languages (9) were scarce compared to those in the Romance ones (10).

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These are cows! JAC: ja, dat is een koe . yes, that is a cow

(10) MAR: lui ha le orecchie nere Marco (2; 02) he has theMASC-PL blackMASC-PL earsMASC-PL

Studies on the topic of acquisition of plural marking (Clark and Nikitina, 2009) also argue that children use expressions such as “more”, “many”, “a lot of”, etc. to help them learning and conveying plural meaning (11). Given this premise I looked for plural nouns used with these kind of expressions throughout the selected transcripts to see how children actually use plural nouns in spontaneous speech.

(11) CHI: more monkeys jumping on the bed. Cameron (1; 08)

6. Results

The data collected was analysed per language and then compared crosslinguistically. What I want to investigate is if, as expected from previous studies that focused mainly on English, children would start using “one” before “two” in every one of the languages under analysis. Furthermore, considering that the Germanic languages are transparent with respect to the indefinite article vs. “one” distinction, I want to see, if possible, if there are differences in the use of the indefinite article and “one”. Earlier productive use of “two” will also influence an earlier acquisition of “one”. In order to show the differences in use and productivity the data collected for the use of “one” will be shown both in instances of “one” used as reference and data for “one” as overall entrances, such as those shown through the CLAN (MacWhinney, 2000) frequency tool. Since the overall entrances of “two” used as frequency are scarce data for the use of “two” are presented only as retrieved from the general frequency data, which means that, to compare entrances of “one” and “two” I had to use the frequency data in the comparison. With respect to plural marking, studies indicated an early use of “two” as an early lexical marker for plurality in languages like French (Kilani-Schoch, 1998) and English (Clark and Nikitina, 2009). Is that actually the case both in Germanic and Romance languages? The spontaneous speech analysed should give me at least an indication of that. If plural marking is productive across languages and instances of “two+ plural noun” are rare, especially in the earliest age points, it will mean that previous analyses were misguided, or at least imprecise.

6.1 Italian Data

Italian does not have a distinction between indefinite articles and number “one”. When used as an article, pronoun, or even when uttered in isolation, “one” has to agree in gender with the noun it refers to (see example 3.a repeated here as 12). From the longitudinal data collected one can see that the children selected tend to use “one” more often at higher age points. Figure 1a shows the number of entrances that every child has of the indefinite article/ “one” when used as correct reference. Marco has an overall high number of entrances for “one” even at the

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earliest age points, but despite a peak at age 1;10 he also seems to follow a pattern of gradual increase in the use of “one”.

(12) CHI: fai una palla grande! Marco (2;00) make aFEM big ballFEM!

Figure 1a- Percentages of entrances of “uno” per utterances used as correct reference

Figure 1b – Percentages of entrances of “uno” per utterances as retrieved from the general frequency data

The entrances of “uno”, “un (')” and “una” in Italian are shown in Figure 1a, where the data are those provided by the search of “one” used as reference2 in the children’s speech transcripts

2_{Using the “kwal” command in CLAN (MacWhinney, 2000)}

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 1.08 1.10 2.00 2.02 2.04 2.06 Marco Martina Diana 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 1.08 1.10 2.00 2.02 2.04 2.06 Marco Martina Diana

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and in Figure 1b, providing the overall entrances for “one” as given by the frequency3. As one can observe from the charts, children’s use of “one”/ indefinite article grows gradually. As for the use of reference at 1;10 Marco has a peak when the entrances for “uno” are 11.05% of his utterances, 5.38% used as reference. Marco’s and Diana’s personal peaks in the use of “uno” as reference are for both at age 2;04 where he uses it 8.74% of the time while she uses it 6.83% of the time. Martina’s peak is at age 2;06 (4.55% of utterances used “one” as reference). It is important to keep in mind that individual differences and peaks in the production are expected given the spontaneous nature of the data which is influenced by many aspects, such as the place or the activity the children are involved in at the moment of the recording The use of “due” (two) of the Italian children can be seen in Figure 2. The data in this case, given the fewer number of entrances, are those of the overall use, as retrieved by the frequency results given by the CLAN programme throughout the transcripts at the different age points. The pattern here is more irregular with children having less entrances, if any, for “two”. Once again Marco has a peak at age 1;10 (3.40% of utterances use “two”). Martina does not use “two” at age 1;08 and 1;10 but starts using the numeral at 2;00 (0.36% of utterances) with a peak in use at age 2;04 (1.81%). There are no entrances at 2;02 but the number word is used again in the remaining two age points. Diana only uses “two” at 1;08 (1.64%), and she does not use “two” as reference: of the three entrances, two are part of a counting sequence and one is spelled out in isolation.

