Children with Deve I op men t a I D ysc a I c u I i a SOME children present with learning difficulties which impede their progress in school, in spite of satisfactory spoken and written language-skills. For example about 6 or 7 per cent of seven- and eight- year-old children have difficulties of co- ordination sufficient to affect their acquisition of motor skills'. Some of these children may also have impairments of speech and language, but often they do not. Although such disorders are not always recognised as specific disabilities, they should be if an adequate assessment is carried out. However, it can be very difficult to identify certain disabilities if they affect an aspect of learning of a particularly subtle kind.

There is no doubt that some children do have considerable difficulties in acquiring the expected skill in numeracy for their age. Sometimes this not due to a specific learning disorder, but to factors such as missing the relevant lessons, emotional disorders, below-average intelligence, and lack of interest and motivation; the last is sometimes related to socio-economic factors2. If the disability is due to a specific developmental dyscalculia, the child may well not be referred for assessment because such a disability is much more socially acceptable than an inability to read or write, and is not thought to be a

serious educational problem. Often people will say, with a degree of pride, 'I was never any good at maths'.

It has been estimated that 6 per cent of the school population has serious problems with arithmetic and, especially if they have behaviour difficulties, there may be little provision for helping these children3. There is no doubt that this disability is particularly complex, and that no single cause can explain all the different types of dyscalculia; and this may well account for the number of theories which try to do this. Dyscalculic children seem to omit facial features in their drawings, especially the nose, and B A D I A ~ suggests that this may be due to lack of visual attention to exact details. Certainly there seems to be evidence that a child's drawing can predict later numerical ability. It has been suggested that children with a severe disability of this kind, but with normal reading ability, have not advanced to the Piagetian stage of concrete operations needed for numerical but not reading skills5. In addition, memory may play an important part, being often related to attainment, especially if it is difficult for a child to recall ways of tackling problems.

Links between dyscalculia and right cerebral hemisphere dysfunction Of particular importance is a link between right cerebral function and dyscalculia, and therefore between spatial and mathematical abilities. This could be due to an inability to point accurately to objects being counted, resulting in errors -a trend which may develop into poor calculation. If inco-ordination resulting

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from visual spatial dysfunction is particularly severe, various other aspects of learning motor skills will be affected, such as speech articulation, and the acquisition of reasonably neat writing; with all the effects this will have on social behaviour6. Abnormal behaviour may be a factor, but it is the link between these two disabilities which is of fundamental importance; thpre can be no doubt about the spatial quality of mathematics, with figures set out in rows, diagrams having crossing lines, and equations having figures with functions dependent on their position in space2. General intelligence, verbal and spatial ability, and specific numerical skills are all involved in the attainment of mathematics, but verbal ability may have only an indirect relation- ship with the latter; those with specific mathematical difficulties usually do better on performance than on verbal tasks. Children with treated phenylketonuria tend to show deficits in conceptual and visual spatial skills, which may explain their reported difficulty with mathematics'. BERRY et a1.* also found that treated phenylketonuric children had no apparent reading and spelling disability, but their arithmetic scores were significantly low. Boys tend to be better than girls at mathematics and also spatial tasks, but this could be due to cultural influences':

ROURKE and FIN LAY SON'^ studied 45 nine- to 14-year-old children with learning disabilities. They were divided into three groups: those who were deficient in reading, spelling and arithmetic; those who were good at arithmetic, compared with their standard in reading and spelling; and those whose reading and spelling were good, but who had diffi- culties with arithmetic. The performance of the first two groups was better than that of the third on measures of visuo- perceptual and visuo-spatial abilities; the third group was better on measures of verbal and auditory-perceptual abilities, as might be expected. The findings indicate that the first two groups performed in a way which suggests left cerebral dys- fumtion, and the third group in a way suggesting right cerebral dysfunction. This is compatible with a right cerebral superiority for certain types of calculation,

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integration. As will be discussed later, some functions of the left cerebral hemisphere play a part in numeracy skills, and obviously it is dangerous to localise cerebral functions too specifically. Certainly the educational approach to the children in the three groups will be different, and the pattern of abilities and deficits exhibited by the various types of learning-disabled children must be care- fully specified before remedial education is planned. The results of psychometric tests in Turner's syndrome show that affected girls do relatively well on verbal tests, but poorly on performance and numerical ones. It is suggested that in this syndrome there is involvement of the right parietal lobe, possibly related to the basic chromosome defects". All this strongly supports the association between per- ceptual motor disabilities and dyscalculia, both being evidence of right cerebral hemisphere dysfunction.

