Calculation difficulties in children of very low birthweightA neural correlate
Summary
Learning difficulties, including problems with numeracy, are common in Western populations. Many children with learning difficulty are survivors of preterm birth. Although some of these children have neurological disabilities, many are neurologically normal, and the latter group provides us with an important opportunity to investigate the neural bases of learning problems. We have conducted a neuroimaging study of adolescent children who had been born preterm at 30 weeks gestation or less, to investigate the relationship between brain structure and a specific difficulty in arithmetic calculation. Using voxelbased morphometry, we have been able to demonstrate that there is an area in the left parietal lobe where children without a deficit in calculation ability have more grey matter than those who do have this deficit. To our knowledge, this is the first report establishing a structural neural correlate of calculation ability in a group of neurologically normal individuals.
 arithmetic calculation
 parietal lobe
 preterm
 voxelbased morphometry
 FD = Freedom from Distractibility Index Score
 MRD = Mathematics Reasoning Deficit
 NOD = Numerical Operations Deficit
 PIQ = Performance IQ
 SPM = statistical parametric map
 VIQ = Verbal IQ
 VLBW = very low birthweight
 WISCIII = Wechsler Intelligence Scale for Children—third edition
 WOND = Wechsler Objective Numeric Dimensions Test
 WORD = Wechsler Objective Reading Dimensions Test
Introduction
Learning difficulties are a significant problem in Western populations but, until recently, the majority of investigations have focused on deficits in literacy. There is now increasing interest, however, in studying specific problems in numeracy. There are indications that difficulties with numeracy may be common within the population of children born preterm (Klein et al., 1989), and we considered that these would provide a suitable group in which to explore the neural bases of such difficulties. There have been almost no studies addressing this question. Rourke speculated that white matter reduction in the right hemisphere might underlie problems with mathematics (Rourke, 1989) and Isaacs and colleagues discussed a possible role for the hippocampus (Isaacs et al., 2000), but there has been no systematic investigation of the neural bases in this group of children.
Despite the lack of studies in children born preterm, and indeed in children generally, a large body of evidence from adults points to areas of the brain that might be implicated. Lesion studies in patients with dyscalculia frequently have identified the left parietal cortex (Grafman et al., 1982; Kahn and Whitaker, 1991), particularly the inferior lobule (Butterworth, 1999), as important in this ability. More recently, functional neuroimaging has been used for investigations in normal subjects (Dehaene et al., 1996, 1999; Rueckert et al., 1996; Menon et al., 2000b). Menon and colleagues state that, despite variation in the aspects of mathematics chosen for investigation, imaging studies collectively suggest the involvement of both prefrontal and parietal cortices in arithmetic tasks (Menon et al., 2000a). Because some areas might also be involved in nonarithmetic operations, they attempted to determine which are unique to numeric computation; they reported that the left and right angular gyri, in the parietal lobe, have a specific role in calculation ability. Cowell and colleagues found evidence to support the involvement of the supramarginal and angular gyri in calculation (Cowell et al., 2000). Rickard and colleagues used three tasks to try to isolate the areas involved in arithmetic calculation and reported bilateral functional MRI (fMRI) activation in the parietal cortices, more prominent on the left (Rickard et al., 2000). These results from patients and normal subjects, taken together, suggest that the parietal lobes are involved bilaterally in normal calculation but that dysfunction in the left parietal lobe alone may lead to impairment.
We hypothesized, therefore, that impaired calculation ability in adolescent children who had been very low birthweight (VLBW) infants would be associated with anomalous structure in the left parietal lobe. We chose to investigate this using voxelbased morphometry (Wright et al., 1995), a method of analysing structural MRIs that can reveal anatomical abnormalities not apparent on visual inspection of the scans. It is particularly appropriate for use in children who were born preterm, in whom any anomalies will have been of early origin. Many of these are likely to be at the level of neural organization, and voxelbased morphometry is suitable for the study of the subtle morphometric differences to which they might lead (Peterson et al., 2000).
