Cross-linguistic relations between quantifiers and numerals in language acquisition : Evidence from Japanese

Journal of Experimental Child Psychology 103 (2009) 421–440
Contents lists available at ScienceDirect
Journal of Experimental Child
Psychology
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j e c p
Cross-linguistic relations between quanti?ers and numerals
in language acquisition: Evidence from Japanese
David Barner a,*, Amanda Libenson b, Pierina Cheung c, Mayu Takasaki c,d
a Department of Psychology, University of California, San Diego, La Jolla, CA 92093, USA
b Department of Communication Sciences and Disorders, MGH Institute of Health Professions, Boston, MA 02114, USA
c Department of Psychology, University of Toronto, Toronto, Ont., Canada M5S 3G3
d Japanese Program, Department of German Language and Literature, Queen’s University, Kingston, Ont., Canada K7L 3N6
a r t i c l e
i n f o
a b s t r a c t
Article history:
A study of 104 Japanese-speaking 2- to 5-year-olds tested the rela-
Received 30 July 2008
tion between numeral and quanti?er acquisition. A ?rst study
Revised 27 November 2008
assessed Japanese children’s comprehension of quanti?ers, numer-
Available online 21 January 2009
als, and classi?ers. Relative to English-speaking counterparts, Japa-
nese children were delayed in numeral comprehension at 2 years
of age but showed no difference at 3 and 4 years of age. Also,
Keywords:
Japanese 2-year-olds had better comprehension of quanti?ers,
Counting
indicating that their delay was speci?c to numerals. A second study
Quanti?ers
Bootstrapping
examined the speech of Japanese and English caregivers to explore
Language acquisition
the syntactic cues that might affect integer acquisition. Quanti?ers
Semantic development
and numerals occurred in similar syntactic positions and
Number
overlapped to a greater degree in English than in Japanese. Also,
Japanese
Japanese nouns were often dropped, and both quanti?ers and
numerals exhibited variable positions relative to the nouns they
modi?ed. We conclude that syntactic cues in English facilitate
bootstrapping numeral meanings from quanti?er meanings and
that such cues are weaker in classi?er languages such as Japanese.
Ó 2008 Elsevier Inc. All rights reserved.
Introduction
Early in language development, children acquire words rapidly, learning up to 10 words a day from
18 months of age (Bates & Goodman, 1997; Caselli, Casadio, & Bates, 1999; Fenson et al., 1994; Gold-
?eld & Reznick, 1990). Children’s early vocabularies are ?lled with names for things and even include a
sprinkling of words that denote actions and events (Nelson, Hampson, & Shaw, 1993). However, before
2 years of age, most children lack words that denote the properties of sets. For example, quanti?ers
* Corresponding author. Fax: +1 858 534 7190.
E-mail address: barner@ucsd.edu (D. Barner).
0022-0965/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.jecp.2008.12.001

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D. Barner et al. / Journal of Experimental Child Psychology 103 (2009) 421–440
and number morphology such as singular–plural marking are largely absent from children’s language
production before 24 months of age (Dale & Fenson, 1996; Fenson et al., 1994). Also, children’s com-
prehension of quanti?ers develops gradually between 2 and 5 years of age. The relative absence of
number marking and set-relational quanti?ers in early language suggests that these words pose a spe-
cial challenge in acquisition (Barner, Chow, & Yang, 2009; Bloom & Wynn, 1997; Wynn, 1992).
Like quanti?ers, numerals such as one, two, and three typically emerge in children’s speech at
around 2 years of age. Also, children’s emerging comprehension of numerals in English is signi?cantly
correlated with their developing comprehension of quanti?ers (Barner et al., 2009). Although many
children can recite numerals in the count list by 2 years of age, learning their meanings normally takes
an additional 18 to 24 months (Fuson, 1988; Le Corre & Carey, 2007; Le Corre, Van de Walle, Brannon,
& Carey, 2006; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007; Schaeffer, Eggleston, &
Scott, 1974; Wynn, 1990; Wynn, 1992). By 2.5 years of age, many English-speaking children have ac-
quired the meaning of the word one. These ‘‘one-knowers” give one object when asked for one but give
more than one for all other numbers. Children often spend a number of months as one-knowers before
they acquire the meaning of two (becoming two-knowers) and then three (becoming three-knowers).
