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Functional Imaging of Numerical Processing

in Adults and 4-y-Old Children

Jessica F. Cantlon1,2*, Elizabeth M. Brannon1,2, Elizabeth J. Carter1, Kevin A. Pelphrey1,3*

1 Department of Psychological and Brain Sciences, Duke University, Durham, North Carolina, United States of America, 2 Center for Cognitive Neuroscience, Duke University,

Durham, North Carolina, United States of America, 3 Brain Imaging and Analysis Center, Duke University, Durham, North Carolina, United States of America

Adult humans, infants, pre-school children, and non-human animals appear to share a system of approximate

numerical processing for non-symbolic stimuli such as arrays of dots or sequences of tones. Behavioral studies of adult

humans implicate a link between these non-symbolic numerical abilities and symbolic numerical processing (e.g.,

similar distance effects in accuracy and reaction-time for arrays of dots and Arabic numerals). However, neuroimaging

studies have remained inconclusive on the neural basis of this link. The intraparietal sulcus (IPS) is known to respond

selectively to symbolic numerical stimuli such as Arabic numerals. Recent studies, however, have arrived at conflicting

conclusions regarding the role of the IPS in processing non-symbolic, numerosity arrays in adulthood, and very little is

known about the brain basis of numerical processing early in development. Addressing the question of whether there

is an early-developing neural basis for abstract numerical processing is essential for understanding the cognitive

origins of our uniquely human capacity for math and science. Using functional magnetic resonance imaging (fMRI) at 4-

Tesla and an event-related fMRI adaptation paradigm, we found that adults showed a greater IPS response to visual

arrays that deviated from standard stimuli in their number of elements, than to stimuli that deviated in local element

shape. These results support previous claims that there is a neurophysiological link between non-symbolic and

symbolic numerical processing in adulthood. In parallel, we tested 4-y-old children with the same fMRI adaptation

paradigm as adults to determine whether the neural locus of non-symbolic numerical activity in adults shows

continuity in function over development. We found that the IPS responded to numerical deviants similarly in 4-y-old

children and adults. To our knowledge, this is the first evidence that the neural locus of adult numerical cognition takes

form early in development, prior to sophisticated symbolic numerical experience. More broadly, this is also, to our

knowledge, the first cognitive fMRI study to test healthy children as young as 4 y, providing new insights into the

neurophysiology of human cognitive development.

Citation: Cantlon JF, Brannon EM, Carter EJ, Pelphrey KA (2006) Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biol 4(5): e125. DOI: 10.1371/

journal.pbio.0040125

Introduction

Intuitively, language influences the way we think about

number. However, substantial evidence indicates that pre-

verbal children and human adults, as well as other animals,

share a fundamental mechanism for representing approx-

imate numerical values that is independent of language [1–

10]. Further, humans appear to possess a common psycho-

logical currency for representing numerical value regardless

of whether the value is communicated symbolically via Arabic

numerals and number words or non-symbolically through the

number of visual objects in a set or the number of tones in an

auditory sequence [3,11–14]. These and other findings have

led researchers to predict that approximate numerical

information, whether symbolic or non-symbolic, is processed

by a common neural substrate [15–17]. Neuroimaging and

lesion studies of adult humans have demonstrated that the

intraparietal sulcus (IPS) plays a central role in processing

symbolic numerical information [18–20]. For example, people

with damage to parietal cortex have difficulty identifying

which of two Arabic numerals is larger, or computing which

numeral falls between two others [19], and damage specif-

ically to the IPS has been reported to cause acalculia, a severe

mathematical deficit [21]. Several neuroimaging studies have

reported increased activity in the IPS when adult participants

perform approximate arithmetic operations on Arabic

numerals relative to control tasks [21–25]. The IPS also

responds more strongly when adult participants engage in a

number word or Arabic numeral detection task than a color

detection task [26]. The IPS further shows the effects of

repetition suppression when numerals are primed at subcon-

scious thresholds and perceptually masked [27]. By adulthood,

the IPS is clearly active during symbolic numerical oper-

ations. However, a critical and controversial question is

whether the IPS is also important for processing non-

symbolic numerical magnitude and therefore processes

number irrespective of notation [28,29,30]. While behavioral

studies of adults implicate a link between approximate

symbolic and non-symbolic numerical processing, neuro-

Academic Editor: Stanislas Dehaene, Service Hospitalier Frederic Joliot, France

Received December 06, 2005; Accepted February 16, 2006; Published April 11,

2006

DOI: 10.1371/journal.pbio.0040125

Copyright: ? 2006 Cantlon et al. This is an open-access article distributed under

the terms of the Creative Commons Attribution License, which permits unrestricted

use, distribution, and reproduction in any medium, provided the original author

and source are credited.

Abbreviations: BA, Broadman’s area; BOLD, blood oxygenation level-dependent;

fMRI, functional magnetic resonance imaging; HDR, hemodynamic response; IPS,

intraparietal sulcus; MNI, Montreal Neurological Institute; SPL, superior parietal

lobule

* To whom correspondence should be addressed. E-mail: jfc2@duke.edu (JFC),

kevin.pelphrey@duke.edu (KAP)

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P PL Lo oS S BIOLOGY

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imaging studies have yielded conflicting results on a link

between these two types of numerical processing.

From an early age, young children are sensitive to the

numerical attributes of stimuli, and their non-symbolic

numerical abilities exhibit important continuities with those

of adults. Like adult humans, when young children compare

the numerical values of sets of objects (e.g., arrays of dots),

their performance is dependent on the ratio between the

values rather than the absolute values (for adults see [3,11,12];

for children see [14,31–33]). For example, both adults and

young children are faster and more accurate at comparing

numerical values when the ratio between them is small (e.g., 6

versus 9¼2/3 ratio) than when it is large (e.g., 4 versus 5¼4/5

ratio). This capacity for approximate non-symbolic numerical

estimation shows the same signature of ratio-dependent

discrimination in human infancy [4,34–39]. Evidence that

number discrimination is ratio-dependent throughout devel-

opment and in adulthood suggests that the physiological basis

for numerical processing is developmentally conserved.