Methods
Subject pool and selection
Children taking part in this study were selected from a larger group of participants in a followup study of a preterm cohort born between 1982 and 1985 at five centres throughout the UK (Lucas et al., 1992). All the children had been born at 30 weeks gestation or less and all had been VLBW infants, weighing 1500 g or less. They were assigned to four groups on the basis of their scores on the Wechsler Objective Numeric Dimensions Test (WOND) and the Wechsler Intelligence Scale for Children—third edition (WISCIII) (tests described below). The scores that a child of any given IQ is expected to obtain on the two subtests of the WOND (Numerical Operations and Mathematical Reasoning) can be determined. The difference between these predicted scores and the actual scores obtained can be evaluated to see if the discrepancy indicates a significant lowering of performance relative to overall cognitive level. Discrepancy scores on the WOND are defined as observed score minus predicted score.
Attainment test and IQ data were available for 80 preterm children at the time of group selection; 18 of these children obtained Numerical Operations subtest scores significantly below IQ predictions (mean discrepancy = 17.3 points, SD = 4.4), while 17 showed a significant deficit in Mathematical Reasoning (mean discrepancy = 14.1, SD = 2.7). Groups were formed by matching children from this pool with VLBW children whose mathematical ability was consistent with IQ predictions. Groups were matched on age, gender and IQ as well as on relevant perinatal variables such as gestational age, birthweight and days of ventilation, thereby controlling these sources of potential confounding of the brain images. The groups did not differ significantly in the frequencies of infants who had had asphyxia or who were smallforgestational age, nor in mean Apgar score at 1 and 5 min. Relevant data are presented in Tables 1 and 2. None of the children involved had any literacy problems, so their mathematical difficulty represented a specific deficit and not a generalized learning difficulty.
Group  Age at test  VIQ  PIQ  FD 

VIQ = verbal IQ; PIQ = performance IQ; FD = Freedom from Distractibility Index score; NOD = Numerical Operations Deficit group; ControlI = control group for NOD group; MRD = Mathematical Reasoning Deficit group; ControlII = control group for MRD group; n = group size. Mean scores for each group are given, with standard deviations in parentheses.  
NOD (n = 12)  15 years 10 months  92.4  95.6  96.4 
(13.2 months)  (10.8)  (14.5)  (12.6)  
ControlI (n = 12)  15 years 8 months  96.1  94.7  97.1 
(10.5 months)  (10.7)  (11.7)  (6.3)  
MRD (n = 12)  15 years 10 months  96.9  98.5  99.6 
(14.6 months)  (13.9)  (11.4)  (12.9)  
ControlII (n = 12)  15 years 7 months  96.6  96.3  96.2 
(10.2 months)  (12.8)  (9.6)  (5.0) 
Group  Gestation weeks  Birthweight (g)  Ventilation (days)  Asphyxia  Small for dates 

NOD = Numerical Operations Deficit group; ControlI = control group for NOD group; MRD = Mathematical Reasoning Deficit group; ControlII = control group for MRD group; n = group size. Data in the first three columns are presented as means, with standard deviations in parentheses. Data in the last two columns are presented as numbers of children with asphyxia or who were small for dates.  
NOD (n = 12)  28.1  1101.8  4.9  0  2 
(1.6)  (240)  (9.8)  
ControlI (n = 12)  29.0  1269.8  5.8  1  3 
(0.9)  (277)  (11.8)  
MRD (n = 12)  28.5  1083.5  2.2  3  3 
(1.5)  (222)  (2.7)  
ControlII (n = 12)  29.1  1242.5  5.4  0  2 
(1.2)  (298)  (8.9) 
Groups
Main groups
Because we had a strong hypothesis about a neural substrate, we were interested primarily in calculation ability. Our two main groups were:

(i) Numerical Operations Deficit (NOD) (n = 12). All children obtained scores on the Numerical Operations subtest of the WOND that were significantly below the scores predicted by IQ; their mean discrepancy score was –15.5 points (SD = 4.2).

(ii) ControlI (n = 12). These children obtained Numerical Operations subtest scores that were consistent with IQ; their mean discrepancy score was 3.3 points (SD = 8.1).
Supplementary groups
In order to determine whether any neural abnormality we were able to demonstrate was specific to calculation ability, we also studied a group of VLBW children who had significant discrepancy scores on the Mathematical Reasoning subtest of the WOND and a group of matched controls. The two supplementary groups were:

(iii) Mathematics Reasoning Deficit (MRD) (n = 12). All children showed a significant discrepancy on the Mathematical Reasoning subtest of the WOND; their mean discrepancy score was –12.7 points (SD = 1.9).

