Age-related Changes in the Activation of the Intraparietal Sulcus during Nonsymbolic Magnitude Processing: An Event-related Functional Magnetic Resonance Imaging Study Daniel Ansari and Bibek Dhital

Abstract & Numerical magnitude processing is an essential everyday skill. Functional brain imaging studies with human adults have repeatedly revealed that bilateral regions of the intraparietal sulcus are correlated with various numerical and mathematical skills. Surprisingly little, however, is known about the development of these brain representations. In the present study, we used functional neuroimaging to compare the neural correlates of nonsymbolic magnitude judgments between children and adults. Although behavioral

INTRODUCTION Functional neuroimaging studies with human adults have consistently shown that areas in and around the left and right intraparietal sulcus (IPS) are engaged during calculation and numerical magnitude processing (Venkatraman, Ansari, & Chee, 2005; Dehaene, Molko, Cohen, & Wilson, 2004; Delazer et al., 2004; Dehaene, Piazza, Pinel, & Cohen, 2003; Delazer et al., 2003; Piazza, Mechelli, Price, & Butterworth, 2002; Gruber, Indefrey, Steinmetz, & Kleinschmidt, 2001; Pesenti, Thioux, Seron, & De Volder, 2000). In particular, the wellreplicated numerical distance effect (where subjects’ reaction times and accuracy are inversely related to the numerical distance between numerical magnitudes) has been used to explore the neural basis of magnitude processing. In studies with adult participants using symbolic stimuli (arabic numerals and number words), it has been revealed that bilateral regions of the IPS are modulated by numerical distance. Pinel and colleagues were able to demonstrate that the amount of activation in bilateral regions of the IPS decreased with increasing numerical distance (Pinel, Dehaene, Riviere, & LeBihan, 2001; Pinel et al., 1999). Moreover, these authors found that the modulation of the IPS by numerical distance is similar for arabic numerals and number words, suggest-

Dartmouth College

D 2006 Massachusetts Institute of Technology

performance was similar across groups, in comparison to the group of children the adult participants exhibited greater effects of numerical distance on the left intraparietal sulcus. Our findings are the first to reveal that even the most basic aspects of numerical cognition are subject to age-related changes in functional neuroanatomy. We propose that developmental impairments of number may be associated with atypical specialization of cortical regions underlying magnitude processing. &

ing that the adult IPS represents numerical magnitude in a stimulus-independent representational format. Convergent evidence has recently been reported by Kaufmann et al. (2005), who also revealed a modulation of the IPS by numerical distance in a functional magnetic resonance imaging (fMRI) study involving single-digit number comparisons. Two recent studies have compared the neural correlates of numerical magnitude comparison with size and luminance comparison (Cohen Kadosh et al., 2005; Pinel, Piazza, Le Bihan, & Dehaene, 2004). In both studies, the authors observed a substantial overlap in the activation patterns underlying the three different types of magnitude comparison. However, both studies revealed some specificity in parietal areas for numerical comparisons. These findings suggest that although comparison of number, size, and luminance all modulate the bilateral IPS, some areas within the IPS are more biased toward number comparison. Some authors have argued that the modulation of the IPS by distance in number comparisons tasks do not reflect underlying representations of numerical magnitude, but instead are indicative of greater attentional resource allocation and response selection. Gobel, Johansen-Berg, Behrens, and Rushworth (2004) compared activations during number comparisons with those observed during a nonnumerical perceptual task with similar response-selection requirements. A direct contrast of the numerical and nonnumerical tasks did

