Trajectories of Infants’ Biobehavioral Development: Timing and Rate of A-Not-B Performance Gains and EEG Maturation

Abstract

This study examined how timing (i.e., relative maturity) and rate (i.e., how quickly infants attain proficiency) of A-not-B performance were related to changes in brain activity from age 6 to 12 months. A-not-B performance and resting EEG (electroencephalography) were measured monthly from age 6 to 12 months in 28 infants and were modeled using logistic and linear growth curve models. Infants with faster performance rates reached performance milestones earlier. Infants with faster rates of increase in A-not-B performance had lower occipital power at 6 months and greater linear increases in occipital power. The results underscore the importance of considering nonlinear change processes for studying infants’ cognitive development, as well as how these changes are related to trajectories of EEG power.

Full text

The title for this Special Section is The Developing Brain: Evidence for Plasticity
during Childhood and Adolescence, edited by Amanda E. Guyer, Koraly P
erez-
Edgar, and Eveline A. Crone
Trajectories of Infants’Biobehavioral Development: Timing and Rate of
A-Not-B Performance Gains and EEG Maturation
Leigha A. MacNeill , and Nilam Ram
The Pennsylvania State University
Martha Ann Bell
Virginia Tech
Nathan A. Fox
University of Maryland
Koraly P
erez-Edgar
The Pennsylvania State University
This study examined how timing (i.e., relative maturity) and rate (i.e., how quickly infants attain proficiency)
of A-not-B performance were related to changes in brain activity from age 6 to 12 months. A-not-B perfor-
mance and resting EEG (electroencephalography) were measured monthly from age 6 to 12 months in 28
infants and were modeled using logistic and linear growth curve models. Infants with faster performance
rates reached performance milestones earlier. Infants with faster rates of increase in A-not-B performance had
lower occipital power at 6 months and greater linear increases in occipital power. The results underscore the
importance of considering nonlinear change processes for studying infants’cognitive development as well as
how these changes are related to trajectories of EEG power.
Infants undergo substantial changes in cognitive
functioning in the second half of the first year (Bell
& Fox, 1992; Cuevas & Bell, 2010; Diamond, 1985).
The A-not-B task, a classic measure of cognitive
development in infancy, was developed by Piaget
(1954) to assess 8- to 12-month-old infants’under-
standing of object permanence (i.e., knowledge that
an object exists when it is no longer in sight).
Although most infants are capable of completing
the task by age 12 months, the timing and rate of
progression toward successful performance differ
among infants across the second half of the first
year. Piaget’s model of qualitative stages in cogni-
tive development implies nonlinearity, in which the
development of children’s thinking is not additive
but undergoes substantial reorganization over time
(van Geert, 1998). Previous work indicates that task
performance is related to variation in brain struc-
ture and function. For example, rhesus monkeys
with bilateral ablations of the dorsolateral pre-
frontal cortex make the A-not-B error at varying
delays, whereas monkeys without these lesions do
not (Diamond, 1990). Prior research with human
infants suggests positive associations between fron-
tal electroencephalogram (EEG) power and object
permanence task performance (Bell & Fox, 1992).
These findings, among others, illustrate that
advancements in children’s cognitive performance
may parallel concurrent changes in the brain (Fis-
cher & Van Geert, 2014).
Although there are individual differences in
infants’development of object permanence, particu-
larly when assessing the amount of delay necessary
to evoke the A-not-B error (Bell & Fox, 1992; Dia-
mond, 1985), we have not yet charted age-related
This study was supported by a grant from the National Insti-
tutes of Health (1R01HD026768) to Nathan Fox. The content of
this article is solely the responsibility of the authors and does not
necessarily represent the official views of the National Institutes
of Health. We thank the many individuals who contributed to
data collection and processing. We especially thank the families
who participated in the study.
Correspondence concerning this article should be addressed to
Leigha A. MacNeill, The Pennsylvania State University, 142
Moore Building, University Park, PA 16802. Electronic mail may
be sent to lam526@psu.edu.
©2018 The Authors
Child Development ©2018 Society for Research in Child Development, Inc.
All rights reserved. 0009-3920/2018/8903-0003
DOI: 10.1111/cdev.13022
Child Development, May/June 2018, Volume 89, Number 3, Pages 711–724

