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Chapter 4. Clinical and neuropsychological validation of a suspected Specific disorder of arithmetical skills

4.1 Selection of probands with a suspected Specific disorder of arithmetical skills

According to the diagnostic criteria for the Specific disorder of arithmetical skills quoted in chapter 1.3. a discrepancy of mathematics performance and other areas of achievement is required to make the diagnosis. Due to the shift of the screening data towards low achievement scores, described in chapter 3.3., it was problematic to identify probands with a significant discrepancy in their test results. The correlation between the teacher‘s ratings and their student‘s test results was equally too weak to be utilized as a diagnostic tool. Considering the low achievement scores, an over-evaluation of the probands‘ potential would be conceivable but under-evaluation of their abilities was just as common. We were not able to find a correlation between differences in test scores and corresponding differences in teacher‘s ratings.

Considering the homogenous distribution of our population‘s test results, we applied specific criteria in order to identify probands with a suspected Specific disorder of arithmetical skills. We selected those probands whose orthographic achievement was above the 50^th percentile of our sample and whose mathematics achievement was below the 25^th percentile of our sample. We thus arrived at the following criteria:

Tab. 3: Selection criteria for a suspected Specific disorder of arithmetical skills

First language	Sex	Score DRE 3	Errors in DRT 3
German	male	<6	<26
	female	<4	<26
Not German	male	<6	<32
	female	<4	<32

The criteria for a suspected Specific disorder of arithmetical skills were met by 12 probands, or 6.59% of the study population. Ten of these probands were girls. Eleven of the probands had German as their first language, six were from the Mitte district and six from the Tiergarten district.

The screening data were obtained in an anonymous fashion. In order to get in touch with the 12 selected probands we gave letters with the request for further participation to the teachers of the probands. We addressed the letters with the proband‘s code. The teachers then identified the probands and forwarded the letters to the families. The parents of five of these probands granted us permission for further investigation. Of these, three were girls and two boys all of them with German as their first language. For detailed case reports of the probands see below.

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4.2 Methods and design of the validation process

4.2.1 Clinico-neurological and psychopathological examination of the probands

The five probands whose families agreed to further testing were given an appointment at the Clinic for Child and Adolescent Psychiatry and Psychotherapy of the Humboldt University Medical School, Charité Campus Mitte. A clinical history was taken and a thorough neurological examination with special attention to laterality preferences and other neurological questions was carried out.

If the parents gave their written permission, an electroencephalogram (EEG), visually evoked event-related potentials (VEP) and acoustically evoked event-related potentials (AEP) as well as cerebral magnetic resonance-imaging (cMRI) of the head were obtained.

4.2.2 Neuropsychological testing of the probands

4.2.2.1 Attention and perseverance

To evaluate attention and perseverance of the probands we used the Vienna Determination Device (VDD) equipped with Program R, a multiple-choice reaction test Schuhfried, Berg, &Fischer, 1994 . The proband‘s data were compared to a standardization sample of our clinic which included the data of 350 tested probands.

At the beginning and the end of the neuropsychological testing the proband works for two minutes with self-determined rapidity on the Vienna Determination Device. The task is to react swiftly an to discern between stimuli. The reaction time and the number of errors from both of the proband‘s test runs are compared and then evaluated in relation to the standardization sample.

4.2.2.2 Laterality preference

As shown in chapter 1.4.2.2.3., hemisphere specialization and hand laterality are crucial issues in the discussion of the Specific disorder of arithmetical skills. For this reason we tested the probands with the Motor Performance Series (MPS) Schuhfried, 1994 using the standardization data of Sturm and Büssing Sturm &Büssing, 1985 . It analyses lateralization, dynamic coordination, accuracy and resting as well as diadochokinesia of the hands.

4.2.2.3 Intelligence testing

The intelligence of the probands was tested with two different methods. For an assessment of overall intelligence we applied a German version of the Hamburg-Wechsler Intelligence Scale for Children in the revised version of 1983 (WISC-R) Tewes, 1984 . We used an abbreviated form of it developed at Zurich University (WISC-R-A). It contains the subtests of Vocabulary

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Von Aster et al. developed the ’Neuropsychological test battery for number processing and calculation in children (NUCALC)‘ to identify children with mathematical deficits. This specific test can be used from grades one through three and examines several basic skills that are necessary for arithmetic and also arithmetical abilities themselves. The examined basic skills are the counting of objects (CO), counting backwards (CB), estimating amounts (EA), estimating (EM) and judging magnitudes (JM), as well as the writing (NW), comparing numbers presented orally (NCO) or in written (NCW) and reading of numbers (NR). Arithmetical abilities are tested with mental addition (MA), mental subtraction (MS), and mathematical text problems (TP). The test was standardized for a German-speaking population sample. The subtests‘ scores can be translated into a quotient. A quotient between 85 and 115 represents an average ability. NUCALC provides the opportunity to identify and specify the profile of mathematical abilities in children with a Specific disorder of arithmetical skills. The instrument has been standardized for the ages 7-11 with a relatively small control sample. Aside from the age limitations and the small standardization sample, the divergent, sometimes considerably small, number of items per subtest (e.g. only 4 text problems), might be criticized and thus do not allow for a very detailed description of single deficits. Nevertheless, it represents a new quality in the description of arithmetic abilities von Aster, Deloche, Gaillard, &Tièche, 1995 .