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not reveal any significantly greater IPS modulation in the numerical tasks. This, together with data showing that this IPS activation was tightly coupled with reaction time changes, led these authors to conclude that magnitude representations in the IPS may be difficult to disentangle from those involved in response selection. Whereas these data call into question the nature of distance effects on the IPS, there is a growing body of studies demonstrating that the IPS is activated by numerical stimuli in the absence of response selection. Eger, Sterzer, Russ, Giraud, and Kleinschmidt (2003) found that even when adults are not instructed to attend or respond to numerical stimuli, numbers activate bilateral regions of the IPS to a greater extent than both letters and colors. This was true for the presentation of both written and spoken stimuli. More recently, Piazza, Izard, Pinel, Le Bihan, and Dehaene (2004) studied numerosity habituation and change detection with nonsymbolic stimuli (arrays of dots). The adult participants in this study were unaware of the purpose of the study and did not have to make any response. The authors found that bilateral regions of the IPS responded to a change in the number of dots presented but not to a change in shape. These findings support the notion that the adult IPS houses the internal representation of approximate nonverbal numerical magnitude independently of attentional modulation or response selection. Although the volume of functional neuroimaging studies of numerical cognition with adults is growing, there are surprisingly few studies that investigate ontogenetic changes in the functional neuroanatomy underlying number processing. An understanding of the typical developmental changes underlying the neural circuitry implicated in number processing may provide a window into how developmental processes go awry, resulting in developmental impairments of number processing such as dyscalculia (Ansari & Karmiloff-Smith, 2002). In the study of dyslexia, functional neuroimaging has been used to evaluate the effects of structured reading interventions (Shaywitz et al., 2004; Temple et al., 2003). With data on typically developing children, such as those reported herein, it will become possible to conduct similar studies to track neural changes associated with number interventions. Among the few developmental neuroimaging studies of numerical cognition, there is, to our knowledge, only one study that has focused on basic magnitude processing. Using event-related potentials, Temple and Posner (1998) investigated the time course of neural activation in 5-year-old children and in adults during symbolic (arabic numerals) and nonsymbolic (arrays of dots) magnitude comparisons. The neurophysiological effects of numerical distance were found to be similar for both symbolic and nonsymbolic stimuli both within and between groups. Although distance effects were found at electrodes placed over parietal sites, the data do not provide sufficient spatial resolution to conclude that the

same neural circuits gave rise to the distance effects in both children and adults. Other than the pioneering study by Temple and Posner (1998), most existing studies have focused on higher level numerical competencies such as mental arithmetic. Using fMRI, Kawashima et al. (2004) compared the neural correlates of addition, subtraction, and multiplication in adults and children. The authors concluded that children and adults show broadly similar functional activation patterns during each operation. More recently, Rivera, Reiss, Eckert, and Menon (2005) studied how the neural correlates underlying mental arithmetic change between the ages of 8 and 19 years. These authors found that activation in and around the left IPS increased over time, whereas activation in the dorsolateral and ventrolateral prefrontal cortex (DLPFC and VLPFC, respectively), as well as anterior cingulate cortex (ACC), decreased. These authors argue for the development of arithmetic representations in the left intraparietal regions and hypothesize that decreasing engagement of frontal areas may ref lect increasing automaticity and decreasing demands on attention and memory resources. These findings, however, cannot explain the extent to which emergent specialization of the IPS is specific for mental arithmetic. Understanding the changes that occur for more basic, less culturally mediated processes, will provide insights into the emergent role of the IPS for the neural representation of numerical magnitude. In the present study, we sought to investigate developmental changes in the functional neuroanatomy underlying magnitude processing by asking adults and children to perform numerical magnitude comparisons with nonsymbolic stimuli (arrays of squares). To investigate age-related changes in the neural correlates of numerical magnitude processing, we manipulated numerical distance and evaluated the effect of numerical distance on cortical networks both within and between groups. We hypothesized that the effect of distance on parietal areas would increase with age, possibly suggesting increasing functional specialization of these cortical areas for numerical magnitude processing.

METHODS Participants Nine healthy, right-handed children (mean age, 10.4 years; range, 9.11–11.11 years; 6 boys) and nine healthy, right-handed adults (mean age, 19.8 years; range, 18.8– 21.10 years; 6 men) participated in this experiment. Seventeen children originally participated in the experiment. To ascertain that participants were drawn from a population of typically developing children, both teachers and parents were asked whether the children presented with any particular difficulties or illnesses. Only those children for whom no such indications were made

