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Variability is prevalent in early language acquisition, however whether it supports or hinders learning is unclear: while target variability has been shown to facilitate word learning, variability in competitor items has been shown to make the task harder. Here we tested whether background variability could boost learning in a referent selection task. Two groups of two-year-old children saw arrays of one novel and two known objects on a screen, and heard a novel or known label. Stimuli were identical across conditions, with the exception that in the constant color condition objects appeared on a uniform white background, and in the variable color condition backgrounds were different, uniform colors. At test, only children in the variable condition showed evidence of retaining label-object associations. These data support findings from the adult memory literature, which suggest that variability supports learning by decontextualizing representations. We argue that these data are consistent with dynamic systems accounts of learning in which low-level entropy adds sufficient noise to the developmental system to precipitate a change in behavior.
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Cognitive Science (2017) 1–26
Copyright ©2017 The Authors. Cognitive Science published by Wiley Periodicals, Inc. on behalf of
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ISSN: 0364-0213 print / 1551-6709 online
DOI: 10.1111/cogs.12539
All the Right Noises: Background Variability Helps Early
Word Learning
Katherine E. Twomey, Lizhi Ma, Gert Westermann
Department of Psychology, Lancaster University
Received 14 September 2016; received in revised form 9 August 2017; accepted 10 August 2017
Abstract
Variability is prevalent in early language acquisition, but, whether it supports or hinders
learning is unclear; while target variability has been shown to facilitate word learning, variability
in competitor items has been shown to make the task harder. Here, we tested whether back-
ground variability could boost learning in a referent selection task. Two groups of 2-year-old
children saw arrays of one novel and two known objects on a screen, and they heard a novel or
known label. Stimuli were identical across conditions, with the exception that in the constant
color condition objects appeared on a uniform white background, and in the variable color con-
dition backgrounds were different, uniform colors. At test, only children in the variable condi-
tion showed evidence of retaining label-object associations. These data support findings from the
adult memory literature, which suggest that variability supports learning by decontextualizing
representations. We argue that these data are consistent with dynamic systems accounts of learn-
ing in which low-level entropy adds sufficient noise to the developmental system to precipitate a
change in behavior.
Keywords: Word learning; Fast mapping; Variability; Entropy; Dynamic systems; Cognitive
development
1. Introduction
Children’s early word learning has long fascinated researchers. When a child hears the
new word spaceship, linking it with a new toy flying machine rather than her toy dog
Correspondence should be sent to Katherine E. Twomey, Department of Psychology, Lancaster University,
Bailrigg, Lancaster, UK LA1 4YF. E-mail: ktwomeyresearch@gmail.com
This is an open access article under the terms of the Creative Commons Attribution License, which
permits use, distribution and reproduction in any medium, provided the original work is properly cited.
or indeed the flying machine’s wings, its color, the way it moves, and so onseems to
pose little problem. Given that the space of potential referents is theoretically infinite
(Quine, 1960), this ability to quickly map a novel word to a novel object is impressive;
so impressive, in fact, that until recently children’s ability to disambiguate has been
attributed to metacognitive rules in the form of innate biases (Markman, 1994) or learned
lexical constraints (Golinkoff, Mervis, & Hirsh-Pasek, 1994). For example, given the
choice between two familiar objects and a new one, children may reason that since the
yellow thing is a banana, and the brown fluffy thing is their much-loved toy dog, then
the new word spaceship must refer to the new toy flying machine (mutual exclusivity or
dysjunctive syllogism; Carey & Bartlett, 1978; Halberda, 2006; Markman & Wachtel,
1988; for other proposed constraints see Golinkoff, Hirsh-Pasek, Bailey, & Wenger,
1992). Recent years have seen the emergence of a new view of word learning as a low-
level phenomenon that can proceed without invoking complex, metalinguistic awareness.
These theories, often based on computational models, argue that low-level associative
processes of excitation and inhibition can give rise to the apparently complex behaviors
children demonstrate during referent selection (RS; Horst, Samuelson, et al., 2011b;
McMurray, Horst, & Samuelson, 2012; Samuelson, Kucker, & Spencer, 2016; Samuelson,
Smith, Perry, & Spencer, 2011; Smith, 2000; Twomey, Morse, Cangelosi, & Horst,
2016).
While the debate as to the mechanisms underlying children’s word learning goes on, it
is clear that memory and language are linked from very early in development (Taylor,
Liu, & Herbert, 2016; Zimmermann et al., 2015). In particular, learning a new word
depends critically on children’s ability to form and retain word-object associations. There
is mounting evidence that a single disambiguation event is not sufficient for full word
learning; rather, children learn word-object associations incrementally, forming in-the-
moment mappings between labels and objects and strengthening memories of these map-
pings across repeated encounters via cross-situational learning (McMurray et al., 2012;
Smith & Yu, 2008; Yurovsky, Fricker, Yu, & Smith, 2014). Consequently, the field has
recently focused on the multiple factors that affect early language acquisition, demonstrat-
ing that RS and word learning are flexible, even fragile processes which depend heavily
on the temporal and visual availability of information in the learning environment, for
example repetition, competition, and timing (e.g., Arias-Trejo & Plunkett, 2010; Horst,
Scott, & Pollard, 2010; Mather & Plunkett, 2009).
In line with the adult literature (Posner & Keele, 1968), developmental research has
demonstrated that variability in target items is a key influencing factor in early learning.
For example, visual variability encountered across target stimuli facilitates categorization
in 6- to 7-month-old infants (Quinn & Bhatt, 2010), and phonological variability in affect
or speaker has been shown to support early word recognition (Rost & McMurray, 2009;
Singh, 2008). Recent work has shown that target variability also affects word learning: In
an RS task, when shown a novel 3D object category with exemplars that varied in color,
30-month-old children learned category labels, but they did not when exemplars were
identical or varied in shape and color simultaneously (Twomey, Ranson, & Horst, 2014;
see also Ankowski, Vlach, & Sandhofer, 2013; Perry, Samuelson, Malloy, & Schiffer,
2K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
2010). Thus, while some target variability supports language learning, too much target
variability appears to disrupt it. However, there are more sources of variability in the
input to language learning than just the to-be-learned item. Findings from RS tasks in
which variability is instantiated in competitor (i.e., non-target) objects suggest that lack
of variability supports word learning. For example, repeating competitor objects across
RS trials, or reducing the number of competitor objects seen during RS, supports 2-year-
old children’s retention of label-object associations (Axelsson & Horst, 2014; Horst et al.,
2011a).