changes in A-not-B task performance as a nonlinear
developmental process. Moreover, questions still
remain concerning whether or how changes in EEG
power map onto children’s cognitive development.
The current study used linear growth models with
logistic model parameters as predictors to examine
the relation between timing (i.e., relative maturity)
and rate (i.e., how quickly infants attain profi-
ciency) of A-not-B performance gains from 6 to
12 months of age. In turn, we mapped performance
changes onto age-related changes in baseline EEG
power.
The A-Not-B Error
In 1954, Piaget published work on the develop-
ment of the object concept, or the understanding
that objects exist as unique entities outside of one’s
own actions (Piaget, 1954). This skill is thought to
be obtained little by little across the six substages of
sensorimotor development. It was argued that chil-
dren do not conceptualize the object as having its
own pattern of movement that is both distinct from
the child and also predictable and logical until the
second year. Piaget argued that children’s attain-
ment of the object concept, or object permanence, is
essential groundwork for building knowledge of
the physical world. He believed that the intellectual
structures of the child change through stages and
that each of these stages is qualitatively different
from the stages that had come before (Flavell,
Miller, & Miller, 1993).
In the 60+years since these observations took
place, researchers have investigated the underlying
skills necessary to correctly display mastery of
object permanence. Arguably, one of the tasks most
often used to measure object permanence is Piaget’s
(1954) own A-not-B task. In this task, an attractive
object is hidden at one location (A) multiple times
in front of the infant until it is switched to another,
adjacent location (B). Furthermore, the experimenter
may impose a time delay between hiding the object
at Band allowing the infant to search. The A-not-B
error lies in the infant reaching toward A, despite
having seen the object’s placement at B.
The skills necessary to perform the A-not-B task
successfully may extend beyond the simple acquisi-
tion of object permanence. Diamond (1985, 1990)
has demonstrated that as infants get older, the
length of delay between hiding the object and
allowing the child to search for the object must
increase for infants to make the perseverative error.
Thus, the A-not-B task is a marker of the infant’s
ability to remember previous events, coupled with
the ability to inhibit a prepotent motor response to
form a correct response. The data also imply that
the infant’s actions are governed by their intention,
as opposed to a developed habit. Diamond (1990)
later also proposed that both the integration of
recall memory and the inhibition of a prepotent
response are jointly necessary for solving the A-not-
B task.
Current conceptualizations contend that the task
can be interpreted as an early measure of children’s
executive function (Diamond, 2006). The delays
between hiding the object and allowing the infant
to search can be taxing on infants’memories, thus
age-related change in A-not-B task performance
may be indicative of improvements in the capacity
and duration of working memory (Marcovitch &
Zelazo, 1999). Smith, Thelen, Titzer, and McLin
(1999) proposed that in order for the infant to cor-
rectly obtain the object at the second location,
infants need to be able to discriminate locations that
look similar as well as be able to reach for the
object. Building on the large perceptual changes
that co-occur with enhanced locomotor skills in the
second half of the first year, infants are able to cou-
ple their looking and reaching abilities, such that
each discrimination and reach emerges from memo-
ries of previous discriminations and reaches (Smith
et al., 1999). The A-not-B error thus may not neces-
sarily represent a failure to obtain object perma-
nence insomuch as it demonstrates the difficulty of
keeping an object’s new location in mind when
exerting control over a motor response. Building on
the various interpretations of the constructs under-
lying the A-not-B task, we argue that the task taps
the intersection of infants’object permanence, exec-
utive functioning, and working memory. Addition-
ally, we agree with the consensus that the task also
requires flexibility in infant cognition and the
deployment of motor behavior (e.g., Smith et al.,
1999).
Given the number of skills required to success-
fully perform the A-not-B task at varying delays, it
comes as no surprise that there are both interindi-
vidual and intraindividual variability in infant per-
formance. Diamond (1985) found large between-
subject differences in the delay at which same-age
children made the A-not-B error through 12 months
of age. Additionally, she demonstrated that infants
persisted in making these errors until 12 months of
age with increases in delay. Other work has found
that performance on the A-not-B task is normally
distributed by 8 months of age, such that there was
a wide range of performance scores with a mode of
3 on a scale from 1 to 6 (Bell & Adams, 1999).
712 MacNeill, Ram, Bell, Fox, and P
erez-Edgar