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were included in the final sample. Due to excessive motion, only nine children were included in the final sample. Only those children and adults whose motion did not exceed one voxel were included in the study. In addition, the time courses of several voxels in each run were inspected for motion artefacts. The procedure was approved by the Committee for the Protection of Human Subjects at Dartmouth College, and all participants and parents (for the group of children) signed informed consent forms. Both teachers and parents reported that children were performing at the level of their peers in mathematics. Children came from relatively affluent parts of northern New England. Adults were recruited from the undergraduate student population at Dartmouth College by means of electronic mail advertisements. Children were recruited through their primary schools. All children who expressed an interest in participating in the study were visited either in their school or in their home by one of the experimenters to introduce them to the tasks as well as to prepare them for the fMRI environment. Parents and children each signed a separate consent form for this visit, which was approved by the Committee for the Protection of Human Subjects at Dartmouth College. During this visit, children were presented with the task on a laptop computer and were asked to complete one run without fixations and one run that used the same stimuli presentation parameters and fixation intervals that were used for the scanner protocol. In this way, children were familiarized both with the task as well as with the stimulus duration characteristics. In addition to practicing the task, children were also presented with pictures of the Dartmouth MRI scanner from various views as well as high-resolution brain images acquired from the instrument. Moreover, children were told that they would have to hold ‘‘really still’’ to avoid making the pictures fuzzy and that there would be quite a lot of different noises. At the conclusion of this visit, children were told to think about whether they would like to participate and that the experimenter would contact the child’s parents the following day to inquire whether the child was interested in the fMRI study. The experimenter contacted parents one day after this visit to discuss the possibility of their child’s further participation in the study.

Figure 1. Example of experimental stimuli and stimulus presentation times. Stimulus presentation was randomized. Each run consisted of 36 stimuli showing two groups of squares containing one to nine squares each. Stimuli were followed by one, two, or three times to repeat (TRs) of fixation (one third of stimuli for each of the three fixation durations).

presented equidistant from a white central fixation in the form of a white dot (see Figure 1). In order to respond, participants held grip handles with a button. Participants were instructed to select the numerically larger group of squares by depressing the button corresponding to the side on which the larger group of squares was presented and to do so as quickly and as accurately as possible. They were presented with three runs of 36 slides each (total of 108 trials). The numerical distance between groups of squares was manipulated in such a way that groups were separated by a numerical distance of 1, 2, 3, 5, 6, or 7. For the analysis, these distances were divided into small (distances 1, 2, and 3) and large (5, 6, and 7) distances. In all the analyses below, ‘‘small distance’’ refers to the average of distances 1, 2, and 3 and ‘‘large distance’’ refers to the average of distances 5, 6, and 7. Therefore, there were a total of 18 stimuli for each distance resulting in 54 small and 54 large distance trials for blood oxygenation level dependent (BOLD) response estimation. Stimuli were presented for a duration of 900 msec followed by 1600 msec of fixation. To achieve jitter in the time series, slides were presented with variable fixation intervals of 2500, 5000, or 7500 msec. Both correct and incorrect responses were included in the analysis of the fMRI data.

Task Design and Stimuli Participants were presented with slides containing two groups of squares (see Figure 1). Squares were equated for area by ensuring that the total area occupied by squares was equated between numerosities. Furthermore, to avoid the use of density cues, the spatial arrangement of squares was randomly varied in such a way that the arrangement was novel each time a given numerosity was presented. Groups of squares were

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Data Acquisition Functional images were acquired in a 1.5T General Electric whole-body MRI scanner (GE Medical Systems, Milwaukee, WI). A standard, quadrature birdcage head coil was used and head movements were restricted through the use of a foam pillow. Using a fast spin-echo sequence, 25 T1-weighted structural slices were acquired in the axial plane. Coplanar to the T1-weighted

