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UNCORRECTED PROOF
Quantifier Spreading in School-Age
Children: An Eye-Tracking Study
Irina A. Sekerina, Patricia J. Brooks, Luca Campanelli
and Anna M. Schwartz
Abstract Children make quantifier-spreading errors in contexts involving sets in
1
partial one-to-one correspondence; e.g., Every bunny is in a box is rejected as a2
description of three bunnies, each in a box, along with two extra boxes. To deter-3
mine whether a signature pattern of visual attention is associated with the classic4
q-spreading error as it occurs in real time, eye-movements were recorded while5
children (N=41; mean 8 y;9 m, range 5;8–12;1) performed a sentence-picture ver-6
ification task, with every modifying either the figure or ground of locative scenes7
(every bunny vs. every box). On trials designed to elicit the classic error, children8
performed at chance (53.3% correct). Errors involved greater numbers of fixations9
to the extra objects/containers, time-locked to regions following the quantified noun10
phrase. Correct responses were associated with longer reaction times, indicating11
additional processing required for quantifier restriction; accuracy was uncorrelated12
with verbal or nonverbal intelligence and only weakly associated with age. The13
findings underscore the susceptibility of school-age children to make errors given a14
default expectation for distributive quantifiers like every to refer to sets in one-to-one15
correspondence and their inattention to sentence structure.16
Keywords Quantifier-spreading (q-spreading) ·Eye movements17
Visual attention ·Children ·Universal quantifier every ·Visual world paradigm18
I. A. Sekerina (B)·P. J. Brooks
Department of Psychology, College of Staten Island, City University of New York, New York, NY
101314, USA
e-mail: Irina.Sekerina@csi.cuny.edu
P. J. Brooks
e-mail: patricia.brooks@csi.cuny.edu
I. A. Sekerina ·P. J. Brooks ·L. Campanelli ·A. M. Schwartz
The Graduate Center, City University of New York, New York, NY 10016, USA
e-mail: luca.campanelli@haskinslabs.org
A. M. Schwartz
e-mail: anna.m.e.schwartz@gmail.com
© Springer International Publishing AG, part of Springer Nature 2019
K. É. Kiss and T. Zétényi (eds.), Linguistic and Cognitive Aspects
of Quantification, Studies in Theoretical Psycholinguistics 47,
https://doi.org/10.1007/978-3-319-91566-1_8
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1 Introduction19
Children’s acquisition of quantifiers has been a topic of great interest due to the com-20
plexity of the mappings between semantic contrasts and lexical-syntactic structures,21
and children’s apparent difficulties in learning these mappings. Inhelder and Piaget22
(1964) seminal work on class inclusion errors led to a proliferation of research on23
children’s difficulties in restricting the domain of a universal quantifier to the appro-24
priate noun phrase (e.g., Brooks and Braine 1996; Bucci 1978; Donaldson and Lloyd25
1974; Freeman 1985; Philip 1995), with the term quantifier-spreading (q-spreading)26
coined as a description of these errors (Roeper and de Villiers 1993). The present27
study aims to shed light on the source of q-spreading errors in school-age children28
by examining patterns of visual attention in sentence processing in real time.
AQ1 29
The terminology used to describe children’s q-spreading errors is unfortunately30
very convoluted. Some authors have emphasized a distinction between bunny-31
spreading and classic q-spreading errors (Roeper et al. 2004), whereas others have32
emphasized under-exhaustive versus over-exhaustive search errors (Freeman 1985).33
Note, however, that the over-exhaustive error is identical to the classic q-spreading34
error. Our intention is not to prioritize one set of terms over the other, but to pay35
homage to both psychological and linguistic traditions in describing these errors.36
Figures 1and 2provide depictions of sets of objects in containers and corresponding37
sentences to illustrate each error type. Bunny-spreading errors occur when children38
extend the scope of a universal quantifier in sentences like Every bunny is in a box39
or Every box has a bunny in it to include extraneous objects that are neither bunnies40
nor boxes (e.g., cats or buckets, as shown in Fig. 1a, b).41
Under-exhaustive and over-exhaustive (i.e., classic) errors occur in contexts42
involving sets in partial one-to-one correspondence—for example, three bunnies43
each in a box, along with one or more extra bunnies or boxes (Fig. 2a, b). Note that44
the specification of error types depends on the pairing of sentences with pictures.45
For the sentence Every box has a bunny in it, rejecting a picture with extra bun-46
nies (Fig. 2a) is an over-exhaustive, classic error (i.e., the scope of the quantifier47
is extended beyond the boxes containing bunnies), and accepting the sentence as a48
B&W IN PRINT
Fig. 1 Sample pictures with extra objects (a) or containers (b) designed to elicit bunny-spreading
errors
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B&W IN PRINT
Fig. 2 Sample pictures of sets in partial one-to-one correspondence with extra objects (a) or con-
tainers (b) designed to elicit over-exhaustive (classic) and under-exhaustive errors
description of a picture with extra boxes (Fig. 2b) is an under-exhaustive error (i.e.,49
some boxes fail to be included within the scope of the quantifier). For the sentence50
Every bunny is in a box, acceptance of Fig. 2a would constitute an under-exhaustive51
error, and rejection of Fig. 2b would constitute an over-exhaustive, classic error.52
Whereas the under-exhaustive error has been documented only in young children53
and appears to be relatively rare (Freeman 1985; Roeper et al. 2004), the classic54
over-exhaustive, classic error has been reported in studies of school-age children55
(Bucci 1978), bilingual adults (Berent et al. 2009; DelliCarpini 2003; Sekerina and56
Sauermann 2015) and even monolingual adults (Brooks and Sekerina 2006; Minai57
et al. 2012).58
Both bunny-spreading and under-exhaustive errors decline rapidly in early child-59
hood and little attention has been paid to these errors in theoretical accounts; hence for60
brevity, we will use the term classic q-spreading to refer to the over-exhaustive error61
throughout the remainder of this chapter. Explanations for the classic error fall into62
two broad categories, linguistic and cognitive, but full treatment of the various expla-63
nations is beyond the scope of this chapter (see Rakhlin 2007). Within the Generative64
Grammar framework of language acquisition, researchers have attributed the error65
to children’s immature, non-adult-like linguistic representations, which may lead66
to quantification over events rather than individuals (Philip 1995) or non-canonical67
mappings from syntax to semantics (Geurts 2003). Classic q-spreading has been68