By the time children understand four, they often demonstrate an understanding of all numerals in the
count sequence that they can recite. These children have transitioned from naming sets on the basis of
associations between words and set sizes to inferring their cardinality based on their understanding of
the cardinal principle, that is, that the last number recited in the counting routine refers to the cardi-
nality of the set (for a review, see Carey, 2004).
As English-speaking children learn the meaning of each numeral, their knowledge of quanti?ers also
grows. For 2- to 5-year-olds, knowledge of quanti?ers and determiners such as a, some, most, all, and none
predicts greater comprehension of numerals (number-knower level) independent of effects due to age
(Barner et al., 2009). Furthermore, this correlation between number knowledge and quanti?er compre-
hension is true of nearly all quanti?ers and determiners individually (i.e., it is not driven by one or two
quanti?ers). Thus, English children who show delayed numeral comprehension also tend to show de-
layed quanti?er comprehension, whereas children who are advanced in one domain are also advanced
in the other domain.
Why does knowledge of integers and quanti?ers emerge so late in language development relative to
other words, and why are the two word types so tightly yoked in acquisition? Wynn (1992) noted that to
learn integers, children must discover that (a) numerals denote the properties of sets, (b) numerals de-
note the cardinalities of sets, and (c) two denotes ‘two,’ three denotes ‘three,’ and so forth—that is, they
must learn which speci?c cardinality each numeral denotes. Quanti?ers pose a similar learning problem.
As with numerals, children must ?rst discover that quanti?ers denote properties of sets rather than prop-
erties of individual things. Second, they must discover that quanti?ers denote set relations (e.g., all, every,
some) or, in certain cases, proportions of sets (e.g., most, many, few). Finally, they must discover which
speci?c relations or proportions quanti?ers denote.
As Wynn (1992) observed, the ?rst step in this process poses a signi?cant problem. By denoting the
properties of sets rather than of individual things, quanti?ers and numerals differ from nearly all other
words that children learn during their ?rst 2 years of life. Words such as ?ve and many (unlike nouns such
as cat) can be applied to a set of things without being true of any single individual in isolation (e.g., in a set
of ?ve cats, no single cat has the property of ‘‘?veness”). As Bloom and Wynn (1997) noted, ‘‘Sets are noto-
riously abstract entities. One can see and hear cats, but nobody has ever been wakened in the middle of
the night by the yowling of a set” (p. 512).
Figuring out that a word denotes the property of a set is surely hard. Harder still, however, would
be to learn this separately for each quanti?er and numeral that is confronted in acquisition. To ease
this burden, Bloom and Wynn (1997) suggested that children might use cues from both the syntax
and semantics of known words to bootstrap the meanings of unknown quanti?ers and numerals.
Bootstrapping mechanisms can take multiple forms involving semantic inferences based on syntactic
facts (Gleitman, 1990), syntactic inferences based on semantics (Grimshaw, 1981; Macnamara, 1982;
Pinker, 1984) or inferences within a domain. Three variations on these bootstrapping mechanisms are
relevant to the problem of acquiring quanti?ers and numerals.
First, as noted by Bloom and Wynn (1997), the syntax and semantics of English noun phrases (NPs)
might signal that both quanti?ers and numerals denote the properties of sets. In English, both can be

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used to modify count nouns, which denote kinds of individuals (see Barner & Snedeker, 2005). Also,
both can occur in partitive constructions, which denote part–whole relations (e.g., six of the dogs/some
of the dogs), and neither can occur between an adjective and a head noun, although other adjectives
that denote the properties of individuals can (e.g., the big smelly dogs, *the big some dogs, *the big ?ve
dogs). Finally, certain NP subdistinctions might provide cues to meaning. For example, both the words
a and one can be used in singular noun phrases (e.g., a/one cat vs. some/two cats), which might lead
children to conclude that both words denote sets of one, whereas other quanti?ers and numerals de-
note sets of ‘‘more than one” (Carey, 2004; Li, Le Corre, Shui, Jia, & Carey, 2003; Sarnecka et al., 2007).
For the purposes of the current discussion, we call this ?rst class of possible mechanisms, by which
quanti?er and numeral meanings are bootstrapped via NP syntax and semantics, NP bootstrapping.