Despite the fundamental similarities in the numerical

cognition of adults and young children, there is enormous

conceptual change in children’s numerical abilities from

early childhood to adulthood [32,33]. For example, by 3 y,

children have memorized some portion of the count

sequence from one to ten, yet they cannot verbally count to

construct a set of items [40–42]. In fact, many children do not

appreciate the link between number words and non-symbolic

quantities by 5 y [43]. Children between the ages of 3½ and

4½ y have typically mastered the verbal count sequence to

ten but make mistakes in the counting sequence between ten

and 20 and have not yet mastered the ordinal structure of the

decade count words (twenty, thirty, etc.) [44]. Lastly, accuracy

and reaction time on non-symbolic numerical tasks change

dramatically between the ages of 2 and 7 y [32,33,45].

By adulthood, humans perform rapid, nonverbal numerical

computations across a wide range of stimuli, sensory modal-

ities, and numerical values with great precision [11]; they are

also proficient at manipulating numerical symbols in com-

plex mathematical operations. Thus, while certain aspects of

numerical performance (such as ratio-dependent discrimi-

nation) remain constant over development, there is also a

great deal of developmental change in numerical compe-

tence. Developmental changes in numerical competence may

relate to changes in the brain regions involved in numerical

processing regardless of whether symbolic and non-symbolic

numerical stimuli are processed by a common substrate in

adulthood. Therefore, an important question is to what

extent a brain region known to be important for numerical

approximation in adults, the IPS, shows continuity in

function over development [17].

Little is known about how the child’s brain comes to

perform the complex mathematical feats of human adults,

with only one study investigating the neural correlates of

numerical processing in pre-school children [14]. That study

employed scalp-recorded event-related potentials. Event-

related potentials provide exquisite information about the

timing of mental processes but lack the spatial resolution for

determining the precise locus of number-related activity in

the brain. Localizing numerical processing to specific brain

structures using techniques such as function magnetic

resonance imaging (fMRI) is crucial for determining whether

common neural circuits are responsible for numerical

performance both early in development and in adulthood.

While there have been several fMRI studies of numerical

processing in adult humans implicating the IPS as a basis of

fundamental numerical processing, there has never been a

parallel fMRI study of numerical processing in pre-school

children. Such a study is essential for addressing the question

of whether number-related activity in the IPS is a source of

fundamental numerical abilities or is, instead, a consequence of

the more sophisticated numerical abilities exhibited in

adulthood.

In this study, we investigated whether the IPS responds to

non-symbolic numerical value in number-sophisticated

adults and 4-y-old children who have limited experience

using symbolic numbers. We sought to determine whether the

IPS responds to numerical values (1) when presented non-

symbolically as visual sets of elements and (2) before

sophisticated symbolic and non-symbolic numerical abilities

emerge. We used an event-related fMRI adaptation paradigm

at 4-Tesla to measure differences in the IPS response to

stimuli that were novel in number compared to stimuli that

were novel in shape. Children and adults were tested with

identical imaging paradigms. Children (n ¼ 8) and adults (n ¼

12) passively viewed a constant stream of visual element

arrays (Figure 1). Arrays consisted of blue circle elements that

Figure 1. Task Design

Participants were given the experiment-irrelevant task of fixating on a

central crosshair and pressing a joystick button when the crosshair

turned red. They passively viewed a stream of visual arrays, the majority

of which contained the same number of elements and element shape.

Occasionally, a stimulus was presented that deviated from the standard

stimuli in either number of elements (number deviants) or local element

shape (shape deviants). Cumulative surface area, density, element size,

and spatial arrangement varied among standard stimuli so that

participants were not habituated to these dimensions. Deviant and

standard stimuli overlapped in cumulative surface area, density, element

size, or spatial arrangement so that these dimensions were never novel

for deviant stimuli. Number deviants differed by a 2:1 ratio from the

standard number of elements such that half of the numerical deviants

had a greater number of elements than the standard, and the other half

had fewer elements. Elements in standard arrays were circles while shape

deviants contained squares or triangles.

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varied in density, cumulative surface area, spatial arrange-

ment, and size, but were constant in both the number of

elements (16 or 32) and in local element shape (circles). Thus,

participants adapted to the constant number and shape of

the elements.

Occasionally, a deviant stimulus was presented that

differed from the standard stimuli either in the number of

elements (number deviant) or in the local element shape

(shape deviant). Number deviants differed by a 2:1 ratio such

that half of the number deviants had a greater number of

elements than the standard stimuli whereas the remaining

half had fewer elements. The standard elements were circles,

whereas half of the shape deviants consisted of square

elements, and the remaining half were triangles. Number

and shape deviants were presented with equal frequency. The

density, cumulative surface area, and element size of the

standard stimuli were continuously varied (i.e., each dimen-

sion changed every 1.5 s) to prevent neural adaptation to

these dimensions. The values of cumulative surface area,

density, and element size for deviant stimuli overlapped with

the values of these dimensions for the standard stimuli. The

cumulative surface area of deviant stimuli was equated with

the middle value of the standard stimuli and the values for the

density and element size of the deviant stimuli were from the

same distribution as the standard stimuli. Therefore, the only

dimensions that repeated among the standard stimuli were

the number and shape of the elements, whereas the only

dimensions of the deviant stimuli that were novel, compared

with standard stimuli, were the number or shape of the

elements. Children and adults were asked to maintain fixation

on a central cross hair. To ensure that they attended to the

stimulus display, they were asked to press a button when the

central cross hair turned red. We examined which brain areas

responded exclusively to each class of deviant stimuli in

adults and children. Then, we compared children’s results

with those of our adult participants. Further methodological

detail is provided in Materials and Methods.