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structural images, functional images were acquired by using a gradient-echo-planar T2* sequence sensitive to BOLD contrast. Image volumes consisted of 25 interleaved slices (4.5-mm thickness, 1-mm gap, 64  64 matrix, repetition time = 2.5 sec, TE = 40 msec, flip angle = 908, field of view = 24  24 cm) covering the whole brain. Each run of functional imaging consisted of the acquisition of 102 volumes. A three-dimensional (3-D) whole-brain high-resolution (0.94  0.94  1.2) T1-weighted image was acquired in the sagittal plane by using a standard GE Spoiled Gradient Recalled (SPGR) 3-D sequence. Data Analysis Structural and functional images were analyzed by using Brain Voyager QX 1.2.8 (Brain Innovation, Maastricht, Netherlands). Functional images were corrected for slice time acquisition differences, head motion, and linear trend. In the spatial domain, data were smoothed with a Gaussian smoothing kernel of 8-mm full width at half maximum. Functional images were aligned to the T1weighted coplanar images and subsequently to the 3-D high-resolution images. The realigned data set was then transformed into Talairach space (Talairach & Tournoux, 1988). Following Boynton, Engel, Glover, and Heeger (1996), the expected BOLD signal change was modeled by using a gamma function (t of 2.5 sec and d of 1.5). Standard random-effects analyses were performed to examine the effect of numerical distance on the BOLD response. Voxels were considered to be significantly activated when they passed a statistical threshold of p < .001, uncorrected. In consideration of a priori hypotheses and a small sample size, this threshold can be considered to be relatively conservative.

RESULTS Behavioral Results

3) distances, F(1,16) = 44.0, p < .0001. There was no significant main effect of group, F(1,16) = < 1, ns, and there was no interaction between distance and group, F(1,16) < 1, ns, thus indicating that the effect of distance on reaction times did not differ between groups. Table 1 shows the mean reaction times and percentage correct by group. Accuracy Data Subjects’ numbers of errors were submitted to the same analysis as described for the reaction time data above. Overall, participants in both groups made fewer errors when groups of squares were separated by large compared with small distances, F(1,16) = 13.8, p < .005, and children made more errors compared with adults, F(1,16) = 10.6, p < .005. In addition, there was an interaction between distance and group, F(1,16) = 9.8, p < .001, indicating that children’s accuracy was more affected by numerical distance than adults’.

fMRI Results Coordinates in parentheses (x, y, z) are Talairach coordinates (Talairach & Tournoux, 1988). These coordinates represent the peak voxel of the significantly activated clusters. The extent of activation (number of significantly activated voxels per cluster) is represented by k. Distance Effect—Children Voxels revealing significantly greater magnitude of activation for small compared with large distances were found in the right DLPFC (43, 27, 19, k = 403), left inferior frontal gyrus (LIFG) ( 49, 18, 13, k = 24), and left IPS ( 26, 59, 37, k = 79). See Figure 2 for activations and bar charts of parameter estimates for small versus large distances.

Reaction Time Data Reaction times were subjected to a 2 (distance)  2 (group) mixed analysis of variance. In general, participants in both groups were faster at making relative magnitude judgments when groups of squares were separated by large (5, 6, 7) compared with small (1, 2,

Distance Effect—Adults In the group of adults, voxels revealing significantly greater activation for magnitude comparison with small compared with large numerical distances was revealed in the left ( 32, 50, 44; k = 231) and right (32, 49, 46;

Table 1. Mean Accuracy and Response Times for Magnitude Comparisons Separated by Small and Large Distances Adults

Children

Accuracy (% Correct)

Reaction Time (msec)

Accuracy (% Correct)

Reaction Time (msec)

Small Distance

99.2 (.97)

697.8 (88.3)

94.4 (4.0)

795.4 (129.3)

Large Distance

99.6 (.81)

639.6 (79.3)

99.4 (1.3)

738.7 (125.4)

Numbers in parentheses denote standard deviations.

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Figure 4. Axial slice showing greater effect of distance on the left IPS ( 35, 48, 38) in the group of adults relative to the group of children. Bar charts show the z scores (parameter estimates) for magnitude comparisons separated by small (1, 2, 3) and large (5, 6, 7) numerical distances for the group of adults and children. Error bars denote the standard error of the mean.

Figure 2. Axial slices showing (A) effects of distance on the left IPS ( 26, 59, 37) and (B) right DLPFC (43, 27, 19) in the group of children. Bar charts show the z scores (parameter estimates) for magnitude comparisons separated by small (1, 2, 3) and large (5, 6, 7) numerical distances. Error bars denote the standard error of the mean.

k = 129) IPS. Furthermore, activation was found in the right superior frontal gyrus (5, 25, 47, k = 870), left ( 2, 23, 28, k = 147) and right (14, 19, 30, k = 114) anterior cingulate gyrus (ACC), posterior cingulate gyrus ( 1, 20, 30; k = 228), as well as LIFG ( 34, 17, 19, k = 120). See Figure 3 for activations and bar charts of parameter estimates for small versus large distances. Interaction of Distance and Group By means of a two-sample t test, we evaluated whether there were differences between groups in the extent

to which brain regions were modulated by numerical distance. This analysis revealed significantly greater modulation of the left IPS in the group of adults ( 35, 48, 38, k = 470). No other areas revealed a significant Group  Distance interaction. See Figure 4 for activations and bar charts of parameter estimates for small versus large distances by group.