In addition, there is good theoretical reason to expect extraneous background variabil-
ityentropyto support word learning. Specifically, evidence from adult problem-sol-
ving studies suggests that introducing entropy to a task facilitates learning. For example,
Stephen, Dixon, and Isenhower (2009) showed adults a series of gear system problems on
a computer screen. Half of the participants saw the problems appear in a consistent spa-
tial location, but for the other half, the task included added entropy in the form of ran-
dom variability in stimulus location. While both groups eventually abstracted a short-cut
solution to the gear problems, the group for whom the task contained more entropy did
so the fastest. The authors explained this finding in the context of dynamic systems theo-
ries of cognition and development. In these approaches, cognitive structure emerges from
the dynamic interactions of multiple, coupled components including the learner’s body,
learning history, and in-the-moment characteristics of the task. Cognitive structure is
instantiated as a stable state (attractor) in the behavior of this complex system. Dynamic
systems of this type exhibit phase shifts from one attractor to another, resulting in qualita-
tive and quantitative changes in the system’s behavior. Because these phase shifts result
in behavioral change, from the dynamic systems perspective, they reflect learning (Kar-
miloff-Smith, 1992; Piaget, 1952; Thelen & Smith, 1996; for an explicit computational
implementation of this theory, see Sch
oner, Spencer, & the DFT Research Group, 2015).
As Stephen et al. (2009) demonstrate, extraneous entropy during learning destabilizes
attractor states, speeding the onset of a phase shift; thus, non-target variability should
speed up early learning by helping new cognitive structure emerge via a shift from one
stable state to another.
Despite this strong theoretical prediction, evidence for the effect of adding noise to
early word learning is mixed. Background variability appears to boost performance in
novel noun generalization tasks, which test children’s ability to extend words heard in-
the-moment to new category exemplars. For example, Goldenberg and Johnson (2015;
see also Goldenberg & Sandhofer, 2013) trained 16- to 20-month-old infants with novel
category exemplars on backgrounds which (a) repeated, (b) varied randomly, or (c) varied
in a nonrandom presentation. Infants were then asked to generalize novel category labels
to a new exemplar. For infants who saw variable but non-random backgrounds, looking
times during training predicted categorization ability. For infants who learned from
repeated contexts or randomly varying backgrounds, however, there was no such relation-
ship. Here, then, additional, structured context variability supported children’s noun
generalization.
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 3
While generalization tasks depend on online processing, typically of never-before seen
stimuli, RS tasks tap multiple timescales of behavior, including children’s long-term
vocabulary (which scaffolds disambiguation) and in-the-moment task characteristics, as
well as the child’s ability to make links across these timescales (Kucker, McMurray, &
Samuelson, 2015). In these tasks, which test children’s memory of already encountered
label-object mappings after a period of time, background variability has been shown to
hinder word learning. For example, teaching 3-year-old children novel words by reading
them the same book every day over a week boosts their word learning relative to teach-
ing the same novel words from multiple, different books (Horst, Parsons, & Bryan,
2011a; Williams & Horst, 2014). Thus, while the generalization literature predicts a bene-
ficial effect of variability on retention, the storybook literature predicts a benefit of con-
textual consistency. Importantly, however, the prediction from dynamic systems theory
(DST) that additional entropy should boost word learning in an RS task has yet to be
explicitly tested.
This study addresses this gap. We added low-level background variability to an RS
paradigm on the hypothesis that variability should support retention of novel labels.
Specifically, we gave 2-year-old children a looking time task in which trials were pre-
sented either on a white background or on multiple colored backgrounds. After a 5-min
break to allow for forgetting, children saw a single warm-up trial followed by six reten-
tion test trials, in which the just-seen novel objects were presented on a gray background
for both groups of children. Based on dynamic systems accounts of learning, we expected
children in the variable color condition to show stronger retention of label-object associa-
tions than children in the constant color condition. Finally, we explored in detail the rela-
tionship between children’s attention to novel targets during RS and their subsequent
retention. Together, these results give a fine-grained picture of children’s looking behav-
ior during RS and its relationship to subsequent word learning.
2. Method
2.1. Participants
Thirty typically developing, monolingual, English-speaking, 2-year-old children (14
girls, M=22.77 months, SD =1.87 months; range =20.026.0 months) with a mean
productive vocabulary of 176.04 words (SD =117.50 words, range =4413 words) and
no family history of colorblindness participated. Children were randomly assigned to the
constant color condition (n=14) or the variable color condition (n=16). Children’s
ages and productive vocabularies did not differ between conditions (age: t(27.31) =0.83,
p=.41; vocabulary: t(16.52) =1.07, p=.30). Data from six additional children were
excluded from analyses due to fussiness as defined as crying/refusal to stay on caregiver’s
lap (1), parental labeling of target objects (3), bilingualism (1), and an eye tracker sample
rate of under 25% (1). Parents were reimbursed for travel expenses and children received
a storybook for participating.
4K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
2.2. Stimuli
The study consisted of three phases: warm-up, RS, and retention (see Figs. 1 and 2).
Critically, stimuli for each phase were identical across conditions with the exception that
during warm-up and RS, in the variable color condition objects appeared on colored
backgrounds, and in the constant color condition backgrounds were always white. We
also presented children with engagement and attention-getting stimuli. We describe the
details of stimuli for the different phases separately below. Overall, however, warm-up,
RS, and retention stimuli were videos containing 2D photographic images of known and/
or novel objects (see Fig. 1). Known objects were an apple, a ball, a banana, a car, a
cup, and a fork, and they were selected because their labels are familiar to children of
this age group (Fenson et al., 1993). Novel objects were a purple, green, and black foam
rocket (labeled zorch), a spherical yellow object with multiple flexible legs capped with
pink and green balls (labeled tife), and a blue kazoo with raised orange spots (labeled
blick), selected from an online database of objects unfamiliar to children of this age
(NOUN Database; Horst & Hout, 2016). Each trial consisted of a single video of three
Fig. 1. Example warm-up and RS trial order, variable color condition. The corresponding trial order in the
constant color condition was identical with the exception that the background color was always white.