attributed to weak quantification (Drozd 2001) and recovery from errors to syntactic69
restructuring (Roeper et al. 2004). In contrast, cognitive approaches attribute classic70
q-spreading to extra-linguistic factors that impact sentence processing, such as the71
pragmatics of the testing situation (Crain et al. 1996), weak cognitive control (Minai72
et al. 2012), or task demands (O’Grady et al. 2010).73
In our prior work, we suggested that classic q-spreading might arise from shal-74
low processing or lack of attention to sentence structure (Brooks and Sekerina 2005,75
2006). Shallow sentence processing is thought to generate ‘good enough’ (under-76
specified) representations of sentence structures that under most circumstances are77
sufficient for comprehension (Clahsen and Felser 2006; Felser and Clahsen 2009;78
Ferreira et al. 2002; Sanford and Sturt 2002). When relying on shallow processing,79
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individuals may associate sentence structures with canonical semantic representa-80
tions by default, such as associating the first noun in the sentence with the role of81
actor, which would lead to an error in processing a passive sentence such as The dog82
was chased by the cat (Ferreira 2003). Brooks and Sekerina (2005,2006) interpreted83
the occurrence of classic q-spreading in college students as evidence of shallow pro-84
cessing (as opposed to having a faulty or immature grammar) resulting in inaccurate85
mappings between syntactic and semantic representations.86
In earlier work, Brooks and Braine (1996) suggested that children might use87
canonical collective and distributive representations as defaults when interpreting88
sentences with universal quantifiers: The canonical collective representation involves89
a group of individuals (or objects) performing an action together (all of the men lifted90
a box, with the interpretation that the men lifted a box together) or assembled in the91
same location (e.g., all of the flowers are in a vase, with the interpretation that the92
flowers are in the same vase). The canonical distributive interpretation assumes one-93
to-one correspondence, with individuals performing the same action but on their own94
(e.g., each man lifted a box, with the interpretation that each man lifted a different95
box) or in their own corresponding locations (e.g., each flower is in a vase, with96
the interpretation that there are as many vases as flowers, with one flower in each).97
For sentences with a distributive universal quantifier like each or every, one-to-one98
correspondence is thought to be the default semantic alignment of the two sets of99
objects. When relying on shallow processing, the child may fail to consider the100
syntactic structure in determining which noun phrase is modified by the quantifier;101
consequently he or she will reject a distributive scene showing sets in partial one-to-102
one correspondence, resulting in a classic q-spreading error.103
In documenting classic errors, researchers have tended to rely on two related104
methodologies: the picture-choice task and the sentence-picture verification task.105
The picture-choice task pits two or more pictures (e.g., one with extra bunnies,106
one with extra boxes) against each other, and asks participants to find the picture107
where, e.g., Every box has a bunny in it. Participants are required to choose one of108
the pictures, where typically only one picture is logically correct; hence the task is109
useful in determining error rates in using sentence structure to restrict the quantifier to110
the appropriate noun phrase. Brooks and Sekerina (2005,2006, Experiment 3) tested111
adults using the picture-choice task with locative scenes (objects in containers) as112
illustrated in Fig. 2, with the position of the quantifier varying from trial to trial (e.g.,113
modifying bunny or box). However, the visual display was more complex, with four114
pictures instead of two. One picture depicted the three pairs of objects in containers115
plus two extra objects, the second one had the three pairs plus two extra containers,116
and the remaining two were foils with two different objects or containers. The authors117
found that college students were only 75% correct (although they had no difficulties118
avoiding the foils that depicted extraneous objects). Street and Da˛browska (2010)119
used the picture-choice task with two options—one with extra objects, one with extra120
containers, and tested adults who had low educational attainment. They attributed121
the group’s poor performance on the task (78% correct for the sentence Every X is122
inaY and 43% correct for Every Y has an X in it) to participants’ lack of experience123
with the sentence structures.124
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The sentence-picture verification task (Clark and Chase 1972) presents pictures125
one at a time along with an accompanying sentence, and asks participants to decide126
whether or not the sentence is an accurate description of the picture. This task is127
advantageous for distinguishing different error types, as features of pictures and128
sentences may be manipulated independently. Studies using this task suggest that129
the number of extra objects influences error rates: In the most extreme case, with one130
extra object (e.g., three turtles each holding an umbrella, with one extra umbrella),131
Japanese adults achieved accuracy of only 59% correct when verifying sentences132
like Dono-kame-mo kasa-o sashi-teruyo ‘Every turtle is holding an umbrella’ (Minai133
et al. 2012). Other studies have reported high rates of classic errors amongst adult134
L2 learners of English with low proficiency (Berent et al. 2009; DelliCarpini 2003).135
2 Current Study136
In the current study, we examined eye-movements during sentence processing in137
school-age children to examine patterns of visual attention associated with classic138
q-spreading in the sentence-picture verification task. To date, only one prior study139
has examined eye-movements associated with susceptibility to classic errors in chil-140
dren. In a study with Japanese preschool-age children, Minai et al. (2012)varied141
the number of extra objects (e.g., umbrellas) in the sentence-picture verification task142
across blocks of trials; they reported very high rates of classic errors when there143
was just one extra umbrella as opposed to three, but only when the more difficult144
one-object condition was presented first. Perhaps due to the small number of children145
who responded correctly in the difficult condition—i.e., 25 of 29 children were cat-146
egorized as SR (symmetric response) for consistently making the classic error—the147
researchers failed to find any evidence that patterns of eye-movements, recorded148