Building on this foundation, we aimed to examine
individual differences in A-not-B task performance
from 6 to 12 months of age using logistic parame-
ters to capture nonlinearities in this development.
The Role of Brain Development in A-Not-B Performance
Differences in individual task performance may
be associated with brain activity over this develop-
mental window (Bell, 2001, 2012; Bell & Fox, 1992,
1997; Cuevas & Bell, 2011; Cuevas, Bell, Marcovitch,
& Calkins, 2012). Fischer and Van Geert (2014)
argued that changes in the rapidly maturing brain
underlie the quick bursts and discontinuities in
behavior and the presumed knowledge base of the
developing infant. Early in development, neurons
that are relatively unused are pruned in order to
increase neural efficiency (Huttenlocher & Dab-
holkar, 1997). With efficiency also comes the coordi-
nation of neural systems involved in newly
emerging behaviors, as in mastering object perma-
nence and the related skills needed to overcome the
A-not-B error. Action systems, such as sustaining
multiple actions, although also inhibiting the prepo-
tent response, must be coordinated for successful
performance (Fischer & Van Geert, 2014). The pre-
frontal cortex plays a role in holding this type of
information in the moment while the individual
engages in other actions. Because the A-not-B task
involves the ability to attend to visual stimuli and
track moving objects in space, we may also expect
to see links to the development of the occipital
region. Occipital power has been positively related
to cognitive performance in infants (Bell & Fox,
1997), and visual processes are more sensitive to
the environment by the end of the first year (Fox,
Kagan, & Weiskopf, 1979).
Much of the research on early brain development
has utilized EEG. EEG has the temporal resolution
to capture quick shifts in brain functioning that
may parallel the rapid cognitive processes that
unfold on the order of milliseconds (Bell, 1998).
EEG power values characterize excitability in a
cluster of neurons and are combined across individ-
ual 1 Hz frequency bins to indicate power measure-
ment in a specific frequency band. The dominant
frequency band during baseline recordings in
infancy is 6–9 Hz (Bell & Fox, 1992; Marshall, Bar-
Haim, & Fox, 2002), reflecting alpha activity in
infancy (Stroganova & Orekhova, 2007). Increases
in EEG power in the alpha frequency band may
suggest extensive organization of neurons (Nunez,
1981) and more neural activity. This neural activity,
in turn, has been associated with increased
cognitive skill in infancy including inhibitory con-
trol (Orekhova, Stroganova, & Posikera, 2001) and
working memory (Cuevas et al., 2012). Linear
increases in baseline power over time are evident
across the scalp at frontal, parietal, and occipital
sites from 7 to 12 months of age in the 6–9 Hz fre-
quency band, with the greatest increase between 9
and 10 months (Bell & Fox, 1994).
Performance on working memory tasks is associ-
ated with increases in baseline EEG power. Bell and
Fox (1992) found that baseline EEG power
increased monthly in the 6–9 Hz range from 7 to
12 months of age, and changes in frontal power
were associated with greater delay tolerance on the
A-not-B task. Bell (2002) tested 8-month-old infants
on a spatial working memory task and assessed
EEG power in the 3–5 Hz, 6–9 Hz, and 10–12 Hz
frequency bands both at baseline and during the
task. She found that the 6–9 Hz band yielded dif-
ferences in baseline and task power values, demon-
strating increased power during the cognitive task.
In addition, 8-month-old infants who successfully
completed the looking version of the A-not-B task
tolerating a 0-s delay or greater demonstrated
increases in frontal, parietal, and occipital power in
the 6–9 Hz frequency band from baseline to task
performance. However, there was no increase in
power for the children who did not complete the
task correctly (Bell, 2001). Finally, 8-month-old
infants who performed successfully on the A-not-B
task with a 0-s delay or greater demonstrated
greater medial frontal and occipital baseline EEG
power in the 6–9 Hz frequency band than infants
who did not successfully complete the task (Bell &
Fox, 1997). These results underscore the evidence
for scalp-wide increases in baseline power for
infants who successfully performed the task com-
pared to infants who did not.
To date, little research has longitudinally
assessed both A-not-B task performance and paral-
lel markers of neural development. Bell and Fox
(1992) examined A-not-B performance from 7 to
12 months (N=13) and collected EEG at rest at
each age. Infants who could tolerate a longer delay
on the A-not-B task at 12 months of age showed a
decrease between 7 and 8 months, and an increase
between 9 and 10 months in frontal EEG power.
The group with a shorter delay period only showed
an increase in frontal power between 10 and
11 months. Additionally, the two groups of infants
first differed on task performance at 10 months of
age, which was also the point in time when the
long-delay group showed the largest increase in
frontal EEG power. These findings suggest that
Trajectories of A-Not-B and EEG 713

toward the end of the first year, the relation
between growth in cortical organization and object
permanence ability becomes more established. The
Bell and Fox (1992) paper was one of the first to
establish that there is interindividual variability in
A-not-B task performance. Although infants demon-
strate remarkable progress on both brain activity
and A-not-B task performance over the latter half
of the first year, the literature has yet to chart the
relations across trajectories over time at the level of
the individual.
Timing and Rate of A-Not-B Performance Gains
If observed behavior and the brain are part of a
dynamic network of systems that co-occur and are
responsible for each other’s change (e.g., Fischer &
Van Geert, 2014), we must model development in
ways that best characterize how particular systems
change over time and how these systems change in
relation to one another. Adolph and Robinson
(2008) argued that the field has been overly reliant
on examining development through differences
between a beginning time point and an end time
point, often as a single difference score. They con-
tended that developmental systems frameworks
should aim to explain processes of change and the
shape of the change across time. Additionally,
development does not unfold in steady increments.
Rather, it speeds up and slows down at different
points in time (Fischer & Rose, 1997; Thatcher,
1994). Research on infant development is often char-
acterized by spurts in behavior that could be due to
distinct developmental processes, such as verbal or
spatial skills and differences in brain activity.
New behaviors can emerge from changes in clusters
of discontinuities (Fischer & Rose, 1997). Around
8 months, for instance, multiple skills undergo
sharp increases, such as crawling ability (Adolph,
1997), vocal imitation (Petitto & Marentette, 1991),
and object search performance (Bell & Fox, 1994).
These dramatic shifts in behavior imply nonlineari-
ties in infant development. Although many aspects
of development are described as nonlinear and
dynamic, the empirical literature has tended toward
using methods that describe stability and linear
change.
Trajectories of cognitive growth can be portrayed
by timing, or how mature infants are in relation to
their same-age peers, and rate, or how quickly or
slowly infants gain proficiency in cognitive perfor-
mance. Infants can be considered early, average,
and late maturers contingent upon their perfor-
mance relative to other infants. They are also
considered as quick, average, or slow maturers
based on the rate at which they progress from no
proficiency to proficiency on the task. The current
study focused on a time window (6–12 months)
that would likely encompass the first emergence
and competence of A-not-B performance.
To our knowledge, A-not-B task performance in
infancy has not been examined using nonlinear
growth models. Although we know that successful
A-not-B performance increases over age (e.g., Bell &
Fox, 1992; Cuevas & Bell, 2010; Diamond, 1985), it
is likely that the shape of the trajectory is nonlinear
and more representative of a sigmoid, or “S”-
shaped, curve. There are known discontinuities in
the development of cognitive processing, in that
spurts of growth are clustered at specific points of
time in the first year (Fischer & Rose, 1997). For
example, Munakata (1998) modeled infants’reaches
at both A and B. The percent of correct responses
for reaching at Awas flat, between 90% and 100%.
The percent of correct responses for reaching at B,
however, revealed a sigmoid shape with upper and
lower asymptotes. Developmental models must
acknowledge potential patterns of nonlinearity in
infants’early cognitive trajectories and ages at
which cognitive performance levels off. The current
study used nonlinear growth curve models, a rela-
tively novel method in the field of infant cognition,
to account for nonlinearities that other studies have
implied but have not directly tested.
Growth models provide a framework for describ-
ing the timing and rate of this change (Grimm,
Ram, & Hamagami, 2011; McArdle, 2009; Ram &
Grimm, 2007). Following previous work using non-
linear growth models to examine between-person
differences in timing and rate of pubertal develop-
ment (Marceau, Ram, Houts, Grimm, & Susman,
2011), our work examines how between-person dif-
ferences in the timing and rate of infants’perfor-
mance on the A-not-B task are related to changes in
EEG power. Given that infants’capabilities change
rapidly over the latter half of the first year and that
there is within-person variability in performance on
these tasks, the present study investigated the tim-
ing and rate of infants’cognitive and brain growth
within this important developmental time window.
We used linear and nonlinear growth models to
relate timing and rate of A-not-B task performance
to change in EEG power from 6 to 12 months of
age. The age range was chosen based on Diamond’s
(1985) work, which assessed A-not-B task develop-
ment every 2 weeks from 6 to 12 months of age.
She found that infants began reaching for the object
at 7.5 months and noted increases in delay
714 MacNeill, Ram, Bell, Fox, and P
erez-Edgar