The role of the left cerebral hemisphere is acquiring numeracy skills This association between numeracy skills and right-hemisphere dysfunction is also recognised in acquired dyscalculia among adults, although the left cerebral hemis- phere does contribute to certain aspects of this disability. Gerstmann syndrome, caused by lesions in the left parieto- occipital region, consists of finger agnosia, right-left disorientation, agraphia and acalculia. However, the last may be more of a manifestation of aphasia than a true disorder of numeracy; for example a difficulty in reading and writing numbers. Also there may be difficulties for the older child in solving arithmetical problems when there is evidence of left cerebral involvement, when instead of using the analytic abilities of this hemi- sphere, the child relies on more immature cognitive strategies of the right cerebral hemisphere. This hypothesis is compatible with a lag in the development of hemi- sphere specialisation'2.

Particularly in the early stages of development, the left cerebral hemisphere may play a signficant role in acquiring numeracy skills. C O H N ~ points out that when a child learns the correspondence of quantities of things with particular sounds he is equipped for arithmetic operations,

at least at the phonetic level. At the time that correspondence between number sounds and quantity occurs, the child appears ready to learn graphic number symbols, and because the number can be kept indelibly on paper while new corres- pondences are made, and also during the process of relational operations, graphic forms of calculations are capable of high accuracy and rapidity of execution.

A developmental type of Gerstmann syndrome has been described, consisting of constructional apraxia, spelling deficits and reading di~abilities'~. A possible cause of the reading and writing retardation could be a difficulty in the correct differentiation or arrangement of parts that constitute a whole, but this is open to doubt. The localising significance of congenital Gerstmann syndrome has still to be established.

Emotional and behavioural disorders and the right cerebral hemisphere There are definite correlations between defective visuo-spatial organisation due to right-hemisphere dysfunction and dis- orders of behaviour. WEINTRAUB and MESULAMI4 have described the syndrome of right cerebral hemisphere dysfunction. Affected children suffer from emotional and interpersonal difficulties, shyness, visuo-spatial disturbances and problems with mathematics, as well as impairment of certain aspects of communication, such as poor eye-contact, absence of gesture and lack of speech prosody. In addition, there may be right-left confusion, poor sense of direction, and difficulty with tasks such as riding a bicycle. Social maturity is low.

Emotional and behavioural disorders are therefore likely to affect children with developmental dyscalculia, who tend to be maladjusted and asocial. In contrast, it has been shown that those who are good at mathematics are more secure, assertive, sociable and well adjusted. Those with right cerebral hemisphere dysfunction and learning disorders have difficulty under- standing the affective state of others, and have a poor comprehension of non-verbal communication; there seems to be no doubt that there are differences in social behaviour associated with high and low verbal and numerical ability4.

Emotional sensitivity involves the right cerebral hemisphere, and those with impaired function of this hemisphere, apart from having a low level of perception and imagery, often have impaired relation- ships with other children and few friends. When difficulties with arithmetic are found among such children with adequate performance on reading and writing, the learning disability can be considered a result of socio-economic disturbances. However, this is not always so, and if the dyscalculia is a specific entity an oppor- tunity for successful remedial teaching can be lost". It has been claimed that socio-emotional disturbances among learning-disabled children are due to central processing deficiencies16.