Results

Adults’ fMRI Results

In adult participants, regions in and around the IPS

(bilaterally) showed significantly greater activity to number

deviants than to shape deviants. A random-effects analysis

that directly compared activity to number and shape deviants

revealed bilateral number-related activity localized to the IPS

and extending into the inferior and superior parietal lobules

consistent with previous studies that tested adults with Arabic

numeral stimuli, symbolic arithmetic operations, and number

words [21,23], as well as a study of non-symbolic number

processing [28] (Figure 2A, MNI coordinates x, y, z: 43, ?47,

59, BA [Broadman’s area] ¼ 40; ?31, ?66, 62, BA ¼ 7). Also

consistent with previous studies [28,29], regions of activity

that responded exclusively to shape deviants were localized to

the ventral temporal-occipital cortex including the fusiform

(32,?70,?14, BA¼19;?34,?47,?19, BA¼37) and lingual gyri

(?27, ?72, ?7, BA ¼ 18) (Figure 2B).

Figure 2C shows the time course of blood oxygenation

level-dependent (BOLD) response to number versus shape

deviants in the IPS (defined on a participant-by-participant

basis) for time points occurring up to 12 s post-stimulus.

Between 3 and 7.5 s post-stimulus onset, the IPS produced a

significantly greater response to stimuli in which the number

of elements changed but the shape remained constant, than

to stimuli in which the local element shape changed but the

number of elements remained constant. This value was

significantly greater than the baseline level of activity across

participants (mean¼.30%, t (11)¼6.63, p , .001) whereas the

hemodynamic response (HDR) to shape deviants in this

region was significantly lower than baseline (mean¼?.17%, t

(11) ¼?6.14, p , .001).

Shape deviants had the same number of elements as the

standard stimuli. Thus, the decreased response to shape

deviants in the IPS likely resulted from a decreasing response

to repeated presentations (1 per 1.5 s) of a numerical value,

relative to a baseline that was set to zero in the baseline-

subtracted epoch averages (but may actually have been much

greater than zero in this rapid presentation, event-related

paradigm). This interpretation is consistent with the pre-

dictions of an fMRI adaptation design for decreased

responding over time with increasing presentations of a

stimulus [46,47]. The adaptation of a BOLD signal increases

gradually as the number of repetitions increases [46–48].

Task- and stimulus-related decreases in BOLD contrast

(deactivations) have been reported in previous fMRI studies

[49–54]. Deactivations have also been correlated with de-

creased blood oxygenation and neural suppression [54].

Therefore, the waveforms from the present study may reflect

relatively high baseline activity that increases slightly when a

numerical deviant is presented but decreases significantly

with repeated presentations of the same numerical stimulus

(i.e., continued adaptation), even in the presence of a non-

numerical change (i.e., shape change). In any case, the IPS

response to numerical deviants is significantly greater than

baseline and significantly different from the IPS response to

shape deviants. This result indicates that the IPS preferen-

tially responds to non-symbolic numerical stimuli.

Activity to deviant stimuli was not asymmetrically influ-

enced by one kind of number deviant or one kind of shape

deviant. There were no significant differences in activity

between the two kinds of number deviants (t (11)¼.95, p¼.36)

in the IPS or the two kinds of shape deviants (t (11)¼ .44, p ¼

.67) in the fusiform and lingual gyri. Thus, the IPS responded

to deviations in number whether the deviant stimulus

contained a larger or smaller number of elements. Similarly,

the ventral temporal-occipital cortex responded to deviations

in local element shape whether the deviant elements were

squares or triangles.

In summary, the IPS of adult participants showed signifi-

cantly greater activity to numerical deviants than shape

deviants. As reviewed above, the IPS is known to respond

selectively to symbolic numerical stimuli such as Arabic

numerals and number words. The IPS response to non-

symbolic numerical deviants in adult participants demon-

strates that the IPS responds to numerical values independ-

ently of notation.

Children’s fMRI Results

We performed direct, random-effects contrasts between

number and shape deviants for child participants as

described above for adults. The average activations across

participants are presented in Figure 3A and 3B in a common

adult template brain space. This analysis revealed significant

activity evoked by numerical deviants (Figure 3A; number .

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shape) in and around the right IPS (MNI coordinates: 45,?44,

62, BA ¼ 5) and right superior parietal lobule (SPL) (18, ?53,

65, BA¼7). We also found significant activations to numerical

deviants in the left precentral gyrus (?56, 2, 62, BA ¼ 6), left

superior frontal gyrus (?21, 1, 62, BA ¼6), left medial frontal

gyrus (0, ?14, 57, BA ¼ 6), left inferior parietal lobule (?62,

?28, 25, BA ¼ 40), and right middle frontal gyrus (46, 28, 20,

BA ¼ 46); although we had no a priori hypotheses regarding

the roles of these latter regions in numerical processing.

Activation maps that reveal significant number-related

activity for individual children overlaid upon their own

anatomical images (without spatial normalization) are pre-

sented in Figure 4. As illustrated, each child exhibited

significant number-specific activity in and around the IPS.

Children showed significantly greater activity to changes in

the local shape of the elements compared with changes in

numerical value (shown in Figure 3B) in the left lateral

occipital-temporal complex (?39, ?78, 4, BA ¼ 19 and

?41,?88, 13, BA ¼ 18) and right fusiform gyrus (45, ?71, ?11,

BA ¼ 19). In addition, we identified significant shape-specific

activations in the right anterior cingulate (17, 39, 11, BA¼32),

right superior frontal gyrus (15, 28, 62, BA ¼ 6), and right

caudate (37, ?38, ?1). Thus, in 4-y-old children, shape

adaptation effects appear to occur in similar regions as those

reported in adults (2,46).