In addition to NP bootstrapping, children might also exploit direct syntactic relations between
quanti?ers and numerals to discover their meanings. By learning their common distributional pro?les,
children could use knowledge of one set of words (e.g., quanti?ers) to inform their hypotheses about
the other set (e.g., numerals). For example, having learned that all refers to the property of a set, chil-
dren could infer that other words used in similar syntactic contexts, such as three or four, also do. In
this way, learning a small set of quanti?ers might permit children to begin the process of integer
acquisition, beginning with the inference that numerals, like quanti?ers, represent sets. Because this
mechanism involves inferences about numeral meanings based on their distributional overlap with
quanti?ers, we call it quanti?er bootstrapping.
Finally, relations between quanti?er and integer acquisition might be mediated conceptually. Dur-
ing their ?rst 2 years of life, children have not yet had the occasion to explicitly represent set relations
in language and may lack the representational resources to do so. Many early utterances may well re-
quire only a basic predicate logic that lacks logical quanti?ers. To explicitly express set relations such
as some and all, however, demands more sophisticated representational resources and minimally a
?rst-order predicate logic that supplies variables and logical quanti?ers (e.g., "x = ‘‘for all x,”
$x = ‘‘there exists an x such that . . .”). Without such variables and logical quanti?ers, children could
perhaps talk about things and sets of things but would be unable to explicitly represent set relations
or their properties. However, having acquired operators that express existential quanti?cation, for
example, children would have the resources needed to represent not only quanti?ers but also numeral
meanings.1 By this account, which we call conceptual bootstrapping, acquiring one or two quanti?ers
might require children to undergo a conceptual change, thereby setting the stage for acquiring other
set relational quanti?ers and numerals (for discussions of conceptual bootstrapping in this and other do-
mains, see Carey, 2004; Gentner, 1989; Perkins & Unger, 1994).
Within a particular language such as English, it is dif?cult to distinguish the relative roles of these
three possible bootstrapping mechanisms. Although we know that quanti?er and numeral compre-
hension are signi?cantly correlated within English, it is dif?cult to say why. The two word types could
be acquired in parallel, each separately facilitated by the presence of count syntax, as with NP boot-
strapping, or they could interact directly via either quanti?er or conceptual bootstrapping. Also pos-
sible is that all three mechanisms play a role.
As Bloom and Wynn (1997) suggested, our best chance to distinguish the roles of particular cues is
to compare acquisition cross-linguistically (see also Dowker, Bala, & Lloyd, 2008). In particular, Bloom
and Wynn (1997) proposed comparing languages such as English and Japanese that differ in several
ways that speak to the hypotheses at hand. Syntactic relations among quanti?ers, numerals, and
nouns may be less consistent and informative in Japanese than in English. For one, Japanese lacks
count syntax at the level of the noun and, thus, does not obligatorily mark individuation syntactically.
As a result, words that denote objects, such as ball, can be used in many of the same syntactic frames
as words that denote nonsolid substances such as water. Also, as a classi?er language, Japanese
requires the use of classi?ers whenever numerals are used. Somewhat like English measure words,
which are often used with mass nouns to permit counting (e.g., six piles of dust), Japanese classi?ers
intervene between numerals and nouns and encode semantic properties of the noun such as shape
1 For example, $x(Px & ($y)(Py & :ðx ¼ yÞ)) means ‘‘there are at least two”; $x(Px & ($y)(Py & :ðx ¼ yÞ)) & :ð9zÞ(Pz & :ðz ¼ xÞ &
:ðz ¼ yÞ) means ‘‘there are exactly two”.

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information. For example, the classi?er -nin is used when counting people, as in Example 1, but is not
used with quanti?ers such as both, as shown in Example 2:
1. [san-nin-no gakusei]-ga aruita
3-CL-GEN student-NOM walked
‘Three students walked’
2. [ryoohoo-no gakusei]-ga aruita
both-GEN student-NOM walked
‘Both students walked’
Because they intervene between numerals and nouns, classi?ers prevent the two word types from
appearing adjacently. Also, in Japanese, classi?ers cause important phonological changes in numerals.
For example, the word one takes the forms ippiki, ichimai, hitotsu, and ikko when used with classi?ers
for naming animals, ?at sheets, generic objects, and small objects, respectively. This can hardly help chil-
dren to converge on a meaning for one, especially when there are more than 100 classi?ers in Japanese, 30
of which are used frequently (Downing, 1996). Children learning Japanese and Chinese acquire classi?er
meanings very gradually, and even some very common classi?ers are not fully understood by 6 years of
age (see Sumiya & Colunga, 2006; Uchida & Imai, 1999; Yamamoto & Keil, 2000; for evidence from Man-
darin Chinese, see Chien, Lust, & Chiang, 2003; Li, Barner, & Huang, 2008). Thus, the use of numerals in
children’s language input is highly variable and different in many respects from the use of quanti?ers.