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4.3 Case summaries of the probands with a suspected Specific disorder of arithmetical skills

4.3.1 M.W.

Sex: female, age: 9 years, 10 months, first language: German.

Screening test results: errors in DRT 3: 9; score in DRE 3: 3.

Teacher‘s evaluation: German: 1; mathematics: 2.

4.3.1.1 Clinico-neurological findings

Family history: No known neuropsychiatric disorders in the family. No family history of learning problems.

Past medical history: Normal pregnancy and delivery. Birth at term without perinatal complications. Normal early childhood development. Developmental milestones met within normal temporal limits. No significant medical or surgical history.

Clinico-neurological examination: No abnormalities found on clinical examination. Normal, age-appropriate neurological status.

Psychological status: Fully oriented and alert. Friendly, cooperative girl. No pathological findings in psychological status.

EEG: Age-appropriately matured wave pattern. Right-hemispheric dominance over the occipito-parietal regions with normal function.

VEP and AEP: Physiologic latency periods with normal amplitude bilaterally.

cMRI: Permission denied.

4.3.1.2 Neuropsychological test results

Normal attention and perseverance as tested by the VDD.

Regular hand-lateralization towards right. Values in the average range for dynamic coordination, accuracy and resting. Diadochokinesia slightly below average.

Homogenous test profile in WISC-R-A with all subtests in the average range, lowest score on mathematical performance.

WISC-R-A-IQ=106. Subtest-scores (scores below average are in bold typeface)

 V: 11                A: 9                S :10                DSp:  11        BD: 10        PA: 9.

Average performance in the test of number processing and calculation abilities. Only text-problem task performance slightly below average.

NUCALC Test-profile:

CO         CB         NW         MA         MS         NR         EA         NCO         EM         JM         TP         NCW

105        107        109        112        105        108        110        110        103        102        80        106.

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In summary: no findings of pathological significance detected in the validation process. Mathematical performance was comparatively weak, however, the working diagnosis Specific disorder of arithmetical skills, as indicated by the results of the screening process, could not be validated. In the absence of other mathematical or cognitive difficulties, the below-average performance on the Text Problem in NUCALC is likely due to a diminished verbal memory capacity. No reason for the particularly low score in the DRE-3 could be detected.

4.3.2 Y.Z.

Sex: female, age: 8 years, 11 months, first language: German.

Screening test results: errors in DRT 3: 9; score in DRE 3: 4.

Teacher‘s evaluation: German: 1; mathematics: 2.

4.3.2.1 Clinico-neurological findings

Family history: No known neuropsychiatric disorders in the family. No family history of learning problems. Father speaks Turkish as first language.

Past medical history: Prematurely ruptured placentar membranes in the fourth month of pregnancy, treated with tocolysis and mild sedation. Birth at term without perinatal complications. Normal early childhood development. Developmental milestones met within normal temporal limits. At the age of six weeks diagnosis and surgical correction of intestinal misplacement.

Clinico-neurological examination: No abnormalities found in clinico-neurological examination. Normal, age-appropriate neurological status.

Psychological status: Fully oriented and alert. Friendly, socially well-adapted girl. No pathological findings in psychological status.

EEG: Age-appropriately matured wave pattern. Hemispheric difference, especially over the occipito-parietal regions, pronounced under hyperventilation. Probable right-sided abnormality.

VEP and AEP: Physiologic latency periods with normal amplitude bilaterally.

cMRI: Hyperintensity of the occipital white matter as seen in myelinization irregularities (see figure 9). Otherwise normal, age-appropriate cMRI.

4.3.2.2 Neuropsychological test results

Normal attention and perseverance as tested by the VDD. Swiftness above average.

Regular hand-lateralization towards right. Values in the average range for dynamic coordination, accuracy and resting. Diadochokinesia slightly below average.

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WISC-R-A-IQ=106. Subtest-scores (scores below average are in bold typeface) :

V: 15                A: 12                S: 15                DSp: 11        BD: 8                PA: 10.

No significant problems in number processing and calculation abilities.