(iv) ControlII (n = 12). Children in this group obtained appropriate Mathematics Reasoning scores, with a mean discrepancy of 4.7 points (SD = 7.2).
Children in the supplementary groups were matched on the same variables as those in the main groups; see Tables 1 and 2.
There was some overlap between groups. Four children were included in both NOD and MRD groups and eight children were in both control groups.
Procedure
Two testing sessions were conducted, one at Great Ormond Street Hospital and a second at the child's choice of home or school, during which neuropsychological and imaging data were collected. All children and parents gave informed, written consent, and the study was approved by the local hospital and regional ethics committees (The GOS/ICH, Norwich District, South Sheffield Research, East Suffolk Local Research and Cambridge Local Research Ethics Committees).
Neuropsychological tests
The WISCIII (Wechsler, 1992) was administered during the first session, and the WOND (Wechsler, 1996) and Wechsler Objective Reading Dimensions (WORD) (Wechsler, 1993) during the second session.
WISCIII
This was administered in full, following standard procedures, to allow the calculation of Verbal IQ (VIQ), Performance IQ (PIQ) and Index scores; only Freedom from Distractibilty Index Scores (FDs) are reported here.
WOND
This consists of two subtests: (i) Numerical Operations—designed to measure skills in mathematics computation, emphasizing the operations of addition, subtraction, multiplication and division; and (ii) Mathematics Reasoning—designed to measure mathematical skills beyond computation, including problem solving, numeration and number concepts, graphs, and statistics and measurement.
WORD
This consists of three subtests: (i) Basic Reading—designed to assess decoding and wordreading ability; (ii) Spelling—measures encoding and spelling ability; and (iii) Reading Comprehension—measures understanding of written material and skills such as recognizing stated detail and making inferences.
Both attainment tests generate standard scores that, like IQs and Index scores, have a mean of 100 and an SD of 15. Discrepancies between IQ and attainment scores were calculated and evaluated statistically according to the prescribed procedures.
Image acquisition
MRI studies were performed on a 1.5 T Siemens Vision system. Investigations included (i) magnetizationprepared rapid acquisition gradient echo (Mugler and Brookeman, 1990) threedimensional volume acquisition with repetition time of 10 ms; echo time, 4 ms; inversion time, 200 ms; flip angle, 12°; matrix size, 256 × 256; field of view, 250 mm; partition thickness, 1.25 mm; 128 sagittal partitions in the third dimension; and acquisition time, 8.3 min; and (ii) coronal and axial turbo spinecho T_{2}weighted scans with repetition time of 4600 ms; echo time, 90 ms; and acquisition time, 4.3 min for each orientation.
Voxelbased morphometry
Prior to statistical analyses, the threedimensional MRI data sets were processed using SPM99 software (Wellcome Department of Cognitive Neurology, Institute of Neurology) (Friston et al., 1995), running in Matlab5, on a SUN workstation. The data sets first were spatially normalized to a template constructed from a collection of 20 data sets obtained from normal children aged between 8 and 17 years [themselves normalized to the template in SPM (statistical parametric mapping)T_{1}imaging]. The normalized scans were then segmented into grey, white, cerebrospinal fluid and scalp images. These are in the form of probability images that classify each voxel to one of the four categories, based on both its signal intensity and its location in the brain. The segmented grey matter images were then smoothed using an 8 mm fullwidth halfmaximum isotropic Gaussian kernel.
The resulting images were then entered into the statistical analyses. Proportional scaling was used to account for global differences in total amount of grey matter between data sets. The SPM design was a twosample ttest with one scan per subject. Two such ttests were conducted within each pair of groups to identify, first, regions where one group had more grey matter than its control and, secondly, where it had less. The tmaps resulting from these analyses were transformed to Zvalues (unit normal distribution) and the significance of the differences estimated using the theory of random Gaussian fields. Because of the very large number of comparisons engendered by studying the entire brain, stringent correction procedures are applied. We used the convention that regions predicted to show differences in advance of the analysis use an uncorrected P value of <0.0005, while regions not predicted a priori must survive a corrected P < 0.05.
