NEUROREPORT

BRAIN IMAGING

Neural correlates of symbolic number processing in children and adults Daniel Ansari, Nicolas Garcia, Elizabeth Lucas, Kathleen Hamon and Bibek Dhital Numerical Cognition Laboratory, Department of Education, Dartmouth College, Hanover, New Hampshire, USA. Sponsorship: This work was supported byThe Dickey Center for International Understanding and the Rockefeller Center for Social Sciences at Dartmouth College. Correspondence and requests for reprints to Daniel Ansari, PhD, Numerical Cognition Laboratory, Department of Education, Dartmouth College, 3 Maynard Street, Raven House, Hanover, NH 03755, USA Tel: + 1 603 646 9043; fax: + 1 603 646 3968; e-mail: [email protected] Received10 August 2005; accepted 24 August 2005

Using functional magnetic resonance imaging, we examined developmental di¡erences in the functional neuroanatomy underlying symbolic number processing. Twelve adults and 12 children had to judge the relative magnitude of two single-digit Arabic numerals. We investigated which brain areas were signi¢cantly (Po0.005, uncorrected) more activated during processing of number pairs with small relative to large numerical distances. In the adult group, symbolic distance modulated bilateral parietal regions. In contrast, the

group of children primarily engaged frontal regions. We conclude that the functional neuroanatomy underlying symbolic numerical magnitude processing undergoes an ontogenetic shift towards greater parietal engagement. This change may re£ect maturation of underlying representations and increasing automaticity in mapping between numerical symbols and the magnitudes they reprec 2005 Lippincott Williams & sent. NeuroReport 16:1769^1773  Wilkins.

Keywords: distance e¡ect, functional magnetic resonance imaging, intraparietal sulcus, number development, numerical cognition

Introduction Almost 40 years ago, Moyer and Landauer [1] reported that, when adults compare which of two digits is numerically larger, their reaction times and accuracy are inversely related to the numerical distance between numbers. This effect has since been replicated many times [2,3] and has provided insights into the representations underlying numerical magnitude processing. It has been suggested that numbers are represented in an analog format on a ‘mental number line’ on which numbers that are close together share more representational space and are thus harder to discriminate from one another than those that are far apart [4]. The distance effect has been found in infants [5], children [3], and animals [6], suggesting that it reveals a system of number representation which is marked by a long evolutionary history and exhibits ontogenetic continuity [7,8]. Many studies have shown that bilateral regions of the inferior parietal sulcus, in particular the intraparietal sulci, are modulated by numerical distance [9–11]. A plethora of functional imaging studies and studies with adult neuropsychological patients have implicated the intraparietal sulcus in number processing [12–14]. While there is some controversy over whether intraparietal sulcus activation reflects attention and response selection rather than number representations [15], recent functional imaging data suggest that this area responds to symbolic and non-symbolic numerical magnitude even when no responses are required [16]. While there is an increasingly sophisticated understanding of the neural basis of number processing in adults

[17], there are currently very few studies that have investigated the development of these neural circuits. Using event-related brain potentials, Temple and Posner [18] investigated the neurophysiological correlates of symbolic (Arabic numerals) and non-symbolic (arrays of squares) number representations in 5-year-old children and adults. Their data suggest similar temporal brain responses in children and adults. Their analysis, however, lacks a direct comparison and event-related brain potentials do not have a sufficiently high spatial resolution to make precise inferences about differences in functional neuroanatomy. More recently, two studies have investigated the neural correlates of arithmetic in children and adults. While Kawashima et al. [19] found that similar brain regions underlie various arithmetic computations in children and adults, Rivera et al. [20] revealed that, over developmental time, activation decreases in frontal areas. At the same time, activation in the left parietal areas was found to increase over developmental time. Against this background, the authors suggest that the left intraparietal areas undergo a process of functional specialization for arithmetic processing, which is coupled with decreasing reliance on attention and working memory circuits in frontal areas. In the present study, we sought to add to the currently very sparse body of studies investigating the ontogenesis of neural representations underlying numerical cognition. Moreover, rather than investigating higher-level number skills, such as mental arithmetic, we investigated more basic representations of number. Namely, using functional

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NEUROREPORT

ANSARI ETAL.

consisted of the acquisition of 102 volumes. A threedimensional whole-brain high-resolution (0.94  0.94 1.2) T1-weighted image was acquired in the saggital plane using a standard GE spoiled gradient recalled acquisition threedimensional sequence.

magnetic resonance imaging, we explored the neural basis of symbolic number processing in both children and adults. We hypothesized that the role of parietal regions in adult number processing is the outcome of an ontogenetic process of specialization. Against this background, we predicted that adults would exhibit relatively greater recruitment of the intraparietal sulcus during symbolic number processing than children.