while the sentence was unfolding, distinguished children as a function of their accu-149
racy in sentence-picture verification. However, they did report that children spent150
more time looking at the extra objects (one or three umbrellas) prior to the onset151
of the sentence, when compared to adults. Minai and colleagues interpreted their152
findings as suggesting that difficulties in the control of attention contribute to the153
occurrence of classic q-spreading in children.154
Extending the study of classic errors to adult bilingual heritage speakers of Rus-155
sian, Sekerina and Sauermann (2015) identified an attentional pattern of eye move-156
ments that distinguished incorrect (20%) from correct (80%) responses in heritage157
Russian-English bilingual adults performing the sentence-picture verification task158
in their weak language (i.e., Russian). This attentional signature was time-locked to159
the occurrence of the verb in the sentences (e.g., Kazhdyj alligator lezhit v vanne160
[Every alligator lies in bathtub]); thus, immediately after processing the quantified161
noun phrase (e.g., kazhdyj alligator), adults who were susceptible to the error showed162
increased looks to the extra objects in the picture.163
The current study attempts to extend the attentional signature pattern associ-164
ated with classic q-spreading to monolingual English-speaking children of ages165
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5–12 years. Children in this age range are still susceptible to classic errors and yet vary166
in performance (Brooks and Braine 1996; Brooks and Sekerina 2005,2006, Exper-167
iments 1 and 2). Using the sentence-picture verification task, we examined visual168
attention as each sentence unfolded in real time. Our goal was to determine whether169
q-spreading would be associated with increased looks to the extra objects/containers170
and whether these looks would be time-locked to the region of interest immedi-171
ately following the quantified noun phrase. We supplemented our analyses of eye172
movements with reaction time data to determine whether q-spreading errors were173
associated with greater or lesser processing time relative to correct responses. Finally,174
in addition to testing children across a broad age range, we administered assessments175
of non-verbal and verbal intelligence to determine whether either of these abilities176
would be associated with error rates after controlling for age.177
Across trials we varied the structure of the sentences, with the quantifier every178
modifying either the object or container in locative events (e.g., bunny vs. box as179
illustrated in Figs. 1and 2). In addition to trials designed to elicit classic errors, we180
also included two other types of trials: One type had the potential to elicit bunny-181
spreading errors and the other had the potential to elicit under-exhaustive errors.182
The latter trial type was treated as a control condition (e.g., Every bunny is in a box183
presented with a picture with extra bunnies), as we expected children to correctly184
detect the violation of one-to-one correspondence between bunnies and boxes with185
near perfect accuracy, and reject these sentences as descriptions of the pictures.186
3Method187
3.1 Participants188
Participants were 41 monolingual English-speaking children (23 girls and 18 boys,189
M=8 y;9 m, SD =1;11, age range = 5;8–12;1). Thirty children were recruited and190
tested in an afterschool program at a private Catholic school in Staten Island, NY;191
an additional 11 children were recruited from a child subject pool and tested in a192
laboratory at the College of Staten Island, CUNY. Informed consent was obtained193
from parents and assent from children. The children were from middle to upper mid-194
dle class families; all had normal or corrected-to-normal vision. Children’s receptive195
knowledge of vocabulary was estimated using the Peabody Picture Vocabulary Test,196
4th Edition (PPVT-4, Form B; Dunn and Dunn 2007), Mraw score = 149.6, SD197
=23.9; Mstandardized score=109.4, SD =11.5; and their nonverbal intelligence198
was estimated with the Test of Nonverbal Intelligence, 3rd Edition (TONI-3; Brown199
et al. 1997), Mraw score=20.0, SD =8.7;Mstandardized score=108.9, SD =15.3.200
Note that standardized scores on the TONI could not be computed for three children201
of ages 5;8–5;10 due to lack of age-referenced norms for children below 6;0. Due to202
lack of time, PPVT-4 and TONI-3 tests were not administered to four children. Due203
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to equipment malfunctioning, eye-tracking data were lost for one child. Children204
received small gifts (e.g., stuffed animals) as rewards for their participation.205
The study was carried out in accordance with the ethical principles of psychol-206
ogists and code of conduct of the American Psychological Association and was207
approved by the Institutional Review Board of the College of Staten Island. In accor-208
dance with the Declaration of Helsinki, informed consent was obtained from parents209
and assent from children.210
3.2 Design and Materials211
Each trial of the sentence-picture verification task presented a picture paired212
with a spoken sentence that either matched or mismatched the picture (correct213
response =‘yes’ or ‘no’). Each sentence was recorded individually by a female native214
English-speaker using mono-mode sampling at 22,050 Hz. Sentences were spoken215
at a normal adult rate. The experiment presented 4 practice trials, 24 quantifier trials216
(i.e., sentences with the quantifier every modifying the figure or ground of a loca-217
tive scene) interspersed with 8 active-voice and 8 passive-voice fillers (i.e., reversible218
sentences with two animate nouns), and 16 additional fillers, with the latter quantifier219
trials and fillers presented in a pseudo-randomized order.220
Table 1presents examples of trials for each condition using the set of bunnies in221
boxes to illustrate the quantifier trials. Note, however, that each trial of the experiment222
depicted a different set of objects in containers, with half of the sets depicting animate223
objects (e.g., alligators in bathtub), and the other half inanimate objects (e.g., eggs in224
frying pans). Quantifier trials presented pictures of objects or animals in containers,225
with three object/container pairs in the foreground and two extraneous objects or226
containers (for bunny-spreading trials) or two extra objects or containers (for classic227
and control trials) in the background. The active/passive fillers depicted transitive228
actions with two animate nouns. The additional fillers used pictures that were visually229
similar to those used for quantifier trials except that they depicted five objects/animals230
in containers (e.g., five flowers in vases; five dogs on mats), with the sentences231