RS =referent selection.
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 5
objects. Videos were created in Microsoft Powerpoint 2010 and converted to AVI format,
using Microsoft Windows Live Movie Maker 2011. Each video was accompanied by
embedded audio consisting of the same female speaker saying, Can you find the [label]?
Look at the [label]! Where’s the [label]?, as well as sound effects to keep children
engaged in the task. Known labels were the appropriate English labels for those objects,
and novel labels were blick (kazoo), tife (legs/balls) and zorch (rocket), selected as plausi-
ble, but unfamiliar English object names. Auditory stimuli commenced 5 s after the start
of each trial. First label onsets occurred from 0.78 to 0.90 s after the beginning of the
auditory stimulus and offsets from 1.27 to 1.58 s; second label onsets from 2.20 to 2.48 s
and offsets from 2.65 to 3.25 s; and third label onsets from 3.54 to 4.21 s and offsets
from 4.22 to 5.19 s.
2.2.1. Engagement stimuli
Engagement stimuli consisted of a 7 s video of a female experimenter on a white
background, smiling and saying, Hello! Let’s play a game! Can you find what I’m looking
for? in child-directed speech.
2.2.2. Warm-up stimuli
Warm-up stimuli were 16 s videos, each depicting a set of three of the known objects
and were designed to encourage children to look at the target object in response to its
label. In the first 0.5 s, a small uniform color rectangle appeared in the center of a black
screen and spun in a circle anticlockwise, growing as it did so until it filled the whole
Fig 2. Example retention trial order. The retention phase was identical across conditions. Ret =retention.
6K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
screen, at which point the rectangle served as the background on which the objects would
appear. In the next 2 s, the three objects appeared in the top left-hand corner of the
screen and bounced diagonally downwards accompanied by a boing sound, coming to a
rest in the center of the screen and remaining there for 9.5 s, during which time the target
object was labeled three times (e.g., Can you find the apple? Look at the apple! Where’s
the apple?). In line with typical 3D object RS tasks in which warm-up trials include
ostensive feedback (e.g., Twomey et al., 2014), during the next 3 s, the target object
rotated accompanied by a twinkling sound, followed by ostensive auditory feedback (e.g.,
There’s the apple!). In the final 1 s, the objects bounced diagonally toward the bottom
right-hand corner and offscreen, accompanied by the sound of children cheering.
2.2.3. Referent selection stimuli
Referent selection trials were 13 s long; they were identical to warm-up trials with the
exception that children saw one novel and two known stimuli, and there was no ostensive
feedback phase. Background colors were either white (constant color) or pseudorandom
(variable color), as in the warm-up trials.
2.2.4. Retention stimuli
Retention trials were 9.5 s; they were proceeded in an identical manner to RS trials
except that the background was always gray and appeared immediately (i.e., there was no
0.5 s period where the background appeared) and all three objects were novel.
2.3. Procedure and design
Before the experiment began, the experimenter showed caregivers pictures of the
known and novel objects to ensure they were appropriately known and novel to the child.
All children were familiar with the known objects and unfamiliar with the novel objects.
Caregivers were asked to complete a UK adaptation (Hamilton, Plunkett, & Schafer,
2000) of the MacArthur-Bates Communicative Development Inventory (Fenson et al.,
1994), a vocabulary index widely used to record receptive and productive vocabulary in
children of this age. Caregivers completed the vocabulary index either before the experi-
ment began or afterwards, depending on the child’s level of engagement.
The eyetracking session took place in a quiet, dimly lit room. Children sat on their
caregiver’s lap 5070 cm in front of a 21.5 in. 1,920 91,080 computer screen. A
Tobii X120 eyetracker (Tobii Pro, Stockholm, Sweden) located beneath the screen
recorded the child’s gaze location at 17 ms intervals, and a video camera above the
screen recorded the caregiver and child throughout the procedure. Caregivers were
instructed not to interact with their child or look at the screen during the task to
avoid biasing their child’s behavior, and they were asked to sit at a 90°angle from
their child to ensure the eyetracker tracked the child’s eyes only.
The eyetracker was first calibrated, using a five-point infant calibration procedure
available in Tobii Studio. A small animation of a cartoon bird accompanied by a jingling
sound appeared in each of the corners and the center of a 3 93 grid on a gray
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 7
background while the eyetracker recorded infants’ gaze direction and duration. Calibra-
tion accuracy was checked for each child; recalibration was not necessary for any child.
Immediately following calibration, children saw the engagement stimulus once.
2.3.1. Warm-up
The three warm-up trials immediately followed the engagement stimulus. An example
warm-up phase for the variable color condition is depicted in Fig. 1. In the constant color
condition, the background on each of the warm-up trials was white. In the variable color
condition, the background varied from trial to trial and was blue, green, pink, purple, or
red. Which objects appeared, which served as targets, and object location were pseudo-
randomized across children such that no object appeared on more than two successive
trials.
2.3.2. Referent selection
Fifteen RS trials immediately followed the warm-up phase. An example RS phase for
the variable color condition is depicted in Fig. 1. Again, the corresponding warm-up
phase in the constant color condition was identical with the exception that backgrounds
were white. RS trials were presented in three blocks of five trials for each set. Sets were
kept constant across trials to maximize children’s retention of novel labels (Axelsson &
Horst, 2014); thus, one child might see a block of five repetitions of the ap-
ple + fork + zorch set, followed by the banana + cup + tife set,andfinallythe
car + ball + blick set, with block order Latin square counterbalanced across children. In
each RS block, children were asked to look at a known object on two trials and a novel
object on three trials. Known/novel trial order and background color (variable color condition
only) were pseudorandomized such that no more than two of the same trial type appeared in
succession. Object location was also pseudorandomized.
During the RS phase, an attention-getting stimulus appeared six times pseudorandomly
such that it was always succeeded by at least one RS trial, and it consisted of a 3 s video
of the speaker saying, What’s next?. Finally, after the RS phase, children saw a 5 s video
of the speaker saying, Well done! All finished! See you soon!