One ?nal cross-linguistic difference that might cause differences in how quanti?ers and numerals
interact in Japanese is ‘‘?oating.” In Japanese, both numerals and quanti?ers can ‘‘?oat” to postnominal
positions, as in Examples 3 and 4:
3. a. [san-nin-no gakusei]-ga aruita
3-CL-GEN student-NOM walked
‘Three students walked’
b. gakusei-ga [san-nin aruita]
student-NOM 3-CL walked
‘Three students walked’
4. a. [ryohoo-no gakusei]-ga aruita
both-GEN student-NOM walked
‘Both students walked’
b. gakusei-ga [ryoohoo aruita]
student-NOM both walked
‘Both students walked’
In contrast, English numerals and quanti?ers normally precede the noun, although quanti?ers can
?oat to postnominal positions, as in Example 5. English numerals never ?oat, as in Example 62:
5. a. All the students walked to the store.
b. The students all walked to the store.
6. a. Four of the students walked to the store.
b. *The students four walked to the store.
As noted by Mintz (2003), detecting distributional relations between words should be easiest in
languages with stable word order and harder in languages that permit relatively freer ordering of con-
stituents. In the current context, freer word order due to ?oating could have two primary effects. First,
relevant to NP bootstrapping, ?oating could obscure the relationship among quanti?ers, numerals, and
the nouns they modify, making it harder for children to recognize that numerals and quanti?ers de-
note properties of sets. Second, in the event that quanti?ers and numerals ?oat with different frequen-
cies in the input, the distributional overlap between quanti?ers and numerals would be reduced,
thereby weakening the signal to distributional learning and, thus, to quanti?er bootstrapping.
In support of Bloom and Wynn’s (1997) prediction that cross-linguistic differences should affect
integer acquisition, recent studies have found delayed integer acquisition in both Japanese and
2 Barbara Sarnecka (personal communication) noted that such uses are possible in English, although they are not productive and
are idiomatic in character: ‘‘Old King Cole was a merry old soul, and a merry old soul was he; he called for his pipe, and he called for
his bowl, and he called for his ?ddlers three.”

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425
Mandarin Chinese (two classi?er languages) relative to English and Russian (two languages with ri-
cher number marking) (Li et al., 2003; Sarnecka et al., 2007). For example, Sarnecka and colleagues
(2007) found that children learning Russian and English began to comprehend numeral meanings ear-
lier than did children learning Japanese. In their study, nearly half of the Japanese children (2 years 9
months to 3 years 6 months of age) had not yet acquired the meaning of one, whereas more than 90%
of English and Russian children knew at least one. Strikingly, these results were found even though
Japanese children typically receive equal exposure to numerals and counting routines and even
though Japanese and Chinese children acquire the count list with greater ease than do English-speak-
ing children (see Miller, Smith, Zhu, & Zhang, 1995; Miller & Stigler, 1987).
This delay of integer acquisition in Japanese provides a case in which it is possible to tease apart the
bootstrapping mechanisms that might be used to discover numeral meanings. For example, if, as
described in the NP bootstrapping hypothesis, both quanti?er and numeral meanings are boot-
strapped in parallel from NP syntax and semantics, then both should be equally delayed in Japanese
because both should be equally affected by the relative lack of number marking on nouns. Similarly, if
acquiring quanti?ers bootstraps integer acquisition conceptually (driving the correlation in English
development), then Japanese children’s delay in integer acquisition should correspond to a similar
delay in quanti?er development. However, if integer acquisition in English is facilitated by the distri-
butional overlap between quanti?ers and integers, as suggested by the quanti?er bootstrapping
hypothesis, then weaker syntactic relations between quanti?ers and numerals in Japanese would
predict a delay that is speci?c to integer acquisition without a corresponding delay in quanti?er
acquisition.
We performed two studies to (a) assess cross-linguistic differences in the acquisition of set representations
and (b) test the possible mechanisms of integer bootstrapping. The ?rst study tested the comprehension of
numerals, quanti?ers, and classi?ers in Japanese 2- to 5-year-olds to determine whether their development
is yoked, as in English, or whether Japanese children’s dif?culty is speci?c to acquiring the meanings of numerals.