tolerance at the average rate of 2 s per month.
However, there were large individual differences in
the delay needed for the error at every age. Our
objectives were to (a) describe nonlinear growth tra-
jectories in the timing and rate of performance gain
in the A-not-B task and (b) examine the associations
between nonlinear performance change and linear
age-related changes in infants’EEG power across
the second half of the first year. We hypothesized
that earlier timing and faster rate of A-not-B task
performance would be associated with higher initial
level of, and linear change in, EEG power.
Method
Given page limitations, an abbreviated discussion
of the methods is presented here with a full
description in Supporting Information.
Participants
Twenty-eight healthy 6-month-old infants (14
boys, 14 girls) and their parents were recruited
through mailing lists to participate in a longitudinal
study of infant development. The participants were
Caucasian from generally middle to upper-middle
class homes in the greater Washington DC
metropolitan area. Infants were born within
3 weeks of their anticipated due date, weighed at
least six pounds at birth, received no special medi-
cal intervention at birth, had no documented neuro-
logical problems, and both parents had at least a
high school education.
Procedures
Families came to the laboratory every month
from 6 to 12 months of age, each time within
5 days of their monthly birthday (total of 7 visits).
At each visit, brain electrical activity (EEG) was
recorded and the infant completed a series of cogni-
tive tasks, including the A-not-B task.
Electrophysiological Recording
Brain electrical activity was recorded during a 2-
min pretask baseline recording session at each visit.
During the recording, the infant watched the exper-
imenter spin balls in a bingo wheel, segmented into
10 s of spinning 1, 3, and 7 balls, each separated by
a 10-s pause. The sequence was then repeated.
Power values were calculated for each electrode site
for each stimulus condition. A composite of EEG
baseline power values were used in the current
analyses.
EEG recordings were taken using an Electro-Cap
(Electro-Cap, Inc., Eaton, OH) stretch cap (10/20
electrode system) from scalp electrodes, left and
right frontal, parietal, and occipital regions (F3, F4,
P3, P4, O1, and O2), as well as channels A1 and A2
located at the ears. All sites were referenced to Cz.
Impedances were kept below 5 KΩ. Electrooculo-
gram (EOG) data were recorded from the external
canthus to the supraorbit of one eye. All leads were
separately amplified by Grass Model 12A5 ampli-
fiers as part of the Neuro-data acquisition system
(Grass Model 12-32; Natus Medical Incorporated,
Pleasonton, CA). The EEG data were digitized
online at a sampling rate of 512 Hz per second for
each channel. The EEG data were re-referenced to
an average reference configuration prior to editing.
The EEG data were edited for eye movement and
gross movement artifact by trained coders. On aver-
age, 50%–59% of the EEG data were artifact free at
each of the measurement occasions. All analyses
used the artifact-free data only. Individual patterns
of available EEG data were not associated with any
study variables (ps>.08). The EEG data were ana-
lyzed using a discrete Fourier transform (DFT) with
a Hanning window of a 1-s width with 50% overlap.
The mean voltage was subtracted from each data
point to remove any power results due to DC offset
before DFT computation. Power in single Hz bands
was computed for frequencies between 1 and 12 Hz,
and power was expressed in mean square micro-
volts. Plots of spectral power indicated that the dom-
inant frequency in all leads at all ages was in the 6–
9 Hz alpha band. Power values were log trans-
formed (ln). Based on missing data patterns across
sessions (see Supporting Information), data were
handled using maximum likelihood estimation.
A-Not-B Task With Delay
After the electrophysiological recording, infants
were assessed on the A-not-B task with delay,
which was modeled after the standard two-location
task. The AB apparatus was a cardboard box with
two wells, A and B (specifics in Supporting Infor-
mation). The apparatus was positioned on the floor
in front of the infant, such that the center of the
box was at midline and the wells were within reach
of the infant. While the parent sat behind the infant,
the experimenter sat on the opposite side of the
apparatus facing the infant and parent.
The experimenter signaled the beginning of a
trial by holding up a toy to engage the infant’s
Trajectories of A-Not-B and EEG 715