DISCUSSION The present results demonstrate that activation of the left IPS during nonsymbolic magnitude processing increases with age. Convergent with the recent report of age-related increases in left IPS activation during mental arithmetic (Rivera et al., 2005), these findings suggest that the left IPS undergoes significant age-related changes during the processing of nonsymbolic magnitude. To our knowledge, these are the first data to demonstrate that there are age-related changes in the engagement of the IPS during basic non-symbolic magnitude processing. Typically, the processing of nonsymbolic numerical

Figure 3. Axial slice showing effects of distance on the left ( 32, 50, 44) and right (32, 49, 46) IPS as well as right superior frontal gyrus in the group of adults. Bar charts show the z scores (parameter estimates) for magnitude comparisons separated by small (1, 2, 3) and large (5, 6, 7) numerical distances. Error bars denote the standard error of the mean.

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magnitude is thought to be independent of processes of enculturation and to be qualitatively similar across species and development (Huntley-Fenner, 2001; Gallistel & Gelman, 2000; Dehaene, Dehaene-Lambertz, & Cohen, 1998; Dehaene, 1997). Although the present findings do reveal a large degree of overlap in the cortical representations of numerical magnitude between children and adults, they do at the same time point to changes that may have important functional consequences. In addition, the present data also suggest that children recruited the right DLPFC during magnitude comparison, perhaps indicating greater reliance on attentional and working memory resources (Rivera et al., 2005). In a recent study of number comparison using arabic numerals, a similar frontoparietal shift was found when comparing children and adults (Ansari, Garcia, Lucas, Hamon, & Dhital, 2005). Our present findings are therefore consistent with the notion that over developmental time, children shift from more controlled and effortful to more automatic processing of numerical magnitude (Rubinsten, Henik, Berger, & Shahar-Shalev, 2002; Girelli, Lucangeli, & Butterworth, 2000). To better understand the significance of these age-related changes, it is important to consider the association between numerical cognition and the left IPS in adulthood. Data from adult neuropsychological studies with patients have repeatedly shown that patients with lesions to the left inferior parietal lobule exhibit severe deficits in calculation (Lemer, Dehaene, Spelke, & Cohen, 2003; Dehaene & Cohen, 1997; Gerstman, 1957). Furthermore, functional neuroimaging studies have implicated the left IPS in calculation (Venkatraman et al., 2005; Gruber et al., 2001), approximation (Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999), number comparison (Kaufmann et al., 2005; Pinel et al., 2004; Pinel et al., 2001), unconscious repetition priming of symbolic numbers (Naccache & Dehaene, 2001), passive habituation, and numerosity change detection (Piazza et al., 2004), as well as subitizing and counting (Piazza et al., 2002; Sathian et al., 1999). Furthermore, in a systematic within-subject comparison of parietal regions implicated in grasping, pointing, saccades, attention, phoneme detection, and calculation, Simon, Mangin, Cohen, Le Bihan, and Dehaene (2002) found that an area in the left IPS horizontal segment was significantly activated only during calculation, suggesting that at least in comparison to the other tasks, calculation is uniquely associated with the left IPS (Simon et al., 2004; Simon et al., 2002). Indeed, the left IPS area reported by Simon et al. (2002) is very close to the area found in the present study to be modulated by distance to a greater extent in adults compared with children. Recent evidence suggests that there may be anatomical differences in the left IPS between individuals with and without calculation deficits. Isaacs, Edmonds, Lucas, and Gadian (2001) compared adolescents with very low birth weight having calculation deficits but normal IQ to