In the second study, we examined caregiver speech in both Japanese and English to determine whether the syn-
tactic relations between quanti?ers and numerals are in fact stronger in English than in Japanese.
Experiment
The ?rst study tested the course of quanti?er and integer acquisition in Japanese children to deter-
mine whether quanti?ers emerge earlier than numerals or are also delayed relative to English. We also
tested comprehension of classi?ers to evaluate their role in integer acquisition.
Method
Participants
Participants were 104 Japanese-speaking children (55 girls and 49 boys) between 23.8 and 59.0
months of age (M = 48.1) recruited from ?ve child care centers and preschools in Fukuoka, Japan. Chil-
dren were divided into three groups: 2-year-olds (n = 32, mean age = 29.7 months, range = 23.8–35.7),
3-year-olds (n = 37, mean age = 42.3 months, range = 36.5–47.7), and 4-year-olds (n = 35, mean
age = 54.3 months, range = 49.1–59.0). Additional pilot participants, used to develop the methods,
were tested in a child care center in Toronto, Canada. Also, 16 Japanese-speaking college students
were recruited and tested at Sapporo University in Japan.
For a subset of analyses, Japanese children were compared with 72 English-speaking children (38
girls and 34 boys) from Barner and colleagues’ (2009) study who were also divided into three closely
age-matched groups: 2-year-olds (n = 44, mean age = 29.3 months, range = 22.8–35.0), 3-year-olds
(n = 12, mean age = 41.4 months, range = 38.4–45.9), and 4-year-olds (n = 16, mean age = 54.3 months,
range = 48.5–60.4). These children were tested in Toronto and Boston, Massachusetts, USA.
Stimuli and procedure
All children were tested individually in a classroom environment in a single session lasting be-
tween 15 and 20 min. Children sat at a child-sized table across from the experimenter (M.T.), who

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was a native speaker of Japanese. A second experimenter sat next to the table to record responses and
videotape sessions. All children were tested in Japanese. Three tasks were used: (a) the Give-Quanti?er
task, (b) the Give-Number task, and (c) the Classi?er Match task. The tasks were always presented in
the above order. Adult controls were tested only with the Give-Quanti?er task.
The Give-Quanti?er task. This task was adapted from Barner and colleagues (2009). Stimuli con-
sisted of a red plastic circle and three sets of small plastic fruit (eight oranges, eight bananas, and eight
strawberries) that were presented in separate piles organized by kind. The experimenter ?rst intro-
duced children to the fruits to ensure that they could distinguish them: ‘‘Kore wa nani?” (‘‘What is this
called?”) or ‘‘Kore shitteru” (‘‘Do you know what this is?”). The experimenter was careful not to use
the target quanti?ers when introducing the items. The experimenter then showed children the red cir-
cle and asked them to put a quantity of a speci?c kind of fruit into it using a quanti?er (e.g., ‘‘Maru no
naka ni mikan wo zenbu iretekureru?” [‘‘Could you put all of the oranges into the red circle?”]). The
following quanti?ers were tested: chotto (a few), takusan (many), nokotteiru (the other Xs), ikutsuka
(some), hotondo (most), zenbu (all), hitotsumo (none), and ryoho (both). These quanti?ers were selected
based on previous studies of quanti?er development (e.g., Hanlon, 1987) due to their relatively early
acquisition in English and to focus on words that were likely to exhibit variability in young children.
Examples of how each quanti?er was used are presented in Table 1. For ryoho (both), we presented
children with one token of each fruit type (one orange, one strawberry, and one banana) and asked,
‘‘Maru no naka ni suki na kudamono wo ryoho iretekureru?” (‘‘Can you ?nd both of the fruits that
you like and put them into the red circle?”). For nokotteiru X (the other Xs), the experimenter told chil-
dren the following: ‘‘Mazu yonko ugokasu ne” (‘‘I will move four of them here”). The experimenter
then moved four of the objects into a separate pile and asked children to put ‘‘the other” things
(e.g., strawberries) into the circle: ‘‘Nokotteru ichigo wo maru no naka ni irete” (nokotteru may also
be translated as the remaining or the rest). Thus, a correct response required selecting the remaining
objects, but not those moved by the experimenter.
After each trial, the experimenter thanked the children and returned all fruit objects to their origi-
nal piles before the next request. The quanti?ers were presented in two different orders across partic-
ipants, and pairings of quanti?ers and kinds of fruit were quasi-randomized. Each word was tested
twice within participants.