Figure 3C shows the time course of number deviant and

shape deviant activity in the IPS. As compared to adults,

children showed a similar BOLD response to deviants in the

IPS: the response to number deviants was significantly greater

than baseline (mean ¼ .15%, t (7) ¼ 3.62, p , .01) while the

response to shape deviants was significantly below baseline

(mean ¼ ?.30%, t (7) ¼ ?7.73, p , .001). Thus, the IPS

continued to habituate to the constant numerical value of the

shape deviant stimuli but showed an increased response to

the novel numerical value of the number deviant stimuli.

A comparison of activity between the two kinds of

numerical deviants revealed no difference in the IPS (t (7) ¼

.24; p . .81) or SPL (t (7) ¼?.89; p . .41) between the larger

Figure 2. Adult Participant’s fMRI Results

(A) Regions that were more active during the presentation of number compared to shape deviants (p , .05, cluster size . six functional voxels). (B)

Regions that were more active during the presentation of shape compared to number deviants (p , .05, cluster size . six functional voxels). (C) Time

course of activity (percent signal change) for number-selective (number . shape) regions in the IPS, averaged from individually-drawn functional

regions of interest from the IPS, from 3 s pre-stimulus to 12 s post-stimulus.

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and smaller numerical deviants. Thus, the IPS responded to

numerical deviants of a 2:1 ratio regardless of the absolute

magnitude of the numerical values. Similarly, a comparison of

activity between the two kinds of shape deviants revealed no

significant difference in the lateral occipital complex (t (7) ¼

.38; p . .72) or fusiform gyrus (t (7) ¼ .75; p . .48). These

analyses indicate that numerical activity was not related to an

increase in visual attention to the number of array elements

nor was shape activity specific to a particular shape. Instead,

children’s number- and shape-related activity in these regions

encompassed the broad classes of deviants in our study.

To summarize, children showed greater activation in the

IPS to numerical deviants than to shape deviants. Number

deviant activity was significantly greater than baseline and

significantly differed from activity related to shape deviants

in the IPS. Our results show that by the age of 4 y, children

show selective activation of the IPS in response to non-

symbolic numerical values.

Comparison of IPS Activity in Children and Adults

Children’s number-related activity in the IPS was strikingly

similar to activity in adult participants tested under identical

conditions. Figure 5 shows brain regions activated by

numerical deviants for children and adult participants in

the present study, tested with identical tasks and stimuli.

While adults tended to show more extensive activations,

numerical activity in the IPS and SPL overlapped consid-

erably in children and adults. Within the right IPS region,

adults and children overlapped for their number . shape

responses on a total of 112 voxels. In the right IPS, where

children overlapped considerably with adults, the extent of

the activation was greater for adults, with adults activating

approximately five times as many voxels as children (586

versus 112 voxels). Note, however, that the more extensive

activation for adults is possibly due to the larger sample of

adult participants (12 adults versus eight children). The key

finding here is that the IPS activity in children exhibited

substantial overlap with that of adults.

The MNI coordinates for the IPS activations in adults were

43, ?47, 59 and ?31, ?66, 62; which can be compared to the

coordinates of the children’s IPS (45, ?44, 62) and SPL (18,

?53, 65) activations. The locus of number-related activity in

our pre-school participants was also comparable to adult

activity reported in similar studies of non-symbolic numerical

processing (1: 36,?60, 52; 28, ?56, 44; 16, ?56, 44) and to

activity related to basic mathematical ability in adults (22: 44,

?36, 52; 20, ?60, 60; ?56, ?44, 52). This finding suggests that

the neural circuitry for processing non-symbolic numerical

information is organized similarly to adults by at least 4 y.

One noteworthy difference between the number-related

brain activity of children and adults in our study is that adults

showed robust bilateral activation in the IPS while children,

on average, showed number-related IPS activation predom-

inantly in the right hemisphere. To evaluate the statistical

significance of this group difference in the laterality of

activation patterns, we conducted a between-groups random-

effects analysis comparing the levels of activity at peak

magnitude in response to numerical deviants for children

and adults. This analysis confirmed the impressions given by

Figure 5: adults had significantly more activity bilaterally in

the IPS region and children had less activity, on average, in

the left IPS region and more bilateral activity in the SPL

region. The MNI coordinates for regions of adults . children

and children . adults number-related activity are provided

in Table 1.

One recent study also found hemispheric asymmetries in

the IPS associated with 8- to 19-y-old children’s developing

numerical abilities [55]. Rivera and colleagues (2005) demon-

strated that an inferior parietal region including the left IPS

Figure 3. Child Participant’s fMRI Results

(A) Regions that were more active during the presentation of number compared to shape deviants (p , .05, cluster size . six functional voxels). (B)

Regions that were more active during the presentation of shape compared to number deviants (p , .05, cluster size . six functional voxels). (C) Time

course of activity (percent signal change) for number-selective (number . shape) regions in the IPS, averaged from individually-drawn functional

regions of interest from the IPS, from 3 s pre-stimulus to 12 s post-stimulus.

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(54: ?51, ?37, 46) becomes increasingly responsive during

symbolic mathematical operations between 8 and 19 y,

whereas a corresponding region in the right hemisphere is

equally active during mathematical processing at all ages.

This study suggests that the left hemisphere may become

functionally specialized for mathematical processing over

development while the right hemisphere shows little devel-

opmental change. Given our finding that more 4-y-old

children show right IPS activation while adults show bilateral

IPS activation, one possibility is that non-symbolic numerical

processing follows a similar trajectory of hemispheric special-

ization over development. However, some studies have found

that the right IPS is also more active than the left IPS during

numerical processing in adults [56]. Further, as shown in

Figure 4, some children exhibited more number-related

activity in the left IPS than others. Therefore, this aspect of

our results should be viewed cautiously until subsequent

studies can confirm that the right lateralization of number-

related IPS activity is unique to young children.