2.3.2.1. Break: Following RS, children took a 5-min break. During this time, they either
remained on their caregiver’s lap and watched an age-appropriate animation or moved to
a seating area in the same room and colored pictures from a book. In line with 3D object
RS studies this break was designed to allow time for forgetting, to ensure the subsequent
retention trials tested robustly learned associations (Horst & Samuelson, 2008).
2.3.2.2. Warm-up: A single warm-up trial followed the break, in an identical manner to
the previous warm-up trials with the exception that objects were presented on a gray
background. Recalibration in Tobii Studio is not required following the break, however
post hoc calibration checks confirmed that calibration was equally accurate for retention
and RS trials, with 85.04% and 85.46% of looks falling in one of the three areas of inter-
est (AOIs) in each phase, respectively.
8K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
2.3.2.3. Retention: Six retention trials immediately followed the warm-up trial. Each
object was labeled on two trials, and trial order and object location were pseudorandom-
ized. Following the retention phase, children saw a 6 s video of the speaker saying, Well
done! It was fun to play with you! Thank you! Bye!
2.4. Coding and data cleaning
Gaze position was calculated automatically in Tobii Studio (v. 3.2) by taking an aver-
age of the gaze position of both eyes during recording. Only timestamps for which the
eyetracker reliably detected one or more eyes were retained (excluded: 88,770; 15.43%).
Left, middle, and right AOIs were 350 pixels wide by 450 pixels tall and centered on
each object’s stationary position after they had bounced into the screen.
Non-AOI looks were discarded, resulting in a final dataset of 309,586 RS and 61,247
retention gaze samples. Individual gaze samples were numerically coded (1 =target look,
0=non-target look), creating a raw looking time measure, which was further collapsed
into 100 ms time bins. All subsequent analyses use this target looking measure, and they
are standardized from the offset of the first label plus 233 ms (to account for saccade ini-
tiation latencies; Swingley, Pinto, & Fernald, 1999) to 6,733 ms post-labeling.
3. Results
3.1. Referent selection
First, we were interested in whether background color variability affected children’s
looking on RS trials. We therefore calculated proportion target looking for each time bin
as [time spent looking at target AOI/total AOI looking time]. We submitted this measure
to a linear mixed effects model with fixed effects of time bin, trial type (novel, known),
and condition (constant color, variable color) and their interactions, with random inter-
cepts for participant and target item.
1
Model output is provided in Table 1.
Table 1
Results from the linear mixed effects model
Effect bSE t v
2
df p
Time bin 0.0022 0.00034 6.544 163.80 1 <.001***
Trial type 0.019 0.070 0.281 0.078 1 .78
Condition 0.051 0.037 1.366 0.59 1 .44
Time bin 3trial type 0.00021 0.00056 0.368 5.28 1 .022*
Time bin 9condition 0.00087 0.000478 1.855 0.084 1 .78
Trial type 9condition 0.060 0.029 2.048 0.29 1 .59
Time bin 3trial type 3condition 0.0020 0.00077 2.65 5.29 1 .0081**
Note. Values in bold were significant at the alpha = 0.05 level. * p< .05, ** p< .01, *** p< .001.
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 9
Overall, children’s looking increased over time (positive main effect of time bin). This
was modulated by an interaction between trial type and time bin, and further by a three-
way interaction between condition, trial type, and time bin. To explore these interactions
further, we ran two separate mixed effects models on proportion target looking for each
condition, each with fixed effects of time bin and trial type and random intercepts for par-
ticipant and target item.
In the constant color condition, looking increased with time (main effect of time bin:
b=0.0022, SE =0.00034, t=6.55, v
2
(1) =73.41, p<.001). However, there was no
effect of trial type (b=0.018, SE =0.083, t=0.22, v
2
(1) =0.024, p=.88) or any
interaction between time bin and trial type (b=0.00022, SE =0.00056, t=0.39,
v
2
(1) =0.015, p=.70). To establish whether children correctly identified target items in
response to labels, we plotted proportion target looking against time bin (Fig. 3).
The t-tests against chance revealed that although children demonstrated some above-
chance looking earlier in known trials (e.g., around 3,500 ms), sustained attention to the
target for did not begin until around 5,500 ms, and then only on novel trials.
In the variable color condition, target looking also increased with time (b=0.0031,
SE =0.00032, t=9.64, v
2
(1) =89.67, p<.001). While there was no independent main
effect of trial type (b=0.042, SE =0.054, t=0.77, v
2
(1) =0.16, p=.69), trial type did
interact with time bin (b=0.0018, SE =0.00052, t=3.51, v
2
(1) =12.29,
p=.00046). Again, to explore the interaction, we ran further separate mixed effects mod-
els on the variable color data for each trial type, with a main effect of time bin and ran-
dom intercepts for participant and target type. These models confirmed that although
0.00
0.25
0.50
0.75
1.00
0123456
Seconds after label offset
Proportion target looking
Trial type known novel
Fig. 3. Proportion target looking in the constant color condition in 100 ms time bins. Error bars represent
95% confidence intervals. Where bins are marked with a point, looking is significantly above chance (0.33;
p<.05, one-sample, two-tailed t-test).
10 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
target looking increased overall on both known and novel RS trials for children in the
variable color condition, it did so faster on known than on novel trials (main effect of
time bin; known: b=0.0031, SE =0.00035, t=8.78, v
2
(1) =76.41, p<.001; novel:
b=0.0013, SE =0.00030, t=4.39, v
2
(1) =19.17, p<.001). Finally, we plotted propor-
tion target looking per time bin. As Fig. 4 shows, target looking reaches above-chance
levels on known trials, but not on novel trials.
Overall, then, children’s looking to the target increased during RS trials. However, this
effect was reduced when children in the variable color condition were asked to identify
novel targets. Only children in the constant color condition showed sustained attention to
the correct referent in response to known and novel words.
3.2. Retention
During RS, background color variability affected children’s performance such that
while children in the constant color condition showed some evidence of sustained atten-
tion to the correct novel referent, in the variable color condition children’s target looking
increased more quickly in response to known labels, although target looking was at
chance overall.