attention. Subsequently, the experimenter lifted the
cloth covering one of the wells (A or B), placed the
toy in that well and then covered the well again
with the cloth, completely obscuring any sight of
the toy. If attention was lost during the trial, the
experimenter gained the infant’s attention and hid
the toy again. A correct response was coded if the
child recovered the toy from side A. Also included
as a correct response was uncovering the correct
well but failing to reach for the toy and uncovering
both wells yet visually fixating on the correct well
(see Supporting Information). Uncovering the
empty well, not reaching for the toy, and not fixat-
ing on the well housing the toy were all deemed
incorrect responses.
The A-not-B task was scored by delay on a scale
from 0 to 4. A score of “0”represented a failure to
complete the task at a 0-s delay. A score of “1”rep-
resented competence at completing the task with a
0-s delay, where the infant was allowed to immedi-
ately search for the toy once it was hidden. Scores
of “2,”“3,”and “4”were given when the infant
completed the task with a 2-, 4-, or 6-s or greater
delay, respectively. During the delay period, the
experimenter broke the infant’s attention from the
task by clapping their hands together. The parent
held the infant’s hands to prevent reaching during
the hiding and delay periods. The delay period
began once the experimenter observed the infant’s
attention breaking from the second well. Two
observers coded A-not-B performance by videotape.
The principal investigator, the experimenter, and
the observer in the session reviewed these codes
independently to resolve any discrepancies.
Data Analysis
We viewed our analyses of this small and very
unique sample as semiexploratory—using linear
and nonlinear growth models to extract meaningful
parameters from the rich and unique repeated mea-
sures data but not claiming or assessing model fits
as confirmatory evidence for statistical inference.
Interindividual Differences in the Development of A-
Not-B Task Performance
Our first aim was to quantify interindividual dif-
ferences in the development of infants’A-not-B task
performance from age 6 to 12 months. The data had
some distinctive characteristics that suggested
description using a logistic growth function (Ram &
Grimm, 2007). By design, the A-not-B task imposes
clear lower and upper bounds on performance.
Theoretically, all children progress from a stage
when they are not able to perform the task at a 0-s
delay (performance =0) to a stage when they per-
form the task at a 6-s or greater delay (perfor-
mance =4). As such, we modeled the seven repeated
observations of each infant’s performance using for-
mula 1, noted in the Supporting Information. The
timing of change was the age at which an infant
would reach a performance score =2 (formally, the
inflection point located halfway between the lower
and upper asymptotes). The rate (i.e., rate governing
change from the lower to the upper asymptote) was
also noted. Higher rate values indicate that the infant
is improving in A-not-B task performance more
quickly over time at the inflection point, relative to
the other infants. Analytically, the logistic growth
model served as a “measurement model”to derive
timing and rate scores (h
2i
and r
i
) that could then be
examined in relation to individual differences in the
development of EEG power. Linearity was accom-
modated in the measurement scale (0–4). Nonlinear-
ity was accommodated in development of cognitive
performance, given the previous research revealing
nonlinearities in infants’cognitive development.
Models were fit to each infant’s repeated measures
data by looping the nls function in R (R Core Team,
2013) with a range of starting values that facilitated
convergence for all N=28 cases.
Associations Between EEG Power and A-Not-B Task
Performance Over Time
Interindividual differences in the development of
EEG power were then modeled using a standard
linear growth model with covariates (Grimm, Ram,
& Estabrook, 2017). As noted in the Supporting
Information with formulas 2 through 4, the seven
repeated observations of EEG power were modeled,
separately for each electrode location while model-
ing the person-specific intercept and linear slope
coefficients. Of particular interest were the relations
of EEG power development with the timing (c
01
and c
11
) and rate (c
02
and c
12
) of A-not-B develop-
ment. Models were fit to the repeated measures
data using the nlme package in R (Pinheiro, Bates,
DebRoy, Sarkar, & Core Team R, 2015) using maxi-
mum likelihood estimation, with incomplete data
(5%) treated using missing at random assumptions.
Results
See Table S1 for descriptive statistics for the core
measures. As expected, the mean level of A-not-B
716 MacNeill, Ram, Bell, Fox, and P
erez-Edgar