Data analysis Structural and functional images were analyzed using Brain Voyager QX 1.2.8 (Brain Innovation, Maastricht, Holland). Functional images were corrected for slice time acquisition differences, head motion, and linear trend. Functional images were aligned to the T1-weighted coplanar images and subsequently to the three-dimensional high-resolution images. The realigned data set was then transformed into Tailarach space [21]. Following Boynton et al. [22], the expected BOLD signal change was modeled using a g function (t of 2.5 s and a d of 1.5). 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 Po0.005, uncorrected.

Study participants and methods Participants Twelve healthy children (mean age: 10.4 years; range: 9.2–11.11 years) and 12 healthy adults (mean age: 19.8 years; range: 19.1–21.10 years) participated in this study. Only those children and adults whose motion did not exceed one voxel were included in the study. 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. Task design and stimuli Participants were instructed to select the Arabic numeral that they judged to be numerically larger, by depressing a button corresponding to the side on which the larger numeral was displayed. They were presented with three runs of 36 slides each. The numerical distance between numerals was manipulated in such a way that Arabic numerals were separated by a numerical distance of 1, 2, 3, 5, 6, or 7. For the analysis, these distances were divided into small (1, 2, and 3) and large (5, 6, and 7) distances. Stimuli were presented for a duration of 900 ms followed by 1600 ms of fixation. Slides were presented with variable fixation intervals of 2500, 5000, or 7500 ms. In the same scanning session, participants also completed another experiment, the results of which are not reported here. The order of the two experiments was counterbalanced across participants.

Results Behavioral results Reaction time data Reaction times were analyzed using a 2 (distance)  2 (group) mixed analysis of variance (ANOVA). This analysis revealed a main effect of distance [F(1,22)¼120.4, P¼0.0001]. Inspection of means in Table 1 reveals that participants in both groups were faster at judging relative magnitude with pairs separated by large (5, 6, 7) rather than small (1, 2, 3) distances. While children were overall significantly slower than adults [F(1,22)¼4.9, P¼0.04], there was no distance  group interaction [F(1,22)¼0.33, P¼NS]. Accuracy data A main effect of distance [F(1,22)¼13.5, P¼0.001] was found. Children made significantly more errors than adults [F(1,22)¼22.2, P¼0.009]. Distance had a greater effect on accuracy in the group of children than in the group of adults, as revealed by the group  distance interaction [F(1,22)¼8.0, P¼0.009].

Data acquisition Functional images were acquired in a 1.5 T General Electric whole body magnetic resonance imaging scanner (GE Medical Systems, Milwaukee, Wisconsin, USA). 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 T1weighted structural images, functional images were acquired using a gradient echo-planar T2*-sequence sensitive to blood-oxygenation level-dependent (BOLD) contrast. Image volumes consisted of 25 interleaved slices (4.5 mm thickness, 1 mm gap, 64  64 matrix, repetition time¼2.5 s, TE¼40 ms, flip angle¼901, field of view¼24  24 cm) covering the whole brain. Each run of functional imaging

Functional magnetic resonance imaging results In the group of adults, activation was found in the parietal and frontal areas. In the group of children, distance was found to primarily modulate frontal areas such as the precentral gyrus and the left inferior frontal gyrus as well as subcortical areas (also see Table 2). Figures 1–3 show several regions of interest for both children and adults. The bar charts reveal the extent to which a region of interest was modulated to a greater extent by numerical distance in one group than in the other.

Table 1 Mean accuracy and response times for magnitude comparisons separated by small and large distances Adults

Small distance Large distance

Children

Accuracy (% correct)

Reaction time (ms)

Accuracy (% correct)

Reaction time (ms)

98.8 (1.4) 99.5 (0.83)

714.4 651.8

93.5 (6.0) 99.5 (1.1)

817.2 747.7

Numbers in parentheses denote standard deviations.