Additionally, as described further in Materials and Meth-

ods, we spatially normalized the data from children and

adults into a common adult template to perform a direct

comparison between these two groups. Although the practice

of normalizing fMRI data from children to make this sort of

direct comparison has been validated by a few previous

studies in older children [57,58], we cannot rule out the

possibility that the nonlinear warping procedures used in the

present study slightly shifted relevant brain loci between the

children and adults. If this were true, the observed differences

between adults and children might be explained, in part, by

the spatial normalization procedures. This possibility seems

unlikely, however, given the relatively coarse resolution of the

fMRI data relative to the anatomical differences caused by

spatial normalization reported in prior studies [57,58]. If the

differences between children and adults resulted from spatial

normalization, there actually may be more overlap in the

parietal activation of children and adults because adults

showed greater number-related activity in the IPS than

children, while children showed greater number-related

activity than adults at an adjacent SPL site. Thus, although

the between-groups random effects analysis revealed differ-

ences in the amount of activation at IPS and SPL sites for

children and adults, our main finding is that the topo-

graphical pattern of parietal activation is remarkably similar

between children and adults.

Behavioral Testing of Children

We tested the same children who participated in the fMRI

study on a non-symbolic numerical discrimination task using

the same numerical values from the fMRI session (8, 16, 32,

and 64). Children were presented with two arrays of dots on a

touch-screen monitor and were instructed to choose the

array with the larger number of dots on each of 50 trials.

Density, cumulative surface area, cumulative perimeter, and

element size were carefully controlled. Overall, children

performed significantly above chance (chance ¼ 50%; mean

¼ 89%; t (7) ¼ 6.89; p , .001), although one child scored near

chance. This result is consistent with previous studies

demonstrating non-symbolic numerical proficiency in young

children [31–33,43,45,59].

We also investigated children’s knowledge of the verbal

counting sequence. Verbal counting ability was assessed for

Figure 4. Data from Individual Children

Each row presents an individual participant’s activation map indicating

regions that were more active during the presentation of number

compared to shape deviants (p , .05, cluster size . eight functional

voxels) overlaid on that child’s own anatomical images. One child moved

during the anatomical scan (which occurred after the functional scan)

and is thus not included in this figure.

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each child using the ‘‘How high?’’ and ‘‘How many?’’ tasks of

Wynn [40]. In the ‘‘How high?’’ task, children were asked to

recite the verbal counting sequence from memory beginning

with ‘‘One’’ whereas in the ‘‘How many?’’ task, children were

asked to verbally count a set of 30 items. For both tasks, we

recorded the highest number to which children could count

without making an error. On the ‘‘How many?’’ task, three

children successfully counted all 30 items without making an

error (i.e., counting an item or count word twice or skipping

an item or count word) in the counting sequence; one child

successfully counted to 14; two children counted to 11; and the

remaining two children counted to ten without making an

error. On the ‘‘How high?’’ task, two children counted to 100

before being stopped by the experimenter; two children

counted to 30 without making an error; one child to 20; and

three children counted to less than 15 before making an error.

Overall, our behavioral tests revealed robust nonverbal

numerical competence among children for the target

numerical values ranging from eight to 64. However, the

majority of children in this study could not count verbally to

64. The numerical values tested in the fMRI session were thus

outside the range of verbal counting proficiency for many of

these children, yet children showed a number-selective

response in the IPS to these values when presented as

numerical deviants.

Discussion

A critical question for the study of numerical cognition is

whether the complex, symbolic mathematical abilities of

adult humans share a neurobiological and developmental

origin with non-symbolic numerical abilities. A growing body

of evidence suggests that the ability to judge numerical values

nonverbally was an important evolutionary precursor to

adult human symbolic numerical abilities [15,60,61], and that

it is a language-independent cognitive capacity [7,9]. Our

study provides additional evidence that there is an important

Table 1. Summary of a Random Effects Analyses Contrasting

Number-Related Activity in Parietal Regions for Children and

Adults

ParticipantsRegionSideXYX BA

Adults . children Intraparietal sulcus

Intraparietal sulcus

Superior parietal lobule

Superior parietal lobule

R

L

R

L

35

?79

?60

?63

?74

38

60

63

62

19

?40

18

?10

7

7

7

Children . adults

X, Y, and Z refer to the stereotaxic MNI coordinates of the center of activation within a

region of interest. R, right hemisphere; L, left hemisphere; BA, Broadman’s area. The

threshold for significance of the clusters reported here was set at a voxel-wise

uncorrected p , 0.05 (two-tailed) and a spatial extent of six functional voxels.

DOI: 10.1371/journal.pbio.0040125.t001

Figure 5. Child and Adult Number-Selective Brain Regions

(Number . shape from Figures 2 and 3) plotted in same space. Adults showed more extensive areas of activation than children; however, the same

brain regions were active for children as for adults in this study.

DOI: 10.1371/journal.pbio.0040125.g005

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Imaging Numerical Processing

Page 8

neurobiological link between symbolic and non-symbolic

numerical cognition in adults and thus helps to resolve

current controversies in the adult literature [28,29]. Most

importantly, our study further demonstrates that the IPS is

recruited for non-symbolic numerical processing early in

development, before formal schooling has begun.

A great many studies have investigated how children

acquire the verbal counting system [2,36,44]. Furthermore,

there are disparate hypotheses about how children begin to

map the meaning of number words onto nonverbal repre-

sentations of number [4,35,36,44,62]. Our study provides new

evidence of a neurobiological link between the early

approximate numerical abilities of children, and the more

sophisticated non-symbolic and approximate symbolic nu-

merical abilities of adults. We therefore suggest that non-

symbolic numerical activity in the IPS may be a developmen-

tal origin of adult mathematical knowledge [15,17]. Ulti-

mately, a full description of how children learn the meaning

of number words must incorporate these new findings.