The Give-Number task. This task was adapted from Wynn (1992) to test numeral comprehension.
Stimuli were the same red plastic circle and a set of eight plastic strawberries. To begin, the experi-
menter presented the strawberries to children and asked, ‘‘A, ichigo ga aru ne. Ikutsu aru kana? Kazo-
ete mite kureru?” (‘‘Oh, there are strawberries. How many do you think there are? Could you count
them for me?”). Then the experimenter showed children the red circle and asked them to put a certain
number of strawberries into it: ‘‘Maru no naka ni ichigo wo rokko irete?” (‘‘Could you put six straw-
berries into the red circle?”). Following Wynn (1992), we used a titration method. When children
Table 1
Experimenter requests in the Give-Quanti?er Task.
Quanti?er
Examples in Japanese and English translation
Some/ikutsuka
‘‘Maru no naka ni mikan wo ikutsuka iretekureru?”
‘‘Could you put some of the oranges into the red circle?
The other/nokotteiru
‘‘Maru no naka ni nokotteru mikan wo iretekureru?”
‘‘Could you put the other oranges into the red circle?”
A few/chotto
‘‘Maru no naka ni mikan wo chotto iretekureru?”
‘‘Could you put a few of the oranges into the red circle?”
Most/hotondo
‘‘Maru no naka ni mikan wo hotondo iretekureru?”
‘‘Could you put most of the oranges into the red circle?”
All/zenbu
‘‘Maru no naka ni mikan wo zenbu iretekureru?”
‘‘Could you put all of the oranges into the red circle?”
None/hitotsumo
‘‘Maru no naka ni mikan wo hitotsumo irenaide.”
‘‘Could you put none of the oranges into the red circle?”
Both/ryoho
‘‘Maru no naka ni suki na kudamono wo ryoho iretekureru?”
‘‘Could you put both of the fruits you like into the red circle?”
Many/takusan
‘‘Maru no naka ni mikan wo takusan iretekureru?”
‘‘Could you put many of the oranges into the red circle?”

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427
successfully gave N strawberries (e.g., 3), they were then asked to give N + 1 strawberries (e.g., 4).
When they failed with N, they were tested on N – 1 (e.g., 2). When they initially failed to give a correct
amount, they were asked, ‘‘Are you sure there are N strawberries?” Following their response, they
were asked, ‘‘Can you count to make sure?” If children counted and the last number of their count
did not match the number requested, they were asked again, ‘‘Is that N strawberries? Can you ?x it
to make it N strawberries?” If they failed to correctly ?x the set, they were tested with N – 1. If they
succeeded, they were tested with N again.
Children were called N-knowers (e.g., two-knowers) if they correctly gave N strawberries two of
three times when they were asked for N but failed to give the correct number two of three times
for N + 1. Children were credited as cardinal principle (CP)-knowers if they could correctly give 6
and 7 strawberries at least two of three times for each.
The Classi?er Match task. This task tested Japanese children’s comprehension of frequently used
classi?ers. In Japanese, classi?ers typically select for nouns with certain semantic properties. For
example, when counting animals, the classi?er -hiki is used, such that the numeral one becomes ippiki.
We tested children with four highly frequent classi?ers3 used with the numeral one: ippiki (one animal),
ichimai (one ?at sheet), hitotsu (one object), and ikko (one small object). Using a two-item forced-choice
paradigm, a distractor stimulus was always paired with a target object for each classi?er (see Chien et al.,
2003). The experimenter then asked the following question: ‘‘‘One-classi?er’ ha docchi?” (‘‘Which is the
‘classi?er-one’?”). Based on the classi?er used, children needed to choose one of the two objects. The tar-
get objects and distractors for each classi?er were as follows: ippiki (a small toy frog vs. a small box-
shaped present), hitotsu (a small box-shaped present vs. a small toy frog), ichimai (a ?at card vs. a small
box-shaped present), and ikko (a small box-shaped present vs. a ?at card). Children received a score of 1
for each correct choice for a maximum score of 4.