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NEUROREPORT

NEURAL BASIS OF NUMBER PROCESSING

Table 2 Tailarach coordinates of activation peaks for the small4large distance comparison for groups of adults and children separately Brain region

Hemisphere

x

y

z

t(11)

k

L R L L L R L L R R R L

52 33 32 50 32 25 18 41 58 37 46 21

16 43 37 5 28 71 71 34 28 25 10 66

53 40 44 40 27 25 29 18 18 13 6 1

3.7 3.9 3.8 4.2 4.0 4.0 3.9 4.0 4.0 3.8 4.4 3.7

31 205 22 495 396 179 78 158 134 117 305 62

R R R L R R R R

51 8 40 60 49 16 36 28

51 20 5 5 7 11 11 21

55 46 34 20 14 8 0 2

3.8 3.8 4.2 3.8 4.5 4.9 3.8 3.8

227 55 751 25 450 887 182 96

Distance e¡ect (small4large) adults Postcentral gyrus Inferior parietal lobe Inferior parietal lobe Middle frontal gyrus Middle frontal gyrus Precuneus Precuneus Superior temporal gyrus Superior temporal gyrus Inferior frontal gyrus Precentral gyrus Lingual gyrus Distance e¡ect (small4large) children Superior parietal lobe Medial frontal gyrus Precentral gyrus Precentral gyrus Inferior frontal gyrus Caudate Claustrum Insula

Peaks obtained from random-e¡ects analysis at Po0.005, uncorrected threshold.

6.00

R (a) 0.8

(b) 0.7

Small Large

0.7 a

0.6

b

0.6

Small Large

0.5

0.4 t

z-score

z-score

0.5 0.4 0.3

0.3 0.2

0.2

0.1

0.1 0

0 Adults

Children Group

3.50

Adults Children Group

Fig. 1 Coronal slice showing e¡ect of numerical distance (small4large) on bilateral precuneus in the group of adults. Bar charts depict the z-scores (parameter estimates): (a) right precuneus (25, 71, 25) and (b) left precuneus (18, 71, 25).

Discussion Our findings suggest both commonalities and differences in the functional neuroanatomy modulated by symbolic distance among children and adults. In the group of adults, a large frontoparietal network of areas was revealed. Many of these regions have previously been shown to be modulated by numerical distance in adults. Convergent with previous data [9,23], we found that numerical distance modulates parietal regions, such as the right and left intraparietal sulci and the bilateral precuneus. In addition, we found sig-

nificant modulation of the middle frontal and precentral gyri by numerical distance. As the bar charts in Figs 1 and 2 suggest, both these frontal and parietal areas exhibited greater modulation by distance in the group of adults than in the group of children. In the group of children, distance was found to have significant effects on areas in the dorsolateral and ventrolateral prefrontal cortex, such as the precentral gyrus and the inferior frontal gyrus. As Fig. 3 illustrates, modulation of these areas by numerical distance was larger in the children relative to the group of adults.

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ANSARI ETAL.

(a) 0.8

6.00

R

Small Large

(b)

1 Small Large

0.9

0.7

0.8 0.6 0.7 db

0.6 t

0.4 0.3

z-score

z-score

0.5

0.5 0.4

a c

0.3

0.2 0.2 0.1

0.1

0 Adults

3.50

Children Group

0 Adults Children Group

Fig. 2 Axial slice showing e¡ect of numerical distance (small4large) on the right intraparietal sulcus and middle frontal gyrus in the group of adults. Bar charts depict z-scores (parameter estimates): (a) right intraparietal sulcus (33, 43, 40) and (b) middle frontal gyrus (50, 5, 40).

(a) 0.8

Small Large

0.7

R

6.00

z-score

0.6 0.5 0.4 a

0.3 0.2 b

0.1 0

(b) 0.8

Adults Children Group

t

Small Large

0.7

z-score

0.6 0.5 0.4 0.3 0.2 0.1

3.50

0 Adults Children Group Fig. 3 Saggital slice showing e¡ect of numerical distance (small4large) on right frontal regions in the group of children. Bar charts depict z-scores (parameter estimates): (a) right precentral gyrus (40, 5, 34) and (b) right inferior frontal gyrus (49, 7,14).

Only one area of the parietal lobe, the superior aspect of the inferior parietal lobe, was significantly modulated by distance in the group of children. Taken together, our findings suggest that the neural networks underlying symbolic number processing undergo

developmental changes between the ages of 9 and 20 years. These developmental changes appear to involve a shift from a strong involvement of right frontal areas to increasing engagement of intraparietal and posterior parietal regions. Similar results have recently been reported for mental

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NEURAL BASIS OF NUMBER PROCESSING

arithmetic [20]. The ontogenetic shift in activation reported here may reflect increasingly flexible mappings between Arabic numerals and the numerical quantities they represent. Such increased automaticity in turn requires less recruitment of frontal areas normally associated with attention, working memory, and executive functions [24]. Moreover, the findings may also suggest that parietal regions become functionally specialized for the processing of numerical magnitude. It is important to note that the parietal cortex has been implicated in many cognitive processes such as attention and response selection [15,25]. It is therefore possible that some of the developmental changes reported here are reflective of the maturation of other cognitive functions associated with parietal cortex that contribute to task performance.