performance increased with age (from M=0.00
at 6 months to M=3.32 at 12 months), with
peak interindividual differences in performance at
9 months (SD =1.41). In parallel, average EEG
power increased with age at all six electrode loca-
tions, but with no clear pattern of change in the
standard deviations.
Interindividual Differences in the Development of
A-Not-B Task Performance
In the logistic growth trajectories derived from
the logistic growth models (Figure 1), the model
(solid lines) provided a good description of the
repeated observations (dotted lines) of performance
(residual standard errors ranged from 0.73 to 9.29,
M=3.68, SD =2.04). The majority of infants were
unsuccessful on A-not-B performance at age
6 months (score =0), developed rapidly between
ages 7 and 11 months, and were able to complete
the task at a 6-s delay or longer (score =4) by age
12 months. The prototypical (average) infant
obtained a score of 2 (i.e., halfway between lower
and upper asymptotes) 3.68 months after the first
observation (i.e., 6 +3.68 =9.68 months), at which
point infants were developing at an average instan-
taneous rate of 2.55 (SD =3.04). There were, of
course, substantial individual differences both in
timing and rate of development (SD
h2
=2.04;
SD
r
=3.04). Notably, interindividual differences in
timing and rate were correlated at 0.49, indicating
that infants growing faster reached the point of
inflection earlier. A pseudo R-squared comparing
the variance of all residuals to the collection of
residuals from the individual models found
substantial variability around parameter estimates
(pseudo R
2
=.842).
Associations Between EEG Power and A-Not-B Task
Performance Over Time
Interindividual differences in timing and rate of
change in A-not-B task performance were examined
in relation to concurrent development of EEG
power at the six electrode locations using linear
growth models (Supporting Information, equations
2–4). We used a stricter criterion of p≤.01 given
the number of tests (Table S2). As expected, all
models indicated that EEG power increased, on
average, across the second half of the first year. For
example, for O2, the prototypical infant had (ln)
power of c
00
=2.51 at the first observation, with
power increasing at c
10
=.07 (SE =0.01, p<.001)
units per month across the seven measurements.
Associations between the interindividual differ-
ences in A-not-B performance derived from the
logistic growth model (timing and rate) and the
interindividual differences in the trajectories of
EEG power emerged for only occipital electrodes.
Individuals with faster rates of increase in A-not-B
performance (Figure 2E) had lower O1 EEG (ln)
power of O1 at age 6 months, c
02
=.08 (p=.01),
and marginally greater increases in O1 EEG power
across the study, c
12
=.01 (p=.08). In parallel (Fig-
ure 2F), individuals with faster rates of increase in
A-not-B performance had lower EEG (ln) power of
O2 at age 6 months, c
02
=.08 (p=.01), and mar-
ginally greater increases in O2 EEG (ln) power across
the study, c
12
=.01 (p=.09).
Discussion
This study is the first to describe the timing and
rate of development of A-not-B performance using
a logistic growth function and to examine how dif-
ferences in the behavioral development of cognitive
performance are related to trajectories of brain
activity. The first aim of the study was to identify
the timing and rate of A-not-B task performance
change, examining the sigmoid-shaped logistic
curve that traversed performance from a score of 0
to 4. As predicted, the logistic growth model pro-
vided a good depiction of repeated A-not-B perfor-
mance across the latter half of the first year,
capturing the observation that the majority of
infants were unsuccessful at the task at 6 months,
rapidly increased in performance from 7 to 11 months,
and succeeded at a 6-s or greater delay by
12 months. This description is consistent with Pia-
get’s theory of qualitative reorganization of chil-
dren’s thinking.
Past research has shown nonlinearities in A-not-
B performance, such as a surge in skill appearing
around 8 months of age (Bell & Fox, 1994), and
another between 10 and 12 months (Smith & The-
len, 2003). Other work has implied a sigmoid-
shaped trajectory of reaching at location Bacross
age in infancy (Munakata, 1998). However, previ-
ous research documented nonlinearities by reveal-
ing surges in performance at various ages, while
often modeling change in behavior as linear (Fis-
cher & Rose, 1997). The current study found that
A-not-B performance is indeed nonlinear, with flat
lower and upper bounds at 6 and 12 months,
respectively, and a spike in performance between 7
and 11 months of age.
Trajectories of A-Not-B and EEG 717

Figure 1. Predicted trajectories of nonlinear intraindividual change of A-not-B performance for N=28 children across seven assess-
ments. Solid lines show the predicted trajectories for each individual; dotted lines show the raw data for each individual. h=timing of
change; r=rate of change. [Color figure can be viewed at wileyonlinelibrary.com]
718 MacNeill, Ram, Bell, Fox, and P
erez-Edgar

AF3 Predicted Trajectories BF4 Predicted Trajectories
CP3 Predicted Trajectories DP4 Predicted Trajectories
EO1 Predicted Trajectories FO2 Predicted Trajectories
High (+1SD) A-not-B Rate
Low (-1SD) A-not-B Rate
Figure 2. Panels A-F represent predicted trajectories of linear intraindividual change of electroencephalography (EEG) power for N=28
children across seven assessments. Bolded lines show the predicted trajectories for each individual; gray lines show the raw data for
each individual. [Color figure can be viewed at wileyonlinelibrary.com]
Trajectories of A-Not-B and EEG 719