Figure 2 – Percentages of entrances of “due” per utterances as retrieved from the general frequency data

Nevertheless the Italian children start using “one”/indefinite article at an early stage and the entrances grow during the time span taken into consideration. The entrances for “two” are scarce throughout the entire time span considered for the analysis. Thus confirming the hypothesis that the number words in questions are learned gradually and one after the other.

3_{Frequency data include counting sequences, reference (correct and incorrect), cases when word analysed was}

uttered in isolation or was ambiguous, repetitions are excluded from the frequency data.

0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 1.08 1.10 2.00 2.02 2.04 2.06

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Figure 3 – Comparison of the average percentages of entrances for “uno” and “due” as retrieved from the general frequency data

Comparing the average entrances, as retrieved from the total frequency data of the three children (figure 3) it is easy to see the difference in use: the number of entrances for “one” is higher even at the earliest age points, while “two” is less used, if used at all. This confirms the previous prediction that children learn “one” before learning “two”, at least in Italian.

6.2 French Data

As it is the case for Italian, French uses the same word for “one” and the indefinite article. Indefinite articles also agree in gender with the noun they refer to, even when they are used as a pronoun (13). A general observation when looking at the collected data is that French children start using “one”/indefinite article gradually and the production grows over time.

(13) CHI: une autre?

another oneFEMM SING? MOT: une autre.

another oneFEMM SING

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 1.08 1.10 2.00 2.02 2.04 2.06 uno due

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Figure 4a – Percentages of entrances of “un” per utterances used as correct reference

Figure 4b – Percentages of entrances of “un” per utterances as retrieved from the general frequency data

Figure 4a shows the use of “one” as correct reference in French. Besides Nathan’s very low use, his peak is at 2;00 where 9.93% of his utterances used “one” as reference, the other children’s use of “one” as reference grows with time, from very low percentages (0.37% for Anais and 4.60% for Marie at 1;08 but 1.16% at 1;10 in the referential use) to higher percentages (10.94% for Anais at 2;06 and 10.32% for Marie at 2;04). The evolution in the use of “un”, as can be seen comparing Figure 4a and 4b does not present many differences, besides an overall higher number of entrances for Marie in the general frequency data at age points 2;00 and 2;02, which does not influence the analysis in any way. As for the production of “two” we can see in Figure 5 that it grows over time. There are no entrances of “two” at 1;08 and, besides for Anais, whose production radically grows at 2;02, the other children’s productions are slower and in a growing curve.

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 1.08 1.10 2.00 2.02 2.04 2.06 Anais Marie Nathan 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 1.08 1.10 2.00 2.02 2.04 2.06 Anais Marie Nathan

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Figure 5- Percentages of entrances of “deux” per utterances as retrieved from the general frequency data

More interesting for the study is to observe the production of “one”/indefinite article and compare it with the production of “two”. The data in Figure 5 and 6 are those retrieved from the percentages of the general frequency per utterance, in order to compare the same type of entrances. The comparison will help answer our first research question and observe how acquisition of number words works.

Figure 6 - Comparison of the average percentages of entrances for “un” and “deux” as retrieved from the general frequency data

In Figure 6 one can easily see that production of “un” starts earlier than the production of “deux”. French children are overall more productive in the use of “one” than in the use of “two” with an average of over 35 entrances (8.59%) for “one” at age 2;06 and less than half the

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 1.08 1.10 2.00 2.02 2.04 2.06 Anais Marie Nathan 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 1.08 1.10 2.00 2.02 2.04 2.06 un deux

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number of entrances for “two” (3.53%). Once again the hypothesis that use of “one” starts earlier than the use of “two” is borne out by the data.

6.3 English Data

English uses two different terms for the numeral and the indefinite article. Therefore my research had to take this difference into account and the data might reveal a different pattern than the one observed for the French and the Italian children so far. The fact that English attributes the two different roles of number word and of indefinite article to two different words is likely to show a different development in the learning pattern.