Next, we divided the retention trials in two blocks (i.e., Trials 13 vs. Trials 46), in
line with existing work, which shows that providing children with a brief reminder of
previously learned stimuli boosts test performance (e.g., Morgan & Hayne, 2006). Fig. 5
depicts looking times during Block 1 and shows little difference in target looking
between the two conditions. This conclusion was supported by a mixed effects model
with main effects of time bin and condition and their interaction, with by-participant and
by-item random intercepts. As in RS, there was a small but robust increase in looking
with time (b=0.0019, SE =0.00063, t=2.99, v
2
(1) =10.49, p=.0012). However,
Fig. 4. Proportion target looking in the variable color condition in 100 ms time bins. Error bars represent
95% confidence intervals. Where bins are marked with a point, looking is significantly above chance (0.33;
p< .05, one-sample, two-tailed t-test).
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 11
condition had no independent effect on looking times, and did not interact with time bin
(main effect of condition: b=0.043, SE =0.00098, t=0.66, v
2
(1) =0.12, p=.73; time
bin 9condition interaction: b=0.0080, SE =0.00098, t=0.81, v
2
(1) =0.67,
p=.41).
0.0
0.2
0.4
0.6
0.8
0123456
Seconds after label offset
Proportion target looking
Condition Constant Variable
Fig. 5. Proportion target looking during Block 1 of retention in 100 ms time bins. Error bars represent 95%
confidence intervals. Where bins are marked with a point, looking is significantly above chance (0.33;
p<.05, one-sample, two-tailed t-test).
0.00
0.25
0.50
0.75
1.00
0123456
Seconds after label offset
Proportion target looking
Condition Constant Variable
Fig. 6. Proportion target looking during Block 2 of retention in 100 ms time bins. Error bars represent 95%
confidence intervals. Where bins are marked with a point, looking is significantly above chance (0.33;
p<.05, one-sample, two-tailed t-test).
12 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
Data from Block 2 show a markedly different pattern, however. As Fig. 6 illustrates,
children in the variable color condition robustly looked at the target at above-chance
levels immediately following labeling and again at around 4,000 ms, suggesting that
encountering variable colored backgrounds during RS facilitated their retention of the
novel label-object mappings. A mixed effects model with the same fixed effects structure
as above and by-participant and by-item random intercepts and slopes for condition
revealed that on these later trials children’s proportion target looking decreased over time
(main effect of condition: b=0.0029, SE =0.00078, t=3.65, v
2
(1) =32.09,
p<.001). This effect was constant for children in either condition (time bin 9condition
interaction: b=0.00084, SE =0.0012, t=0.71, v
2
(1) =0.52, p=.47). Critically,
however, proportion target looking was greater for children in the variable color condition
than in the constant color condition (main effect of condition: b=0.25, SE =0.078,
t=3.26, v
2
(1) =9.38, p=.0022).
3.3. The relationship between RS and retention
Clearly, only children in the variable color condition retained label-object mappings in
Block 2; however, these children did not look at targets at above-chance levels during
RS. We reasoned that despite this apparent failure during RS, children must have learned
something in order to show retention. If so, we expected a relationship between looking
times during RS and children’s retention. To test for this possibility, we calculated chil-
dren’s raw looking to both known and novel targets for the entirety of each RS trial. We
then correlated these raw looking time scores with children’s post-label target looking
during all six retention trials, excluding RS data from two children who looked away dur-
ing the retention phase (variable: 2). In neither condition did we find a relationship
between known target looking and retention (constant: r(12) =.50, p=.071, 95% CI
[0.05, 0.80]; variable: r(12) =.20, p=.50, 95% CI [0.37, 0.65]). However, there was
a positive correlation between novel target looking and retention, again in both conditions
(constant: r(12) =.64, p=.014, 95% CI [0.16, 0.87]; variable: r(12) =.74, p=.0024,
95% CI [0.34, 0.91]). Thus, although children did not consistently direct their attention to
targets during RS, they were nonetheless learning, with a stronger relationship between
looking time and retention in the variable color condition.
3.4. Characterizing looking during RS
Although the correlations do not establish a causal link between looking times during
RS and retention, they do suggest that children were learning during RS despite appar-
ently not looking at target objects at levels greater than expected by chance. We therefore
conducted a series of exploratory analyses to shed light on this unexpected finding. A
possible explanation for these results is that some children were not responding correctly.
If somebut not allchildren looked consistently at competitor objects in response to
the label instead of the target, overall looking would be at chance levels. Alternatively,
infants may have been comparing stimuli (Kovack-Lesh, Horst, & Oakes, 2008; Kovack-
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 13
Lesh, Oakes, & McMurray, 2012) or disambiguating (Halberda, 2006; Horst et al., 2010)
during RS; in this case we would expect to see switching between stimuli on these trials.
We therefore calculated the number of post-labeling stimulus-to-stimulus transitions
(Gabadinho, Ritschard, Mueller, & Studer, 2011) for each child on each RS trial, ignoring
background looking and looks away (note that including transitions between stimuli and
background would increase the overall number of transitions; this is therefore the most
conservative approach to the following analysis).
Fig. 7 depicts switching post-labeling for each trial. If, as a group, children were
responding by attending to a single object (whether target or competitor), switching rates
should be consistent and close to 1. In fact, the height of the bars indicates that children
varied in their switching behavior; further, mean switches were higher than 1. Interest-
ingly, across trials, the probability of low switching rates increased, as indicated by
shorter bars with wider basesthis is the pattern we would expect if children were learn-
ing during RS. On the other hand, the more variable responding earlier in RS indicates
higher rates of switching.
Next, we quantified the variability in children’s switching by calculating a Shannon
entropy score (Gabadinho et al., 2011) for the sequences of looks generated by each child
on each trial. Mean entropy scores per trial are depicted in Fig. 8. On a given trial, reli-
able looking to a single object would yield a Shannon entropy score of 0, while looking
distributed evenly across stimuli would yield a score of 1. Clearly, looking behavior dur-
ing RS is not consistent; rather, it is characterized by switching between stimuli. Entropy
drops around trials 10 and 11, suggesting that children were responding more reliably
toward the end of RSagain consistent with learning across trials.
0
5
10
15
123456789101112131415
Trial number
Switches
Condition Constant Variable
Fig. 7. Switches between stimuli during referent selection. Bar width represents probability density. Black
points represent mean switches.