As mentioned, previous work with adult participants has

implicated the IPS in processing Arabic numerals and

number words but has remained inconclusive on the role of

the IPS in processing non-symbolic number [28,29,30]. One

study [28] used an event-related adaptation design and found

that activity in the IPS correlated with the numerical distance

between standard numerical stimuli and numerical deviants.

However, unlike the present study, in the study by Piazza and

colleagues [28], number-related activity in the IPS was not

directly contrasted with activity related to a class of non-

numerical stimuli in a random-effects analysis and compared

against baseline activity. Thus, the authors could not

definitively demonstrate number-specific brain activity for

visual arrays. Similarly, number specificity in the IPS was not

definitively demonstrated in a study by Ansari et al. [30],

which nicely demonstrated parametric modulation of IPS

activity by numerical distance but did not test whether the

IPS responds significantly above baseline to non-numerical

stimuli. The current study directly contrasted number-related

activity in the IPS with activity related to shape changes in a

random-effects analysis and compared this against baseline

activity, providing strong evidence in favor of the argument

that the IPS is sensitive to numerical changes for sets of visual

objects and that this region does not respond equally to all

stimulus changes (i.e., shape changes; [28]).

In contrast to our result, Shuman and Kanwisher [29] found

no difference in IPS activity between blocks in which number

varied and those in which number was held constant. One

possible explanation of the conflicting results between these

two studies is that in the study by Shuman and Kanwisher

[29], surface area varied in the ‘‘number constant’’ blocks,

which could have elicited IPS activity because the IPS has

been shown to respond to changes in surface area [63].

Consequently, the IPS may have responded to number

changes in the ‘‘number varied’’ condition, but responded

to surface area changes in the ‘‘number constant’’ condition.

These two responses in the IPS could have canceled each

other out in a statistical contrast [30]. This explanation of the

Shuman and Kanwisher [29] result assumes that the IPS plays

a more general role in magnitude judgments and is not

selective for number per se. Yet it leaves open the possibility

that the IPS responds to changes in magnitude as suggested

by Pinel and colleagues [63] but not to changes along other

dimensions (e.g., shape).

Alternative explanations of the IPS response to numerical

deviants such as a non-numerical recovery response, a non-

numerical novelty response, a general novelty response, or a

response reflecting changes in visual attention cannot

account for our result. First, the recovery response exhibited

by the IPS to numerical deviants cannot be attributed to non-

numerical dimensions such as cumulative surface area,

density, or element size because these non-numerical

dimensions were constantly varied in the standard stimuli

while number and shape were held constant. Thus, given the

known characteristics of an fMRI-adaptation design [48], the

IPS could not adapt to these dimensions. Second, the IPS

response to numerical deviants cannot be explained as a

novelty effect evoked by the non-numerical dimensions of

cumulative surface area or density because shape and number

deviants were equated on these dimensions and their effect, if

any, would cancel out in the number . shape contrast. The

element size of the deviant stimuli would also fail to evoke a

novelty response because element sizes for deviant stimuli

were taken from the distribution of values from the standard

stimuli and were thus never novel compared to the range of

standard stimuli to which the IPS adapted. Third, because we

directly contrasted the brain response to two categories of

deviant stimuli, alternate explanations of IPS activity, such as

a general novelty effect, cannot easily account for our result.

Additionally, the IPS responded to numerical deviants

regardless of whether deviants increased or decreased in

their number of elements from the standard stimuli. This

result indicates that a greater IPS response to numerical

deviants does not simply reflect increased attention with the

number of visual objects presented. Lastly, our study did not

require participants to perform an explicit number-related

task, indicating that task difficulty is not necessarily a

correlate of IPS activity. An implication of this finding is

that the IPS responds automatically to numerical information

when participants passively view numerically relevant stimuli.

Taken together with previous studies, our results suggest that

the IPS plays a role in both symbolic and non-symbolic

numerical processing and is thus important for processing

number independent of notation. Further, our comparable

results from both children and adults make a case for an

early-developing neural substrate for notation-independent

numerical processing.

Behavioral studies of children’s developing numerical

abilities have highlighted important similarities and differ-

ences in numerical competence over development

[4,17,35,59]. Studies of numerical processing in adults have

revealed number-selective brain regions in and around the

IPS [28,21,30]. Our study provides evidence that numerical

processing invokes a common neural substrate in adults and

children during the presentation of non-symbolic numerical

stimuli; by 4 y, the IPS responds more strongly to numerical

changes than to shape changes. Therefore, the similarities in

numerical performance across ontogeny may reflect reliance

on a single substrate for numerical processing from child-

hood to adulthood. However, symbolic numerical abilities are

reported to recruit a broader network of number-specific

brain regions than the IPS alone [21]. For example, the ability

to solve multiplication tables and other math facts appears to

recruit regions in and around the left angular gyrus

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Imaging Numerical Processing

Page 9

[20,21,64–66]. Some researchers have suggested that this brain

region is important for the explicit manipulation of

numerical values that is characteristic of adult human

mathematics [35,66]. Thus, conceptual development related

to cultural, linguistic, and symbolic numerical practices might

cause changes in the network of brain regions involved in

precise, sophisticated adult mathematics [2,20]. However, the

neural basis of notation-independent numerical processes in

the IPS may be the nucleus of this sophisticated mathematical

network over development.

It is possible that the IPS also supports non-symbolic

numerical discrimination in infancy. As mentioned, the

behavioral signatures of non-symbolic numerical processing

in infants, children, and adults indicate that numerical

discrimination employs similar psychological mechanisms

over development. Studies with human infants in the 6th mo

of life have demonstrated that, like adults and children,

infants also show ratio-dependent numerical discrimination

[37–39]. Similarly, studies of non-human animals also show

striking parallels in the behavioral and neural signatures of

number processing [1–8,15,16,67–69]. The neural bases of

numerical cognition may be, therefore, both ontogenetically

and phylogenetically primitive.