Conclusion Our findings indicate that there are developmental differences in the functional neuroanatomy underlying the symbolic distance effect. While distance was found primarily to modulate frontal areas in the group of children, the group of adults exhibited greater effects of distance on parietal areas. These data may suggest an ontogenetic frontoparietal shift in the processing of symbolic magnitude processing.

Acknowledgement We are especially grateful to Dr Steve Michlovitz and the Windsor Central Supervisory Union. We would like to thank the Dartmouth Brain Imaging Center for technical support, and the National Science Foundation for funding to the Center for Cognitive and Educational Neuroscience.

References 1. Moyer RS, Landauer TK. Time required for judgements of numerical inequality. Nature 1967; 215:1519–1520. 2. Dehaene S, Dupoux E, Mehler J. Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. J Exp Psychol Hum Percept Perform 1990; 16:626–641. 3. Sekuler R, Mierkiewicz D. Children’s judgments of numerical inequality. Child Dev 1977; 48:630–633. 4. Dehaene S. The number sense: how the mind creates mathematics. Oxford University Press: Oxford; 1997. 5. Xu F, Spelke ES. Large number discrimination in 6-month-old infants. Cognition 2000; 74:B1–B11.

NEUROREPORT 6. Brannon EM, Terrace HS. Ordering of the numerosities 1 to 9 by monkeys. Science 1998; 282:746–749. 7. Feigenson L, Dehaene S, Spelke E. Core systems of number. Trends Cogn Sci 2004; 8:307–314. 8. Domijan D. A neural model of quantity discrimination. Neuroreport 2004; 15:2077–2081. 9. Pinel P, Dehaene S, Riviere D, LeBihan D. Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage 2001; 14:1013–1026. 10. Kadosh RC, Henik A, Rubinsten O, Mohr H, Dori H, van de Ven V, et al. Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia 2005; 43:1238–1248. 11. Kaufmann L, Handl P, Thony B. Evaluation of a numeracy intervention program focusing on basic numerical knowledge and conceptual knowledge: a pilot study. J Learn Disabil 2003; 36:564–573. 12. Dehaene S, Cohen L. Towards an anatomical and functional model of number processing. Math Cogn 1995; 1:83–120. 13. Butterworth B. The mathematical brain. Macmillan: London; 1999. 14. Lemer C, Dehaene S, Spelke E, Cohen L. Approximate quantities and exact number words: dissociable systems. Neuropsychologia 2003; 41: 1942–1958. 15. Gobel SM, Johansen-Berg H, Behrens T, Rushworth MF. Responseselection-related parietal activation during number comparison. J Cogn Neurosci 2004; 16:1536–1551. 16. Piazza M, Izard V, Pinel P, Le Bihan D, Dehaene S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 2004; 44:547–555. 17. Dehaene S, Piazza M, Pinel P, Cohen L. Three parietal circuits for number processing. Cogn Neuropsychol 2003; 20:487–506. 18. Temple E, Posner MI. Brain mechanisms of quantity are similar in 5-year-old children and adults. Proc Natl Acad Sci USA 1998; 95: 7836–7841. 19. Kawashima R, Taira M, Okita K, Inoue K, Tajima N, Yoshida H, et al. A functional MRI study of simple arithmetic: a comparison between children and adults. Brain Res Cogn Brain Res 2004; 18:227–233. 20. Rivera SM, Reiss AL, Eckert MA, Menon V. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb Cortex [Advance access published on 16 February 2005] doi: 10.1093/cercor/bhi055. 21. Tailarach J, Tournoux P. Co-planar stereotaxic atlas of the human brain. Thieme: New York; 1988. 22. Boynton GM, Engel SA, Glover GH, Heeger DJ. Linear systems analysis of functional magnetic resonance imaging in human V1. J Neurosci 1996; 16:4207–4221. 23. Pinel P, Le Clec HG, van de Moortele PF, Naccache L, Le Bihan D, Dehaene S. Event-related fMRI analysis of the cerebral circuit for number comparison. Neuroreport 1999; 10:1473–1479. 24. Baddeley TC, Davidson IG, Glidewell C, Low JN, Skakle JM, Wardell JL. Supramolecular structures of substituted alpha,alpha0 -trehalose derivatives. Acta Crystallogr B 2004; 60:461–471. 25. Culham JC, Kanwisher NG. Neuroimaging of cognitive functions in human parietal cortex. Curr Opin Neurobiol 2001; 11:157–163.

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