referring to the number of objects, their color, or including a comparison (e.g., There232
are more blue chairs than green ones). These additional fillers were used to balance233
the number of trials where ‘yes’ versus ‘no’ was the correct response, while reducing234
the proportion of quantifier trials overall.235
Six lists were created, using a Latin square to counterbalance sets across condi-236
tions, with children at each age randomly assigned to each list. The lists presented237
8 trials in each of the three quantifier conditions: bunny-spreading, control (under-238
exhaustive), and classic (over-exhaustive), using object sentences (Every X is in/on239
aY) in half of the trials and container sentences (Every Y has an X in/on it)inthe240
other half. Note that the correct response for bunny-spreading and classic trials was241
always ‘yes’ whereas the correct response for control trials was always ‘no.’ Each242
list also included 8 active and 8 passive fillers, with half of the trials per condition243
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Table 1 Examples of sentences and pictures for each task condition
Condition Sentence type Example sentence Example picture
Bunny-spreading Object Everybunnyisinabox
(correct=‘yes’)
Bunny-spreading Container Every box has a bunny in it
(correct=‘yes’)
Classic Object Everybunnyisinabox
(correct=‘yes’)
Classic Container Every box has a bunny in it
(correct=‘yes’)
Control Object Everybunnyisinabox
(correct=‘no’)
(continued)
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Table 1 (continued)
Condition Sentence type Example sentence Example picture
Control Container Every box has a bunny in it
(correct=‘no’)
Filler Active The cow is pulling the horse
(correct=‘yes’)
OR
The horse is pulling the cow
(correct=‘no’)
Filler Passive The cow is being pulled by
the horse (correct=‘yes’)
OR
The horse is being pulled by
the cow (correct= ‘no’)
Filler Additional Therearemorebluechairs
than green ones
(correct=‘no’)
associated with a correct response of ‘yes’ and the other half with a correct response244
of ‘no.’245
3.3 Procedure246
The sentence-picture verification task was programmed into a script run by DMDX,247
a free Windows-based software for language processing experiments (Forster and248
Forster 2003). Stimuli were presented on a 19-inch HP laptop computer to which a249
remote eye-tracking camera was attached. On each trial, the picture appeared on the250
screen simultaneously with the onset of the spoken sentence. Children were instructed251
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to answer ‘yes’ if they thought that the sentence correctly described the picture, and252
‘no’ otherwise. Accuracy was recorded using a gamepad attached to the computer.253
The gamepad had three buttons, ‘yes’, ‘no’, and ‘next’. Only a few children, mostly254
the oldest ones, were able to manipulate the gamepad successfully, as was determined255
during the practice trials. The rest of the child participants provided their answers256
by saying ‘yes’ or ‘no’ out loud while the experimenter used the gamepad to record257
their answers.258
Children’s eye movements were recorded using the ISCAN remote portable eye-259
tracking system (ETL-500). Eye movements were sampled at a rate of 30 times per260
second and were recorded on a digital SONY DSR-30 video tape-recorder. Spo-261
ken sentences were played through speakers connected to the computer and were262
recorded simultaneously with eye movements. Each child underwent a short calibra-263
tion procedure prior to the experiment.264
3.4 Data Treatment and Analyses265
Eye movements were extracted from videotape using a SONY DSR-30 video tape-266
recorder with frame-by-frame control and synchronized audio and video. Nine trials267
(0.9%) were not recorded due to equipment malfunctioning and constituted missing268
data for the eye-movement analyses. For each trial, four categories were coded: looks269
to the three pairs of entities in the front of the picture, looks to the two ‘distractors’270
(e.g., cats or buckets in the bunny-spreading condition), looks to the two ‘extra’271
objects/containers (bunnies or boxes in the control and classic conditions), looks272
elsewhere in the picture, and track loss. Track loss and looks elsewhere constituted273
a small proportion of total looks (8.6%) and were removed from the eye-movement274
analyses; thus, fixations to the three object/container pairs in the foreground of each275
picture were in complimentary distribution with fixations to the distractors/extras in276
the back. We hypothesized that allocation of visual attention to irrelevant distrac-277
tors/extras would co-occur with q-spreading errors; hence statistical analyses focus278
on proportions of looks to the distractors/extras as a function of response accuracy.279
Using fine-grain analyses, proportions of looks to the distractors/extras were ana-280
lyzed in three separate time windows or regions of interests (ROIs) defined relative281
to the onset of each phrase (Table 2). Note that ROI 3 terminated when the child282
responded or one second after the offset of the stimulus sentence, whichever was283
earlier.284
We conducted three sets of analyses with response accuracy, eye movements to285
distractors/extras, and reaction times as dependent variables. Mixed-effects logistic286
regression was used to analyze response accuracy and eye-movement data. The logis-287
tic part allows for modeling the nonlinear nature of the dependent variable, which is288
bounded by 0 and 1; this approach has been shown to be superior to an analysis of289
variance approach on transformed data (Jaeger 2008).290
Response times were analyzed using linear mixed-effects regression with max-291
imum likelihood as the estimation method. Although the distribution was slightly292
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Table 2 Regions of interest (ROIs) for each sentence type
Sentence type ROI 1 ROI 2 ROI 3
Object Quantified NP Verb–PP–NP-Loc Silence
Every bunny Is in a box
Container Quantified NP Verb–NP–PP
Every box Has a bunny in it
skewed, response time data were kept in their original scale as analyses on trans-293
formed data produced the same pattern of results.294
All models included crossed random intercepts for subjects and items (Baayen295
et al. 2008). Fixed effects and random slopes were examined during the model build-296
ing process and retained only when they improved the model fit. We used a model297
comparison framework to contrast alternative models that were progressively more298
complex. This approach is preferable to significance tests of individual parameters299
in arriving at correct statistical inferences (Bliese and Ployhart 2002). The likelihood300
ratio test was used to compare the fit of competing models. Only age was retained301