Different types of developmental dyscalculia Various types of developmental dyscalculia have been identified by B A D I A ~ . (1) Alexia and agraphia for numbers and words, which may be uncommon com- pared with other types of developmental dyscalculia and be obscured by the many different problems of children with dyslexia. However, these children may well have difficulties with the syntactical properties of numbers, being apt to reverse the position of numbers and add additional zeros which impairs their mathematical skills. (2) Spatial dyscalculia; for which there is considerable evidence. In written addition and subtraction this is exhibited by both horizontal and vertical confusion, and there can be considerable disorganisation when arranging rows and columns of figures. Telling the time proves difficult, with confusion of the hands of the clock and reversal of the hours and minutes when writing times. Oral mathematics and numerical reasoning is often superior to written calculation skills. The fact that numbering digits backwards is particularly difficult for these children may depend on the visuo-spatial component in this task. (3) Anarithmetia, with a mix-up of the procedures involved in addition, sub- traction and multiplication. There may also be extreme confusion in carrying out the tasks of written arithmetic. There are problems of memory, but the important defect is the muddle between one mathematical task and another. 461

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(4) Attention-sequential dyscalculia, in which addition and subtraction are in- accurate, and there are difficulties in learning and recalling multiplication tables and the decimal point is often forgotten. This type is found among children with attention deficit syndrome. ( 5 ) Mixed types of dyscalculia, as in Gerstmann syndrome, comparable to the mixed types of dyslexia in BODER’S classification of this disability”. Although developmental dyscalculia reflects a con- genital cerebral dysfunction, mixed types can simulate acquired dyscalculia in adults.

KOSC’* uses a different classification of developmental dyscalculia: verbal, with difficulties in naming mathematical terms and relations; practognostic, with a dis- turbance of mathematical manipulation of real or pictured objects; lexical, with a disability in reading mathematical symbols; graphical, with a similar disability in manipulating mathematical symbols in writing; ideognostical, with an inability to understand mathematical ideas and relations in ‘doing mental calculations; and operational, with the skill for carrying out mathematical operations directly disturbed. This type is also called anarithmetia, as in BADIAN’S classifi- cation, and a typical example is an inter- change of operations: addition instead of multiplication, subtraction instead of division, or the substitution of complex operations by simple ones.

Conclusions Developmental dyscalculia, a develop- mental lag in the acquisition of numerical skills, can be manifested in a number of ways, including: inability to recognise number symbols; stephosymbolia or mirror writing: failure to recognise the basic mathematical operations or use of operator or separator symbols; inability to recall tables and ‘carry’ numbers in multiplication; and failure to main- tain the proper order of numbers in calculation6.

Some children seem to be born with a defective ability to discriminate and manipulate spatial and numerical relation- ships, and lack the basic tools of mathematics. Such children can make progress at first using learning by rote, but as they grow, older they will find

mathematics increasingly difficult; and this is likely to cause anxiety2. If teaching is inappropriate and there are adverse socio-economic conditions, there is a strong possibility that depression and anxiety will occur, with poor self-image, failure to reach full potential and a variety of behaviour disorders; common findings among children with learning difficulties. However, many children wilh learning disorders are not held in low esteem by their teachers, parents and peers, and can be popular, although they are always at risk of acquiring low social status”. Developmental dyscalculia may not have the stigma of some of the other learning disorders, but it is important that it is recognised when it occurs as a specific entity, and that the child is referred for a full assessment. Only then can manage- ment and educational help be logically planned.

SEMRUD-CLIKERMAN and HYND” have reviewed recent research on non-verbal learning disabilities and make recom- mendations for the future. There are inconsistencies among studies on children with learning disabilities and their social perception and interaction skills, but considering the great variation in method- ology perhaps this is not surprising; and more studies are needed. Both cerebral hemispheres seem to contribute to mathematical skills in different ways, and it may be that only very specific deficits in arithmetic are manifested in children with learning disabilities of right cerebral origin. It is of special interest that experiments show that the thalamus on both sides is also involved. Dysfunction at this level may impede allocation of hemisphereic attentional resources impli- cated in developmental dyslexia, and deficits in sensory processing may involve subcortical structures, especially in right- hemisphere learning disorders related to visual-spatial input, and expression of emotion.

The delineation of subgroups is im- portant for research, as is the link be- tween dyscalculia and social perception, where both are manifestations of right cerebral hemisphere dysfunction. More may be learned from the study of acquired dyscalculia and the way this affects cerebral function, and the results applied

to the developmental type. New remedial techniques can then be formulated.