In conclusion, our data provide strong evidence in favor of

the view that the IPS, known to be part of a cerebral network

important for symbolic number processing, is also recruited

in non-symbolic numerical processing. Further, by testing

one of the youngest samples of healthy children in a cognitive

fMRI study, we have shown that by 4 y, the IPS is already

recruited when children represent number non-symbolically.

Our results are therefore consistent with the view that the IPS

is the ontogenetic and phylogenetic origin of non-symbolic

number processing and serves as a foundation upon which

symbolic number processing is built. Although our data

further demonstrate the ubiquitous role of the IPS in

numerical processing, additional work is necessary to

determine whether any region of the IPS is truly number-

specific or instead plays a more general role in magnitude

processing.

Materials and Methods

Participants. Twelve healthy young adult volunteers (five females,

seven males; M¼25 y, range¼21–37 y) and eight typically developing

4-y-old children (five females, three males; M¼4.75 y, range 4.25–4.95

y) participated in this study. All participants had normal or

corrected-to-normal vision and were screened against neurological

and psychiatric illnesses. The parents of the child participants gave

informed consent prior to participation, and the families were given

a toy as a token of our appreciation and financial compensation for

their time. Adult volunteers gave informed consent and were given

financial compensation for their time. The Institutional Review

Board of Duke University Medical Center, Durham, North Carolina,

United States approved this project.

In all, 17 children were brought in for scans. They were first

trained in our mock scanner. The practice scans are described in

more detail below. Of these 17 children, only anatomical scans were

obtained for two children. All 15 of the remaining children

performed both functional runs, although seven of them moved

excessively during both runs and could not be used in the analyses.

All 12 adults provided useable data. Comparison of movement values

for the adults and children revealed no significant differences in the

amount of movement between these two groups during the scans.

Experimental design. Stimuli were visual arrays of circles (Figure

1). The experiment consisted of two blocks counterbalanced for the

numerical quantity of the habituation arrays (16 or 32). Each block

consisted of 238 stimuli presented at a rate of 1 every 1,200 ms for a

duration of 300 ms. Participants fixated on a central fixation cross

and were given the experiment-irrelevant task of pressing a joystick

button when the central fixation cross turned red to ensure that they

attended to the stimuli. This happened three times per block: once

near the beginning of the block, once in the middle, and once near

the end of the block.

Twenty deviants were presented in each block. Half of the deviants

differed from the habituation stimuli in their number of elements.

The other half differed in the local shape of the elements. Deviant

stimuli occurred randomly in the stimulus train with the constraint

that two successive deviants were separated by at least eight and at

most 11 habituation stimuli. Deviants appeared in a pseudo-random

order with each type of deviant presented once without replacement

and then the deviant order was re-randomized. The numerical

quantity of the elements in number-deviant stimuli differed from the

habituation quantity by a ratio of 2:1. Thus, for blocks in which the

number of elements in the habituation stimulus was 16, half of the

number deviants contained eight elements and the other half

contained 32 elements, while for blocks with a habituation number

of 32, half of the number deviants contained 16 and the other half

contained 64 elements. The local element shape of habituation

stimuli was circles. Half of the shape deviants had square elements

and the other half had triangular elements. All deviant stimuli were

equally probable.

Segments of the IPS have been shown to respond to changes in

continuous magnitude such as surface area, in addition to the

numerical magnitude represented by Arabic numerals [63]. To ensure

that participants were being habituated to numerical magnitude and

not non-numerical magnitude of arrays, we varied the cumulative

surface area, element size, and density of the elements within each

array across habituation trials. For habituation arrays, there were

seven different values for element size and cumulative surface area

and three different values for density (Standard stimuli: cumulative

area, range ¼ 15,000–60,000 pixels; element size, range ¼ 937.5–3,750

pixels; density, range ¼ 0.00007–0.00025 pixels). The different values

for these dimensions were presented pseudo-randomly in that they

were randomly ordered and presented without replacement, and

then re-randomized. The values of these dimensions for all deviant

stimuli overlapped with the range of values for habituation stimuli

(Deviant stimuli: cumulative area ¼ 30,000 pixels; element size, range

¼ 937.5–3,750 pixels; density range ¼ 0.00007–0.00025 pixels). All

deviant stimuli were equal in cumulative surface area (30,000 pixels)

and the value chosen was equal to the middle value used for

habituation stimuli. For example, a pseudo-randomly ordered

sequence of eight standard stimuli with a constant number (16) and

local element shape (circles) could have the values (in pixels) 2,727.5,

1,250, 937.5, 2,250, 1,875, 3,750, 1,500, and 2,727.5 for element size;

43,640, 20,000, 15,000, 36,000, 30,000, 60,000, 24,000, and 43,640 for

cumulative surface area; and .00025, 0.0001, 0.00007, 0.0001, 0.00025,

0.00007, 0.00025, and 0.0001 for density. A number deviant stimulus

with eight circles following such an array would have an element size

of 3,750, a cumulative surface area of 30,000, and a density of 0.00007

in pixels. Thus, the only candidate dimension for neural adaptation

in the standard stimuli was the number and shape of the elements;

similarly, the only novel dimension of the deviant stimuli was the

number or shape of elements.

Imaging protocol. Scanning was performed on a General Electric

Health Technologies, 4T LX NVi MRI scanner system, equipped with

a quadrature birdcage radio frequency head coil. Sixty-eight high-

resolution images were acquired using a 3D fast SPGR pulse sequence

(TR ¼ 500 ms; TE ¼ 20 ms; FOV ¼ 24 cm; image matrix ¼ 2562; voxel

size¼0.937530.937531.9 mm). Whole brain functional images were

acquired using a gradient-recalled inward spiral pulse sequence

[70,71] sensitive to BOLD contrast (TR, 1,500 ms; TE, 35 ms; FOV, 24

cm; image matrix, 642; a ¼ 62 8; voxel size, 3.75 3 3.75 3 3.8 mm; 34

axial slices). These functional images were aligned to the structural

images.