as a covariate in all models independently of its statistical significance.302
Outliers were trimmed in two steps: First, for each experimental condition, partic-303
ipants with average performance more than 3 standard deviations above or below the304
grand mean were excluded. Second, for each model, we examined its residuals and305
re-fitted it after removing observations with standardized residuals greater than 3 or306
smaller than −3. In none of the analyses were more than 3.5% of the data excluded.307
Data were analyzed with R version 3.1.0 (R Core Team 2014)usingthelmer and308
glmer functions from the lme4 package, version 1.1–8 (Bates et al. 2015).309
4 Results310
4.1 Accuracy311
To examine associations between accuracy in sentence comprehension and individ-312
ual differences in verbal and nonverbal abilities, we computed partial correlations,313
between accuracy and PPVT and TONI raw scores for each sentence type and con-314
dition, controlling for age in months. Note that use of raw scores was necessitated315
by lack of age norms for 5-year-olds on the TONI. The partial correlation between316
TONI and PPVT raw scores approached statistical significance and showed a weak317
positive association (r=0.30, p=0.076).318
As shown in Table 3, none of the correlations involving PPVT or TONI scores,319
except for one, reached statistical significance or showed a clear trend, thus pointing320
to the absence of any linear relationship between comprehension accuracy and verbal321
and nonverbal skills after controlling for age. The only significant association was322
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Table 3 Response accuracy (N= 41) and partial correlations with PPVT and TONI raw scores
(controlling for age in months) (N=37)
Condition Sentence type Means (SD) Partial correlations
PPVT (raw) TONI (raw)
Bunny-spreading Object 80.3% (29.9) 0.26 0.21
Container 82.3% (31.2) 0.25 0.13
Classic Object 53.0% (35.4) 0.20 –0.07
Container 53.5% (36.4) 0.02 –0.01
Control Object 89.6% (21.6) 0.02 0.16
Container 90.2% (23.6) −0.08 0.15
Filler Active 96.3% (7.0) 0.38* 0.12
Passive 89.0% (13.7) −0.22 0.19
Significance levels: *p<0.05; **p<0.01; ***p< 0.001
between the filler active sentences and PPVT, which should be interpreted with323
caution because of the ceiling effect (comprehension accuracy=96%). The high324
accuracy on both active and passive fillers indicates that children understood the325
instructions for the sentence-picture verification task and could process complex326
reversible passive sentences with a high degree of accuracy. We did not examine327
children’s performance on the fillers sentences further, as it was unrelated to the328
main aims of the study.329
In line with the previous findings in the literature, children’s response accu-330
racy in the classic condition was at chance (M=53.3%; 95% CI=43.5–62.8)331
whereas performance on the control condition approached ceiling (M= 89.9%; 95%332
CI=87.3–96.7). Children averaged 81.3% correct in the bunny-spreading condition333
(95% CI=69.1–94.0).334
Figure 3provides a histogram of children’s scores (out of 8 trials) on the classic335
condition. Given that prior studies (Minai et al. 2012) split samples into subgroups336
of children who consistently made q-spreading errors versus logical responses, we337
examined our data for evidence of a bimodal distribution. To assess the likelihood338
that the children’s scores on classic condition came from a normal distribution, we339
employed the Shapiro–Wilk test and the Anderson-Darling test of normality. Note340
that the null hypothesis is that the scores in the population are normally distributed.341
Results from Shapiro to Wilk test indicated that a normal distribution could not342
be assumed (W=0.94, p=0.034) whereas results from the Anderson-Darling test343
yielded a non-significant trend, suggesting a normal distribution could be assumed344
(A=0.70, p=0.063).345
Given these ambiguous results, we did not attempt to split the sample to compare346
children who were consistently correct versus incorrect in the classic condition.347
Instead, we used logistic mixed-effects regression analyses to examine effects of348
age and sentence type (object or container) on response accuracy across conditions.349
These analyses included crossed random effects for subjects and items.350
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Fig. 3 Histogram of the number of correct responses (out of 8) for the classic condition (N=41)
Bunny-Spreading Condition Response accuracy increased significantly with351
age, β=0.07, SE =0.04, z=1.99, p=0.046, indicating that errors in this condition352
tended to be made only by younger children. The effect of sentence type was not353
statistically significant, χ2(1)=0.5, p=0.818.354
Classic Condition The effect of age only approached significance, β=0.02, SE355
=0.01, z=1.72, p=0.086, indicating the occurrence of classic errors across the age356
range tested. There was no effect of sentence type, with children showing equivalently357
low accuracy on object and container sentences, χ2(1)=0.04, p=0.847.358
Control Condition Similarly to the bunny-spreading condition, age was posi-359
tively related to response accuracy, β= 0.08, SE = 0.02, z= 3.70, p< 0.001, indicating360
that the rare errors were made by younger children. As in the other conditions, there361
was no effect of sentence type on response accuracy, χ2(1) =0.05, p= 0.820.362
4.2 Eye Movements363
Eye-movement analyses compared the proportions of looks to the distractors (bunny-364
spreading condition) or extras (classic condition) in the pictures as a function of com-365
prehension accuracy. (The control condition was not included due to ceiling effects366
on accuracy.) Figure 4and Table 4present the results for each region of interest (ROI),367
as defined in Table 2. We used logistic mixed-effects regression models with crossed368
random effects for subjects and items and by-subject and by-item random slopes for369
sentence type. The analyses examined effects of age, accuracy, and sentence type on370
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Fig. 4 Proportions of fixations to the distractors (bunny-spreading condition) or extras (classic
condition) in each ROI. Solid line: correct trials, dashed line: incorrect trials
patterns of visual attention. Note that we retained the effect of age as a covariate in371
all models irrespective of its statistical significance. We also retained non-significant372
main effects of accuracy and sentence type if the interaction was significant.373
Bunny-Spreading Condition (Fig. 4a)374
ROI 1 The first region of interest (ROI) consisted of the quantified noun phrase (e.g.,375
Every rabbit or Every box). There was a significant effect of sentence type, qualified376
by a significant interaction of sentence type ×accuracy. Children exhibited more377