14 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
3.5. A relationship between switching during RS and retention?
We then asked whether switching rates related to retention, based on findings from the cat-
egorization literature with infants demonstrating that infants who switched frequently
between stimuli showed better categorization (Kovack-Lesh et al., 2012). For this analysis,
we included all switches made during both the pre- and post-labeling phase, assuming that
children could learn about the objects on screen before the label was heard. Overall switching
rates did not differ between conditions (constant: M=146.64, SD =41.91, range =36215;
variable: M=151.75, SD =36.06, range =39204; t(25.84) =0.35, p=.73, 95% CI
[34.66, 24.45]). Because children with overall longer looking times had more opportunity
to switch, we performed partial correlations on total switching during RS and retention scores
(post-label target looking times during retention), controlling for total looking times to all
objects during RS. We removed data from two children whose total number of switches was
more than two standard deviations outside the overall mean (constant: 1; variable: 1). These
tests revealed no relationship between switching and retention scores either overall (r
(28) =.33, p=.09, 95% CI [0.63, 0.057]) or separately by condition (constant: r
(12) =.46, p=.13, 95% CI [0.81, 0.15]; variable: r(14) =.39, p=.16, 95% CI
[0.73, 0.24]). Interestingly, then, we found no influence of background variability on
switching rates as might be expected if infants in the variable condition were more distracted,
for example.
3.6. Block effects and switching in retention
The final question posed by these data is why children in the variable color condition
did not show retention until Block 2 of the test trials. One possibility is that switching
0.3
0.4
0.5
0.6
0.7
123456789101112131415
Trial number
Entropy
Condition
Constan
t
Variable
Fig. 8. Mean entropy scores across referent selection trials.
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 15
between stimuli on Block 1 could have reactivated previously learned mappings, allowing
them to respond correctly to the label on Block 2; if so, as in RS, looking times during
Block 1 could be related to retention on Block 2. Thus, we correlated raw target looking
times during the entirety of Block 1 with retention on Block 2 as indexed by post-label
target looking, removing data from three children who looked away for one or both
blocks (constant: 1; variable: 2). Looking times on Block 1 were related to retention in
the variable condition only (constant: r(11) =.37, p=.22, 95% CI [0.23, 0.76]; vari-
able: r(12) =.64, p=.014, 95% CI [0.16, 0.87]), reflecting our earlier finding that novel
target looking during RS was related to retention for these children. Although there was
no relationship between switching during RS and retention on Block 2, it remains possi-
ble that this relationship could hold for switching on Block 1 and retention. We therefore
calculated total switching during retention for all children on Block 1 and correlated this
with retention scores on Block 2, controlling for total looking times during Block 1. No
relationship between switching and retention was found, either overall (r(28) =.18,
p=.38, 95% CI [0.52, 0.21]) or for each condition individually (constant: r(14) =.19,
p=.53, 95% CI [0.40, 0.67]; variable: r(14) =.20, p=.51, 95% CI [0.68, 0.39]).
As in RS, then, while we found no evidence that the amount of switching between stimuli
related to retention, the amount of looking time accumulated as a consequence of switch-
ing was related to retention. Overall, these exploratory analyses of children’s raw looking
time data suggest that “chance” responding is a statistical artifact of more complex
exploratory behavior which can lead to learning without prolonged target fixation (cf.,
Kovack-Lesh et al., 2012).
4. Discussion
This study explored whether extraneous background variability would boost young
children’s word learning. We trained two groups of 2-year-old children with novel label-
object associations via multiple RS trials. Stimuli presented to both groups were identical
except that during RS half the children saw arrays of novel objects displayed on a white
background each time (constant color condition), and half saw objects on multiple col-
ored backgrounds (variable color condition). During RS, children in both conditions
increased their looking to target objects across trials but showed little evidence of sus-
tained target looking at levels greater than expected by chance. Overall, then, the effect
of background variability during this learning phase was weak. In contrast, at test there
was a clear effect of background variability: In the second block of retention trials, chil-
dren who had seen variable backgrounds during RS looked for longer at target objects
than did children who had seen constant colored backgrounds, and they did so at levels
greater than would be expected by chance. Thus, infants who had seen objects on vari-
able backgrounds learned and retained the novel object-label mappings, but infants who
had seen the objects on a constant background did not. These results indicate that back-
ground variability facilitated word learning, raising several interesting issues.
16 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
4.1. How does “poor” performance during RS lead to retention?
The variable color condition is one of the first word learning experiments to show chil-
dren performing apparently poorly during RS but successfully at test. In typical analyses
of word learning tasks with 3D objects, test trials for which children have not correctly
mapped novel labels during RS are excluded, with the rationale that children do not learn
(correct) novel label-novel object mappings when (incorrectly) mapping novel labels to
known objects (e.g., Hilton & Westermann, 2016; Twomey et al., 2014). From this per-
spective, it is surprising that children in the variable color condition were the only ones
to show robust retention: If during training these children were not looking to novel
objects at above-chance levels, how then did they retain?
Importantly, the canonical measure of attention on word learning tasks is proportion
target looking out of all AOI looking, and it was on this measure that children seemed to
be unsuccessful during RS and should therefore not be learning label-object mappings. In
contrast, our correlation analyses of raw looking times showed that children in the vari-
able condition who spent longer looking at novel targets during RS (and the first block of
retention) did indeed show better learning (for a similar result in a noun generalization
task, see Goldenberg & Johnson, 2015). Then, our exploratory analyses revealed that this
learning occurred while children were distributing their attention between targets and
competitors (see also Fitneva & Christiansen, 2011). In particular, incorrect but reliable
responding would lead to low entropy in the sequences of children’s switching between
stimuli, whereas entropy during RS was initially high for both known and novel trials.
This finding is convergent with new empirical and computational evidence suggesting that
word learning is a multiple-stage process which entails (a) learning about non-target as
well as target objects and (b) encoding new objects as well as new word forms (Bion,
Borovsky, & Fernald, 2013; Halberda, 2006; Horst et al., 2010; McMurray, Horst,
Samuelson et al., 2011b; Yurovsky et al., 2014). These incremental accounts of word
learning also suggest that low levels of looking during RS may be sufficient for children
to demonstrate retention (cf., Yurovsky et al., 2014)and this is what we found.