NEIL GORDON Huntly wood, 3 Styal Road, Wilmslo w, Cheshire SK9 4AE.

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8. Berry, H. K., O’Grady, D. J., Perlmutter, L. J., Bofinger, M. K. (1979) ‘Intellectual develop- ment and academic achievement of children treated early for phenylketonuria.’ Develop-

Febrile Seizures Venice; Italy, 18th and 19th June 1992

This meeting is being organised by the International School of Neurological Sciences in Venice. Main topics include: clinical predictors; EEG; natural history; acute management; emergency care; differential diagnosis; long-term management; continuous therapy; intermittent therapy; Severe myoclonic epilepsy of infancy and febrile seizures; relationship of other types of epilepsy to febrile seizures; genetic aspects; counselling families. Further information from Prof. F. Paladin, Secretary ISNV, Santa Croce 1591, 30135 Venice. Tel.: (39) 41 721053; Fax: (39) 41 5294555.

mental Medicine and Child Neurology, 2 1, 1 1 1-72n

rn W 9 --. h

Psychology of Sex Differences. Stanford: 0

d Stanford University Press. r?

N* 10. Rourke, B. P., Finlayson, M. A. J. (1978)

‘Neurophysiological significance of variations Q\

in patterns of academic performance: verbal z s and visual-spatial abilities.’ Journal of 3 Abnormal Child Psychology, 6, 121-133. 2 11. Money, J. (1973) ‘Turner’s syndrome and

parietal lobe functions.’ Cortex, 9, 387-393. 12. Weinstein, M. A. (1980) ‘A neurophysiological

p approach to math disability.’ New York

5 University Education Quarterly, 11, 22-28. 13. Kinsbourne, M., Warrington. E. K. (1968) ‘The

developmental Gerstmann’s syndrome.’ b Archives of Neurology, 8,490-501. 8

14. Weintraub, S., Mesulam, M. M. (1983) ‘Develop- mental learning disabilities of the right hemi- * sphere.’ Archives of Neurology, 40,464468.

IS. Rourke, B. P., Strang, J. (1978) ‘Neuro- 4 physiological significance of vairations in .

2 E patterns of academic performance: motor, 5 psychomotor and tactile-perceptual abilities.’

Journal of Pediatric Psychology. 3, 62-66. 16. Rourke, B. P., Fisk, J. L. (1981) ‘Socio-emotional 2

disturbances of learning disabled children: the 3 role of central orocessine deficits.’ Bulletin of 4“

9. Maccoby, E. M., Jacklin, C. N. (1974) The m

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the Orton Sociky, 31, 77. 17. Boder, E. (1973) ‘Developmental dyslexia: a

diagnostic ‘approach basid ,on three atypical reading-spelling patterns. Developmental Medicine and Child Neurology, 15, 663-687.

18. Kosc, L. (1974) ‘Developmental dyscalculia.’ Journal of Learning Disobililies, 7, 164-1 77.

19. Dudley-Marling, C. C., Edmiaston, R. (1985) Social status of learningdisabled children and

adolescents: a review.’ Learning Disabilify Quarterh, 8, 189-204.

20. Semrud-Clikeman, M., Hynd, G. W. (1990) ‘Right hemispheric dysfunction in non-verbal learning disabilities: social, academic an! adaptive functioning in adults and children.

* Psychological Bulletin, 107, 196-209.

Fourth International Workshop on Childhood Epilepsies Marseille, France, 23rd to 26th June 1992

This NATO Advanced Research Workshop is being organised by Charlotte Dravet (Marseille), Fritz Dreifuss (Charlottesville, VA) and Cesare Lombroso (Boston, MA). The topic is Epilepsies and. Generalised Epileptic Syndromes Before rhe Age of Sir. The workshop will be followed on 27th June by a Scientific Day in honour of Joseph Roger. Further information from Dr. Michelle Bureau, AREP, 300 Bd. de Sainte-Marguerite, 13009 Marseille, France. Tel.: 33 91 75 13 40.

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