Preparing children for fMRI scans. Acquisition of neuroimaging

data from children involves several methodological challenges.

Perhaps the most noteworthy of these is the child’s compliance with

the requirement to remain motionless during the scan. A key

methodological advance in our laboratory’s establishment of child

neuroimaging research has been to develop ‘‘mock scanning’’

facilities. We constructed an MRI simulator for use in acclimating

children to the scanner environment and for training these

participants to minimize head motion. We also developed a protocol

and computer software for use with the MRI simulator to limit head

motion by training children to remain still during fMRI scanning.

Children were ‘‘trained’’ using operant-conditioning procedures

implemented in custom-written software that receives input from a

head motion sensor and uses that input to direct the operation of a

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Imaging Numerical Processing

Page 10

video player. The child watched a favorite movie, and the movie was

halted whenever the child exhibits head motion above a progressively

stricter threshold.

Data analysis. Image preprocessing was performed with custom

programs and SPM 99 modules (Wellcome Department of Cognitive

Neurology, United Kingdom). Images were time-adjusted to compen-

sate for the interleaved slice acquisition and realigned to the tenth

image to correct for head movements between scans. The realigned

scans were then spatially normalized to the Montre ´al Neurologic

Institute (MNI) template found in SPM 99 using the standard two-

part procedure involving first a 12-parameter affine registration for

global normalization followed by a non-linear basis function

registration for regional transformations. The functional data were

high-pass filtered and spatially smoothed with an 8 mm isotropic

Gaussian kernel prior to statistical analysis. Except where otherwise

noted, these normalized and smoothed data were used in most of the

analysis procedures described below. By normalizing the children’s

imaging data to the MNI space, we were able to compare functional

activation foci in children and adults within a common template.

Kang et al. [57] recently provided an empirical validation of

normalization for analysis of fMRI data from children. Kang et al.

found very small differences (relative to the resolution of fMRI data)

in the spatial correspondence among several brain loci between

young children and adults after a standard, nonlinear transformation

that warped child and adult fMRI data into a common adult Talairach

space. Based on these and other similar findings [56], we directly

compared data from adults and children in common, adult stereo-

tactic space in this study.

The primary analysis consisted of a random-effects assessment of

the differences between the shape and number deviant conditions at

the expected peak of the hemodynamic response (HDR). This analysis

consisted of the following steps: (1) The epoch of image volumes

beginning 3.0 s before and 12 s after the onset of each deviant

stimulus was excised from the continuous time series of volumes. (2)

The average intensity of the HDR at expected peak was computed for

the time interval ranging from 4.5–7 s by deviant type. A t-statistic

was then computed at each voxel within the brain to quantify the

HDR differences between shape and number deviants. This process

was performed separately for each participant. (3) The shape .

number and number . shape t-maps were then subjected to a

random-effects analysis that assessed the significance of differences

across participants. To reduce the number of statistical comparisons

and thus the false-positive rate, the results of the random-effects

analyses were then restricted to only those voxels in which a

significant (p , .05, uncorrected) HDR was evoked by either of the

two conditions. The threshold for significance of a difference in the

HDR peak was set at p , .05 (two-tailed, uncorrected) and a minimal

spatial extent of six uninterpolated voxels. We performed this

analysis separately for the adult and child samples. We localized each

cluster of number . shape and shape . number activation by

anatomical location, MNI coordinates of the center of the activation,

and BA.

We also conducted a between-participant random-effects analysis

to evaluate the statistical significance of observed differences

between adults and children in patterns of number-related activity

in the parietal cortex. This analysis compared levels of number-

related activity at the peak of the HDR (4.5 s ?7 s). For this analysis,

we randomly selected eight of our 12 adult participants, so that the

samples sizes would be equivalent for adults and children. The

threshold for significance of adult versus child (adults . children,

children . adults) difference in the HDR peak was set at p , .05 (two-

tailed, uncorrected) and a minimal spatial extent of six voxels.

For an additional set of analyses, we used the acquisition aligned

and motion-corrected, un-normalized imaging data. Using this data,

overlaid on each participant’s own anatomical images, we identified,

on a participant-by-participant basis, regions of activation within the

IPS that were: (1) significantly above baseline in their response to

number (p , .05, uncorrected), (2) exhibited significantly greater

activity to number compared to shape deviants at expected peak (t ¼

1.96, p , .05, uncorrected), and (3) encompassed an area greater than

eight functional voxels. The average shape and number epochs were

then calculated for the voxels that meet these criteria and were

averaged across participants for inspection.

Acknowledgments

We thank Brian Butterworth, Nancy Kanwisher, Warren Meck, Miles

Shuman, and Elizabeth Spelke for helpful commentary on this study.

We also thank Mat Fleck, Kerry Jordan, Melissa Libertus, Heather

Lucas, Evan MacLean, James Morris, and Kelley Safford for help

collecting, analyzing, and discussing these data.

Author contributions. JFC, EMB, and KAP conceived and designed

the experiments. JFC and EJC performed the experiments. JFC, EJC,

and KAP analyzed the data. JFC, EMB, and KAP wrote the paper.

Funding. This study was funded by a Career Development Award

to KAP from the National Institute of Mental Health (MH071284), by

a National Science Foundation Graduate Student Fellowship to JFC,

by a John Merck Fund fellowship to EMB, and by funds to KAP from

Duke University.

Competing interests. The authors have declared that no competing

interests exist.

&

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PLoS Biology | www.plosbiology.orgMay 2006 | Volume 4 | Issue 5 | e125 0854

Imaging Numerical Processing