a matched group of adolescents with very low birth weight but without calculation deficits. Voxel-based morphometry revealed that children without calculation deficits had more gray matter volume in a region in the left IPS than those with calculation difficulties. The coordinates reported by Isaacs et al. are close, although slightly anterior, to left IPS activations revealed in the present study. Interestingly, this reduction appeared to be specific to calculation, as low-birth weightadolescents with a deficit in mathematical reasoning did not exhibit any volumetric brain differences in comparison to the group of low-birth-weight adolescents without any numerical difficulties. These findings highlight the importance of the left IPS for calculation and suggest that atypical development of this area may prevent successful mathematical development. It is possible that this cortical area, over the course of development, comes to represent numerical magnitude in an increasingly less approximate fashion, allowing for the developmental construction of exact number processing, such as calculation. Taken together, the available evidence suggests that the areas in and around the left IPS play a crucial role in various kinds of number processing. The present findings add to this body of knowledge by revealing that magnitude-related activation in the left IPS increases with age. Data such as those reported here highlight the importance of taking a developmental perspective on functional specialization of cortical areas for higher level cognitive functions (Casey, Tottenham, Liston, & Durston, 2005; Davidson, Thomas, & Casey, 2003). The present results further elucidate the functional role of the IPS in number processing by showing that it assumes an increasingly important function in numerical magnitude processing with age. From a clinical point of view, developmental neuroimaging studies with typically developing children provide important insights into the typical developmental trajectory of functional neuroanatomy underlying higher level cortical functioning, which could be used to both diagnose and remediate atypical cognitive functioning. In the case of mathematics, for example, it is possible that children with dyscalculia do not exhibit the functional specialization of the left IPS for magnitude processing observed here. Data from intervention studies suggest that children with dyscalculia have difficulties in forming flexible and automatically accessible representations of quantity (Griffin, 2004; Gersten & Chard, 1999; Griffin & Case, 1999). It remains for future studies to investigate whether such difficulties are associated with atypical age-related changes in the role played by cortical areas normally implicated in quantity processing. It is important to note that a recent fMRI adaptation study (Cantlon, Brannon, Carter, & Pelphrey, 2006) comparing the BOLD response to nonsymbolic numerical and nonnumerical shape deviants between 4-yearolds and adults revealed similar responses to numerical

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but not shape deviants in the bilateral IPS. In contrast to the present results, these findings suggest age-invariant and domain-specific engagement of the IPS in nonsymbolic number processing. It is important, however, to note that the study by Cantlon et al. (2006) did not require participants to attend to number or make any number-related responses, which could explain why the results differed from the present study. In this context, one could question whether the current findings are indeed reflective of a process of functional specialization or age-related changes in performance and response selection (Schlaggar et al., 2002). We argue that an explanation based on general differences unrelated to functional changes in magnitude processing is unlikely to provide a convincing account of the current findings. First, we did not observe any significant differences in either overall reaction times or modulation of reaction times by distance between the groups of children and adults. Furthermore, although children were less accurate and their accuracy was affected by numerical distance to a greater extent than was the case for the group of adults, we found that in fact the group of adults showed significantly greater activation in the left IPS. If the left IPS activation was purely related to differences in reaction time or accuracy, we would have expected to find greater modulation of this cortical area in the group of children. Given that children were, on average, less accurate than adults, it could be suggested that a speed–accuracy trade-off may explain the absence of reaction time differences between the groups of children and adults. If indeed a speed–accuracy trade-off existed in the group of children, then there should be a negative relationship between number of errors and reaction time (with greater number of errors correlating with faster reaction times). However, there was no significant negative correlation between reaction time and accuracy. Furthermore, we inspected individual data sets and could find no evidence for an association between high number of errors and low reaction times. Thus, there does not seem to be a systematic relationship that would point to a speed–accuracy trade-off. It is important to note that there are noticeable structural changes in the parietal cortex with age. It has been reported that gray matter density decreases in parietal areas with age (Gogtay et al., 2003; Sowell et al., 2003). These structural changes may interact with the functional changes observed here. It is possible that the functional changes are the consequence of structural changes. Recent work by Rivera et al. (2005) sheds light on the interaction between structural changes in the parietal lobe and functional changes associated with mental arithmetic. These authors found that age-related changes in functional activation were greater than those associated with structural change, suggesting that functional changes cannot solely be explained by maturation of the cortical areas engaged by tasks.