Thus, children in this study learned by accumulating experience with objects by
switching between them. Importantly, however, it was the amount of experience gained
rather than the number of switches that related to retention. This finding contrasts with
work in the categorization literature, which demonstrates that the frequency of switching
between stimuli is related to category learning. For example, Kovack-Lesh et al. (2012)
demonstrated that 4-month-old infants showed better category learning when they had
switched more frequently between stimuli during familiarization (see also Kovack-Lesh,
McMurray, & Oakes, 2014; Kovack-Lesh et al., 2008). However, there are many differ-
ences between these studies and the current work: The children who took part in the
categorization studies were much younger, stimuli were displayed individually on two
separate monitors rather than side by side on a single screen, and there was no labeling,
to name a few. Thus, we interpret the lack of relationship between switching and learning
in this study as inconclusive. Rather, our results suggest that the fine-grained temporal
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 17
dynamics of children’s looking in word learning task is a rich topic for further investiga-
tion.
Finally, there remains the question of why the correlations between raw looking times dur-
ing RS and retention only hold for the variable color condition. While it is impossible to draw
firm conclusions from the null results in the constant color condition, we believe that the most
likely explanation for this is a floor effect. Specifically, children in the color condition may
have been learning during RS, but some other aspect of the task may have prevented them
from responding correctly during retention. We discuss a possible mechanism below.
This study makes the empirical point that even if children are not responding at above-
chance levels during RS on proportion-based analyses, they can learn enough about novel
labels and novel objects to form partial label-object mappings sufficient to support correct
responses at test. This finding has implications for future work in word learning and,
more broadly, developmental work involving forced-choice tasks. First, when analyzing
rich eye tracking data, proportion target looking may not be the only informative measure
of children’s performance: Analyses of raw looking times may reveal additional patterns
in the data. Second, we provide strong evidence that children learn something about
label-object mappings even when they do not show a clear label response. Thus, research-
ers should consider including in their analyses test trials for which children did not cor-
rectly map novel labels during earlier training trialseven in 3D object paradigms
because children may well learn something from these trials even when making an erro-
neous mapping. Third, tasks involving a pointing response require infants to make an
explicit choice via a point or a reach, resulting in substantially less noisy scores than seen
in looking time measures (Ambridge & Lieven, 2011). In contrast, infants’ and children’s
looking times in general, and label responding in particular, are noisy and highly sensitive
to individual differences in processing speed (Fernald, Perfors, & Marchman, 2006;
Marchman & Fernald, 2008). These individual differences may have compounded chil-
dren’s apparently poor RS performance in this study, given that children of the same age
in 3D object studies have repeatedly been shown to succeed at this type of task (e.g.,
Axelsson, Churchley, & Horst, 2012; Horst & Samuelson, 2008; Horst et al., 2010;
Kucker & Samuelson, 2012; Twomey et al., 2014). Thus, this work underscores the
importance of understanding the relationship between the explicit measures obtained from
children’s behavioral responses and the implicit measures provided by eye tracking, both
in early language acquisition tasks and in developmental science more broadly (cf., Mac-
donald, Brandt, Theakston, Lieven & Serratrice, 2017; Noble, Rowland, & Pine, 2011).
Future work is planned to explore this critical methodological issue.
4.2. Memory reactivation in word learning tasks?
Children in the variable color condition looked at target objects at chance levels on the
first block of retention trials, but they responded systematically to labels on the second
block. This behavior is consistent with the infant and adult memory literatures, which
demonstrate that memory recall is boosted when participants are reminded of the previ-
ously studied materials before test (Hildreth & Rovee-Collier, 1999; Hsu, Rovee-Collier,
18 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
Hill, Grodkiewicz, & Joh, 2005; Rovee-Collier, Sullivan, Enright, Lucas, & Fagen, 1980;
Smith & Handy, 2014). This phenomenon has been demonstrated in visual recognition
studies in infants of this age group, for whom a 1 s visual reminder of previously learned
stimuli is sufficient to trigger retention effects for novel stimuli (Morgan & Hayne,
2006).
Our exploratory analyses offer a mechanism for this effect: In Block 1, children
explored stimuli without showing systematic responses to the label, but in doing so they
reactivated their memory for the label-object mappings learned during RS, which allowed
them to demonstrate retention in Block 2. Often in word learning studies children are pro-
vided with only a single retention trial for each object, but the current data suggest that
null findings could be due to difficulty in recall rather than a lack of learning. Future
work is necessary to explore in detail whether the inclusion of memory reactivation-type
trials in retention tasks will provide a useful means of teasing apart “true” lack of reten-
tion from lack of responding. Moreover, whether the relationship exists between this phe-
nomenon as seen in our data and other word learning paradigms such as the 3D object
task is unknown. For example, Horst and Samuelson (2008) analyzed retention by block
and found no such reactivation effect. Thus, establishing the locus of the effect of mem-
ory reactivation in the word learning field is critical for a thorough understanding of the
delicate memory processes underlying early language acquisition.
4.3. Decontextualization in children’s representational development
The fact that children in the constant color condition failed to retain newly formed
label-object associations is surprising. Indeed, related work indicates that consistency in
context supports learning in related tasks in children of this age (e.g., Horst, Samuelson,
et al., 2011b; Williams & Horst, 2014)the opposite of the current findings. For exam-
ple, Vlach and Sandhofer (2011) demonstrated that 2.5-year-old children’s noun general-
izations were supported by matching training and test contexts (i.e., same color), while
only older children were able to generalize after training with variable contexts. Simi-
larly, Axelsson and Horst (2014) showed that contextual consistency in the form of
repeating rather than varying competitor objects supported children’s word learning in an
RS task similar to the one presented here. These studies suggest that simplification of
non-target information helps children learn about the target. From this perspective, chil-
dren in the constant color condition should show better, not worse, learning than children
in the variable color condition.
However, this is not what we found. Why, then, should a simpler task (i.e., constant
color vs. variable color backgrounds) lead to worse learning? In fact, our results are in
line with a wealth of adult memory work that demonstrates that background variability
supports recall of learned information in a new context (e.g., Gartman & Johnson, 1972;
Godden & Baddeley, 1975, 1980). More recent work has explored the effect of context
on adults’ category learning. For example, Smith and Handy (2014) demonstrated that
encountering faces on variable video backgrounds facilitated retention of names learned
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 19
for those faces, while Finch, Carvalho, and Goldstone (2016) showed that variable back-
grounds led to better retention of previously seen exemplars of a bird category.