Results
IQ and attainments scores
Participants in this study were selected from a total group of 80 VLBW children on whom we had both IQ and attainment data; mean IQ of this total group was close to the population average of 100 (VIQ = 98.3, PIQ = 97.8). As expected, however, there was an increased incidence of significant discrepancies between observed and predicted scores compared with the normative population, more pronounced for numeracy than literacy. Of the VLBW children, 23.8% had significantly low scores on Numerical Operations and 22.5% on Mathematics Reasoning. These percentages compare with ~7% in the normative group (Wechsler, 1996). The incidence of significant discrepancies in literacy was (normative percentages in parentheses; Wechsler, 1993): Basic Reading, 10% (3%); Spelling, 16.3% (4%); and Reading Comprehension, 11.3% (~5%). Children with literacy deficits were not selected for this study.
VIQ, PIQ and FD scores for the four groups are reported in Table 1. There were no significant differences between the means of either pair of groups, and all four groups fell within the average range of 90–109 (Wechsler, 1992) on all three measures.
In accordance with selection procedures, there were large and statistically significant differences between the groups on the relevant subtests. The NOD group had a mean Numerical Operations score of 80.3 (SD = 8.6) and the matched ControlI group a mean score of 100.0 (SD = 9.2) (P < 0.0001). The MRD group had a mean Mathematical Reasoning score of 85.2 (SD = 7.4) and the matched ControlII group a mean score of 102.2 (SD = 12.4) (P < 0.001).
Voxelbased morphometry
Results of the neuroimaging analyses are presented in the form of statistical parametric maps (SPMs). The SPM showing regions where the ControlI group had a significantly higher grey matter probability than the NOD group is shown in Fig. 1. Neurological convention is used in these maps, so left is left. The most visually prominent region is in the area of the left intraparietal sulcus (Talaraich coordinates of peak voxel: –39, –39, 45). This area, predicted by our hypothesis, has an uncorrected P value of <0.0001. There are no other regions that reached the required level of significance in this analysis. Neither were any significant areas found in the analysis of regions where the NOD group had more grey matter, rather than less.
The same analyses were carried out in the MRD and ControlII groups. There were no regions of difference for either contrast where the significance level survived the correction for multiple comparisons.
Discussion
Our aim was to identify a neural correlate for the deficit in calculation seen in a group of children who had been VLBW preterm infants. Our results clearly show that there is an area in the left parietal lobe where VLBW children without a deficit in calculation ability have more grey matter than those who do have this deficit. Since this area has been implicated repeatedly in mathematics functioning, it seems reasonable to conclude that this is the neural correlate of this disability in these children. This conclusion is strengthened by the fact that we did not find a similar anomalous region in the group of children with a deficit in a different aspect of mathematical processing.
The left parietal area identified in this study accords well with the findings of previous research. Although most of these studies have used fMRI methodology, a recent report by Levy and colleagues, based on proton magnetic resonance spectroscopy, is also of interest (Levy et al., 2000). They studied an 18yearold subject with developmental dyscalculia, reporting a focal defect in the left temperoparietal area of the brain where decreased signal of neural metabolites suggested an alteration in the pattern of cell density. The area we have identified is within a few millimetres of the main peak described by Dehaene and colleagues (Dehaene et al., 1999) as activated during arithmetic tasks requiring approximation rather than exact calculation.
These authors suggest that approximation relies on nonverbal visuospatial networks while exact calculation is language based. The calculation task used in this study did not allow us to draw more specific conclusions about the nature of the deficit, but it is of interest that the children all had welldeveloped literacy skills and no apparent language deficits; their calculation deficit occurred in the context, therefore, of an appropriate level of language development. The study of abilities such as sensitivity to numerosity and the comparison of numerosities (Butterworth, 1999), thought to be more biologically basic, would also be of great interest in this group.