looks to distractors when every modified the object rather than the container noun378
(i.e., they looked more at distractor cats than buckets). As shown in the left panel of379
Fig. 4a, sentence type yielded more of an effect on correct trials than on incorrect380
trials. Note also that while the left panel of Fig. 4a appears to suggest that children381
looked more often at distractors on incorrect trials, the main effect of accuracy failed382
to reach significance in ROI 1, p=0.064.383
ROI 2 The second ROI started at the verb (is/has) and continued to the end of the384
sentence (middle panel of Fig. 4A). Here looks to the distractors varied significantly385
as a function of accuracy, with children fixating more often on the distractors on incor-386
rect trials. The effects of sentence type and the interaction of sentence type ×accuracy387
were not statistically significant, χ2(1) = 3.237, p= 0.072 and χ2(2) = 3.889, p=0.143,388
respectively.389
ROI 3 The third region of interest consisted of the period of silence after the end390
of the sentence (right panel of Fig. 4a). Again, fixations to the distractors varied as a391
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Table 4 Summary of the mixed logistic analyses by ROI (fixed effects only) examining propor-
tion of looks to the distractors (bunny-spreading condition) and extra objects/containers (classic
condition)
βSE Z p-Value
Bunny-spreading condition ROI 1: quantified NP
(Intercept) −1.33 0.53 −2.53 0.011
Age (months) 0.01 0.01 0.81 0.420
Accuracy (0=incorrect) −0.48 0.26 −1.85 0.064
Sentence Type (0= container) 1.43 0.53 2.69 0.007**
Accuracy×sentence type −0.75 0.32 −2.33 0.020*
ROI 2: verb to end of sentence
(Intercept) −0.01 0.23 −0.03 0.976
Age (months) −0.01 0.01 −1.26 0.210
Accuracy (0=incorrect) −0.55 0.13 −4.14 <0.001***
ROI3:silence
(Intercept) 0.23 0.21 1.09 .277
Age (months) 0.01 0.01 2.03 .042*
Accuracy (0=incorrect) −0.55 0.12 −4.48 <0.001***
Classic condition ROI 1: quantified NP
(Intercept) −1.56 0.37 −4.22 <0.001
Age (months) 0.01 0.01 0.72 0.471
Accuracy (0=incorrect) 0.16 0.17 0.95 0.341
Sentence type (0=container) −0.54 0.46 −1.18 0.238
Accuracy×sentence type 0.63 0.24 2.66 0.007**
ROI 2: verb to end of sentence
(Intercept) 0.13 0.23 0.54 0.587
Age (months) −0.004 0.01 −0.74 0.462
Accuracy (0=incorrect) −0.46 0.09 −5.19 <0.001***
Sentence type (0=container) −0.93 0.37 −2.49 0.013*
ROI3:silence
(Intercept) 0.04 0.34 0.11 0.911
Age (months) −0.01 0.01 −0.95 0.344
Accuracy (0=incorrect) −0.28 0.11 −2.42 0.015*
Sentence type (0=container) −1.06 0.39 −2.70 0.007**
Accuracy×sentence type 0.52 0.17 3.06 0.002**
Significance levels: *p<0.05; **p<0.01; ***p< 0.001
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Table 5 Mean reaction times for each condition as a function of response accuracy. Standard
deviations are in parentheses
Condition Sentence type Correct trials Incorrect trials
Bunny-spreading Object 3256 (657) 3545 (893)
Container 3311 (636) 3647 (1056)
Control Object 3000 (599) –
Container 2822 (588) –
Classic Object 3433 (629) 3024 (695)
Container 3767 (830) 3444 (764)
function of accuracy, with children looking more at the distractors on incorrect trials.392
Perhaps spuriously, age was also significant in the model, with older children tending393
to make more fixations to the distractors than younger children, although the older394
children made fewer incorrect responses. The effects of sentence type and the inter-395
action of sentence type×accuracy were not statistically significant (χ2(1)=1.412, p396
=0.235 and χ2(2)=4.665, p=0.097).397
Classic Condition (Fig. 4b)398
ROI 1 In the first ROI, the only significant effect was a weak interaction of sentence399
type×accuracy (left panel of Fig. 4b).400
ROI 2 In ROI 2, there were a significant effect of accuracy, with more looks to the401
extra objects/containers on incorrect trials. There was also a main effect of sentence402
type: Children looked more often at the extras in the pictures paired with container403
sentences than the extras in the pictures paired with object sentences (middle panel404
of Fig. 4b), perhaps because the extras were animate in half of the trials in the405
former condition. The interaction of sentence type×accuracy was not significant406
(χ2(1)=0.654, p=0.419).407
ROI 3 In ROI 3, there were significant main effects of accuracy and sentence type,408
as well as an interaction of sentence type×accuracy. As shown in the right panel409
of Fig. 4b, the effect of accuracy on fixations to ‘extras’ was stronger for container410
sentences than for object sentences.411
4.3 Reaction Time412
Table 5presents mean reaction times for each condition and sentence type, as a413
function of response accuracy. Note that in the control condition we did not examine414
response times for incorrect trials due to high accuracy (89.9%) yielding insufficient415
data for analysis.416
Linear mixed-effects regression analyses were used to examine effects of age,417
sentence type (object vs. container) and accuracy (correct vs. incorrect trials) on418
children’s response times.419
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Bunny-Spreading Condition Reaction times for the bunny-spreading condition420
varied significantly with age, β=−14.3, SE =3.5, t=−4.10, p<0.001, with older421
children responding more quickly than younger children. Adding effects of accuracy,422
sentence type, and their interaction did not improve the model fit: χ2(1)=2.71, p423
=0.099, χ2(1)=0.13, p=0.716, and χ2(3)=4.01, p=0.261, respectively.424
Classic Condition Likewise for the classic conditions, reaction times decreased425
significantly with age, β=−13.3, SE =2.9, t=−4.52, p<0.001. Reaction times426
also varied significantly as a function of accuracy, with slower responses on correct427
trials than on incorrect trials, β=368.5, SE =113.5, t=3.25, p=0.001, indicating428
that additional processing time was necessary for children to correctly restrict the429
universal quantifier. Reaction times also varied across sentence types, with faster430
responses when the quantifier every modified the object than when it modified the431
container (β=−342.2, SE =104.80, t=−3.27, p=0.001). Including the interaction432
of accuracy×sentence type did not improve the model fit, χ2(1)=0.02, p=0.896.433
Classic Versus Control Conditions Next we compared the reaction times for434
children’s correct responses in the classic and control conditions. In this analysis,435
the effect of age remained significant, β=−13.6, SE =2.6, t=−5.33, p<0.001,436
confirming faster responses in older children. The main effect of condition was also437
significant, β=867.8, SE =110.1, t=7.68, p<0.001, with slower correct responses438
to classic trials than control trials, which suggests that additional processing time439
was required for participants to avoid q-spreading errors. There was also significant440