Regarding timing, infants reached the point of
inflection on the A-not-B task on average at age
9.68 months. Nine months of age may be an impor-
tant time for coordinating multiple systems
involved in the A-not-B task, such as motor control,
attending to and tracking visual stimuli, inhibitory
control, and working memory. Previous work
found a sharp increase in performance at 8 months
of age (Bell & Fox, 1994) and that task performance
at 8 months is normally distributed (Bell & Adams,
1999). A second study with eight infants (Fox et al.,
1979) found that all 9-month-old infants were able
to complete the A-not-B task at a 3-s delay, whereas
by 10 months, all infants completed the task at a 7-
s delay. These findings indicate that between 9 and
10 months, infants experience a rapid increase in
performance on the A-not-B task. It is, however,
important to note that the 7-s delay in Fox et al.
(1979) study is larger than the 2-s delay at the point
of inflection in the current study. This difference
could be due to the disparity in sample size.
Although the greatest shift in behavior occurred at
around 9 months of age for both studies, this was
also the age when individual differences were
greatest, and many infants were tolerating delays of
6 s or greater.
The substantial interindividual differences in the
timing of task proficiency gains are consistent with
previous work. Diamond (1985) and Bell and Fox
(1992) found large variability at 8 and 7 months of
age, respectively, in delay tolerance. Although pre-
vious work has found that A-not-B performance
increases monthly for at least 6 months (Bell & Fox,
1992; Cuevas & Bell, 2010; Diamond, 1985; Fox
et al., 1979), the present study is the first to quan-
tify those increases with respect to a logistic func-
tion that accommodates the nonlinear age-related
changes in behavior across this time window.
Indeed, although the relative rate at the point of
inflection was 2.55 on average, the range was from
0.25 to 13.04.
This study is the first to identify significant indi-
vidual differences in how quickly or slowly infants
attain proficiency relative to their peers. Because
there was variation in both timing and rate A-not-B
task performance, we can assume that whereas the
sigmoid-shaped curve describes the infants’perfor-
mance gains across 6–12 months, the trajectories for
the 28 infants are all somewhat unique (see Fig-
ure 1). Furthermore, the negative correlation of tim-
ing and rate illustrates that earlier timing on the
task is related to faster rates of acquisition, such
that children who reach the halfway point in task
performance at younger ages are mostly the same
individuals who are making successful task gains
more quickly. These findings suggest that, although
the latter half of the first year is a time during
which there is substantial normative change, there
is already substantial idiosyncrasy in individual
development.
Our second aim was to examine the associations
between linear change in baseline EEG power and
nonlinear change in A-not-B performance. First, the
results demonstrated that for all electrode sites,
there was a linear increase in baseline EEG power
values across 6–12 months of age. These findings
are consistent with previous work that has
described an overall linear increase in power at
frontal, parietal, and occipital sites across the first
year (Bell & Fox, 1992; Cuevas & Bell, 2011). The
fact that the 6–9 Hz alpha band captured increases
in power validates the existing literature that this is
an appropriate frequency band for measuring brain
electrical activity during infancy (Marshall et al.,
2002). Previous work has suggested that increases
in baseline EEG power in the infancy are indicative
of emerging neural organization (Nunez, 1981). The
increase in baseline power at all six electrode sites
over time is suggestive of neural maturation and
myelination that support the coordination of higher
order systems (Fischer & Van Geert, 2014). In order
to capture the functional consequences of brain
activity, it is necessary to investigate how changes
in baseline EEG power are related to changes in
cognitive processing.
Interestingly, the current study found that infants
with a faster rate of increase in A-not-B perfor-
mance had lower baseline EEG power of O1 and
O2 at 6 months of age, and they had larger
increases in baseline power at these electrode loca-
tions across the 7-month period. Infants with higher
power at the first time point (6 months of age)
tended to advance on the A-not-B task more slowly
over time. It may be that these infants were already
performing the A-not-B task more successfully with
longer delays and were thus ahead of infants with
lower levels of initial power. Infants with lower ini-
tial levels of baseline EEG power had relatively
more catching up to do, which required steeper (or
faster) rates of performance over time.
Specific to occipital power, previous work has
found that infants who could tolerate longer delays
in A-not-B task performance also demonstrated
greater baseline left hemisphere occipital power
over age (Bell & Fox, 1992). Additionally, infants
who did not complete the A-not-B task at 8 months
had significantly lower baseline occipital power
values than children who could complete the task
720 MacNeill, Ram, Bell, Fox, and P
erez-Edgar