These results are attributed to a decontextualization mechanism. When memories are
formed after a single encounter, the context as well as the target is encoded. On subse-
quent encounters, if the context is unchanged, it remains part of the representation. For
these context-dependent memories, recall is impaired when the context changes. Godden
and Baddeley (1975) describe a classic example of this context effect on memory,
showing that divers who had learned word lists either on dry land or underwater were
better at recalling words learned underwater when tested underwater, and better at
recalling words learned on dry land when tested on dry land. When an item is encoun-
tered in multiple different environments, however, the representation becomes decontex-
tualized: The context becomes less important to the representation, increasing the
signal-to-noise ratio (Hintzman, 1984). If an item with a decontextualized representation
is encountered in a new environment, then, it is easier to recall than if the representa-
tion were context dependent.
The same mechanisms that explain these adult data can account for children’s word
learning in this study. During RS, children in the constant color condition learned con-
text-dependent representations in which label-object mappings were only associated with
a white background. In contrast, children in the variable color condition learned decontex-
tualized representations, where label-object mappings were associated with multiple dif-
ferent backgrounds. At test, children encountered novel objects on a gray screenand
critically, neither group had seen these objects in this context until this point. Thus, any
correlation between novel target looking during RS and retention for children in the con-
stant color condition was likely washed out by the difficulty for these children of general-
izing novel label-object mappings to a new context for the first time (for a related
argument, see Goldenberg & Johnson, 2015).
This raises the question of why contextual consistency in previous studies supports word
learning. It is possible that different types of context have qualitatively different effects. In
the current RS task, in line with Stephen et al. (2009), “context” was low-level background
variability (cf., Goldenberg & Johnson, 2015; Goldenberg & Sandhofer, 2013). In contrast,
the contexts in the storybook literature are rich and salient: In these studies, books were con-
structed from photograph-like images, resulting in a complex visual scene that varied from
page to page. In addition, the sentence contexts in which novel words appeared also varied
(Horst, Samuelson, et al., 2011b; Williams & Horst, 2014). Similarly, in the RS work, “con-
text” consisted of the competitor objects presented alongside the targets, which were consid-
erably more complex than a simple block of color (Axelsson & Horst, 2014). Thus, it may
be that in rich learning environments, restricting complexity supports learning (e.g.,
Radesky & Christakis, 2016), while in simpler learning environments, increasing complex-
ity by adding low-level background noise helps learning. Clearly, the current data indicate
that the relationship between RS and retention is not as straightforward as accurate respond-
ing during learning leading to accurate recall, and it deserves more in-depth work (for a sim-
ilar argument, see Samuelson et al., 2016).
20 K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017)
4.4. Relationship to dynamic systems accounts of learning
Decontextualization of memory traces can account for the current data. However, we
view this explanation as part of a much broader, more complex mechanism which can
account for learning and development across multiple domains: dynamic systems, and in
particular, the DST of development (Thelen & Smith, 1996). In DST, behavior emerges
as a stable state of a complex system of multiple interacting components, and develop-
mentlearningis the transition between these stable states. Importantly, the developing
child is not a closed system: S/he is embedded in a system consisting of myriad and
constantly changing inputs, for example, the learning environment, the child’s learning
history, the child’s own body, and subtle changes in the task at hand (e.g., Clerkin, Hart,
Rehg, Yu, & Smith, 2017; Fausey, Jayaraman, & Smith, 2016; Morse, Benitez, Bel-
paeme, Cangelosi, & Smith, 2015; Samuelson & Horst, 2007; for a review, see Sch
oner
et al., 2015). Changes to any of these components can have cascading and often unpre-
dictable effects on the interactions at work in the learning system. Here, we tested the
broad theoretical prediction from the dynamic systems approach that adding background
entropy to the learning system should facilitate learning by speeding up the emergence of
new stable behavioral states (Dixon, Stephen, Boncoddo, & Anastas, 2010; Stephen &
Dixon, 2009). The current data support this account: Only the children who were trained
in a higher entropy environment showed evidence of learning. Thus, decontextualization
may serve as a mechanistic description of a phenomenon emerging from a higher order
dynamic system.
Importantly, visual variability may be only part of the story: Other types of entropy may
also support learning, raising the intriguing possibility for future work that entropy intro-
duced in a different modality, for example sound or spatial location, could also support word
learning. Further, this experimental work motivates further naturalistic studies to explore
the effect of entropy in early language learning in the noisy, unconstrained real-world envi-
ronment encountered by children outside the lab (e.g., Clerkin et al., 2017). Overall, how-
ever, the current work provides evidence that word learning is just one component of a
developmental system; critically, then, to understand language development, we must
endeavor to understand the interactions of the components of the system as a whole.
Acknowledgments
This work was supported by the ERSC International Centre for Language and Commu-
nicative Development (LuCiD; ES/L008955/1), an ESRC Future Research Leaders grant
to KT (ES/N01703X/1). GW was further supported by a British Academy/Leverhulme
Trust Senior Research Fellowship (SF150163). We are very grateful to the caregivers and
infants who made this work possible. We also thank Rebecca Frost, Gemma Taylor, and
Matt Hilton for their generosity with their time in stimulus preparation, analyses, and dis-
cussion, and three anonymous reviewers for their insightful comments. Anonymized data
and scripts are available via Open Science Framework (https://osf.io/mtr8a/).
K. E. Twomey, L. Ma, G. Westermann / Cognitive Science (2017) 21
Note
1. Mixed effects models were run in the R package lme4.0 (v.1.1-12; Bates, M
achler,
Bolker, & Walker, 2015) in R Studio 0.99.903 (R Studio Team, 2015) running R
version 3.2.4 (R Core Team, 2016). All random effects structures reported were the
maximal that converged (Barr, Levy, Scheepers, & Tily, 2013), and all p-values
associated with mixed effects models were obtained, using the likelihood ratio test
(anova()) and Type I sequential sum of squares.
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... Applied to data of first language development, it has been confirmed that MLU is highly variable, and that this may be meaningful for development (Van Dijk et al., 2001). There are also some experimental studies that investigate the role of temporal variability, for instance the one by Twomey et al. (2018) on word learning. In their design, 2-year-old children watched novel and known objects, and simultaneously heard a novel or known word. ...
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