effect of sentence type, β=227.5, SE =91.4, t=2.49, p=0.013, moderated by a441
significant interaction of condition and sentence type, β=−568.6, SE =156.4, t442
=−3.63, p<0.001). The reaction time difference that favored object over container443
sentences in the classic condition was absent (i.e., slightly reversed) in the control444
condition.445
5 Discussion446
The current study explored patterns of visual attention associated with q-spreading447
errors in school-age children (age range 5–12 years). At this age, performance of the448
group was expected to be at chance (~50% correct) on trials designed to elicit the449
classic error; thus, we sought to compare patterns of visual attention over roughly450
equal numbers of correct and incorrect trials with the goal of identifying a signa-451
ture pattern of attention associated with committing the error. We administered the452
sentence-picture verification task using two distinct locative constructions: In object453
sentences, the universal quantifier every modifying the designated objects (as in Every454
bunny is in a box), and in container sentences, it modified the designated containers455
(as in Every box has a bunny in it). Across trials, we varied the pictures to elicit differ-456
ent types of errors. For the bunny-spreading condition, we presented three bunny-box457
pairs along with two unrelated distractors (e.g., cats or buckets, as depicted in Fig. 1a,458
b). For classic and control conditions, we presented three bunny-box pairs along with459
two extra objects or containers (e.g., bunnies or boxes, as depicted in Fig. 2a, b). The460
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classic condition was expected to elicit (over-exhaustive) q-spreading wherein the461
scope of the universal quantifier spreads beyond its subject. That is, we expected462
children to incorrectly reject the sentence Every bunny is in a box as a description463
of a scene with extra boxes. By swapping the pairings of sentences and pictures, the464
same stimuli were used for the control condition, wherein children were expected to465
correctly reject the sentence Every box has a bunny in it as a description of a scene466
with extra boxes.467
The task was conceptually identical to the truth-value judgment task used in468
previous offline studies of classic q-spreading in children (see Rakhlin 2007,for469
an overview). We adapted procedures to allow for concurrent online recordings of470
eye-movements using the visual world paradigm (cf. Minai et al. 2012; Sekerina471
and Sauermann 2015). The paradigm allowed us to examine how children allocated472
their visual attention as each sentence unfolded in real time in order to determine473
whether increased looks to the distractors (bunny-spreading condition) or extras474
(classic condition) were time-locked to the region of interest immediately following475
the quantified NP. In addition to exploring how specific eye-movement patterns might476
be associated with q-spreading, we examined susceptibility to errors in relation to477
individual differences in non-verbal and verbal intelligence as well as age. We also478
measured reaction times as an additional variable to determine whether errors were479
associated with greater or lesser processing time relative to correct responses.480
With regards to accuracy in performing the sentence-picture verification task, the481
children did quite well on the control (89.9% correct) and bunny-spreading (81.3%)482
conditions, as well as on the reversible active (96.3%) and passive (89.0%) sentences483
used as fillers. These findings indicate that children understood the task instructions484
and could succeed in sentence-picture verification with a variety of sentence struc-485
tures. In contrast, the children exhibited the well-established classic error on trials486
that depicted extra objects and containers that were outside the scope of the universal487
quantifier, with the group performing at chance (53.3% correct).488
For the bunny-spreading condition, accuracy increased with age, in line with489
prior work associating these errors with young children (Roeper et al. 2004). For490
the classic condition, the correlation between accuracy and age was not statistically491
significant (p=0.086). The lack of a robust effect of age on classic q-spreading492
makes sense in light of findings from a group of college students performing the493
sentence-picture verification task with the same set of materials used in the current494
study (Brooks and Sekerina 2006), wherein one in five adults performed at chance in495
the classic condition. Taken together with other findings demonstrating classic errors496
in college students performing the picture-choice task (Brooks and Sekerina 2005,497
2006, Experiment 3), the results suggest that classic q-spreading is less constrained498
by maturation than was previously thought and persists into adulthood. This set of499
findings is difficult to accommodate within frameworks that assume faulty grammar500
to be the source of children’s errors (e.g., Philip 1995; Roeper et al. 2004), and are501
more consistent with shallow processing accounts that attribute errors to superficial502
processing of sentence structure (Brooks and Sekerina 2005,2006).503
In examining individual differences in relation to adult performance on the504
sentence-picture verification task, Brooks and Sekerina (2006) reported significant505
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correlations between accuracy on classic trials and nonverbal intelligence (estimated506
using the Culture Fair Intelligence Test; Cattell and Cattell 1973) and need for cog-507
nition scores (Cacioppo et al. 1984) Similarly, in accounting for individual differ-508
ences in adult performance on the picture-choice task, Street and Da˛browska (2010)509
reported an association between classic errors and need for cognition, while also510
finding an association with self-reported time spent reading for pleasure. However,511
in the current study, we failed to find evidence in children for a relationship between512
comprehension accuracy and individual differences in either nonverbal or verbal513
intelligence (estimated using TONI-3 and PPVT-4 standardized assessment tests,514
respectively). Although the topic of individual differences in children’s sentence515
processing clearly warrants additional research, the lack of any clear predictive rela-516
tionships between classic q-spreading and nonverbal or verbal intelligence in children517
appears to underscore their broad susceptibility to the classic error.518
Prior work with heritage speakers of Russian documented a signature pattern of519
visual attention associated with classic q-spreading in bilingual adults (Sekerina and520
Sauermann 2015): When committing the error, adults made a greater number of521