at 0- or 2-s delays (Bell & Fox, 1997). The A-not-B
task is a spatial working memory task, which
requires attending to objects in space and tracking
moving objects. Infants show an increase in general
attentiveness to their environment by the end of the
first year (Fox et al., 1979), which may provide fur-
ther support for the relations noted here. In other
words, infants’ability to advance quickly on cogni-
tive tasks may be in part linked to their increasing
capability to attend to nonsocial visual events. Tim-
ing of A-not-B performance, on the other hand, was
not related to initial levels or change in baseline
occipital power. This suggests that the average
point of change in the curvature of the A-not-B tra-
jectory is not dependent on levels or changes in
occipital power.
Substantial changes in children’s cognitive ability
can be attributed to the coordination of multiple
brain and behavior systems (Fischer & Van Geert,
2014). It is somewhat surprising, then, that the fron-
tal sites were not significantly associated with rates
of increase in A-not-B performance for our sample,
given previous literature suggesting that the pre-
frontal cortex plays an important role in infants’
development of object permanence (Bell, 2001, 2012;
Bell & Fox, 1992, 1997; Cuevas et al., 2012). Occipi-
tal development may be more robust than frontal
development in the first year. Past research sug-
gests that the occipital lobe typically develops ear-
lier in infancy, whereas frontal development is
particularly variable and develops at differing rates
in the latter half of the first year (Johnson, 2001).
The stability of occipital development may con-
tribute to the significant associations between
A-not-B task performance and occipital power
changes. However, we are hesitant to suggest that
changes in baseline occipital power are the only
neural correlates of performance on the A-not-B
task. Future research should replicate these analyses
with a larger sample size to generalize these find-
ings and isolate the mechanism of A-not-B perfor-
mance associated with baseline occipital power.
In sum, the current findings demonstrate that
faster improvement in A-not-B performance could
reflect changes in the organization and excitability
of neurons in the occipital region. The use of associ-
ations between nonlinear cognitive performance
change and linear baseline EEG power change is an
innovative way of examining interrelated develop-
mental processes. However, increases in occipital
power need not cause increased cognitive
performance or vice versa. Additionally, it is only
assumed that scalp electrodes are indicative
of brain activity from specific cortical regions
underlying the electrodes, and we have not directly
tested whether changes in baseline EEG power are
reflective of brain maturation. Although this work
does not measure brain maturation directly or EEG
power in-task, knowledge of these patterns of brain
activity in infants, in conjunction with cognitive
performance, opens up the possibility to predict,
and eventually understand, individual differences
in executive function over time.
This study is the first to use growth curve mod-
eling to delineate trajectories of infants’cognitive
growth in relation to their brain development. Bell
and Fox’s (1992) study was pivotal in longitudinally
assessing change in baseline EEG power over time
for two groups of infants varying in A-not-B task
performance, but the longitudinal sample was smal-
ler (N=13), and sensitive analytic techniques could
not be applied. Conversely, Cuevas et al. (2012)
used a much larger sample (N=290) but fewer
time points (5 and 10 months) and traditional
regression analyses. We used nonlinear growth
curves of task performance to more accurately
describe the monthly change occurring for infants
(N=28) from 6 to 12 months of age. In this way,
we illustrate how contemporary analytic tools can
be used to assess, and reassess, classic developmen-
tal phenomena. Using nonlinear mixed-effects mod-
els allowed us to most effectively describe trends in
A-not-B development that support the discontinu-
ities central to Piaget’s theory of cognitive develop-
ment while also revealing how brain development
maps onto the rates at which children advance in
task attainment. Additionally, individual differences
in timing and rate of A-not-B performance were
shown in the sigmoid shape of the trajectories, per-
mitting a closer and more comprehensive under-
standing of how variable cognitive development is
in the first year. It is important to mention that the
sigmoid shape of the A-not-B performance trajec-
tory is dependent on the sampling method
(Adolph, Robinson, Young, & Gill-Alvarez, 2008),
and more frequent assessments within the age win-
dow could have demonstrated linear development.
However, we found little change between 6 and
7 months, and noted that between 11 and
12 months performance levels off. Without the
addition of these beginning and end time points,
one might assume linear increases between these
missing time points. Moreover, individuals vastly
differed in their A-not-B performance (Figure 1),
and the inclusion of initial emergence through to
competence therefore allowed us to capture the full
developmental progression for most of the infants
in the study.
Trajectories of A-Not-B and EEG 721

The current results should be viewed in the con-
text of study limitations. Primarily, the sample was
small for detecting interindividual differences in
intraindividual change. More participants will be
needed to generalize these findings. Second, the
A-not-B task involved a well that was uncovered
then recovered again once the toy was placed
rather than having both wells covered simultane-
ously. The procedure we used may have primed
the infant to maintain attention on the correct well
(Diamond, Cruttenden, & Neiderman, 1994). Third,
infant behavior was not coded during the EEG
baseline session. Had there been information
regarding the time the infant spent attending to the
spinning wheel or amount of infant motor move-
ment, we may have been able to more closely tie
individual differences in occipital power to individ-
ual differences in visual attention. Fourth, EEG was
not recorded during the A-not-B task so we could
not capture any task-related variations in power.
Fifth, the mathematical equation used in the analysis
relied on the inflection point to measure interindivid-
ual differences at a score of 2. As this score is in the
middle of the continuous scale from 0 to 4, its mean-
ing on the scale is somewhat unclear. Moving the
inflection point to different locations on the growth
curve would likely reveal how rate changes across
the logistic function. The selection of the score of 2
was simply to have a common point, or a parame-
terized feature of the trajectory, on which to com-
pare individuals parsimoniously using the entire
measurement scale. Moreover, we assumed that the
measurement scale was linear and that cognitive
development was nonlinear. An alternative approach
would be to accommodate a nonlinear measurement
scale and linear development. Finally, the current
study did not assess outcome behaviors beyond the
age of 12 months, so the implications of these vary-
ing trajectories on later developmental processes and
outcomes remain unknown. Future research should
assess larger samples and extend measurement of
these constructs beyond the age of 12 months so that
we may better understand the role of early brain
maturation in the long-term development of cogni-
tive skills.
Nevertheless, this work provides evidence for
the relations between brain activity and cognitive
performance trajectories across the second half of
the first year. By capturing the initial emergence of
a skill and tracing attainment from absence through
to advanced performance, this approach has the
potential to not only inform our understanding of
cognitive processing in infancy but also provide
theoretical and methodological foundations for
future investigations of emerging developmental
pathways. The contemporary analytic techniques
illustrated here provide an exciting opportunity to
empirically reassess our theoretical understanding
of core developmental functions and processes.
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Supporting Information
Additional supporting information may be found in
the online version of this article at the publisher’s
website:
Table S1. Descriptive Statistics for the Seven
Monthly Repeated Measurements of Behavior (A-
Not-B Performance) and Brain Activity (Electroen-
cephalography [EEG] Power)
Table S2. Results From the Linear Growth Mod-
els With Logistic Model Parameters as Predictors
Data S1. Method
724 MacNeill, Ram, Bell, Fox, and P
erez-Edgar