The implication of these results is that the integrity of the left intraparietal sulcal area is necessary for the appropriate levels of calculation ability in these children. However, the results should not be interpreted to mean that this area is the only important region for calculation. A whole network of regions could participate in normal processing; at the very least, the homologous area in the right hemisphere may be involved, in view of the bilateral activation shown by some functional studies (Rueckert et al., 1996; Dehaene et al., 1999). Nevertheless, whether other regions are involved or not, we conclude that less grey matter in the left intraparietal sulcus in these children is associated with a deficit in calculation.
The design of this study has produced very clear imaging findings. We feel that this is partly because our groups are well matched on a series of potentially confounding variables such as age, gender and intelligence. In addition, however, we have chosen to make our comparisons between two preterm groups and not between preterm and full term. This allows us to control for another set of variables, such as gestational age and birthweight, that might produce differences between preterm and full term brains. We wanted our analyses to demonstrate neural effects associated with calculation ability and not to reflect differences associated with birth status.
The high incidence of learning difficulties in this group was not unexpected (Hack and Taylor, 2000), but our results make the point that problems with numeracy are at least as prevalent as those with literacy. Families and children were well aware of these in their individual cases but had never been informed that such problems might be a consequence of VLBW birth. These children are not acalculic, of course, and are able to carry out simple calculations, albeit at a level far below their chronological age. They generally can complete simple addition and subtraction sums correctly, but encounter difficulty with more complex operations such as carrying and borrowing with multidigit numbers. It is possible that they rely heavily on number fact retrieval from semantic memory for the completion of simple sums (Ashcraft, 1992) and are not calculating at all. Alternatively, there may be enough neural substrate to support simple but not complex operations. Whatever the case, it is clear that the calculation deficits cannot be attributed to difficulty in attention/concentration, since there was no significant difference in FDs between the groups (see Table 1).
Why only some preterm babies have a deficit in calculation ability with an associated anomaly in the parietal lobe is interesting and requires further explanation. We and others have shown previously that perinatal factors such as the severity of respiratory disease (Stewart and Reynolds, 1974), nutritional variables (Lucas et al., 1998, 1990) (including diet, growth and minimum plasma taurine; A. Lucas, unpublished data) and metabolic disturbances, notably duration of hypoglycaemia (Lucas et al., 1988) and low thyroid status (Lucas et al., 1996), are all strongly related to later cognitive performance. In order to determine whether any aspects of perinatal status might explain a specific effect of numeracy in this population, we performed a series of additional analyses on the total group (n = 80). Using multiple regression, with the magnitude of the discrepancy between predicted and observed Numerical Operations scores as the dependent variable, we found that number of days in 30% or more inspired oxygen concentration (a measure of respiratory illness) and minimum plasma taurine were both significant predictors, independently of age of gestation. The tvalues and significance levels were: oxygen, t = –2.48, P < 0.02; and taurine, t = 2.61, P < 0.02. Neither factor was significantly related to IQ. None of the other factors screened was related to numeracy skills. Our preliminary analyses, therefore, indicate a relationship between calculation ability and both the duration of respiratory illness and low concentrations of plasma taurine, a nutrient factor believed to be important in neural development (Sturman, 1993) and not routinely added to artificial feeds at the time this cohort was born. Our recent (unpublished) data indicate that taurine status could, at least in part, explain the major longterm effects of early diet on later cognitive function that we have reported in prospective experimental studies of this population (Lucas et al., 1990, 1998). These data raise hypotheses concerning the possible influence of nutrition and hypoxia on specific aspects of grey matter development.
The children studied here were all VLBW, so we cannot say that the parietal lobe anomaly would be found in all children with calculation ability deficits. However, since the area we have identified is similar to that revealed in adult studies, it seems likely that this might be the case across the age spectrum; neuroimaging studies in groups of wellmatched full term children will be necessary to determine if this is so. Meanwhile, this study demonstrates a neural correlate of a specific learning difficulty in preterm children, and adds to the body of evidence that implicates the left parietal lobe in calculation. Future investigations of this population of children should provide the opportunity to identify the neural underpinnings of a wide variety of cognitive deficits.
Acknowledgments
We wish to thank the children and their families as well as the staff at the hospitals involved in the early stages of this research. The Medical Research Council and the Wellcome Trust provided financial support. Research at the Institute of Child Health and Great Ormond Street Hospital NHS Trust benefits from Research and Development funding from the NHS Executive.
 © Oxford University Press 2001