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With respect to the design of the stimuli, it may be contended that children and adults could have relied on cues other than numerosity to successfully perform the magnitude comparisons. Against the background of recent studies in infants highlighting the strong cue that overall area represents in nonsymbolic numerosity discrimination studies (Feigenson, Carey, & Spelke, 2002; Clearfield & Mix, 1999), we decided to control for overall area by ensuring that all groups of squares occupied the same amount of space in the slides. This resulted in a negative correlation between individual square size and numerical magnitude. In other words, individual square size decreased with increasing numerosity. It is therefore possible that participants compared individual square size rather than numerical magnitude. We contend that this is an unlikely explanation for several reasons. First, this would require participants to focus on individual square size rather than overall number in arrays and continuously remind themselves that larger square size implies smaller numerosity. This would be a difficult strategy to maintain because overall display size was relatively small and therefore individual squares harder to identify than overall numerosity. It could also be argued that children and adults engaged in different strategies, with one group focusing on individual square size and the other attending to overall numerosity. We think this is unlikely because if there had been a significant difference between children and adults in the strategy used to perform the nonsymbolic magnitude judgment, then we should have expected to find that the direct contrast of children and adults should have revealed areas that were modulated by numerical distance to a significantly greater degree in the group of children than in the group of adults. Together with the fact that both groups exhibited significant modulation of the left IPS, the absence of such an effect suggests age-related changes in the recruitment of the IPS for comparable strategies. Although we deem it unlikely that either children or adults relied on individual square size rather than numerosity for the reasons discussed above, it is important that future studies include both trials in which area is confounded and area is controlled to seek convergent data. Future studies should also seek to test larger sample sizes of both children and adults. Finally, it is important to note that there is some evidence to suggest that adults ignore size in favor of numerosity (Allik & Tuulmets, 1991). Recent evidence from 5-yearold children also suggests that nonnumerical cues do not significantly affect the ability to perform numerical comparison and addition of nonsymbolic arrays (Barth, La Mont, Lipton, & Spelke, 2005). In their study, Barth et al. found that nonsymbolic number processing was unaffected by whether individual stimulus area was confounded with or disconfounded from numerosity. In addition, evidence from infants suggests that even 6-month-old infants are less likely to detect changes

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in surface area than number for large numerosities (Brannon et al., 2004). Moreover, in view of recent evidence showing overlapping activations of the IPS for size and number (Pinel et al., 2004), it seems likely that there is a substantial overlap in their developmental trajectories. Future studies should ascertain how the use of nonnumerical cues in nonsymbolic numerosity tasks changes over developmental time. Conclusion Using numerical distance effect as our dependent measure, we showed that modulation of the left IPS by numerical distance is greater in adults than in children. The left IPS has been implicated in various studies of impaired and normal numerical cognition. The present data suggest that even the most basic processes of numerical cognition are subject to ontogenetic changes in their underlying functional neuroanatomy. Against the background of these findings, it may be hypothesized that children with developmental dyscalculia fail to undergo the typical age-related changes in the engagement of the IPS during magnitude processing reported here. It is crucial that future studies clearly distinguish between the developmental trajectories underlying individual size versus overall numerosity comparisons in an effort to ascertain both similarities and differences in associated age-related changes in functional neuroanatomy. Moreover, future investigations could use paradigms such as the one reported here to study atypical and typical development of numerical cognition and track changes in cortical activation patterns associated with structured intervention programs. Acknowledgments This work was supported by grants from the NSF Science of Learning Center (Center for Cognitive and Educational Neuroscience [CCEN], SBE-0354400), the Dickey Center for International Understanding, and the Rockefeller Center for Social Sciences at Dartmouth College to D. A. We are especially grateful to Dr. Steve Michlovitz and the Windsor Central Supervisory Union for assisting us in the recruitment of children for this study. We thank the Dartmouth Brain Imaging Center for technical support. We are grateful to Hwee Ling Lee, Craig Bennett, Gwyn Taylor, and Lucia van Eimeren for their helpful comments on an earlier draft. Reprint requests should be sent to Daniel Ansari, Department of Psychology, University of Western Ontario, London, ON, N6A 5C2, Canada, or via e-mail: [email protected].

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