fixations to the extra objects/containers in the pictures, with the increased rate of522
fixations time-locked to the ROI immediately following the quantified noun phrase523
(ROI 2, defined as the verb). In line with well-established results from other stud-524
ies using the Visual World Paradigm (Trueswell and Tanenhaus 2004), Sekerina and525
Sauermann (2015) interpreted the changing patterns of eye-movements to be a reflec-526
tion of the participant’s interpretation of the sentence as it unfolded in time. Thus,527
increased looks to the extras were a direct index of their spreading the domain of528
the universal quantifier beyond its subject, to encompass both the object and con-529
tainer nouns. Sekerina and Sauermann’s findings contrast with those of Minai and530
colleagues (2012) who focused on executive control of attention in relation to classic531
errors in preschool-age children. In support of their hypothesis that a lack of control532
of attention in children increases their susceptibility to classic errors, the children533
showed a large increase in fixations to the extra object(s) prior to the onset of the534
sentence, when compared with adults. However, no evidence of aberrant patterns of535
visual attention during sentence processing was found.536
Given these conflicting reports, the current study sought evidence for a signature537
pattern of visual attention associated with classic errors in a sample of school-age538
children. If classic errors involve a spread of visual attention as the scope of the539
universal quantifier is extended beyond its complement NP, we should see increased540
fixations to the extra objects/containers that are time-locked to when the error is made541
in sentence processing—presumably just as soon as the children have interpreted542
the quantified noun phrase (every bunny or every box). This is indeed what we543
found: q-spreading errors were associated with increased looks to the distractors544
(bunny-spreading trials) and the extras (classic trials) relative to correct responses.545
The increased fixations became significant in ROI 2 (extending from the verb to546
the end of the sentence), and remained significant throughout ROI 3 (silence). In547
other words, the eye-movement patterns associated with q-spreading gained strength548
as the spoken sentence unfolded, in line with the view that incremental sentence549
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20 I. A. Sekerina et al.
interpretation guides visual attention (for an overview, see Huettig et al. 2011), with550
the acknowledgement that effects can be bi-directional.551
We analyzed reaction times as an additional dependent variable to determine552
whether classic errors were associated with greater or lesser processing time rela-553
tive to correct responses. The analyses indicated a significant age-related decrease in554
overall reaction times; however this effect should be interpreted with caution as older555
children responded directly using the gamepad whereas younger children responded556
orally, with the experimenter registering their responses on the gamepad. In addi-557
tion to the main effect, we found significantly slower responses on correct trials558
(3600 ms) than on incorrect trials (3234 ms) in the classic condition. This pattern is559
compatible with our hypothesis that additional processing time and effort are neces-560
sary for children to overcome shallow processing of sentence structure to correctly561
restrict the universal quantifier to the appropriate noun phrase. It argues against the562
hypothesis that errors are driven by distraction from the extra object/containers (i.e.,563
a failure in executive control of attention), as distraction should lead to slower reac-564
tion times for incorrect trials. The faster response times associated with the classic565
error (and also with correct rejections of sentences in the control condition) sup-566
port the view, initially proposed in Brooks and Braine (1996), that children adopt567
a default expectation that distributive quantifiers (e.g., each and every) refer to sets568
in one-to-one correspondence. Reliance on this default assumption leads to a quick569
rejection of pictures showing sets in partial one-to-one correspondence, which is570
overcome when children attend to linguistic cues that provide additional constraints571
on sentence interpretation.572
Notably, in the classic condition, the children did not show higher accuracy for573
object sentences in comparison to container sentences, as had been reported in a prior574
study of classic errors in adults using the picture-choice task (Street and Da˛browska575
2010). Children did, however, show faster reaction times for object sentences than576
container sentences, which suggests that these sentences were somewhat easier to577
process. Eye-movement analyses also revealed an influence of sentence type on pat-578
terns of visual attention. In the bunny-spreading condition, object-sentences elicited579
greater numbers of looks to the distractors than container-sentences. That is, dis-580
tractor cats in the context of the sentence Every bunny is in a box attracted greater581
attention than distractor buckets in the context of the sentence Every box has a bunny582
in it. In the classic condition, container-sentences tended to attract greater looks583
to the extra objects (e.g., bunnies) than object-sentences to extra containers (e.g.,584
boxes). Thus, across both of these conditions, children’s attention was drawn to dis-585
tractors/extras that constituted the figure/object, as opposed to the ground/container,586
perhaps because the figure/object was animate in half of the trials. These findings587
complement research by Freeman (1985) demonstrating the impact of the visual588
context on children’s errors in sentence comprehension.589
In conclusion, the current study contributes to the vast literature on q-spreading590
in children by identifying a pattern of visual attention associated with committing591
the error in real time. We offer a unified account of school-age children’s classic592
errors and the less-than-perfect performance of monolingual and bilingual adults that593
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attributes errors to shallow sentence-processing strategies as opposed to immature594
or faulty grammar.595
Acknowledgements Irina Sekerina and Patricia Brooks share first authorship and made equal596
contributions to the study. We extend our gratitude to the parents, teachers, and children at St.597
Thomas-St. Joseph School in Staten Island, NY, for their involvement in the study. We also thank598
Annemarie Donachie, Carolin Obermann Linxen, and Kasey Powers for their assistance in collecting599
and tabulating the data.600
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