Figure 7a – Percentages of entrances of “one” per utterances used as correct reference

Figure 7b – Percentages of entrances of “one” per utterances as retrieved from the general frequency data. 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 1.08 1.10 2.00 2.02 2.04 2.06 Cameron Charlotte Naomi 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 1.08 1.10 2.00 2.02 2.04 2.06 Cameron Charlotte Naomi

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The data on Figures 7a and 7b show an irregular distribution in the use of “one”. Taking into consideration the overall entrances as retrieved by the frequency (Figure 7b), one can see that the individual differences play a role in the evolution of the acquisition of “one”, especially in the case of Cameron who uses “one” several times in the first three age points (Figure 7b: 12 times, i.e. 7.14% of his utterances use “one” at 1;08; 27 entrances, i.e. 14.21% at 1;10 and 21 entrances, i.e. 10.99% at 2; 00), but after 2;00 the entrances drop and he does not use “one” more than three times in the following age points with 1.52% being the highest percentage at 2;04. Comparing Cameron’s data in Figures 7a and 7b it is easy to observe that “one” is mostly used as reference, with the exception of 15 counting sequences at age 1;10, reason for the peak at this age point in Figure 7b. With respect to the other children Charlotte’s use of “one” increases gradually with age. A similar analysis can be done for Naomi, using the frequency data (Figure 7b) we can see she has a peak at age 2;02 (6.02%, all entrances were used as reference) and uses again “one” at 2;04 (3.95%). The analysis of her use of the number word also shows entrances for “one” in a counting sequence at age 1;10.

As for the use of the indefinite article in English, as Figure 8a suggests, there is a more gradual development.

Figure 8a – Percentages of entrances of “a/an” per utterances used as correct reference

0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 1.08 1.10 2.00 2.02 2.04 2.06 Cameron Charlotte Naomi

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Figure 8b – Percentages of entrances of “a/an” per utterances as retrieved from the general frequency data

As it is expected the indefinite article is never used in a counting sequence or in isolation, in those type of utterances I observed the use of number words instead. Figure 8a and 8b are in fact showing almost the same data, with a few differences due to incorrect use of “a/an” as reference or ambiguous entrances. Data indicates that children learn to use and distinguish indefinite articles from the number word “one”, more details can be seen in the comparison in Figure 10. Taking into considerations all the reference entrances for “one” and “a/an” I observed that at 20 months Cameron uses “one” as reference 7.14 % of the times, opposed to the use of “a” 3.57% of the times. At 24 months his use of “one” as reference increases to 8.38% and “a/an” also increases to 8.90%. Besides Cameron’s production of “one” and “a” the other children have very low productions of “one” as reference before age 2;02. Charlotte usage of “one” is 0.81 % of the utterances at 22 months and 1.43% at 24 months and the usage increases to 4.52% at 2;02, with a lower usage of “a” (1.94%). Charlotte’s usage of the indefinite article has overall low percentages with a peak at age 2;06 (2.53% used as reference, 3.03% in the general number of entrances for “a/an”). Naomi does not use one as reference until 2;02 where she uses it as reference in 6.02% of her utterances, in contrast with 4.17 % for “a/an”. Her peak in the usage of “a/an” is at age 2;04 with 12.5% of her utterances.

When do English speaking children learn “two”? Given the data collected in the longitudinal study (figure 9) we see that the use of “two” is very rare throughout the entire time span taken into consideration. The peak at 1;10 observed in Cameron also corresponds to his peak in the use of “one” (figure 7b) but it is due to the fact that he uses “one” in a rather long and repetitive counting sequence. The reason for this peak in use is likely to be found in the activity the child is involved in, going through the transcript it seems that Cameron and his mother are playing a game involving jumping and bouncing and the child counts before jumping. Unfortunately there are no further comments in the transcripts that could help to have a better understanding of the event. 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 1.08 1.10 2.00 2.02 2.04 2.06 Cameron Charlotte Naomi

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Figure 9 – Percentages of entrances for “two” per utterances as retrieved from the general frequency data

Charlotte’s and Naomi’s use of “two” develops, as expected, more slowly and starts later with only one entrance before 2;04 for Naomi. Trying to compare the data of the three children in the use of “one”, “two” and “a/an” I calculated the average percentages of use per utterances of all the three children as shown in the frequency per every age point (figure 10).

Figure 10 - Comparison of the average percentages of entrances for “one”, “a/an” and “two” as retrieved from the general frequency data

As expected from our hypothesis children start using “one” and “a/an” before they learn “two”. It is also possible to observe a difference in the use of “one” and “a/an”. The evolution in the use of the indefinite article increases over time while the use of “one” seems to decrease. The analysis of the data did not, however suggest any particular correlation in the use of one over the other. Looking at the individual growth of every child (figure 7b and 8b) it is safe to say

0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 1.08 1.10 2.00 2.02 2.04 2.06 Cameron Charlotte Naomi 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 1.08 1.10 2.00 2.02 2.04 2.06 one a/an two

First language acquisition of number words and its relation with the acquisition of indefinite articles and plural marking