Results
For quanti?ers and numerals, we performed three analyses. First, we examined Japanese children’s
comprehension of numerals to determine whether they were delayed relative to children acquiring
English, as reported previously by Sarnecka and colleagues (2007). Second, we compared quanti?er
comprehension in Japanese and English. Third, we analyzed the relation between quanti?er compre-
hension and number-knower level to determine whether quanti?er and integer acquisition are corre-
lated in Japanese as they are in English. In each analysis, Japanese children were compared with
English-speaking children from Barner and colleagues’ (2009) study who were tested using exactly
the same procedures and materials described above but in English and with the words a, some, all,
most, most, both, none, another, and the other X’s. English sentences are shown in Table 1.
For classi?ers, we determined the number of trials on which children matched classi?ers to their
appropriate objects and compared behavior among 2-, 3-, and 4-year-olds.
Numeral comprehension
We assigned each child a number-knower level using the criteria described above. To compare the
number-knower levels of Japanese and English-speaking children, number-knower level was entered
into an analysis of variance (ANOVA) with two between-participants factors: Age (2-year-olds vs. 3-
year-olds vs. 4-year-olds) and Language (Japanese vs. English). The analysis found a main effect of
age, F(2, 166) = 108.09, p < .001, but no main effect of language, F(1, 166) = 0.18, p > .50, indicating that
there was no overall difference in number-knower levels between children acquiring the two lan-
guages. However, crucially, there was a signi?cant interaction between age and language, F(2,
166) = 5.47, p < .01.
To investigate this interaction, we compared the average number-knower levels of English and Jap-
anese children at 2, 3, and 4 years of age (see Fig. 1). At 2 years of age, Japanese children had a signif-
icantly lower number-knower level (M = 0.44) than did English-speaking children (M = 1.14),
3 According to Tamiko Ogura (personal communication), data from the Japanese Communicative Development Inventory (a
parental report measure) indicate that -tsu, -ko, -mai, and -hiki are the most frequent classi?ers in the speech of Japanese children
at 30 months of age (tsu is used by 72.0% of children, ko by 62.2%, mai by 23.2%, and hiki by 13.3%) (see also Naka, 1999).

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D. Barner et al. / Journal of Experimental Child Psychology 103 (2009) 421–440
Fig. 1. Average number-knower levels for Japanese and English children at 2, 3, and 4 years of age.
t(75) = 3.11, p < .003. However, there was no effect of language at 3 years of age (Japanese = 2.62, Eng-
lish = 2.25) or at 4 years of age (Japanese = 3.89, English = 3.38, both ps > .05).
The cross-linguistic difference for 2-year-olds re?ected the fact that signi?cantly more Japanese 2-
year-olds were non-number-knowers (25 of 32) relative to English 2-year-olds (11 of 42),
v2(1) = 17.60, p < .001. There were more one-knowers in the English sample (19 of 42) than in the Jap-
anese sample (2 of 32), v2(1) = 11.23, p < .001, but no difference in the proportion of two-knowers,
three-knowers, or CP-knowers (all ps > .05).4 Thus, following Sarnecka and colleagues (2007), we found
a signi?cant difference in the development of numeral meanings across Japanese and English. Whereas
hardly any Japanese children had acquired the meaning of one before their third birthday, nearly half of
English-speaking children had done so.
At later ages, there were no cross-linguistic differences in the proportion of children at each num-
ber-knower level (all ps > .05) (see Fig. 2). Thus, Japanese children caught up to their English counter-
parts and acquired numeral meanings quickly after having acquired one. This suggests that the delay
in Japanese is not attributable to a dif?culty in acquiring speci?c numeral meanings given that they
acquire the meanings of two, three, and beyond as early as do children learning English. Instead, the
result suggests a more general delay, consistent with a failure to recognize that numerals denote
the cardinalities of sets.
Quanti?er comprehension
To evaluate Japanese children’s comprehension of quanti?ers, we de?ned ‘‘correct” responses for
each quanti?er as in Table 2. These criteria were based on the judgments of adult speakers of Japanese
(n = 16). For each word, 100% of adult participants gave a quantity of objects that was consistent with
these criteria on two trials.
Japanese children’s comprehension of the quanti?ers and determiners was analyzed based on the
number of correct responses that they provided over two test trials for each word (resulting in scores
of 0, 1, or 2). For each quanti?er, we determined whether the rate of correct responses differed from
chance using one-sample t tests. We de?ned chance based on the assumption that there were nine
possible responses, giving 0, 1, 2, . . . 8 objects on each trial. With a word such as all, for which there
was only one correct response (i.e., 8 objects), the number of correct responses expected by chance
over two trials would be 2/9 (i.e., 1/9 + 1/9 = .222).
Fig. 3 presents data for each age group (2-, 3-, and 4-year-olds) for each quanti?er. Items are pre-
sented according to the average percentage of trials on which children responded correctly for each,
thereby providing an estimate of their order of acquisition: hitotsumo (none), zenbu (all), takusan
4 There was one four-knower. To simplify analysis, this child was classi?ed as a CP-knower.

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D. Barner et al. / Journal of Experimental Child Psychology 103 (2009) 421–440
429
Fig. 2. Distribution of non-knowers, subset-knowers, and CP-knowers in English and Japanese children at 2, 3, and 4 years of
age.
Table 2
Correct (adult) responses for each Japanese quanti?er.
Quanti?er
Correct responses
Some/ikutsuka
1–7
The other/nokotteiru
4 objects not moved by experimenter
A few/chotto
1–7
Most/hotondo
5–7
All/zenbu
8
None/hitotsumo
0
Both/ryoho
2
Many/takusan
5–8
Note. Total numbers of objects: 8 for some, the other, a few, most, all, none, and many; 3 for both).
(many), chotto (a few), ikutsuka (some), nokotteiru (the other Xs), ryoho (both), and hotondo (most).
Combined, the performance of Japanese 2- to 5-year-olds was signi?cantly better than chance for
all words (all ps < .001) except for ikutsuka (some) and chotto (a few), which did not differ from chance
(p > .05), and hotondo (most), which was below chance (p > .001). The Japanese 2-year-olds, who were
delayed in integer acquisition, exhibited better than chance comprehension of zenbu (all), hitotsumo
(none), and nokotteiru (the others) (ps < .001).5 Comprehension was at chance for takusan (many),
chotto (a few), ryoho (both), and ikutsuka (some) (ps > .10) and was below chance for hotondo (most)
(p < .001).
To compare quanti?er comprehension between Japanese and English, each child was assigned a
quanti?er score, which was de?ned as the average number of correct responses (of 2) across all quan-
5 Interestingly, children succeeded at hitotsumo (none), although few were yet one-knowers. This suggests that knowing hitotsu
(one) did not likely contribute to understanding hitotsumo.

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D. Barner et al. / Journal of Experimental Child Psychology 103 (2009) 421–440
Fig. 3. Average percentages of trials on which Japanese children gave adult-like responses for the quanti?ers hitotsumo (none),
zenbu (all), takusan (many), chotto (a few), ikutsuka (some), nokotteiru (the other Xs), ryoho (both), and hotondo (most).
ti?ers (see Fig. 4). An ANOVA assessed the effects of Age (2-year-olds vs. 3-year-olds vs. 4-year-
olds) and Language (Japanese vs. English) on quanti?er score. There was a signi?cant effect of
age, F(2, 169) = 120.1, p < .001, driven by an overall increase in scores with age. Also, Japanese chil-
dren had higher quanti?er scores, on average, than did English-speaking children, resulting in a
main effect of language, F(1, 169) = 9.4, p < .005. Finally, there was a signi?cant interaction between
age and language, F(2, 169) = 11.3, p < .001, which was due to a difference between English and
Japanese children at 2 years of age (English = 0.48, Japanese = 0.93), t(73) = 7.27, p < .05, but not
at 3 years of age (English = 1.19, Japanese = 1.33) or 4 years of age (English = 1.63, Japanese = 1.53),
both ps > .05. Thus, Japanese children had a slightly greater comprehension of quanti?ers at 2 years
of age but did not differ at 3 and 4 years of age. Whereas the Japanese children were initially de-
layed in acquiring numeral meanings relative to English children, they were relatively advanced in
quanti?er acquisition, suggesting that for them quanti?er and numeral comprehension were not
yoked in early acquisition.6
6 Unlike Japanese 2-year-olds, who were tested on all quanti?ers used for older groups, English-speaking 2-year-olds were
tested only on a, some, all, and none. To verify that this did not drive the difference between groups, we did two analyses. First, a
comparison of only overlapping items (some, all, and none) found the same signi?cant difference (English = 0.91, Japanese = 1.27),
t(74) = 3.33, p < .001. Second, Japanese children’s comprehension of nonoverlapping words (M = 0.70) was signi?cantly worse than
their comprehension of overlapping words (M = 1.27), t(31) = 6.85, p < .001, suggesting that the added words did not drive the
cross-linguistic difference.

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