NUCALC Test-profile (scores below average are in bold typeface):

CO         CB         NW         MA         MS         NR         EA         NCO         EM         JM         TP         NCW

105        107        117        112         99        113        112        116        104        116        119        110.

In summary: average to above-average results in most neuropsychologic tests. The working diagnosis Specific disorder of arithmetical skills indicated by the results of the screening process could be disproved in the validation process.

Fig. 9: cMRI of proband Y.Z. Note the poor differentiation between cortex and white matter in the occipital region. T2-weighted images.

4.3.3 S.P.

Sex: male, age: 9 years, 6 months, first language: German.

Screening test results: errors in DRT 3: 21; score in DRE 3: 6.

Teacher‘s evaluation: German: 2; mathematics: 2.

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4.3.3.1 Clinico-neurological findings

Family history: No known neuropsychiatric disorders in the family. Both parents have a very good command of arithmetical tasks and had good grades in school mathematics. A 19 year-old half-sister of the proband from the mother‘s first marriage strongly disliked school mathematics, but had average grades. A 16 year-old half-brother from another father, born out of wedlock, is a mathematic prodigy and has an overall excellent academic performance.

Past medical history: Pregnancy originally was of twins, spontaneous abort of one fetus in the 3^rd month of gestation. Mother was then admitted as a risk-pregnancy to the hospital and put under mild sedation. Birth induced at term without perinatal complications. Apgar (1/5/10 min): 8/9/10. Birthweight: 4200 g, length at birth: 52 cm. Normal early childhood development. Developmental milestones met within normal temporal limits. Cerebral commotion in 1995 with mild posttraumatic dysfunction shown on EEG. Gradual worsening of mathematics grades in school (Mark 1 in the second grade, mark 2 in the first semester of third grade, mark 3 in the second semester of third grade.) No past surgical history.

Clinical examination: Macrocephalic skull configuration, mild right-convex facial skoliosis. Inward-strabism of the left eye. Otherwise normal clinical examination.

Neurological examination: mild deficits in fine-motor coordination in upper and lower extremities on both sides. Normal reflex status. No focal signs. Normal, age-appropriate neurological status.

Psychological status: Fully oriented and alert. Slow reactions towards stimuli, absent-minded, daydreaming. Shy, contact-avoiding, internalizing. No other significant findings in psychological status.

EEG: Age-appropriately matured wave pattern without residues of the mild posttraumatic dysfunction of the previous EEG.

VEP: Physiologic latency periods with normal amplitude bilaterally.

AEP: Physiologic latency periods bilaterally of most waves. Wave 3 markedly delayed on the left side, indicating a dysfunction in the left pontine area.

cMRI: Normal, age-appropriate cMRI.

4.3.3.2 Neuropsychological test results

Normal attention and perseverance as tested by the VDD. Swiftness above average.

Regular hand-lateralization towards right. Values in the average range for dynamic coordination. Accuracy and resting in the low average range. Diadochokinesia at the lowest testable limit.

In WISC-R-A most subtests in the high-average range. Vocabulary and visuo-constructive performance above average. Logical thinking, numeric short-term memory and detection of visual contexts in the average range. Calculation ability in the low-average range.

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V: 13                A: 9                S: 10                DSp: 11        BD: 12        PA 11.

Deficits in magnitude representation. No other significant problems in the test of number processing and calculation abilities.

NUCALC Test-profile (scores below average are in bold typeface):

CO         CB         NW         MA         MS         NR         EA         NCO         EM         JM         TP         NCW

70        107        109        111         89        108        110        101        103        102        107        76.

In summary: mostly above-average results in most neuropsychologic tests. The arithmetical skills are distinctly weaker, most likely due to an impaired magnitude representation. However, the discrepancy between the mathematical performance and the overall performance is not sufficient to meet the ICD-10 criteria for a Specific disorder of arithmetical skills.

4.3.4 T.H.

Sex: female, age: 9 years, 2 months, first language: German.

Screening test results: errors in DRT 3: 20; score in DRE 3: 1.

Teacher‘s evaluation: German: 2; mathematics: 2.

4.3.4.1 Clinico-neurological findings

Family history: No known neuropsychiatric disorders in the family. Parents divorced. Mother works as a teacher, does not report any problems with mathematics. Mother‘s parents are both teachers for mathematics. No known family history of learning difficulties.

Past medical history: Diagnosis of maternal cholestasis in the 27^th week of gestation, short hospital admission with ready clinical improvement. Birth at term. Length of labor: 4.5 hours, birthweight 3720 g, length at birth: 53 cm. Reflex-status diagnosed as pathological from 1 month of age. Delayed early childhood development: sitting upright from 10 months of age, first free steps with 16 months, first words with 18 months, first sentences at approximately 3 years. Diagnosis of a bilateral conduction hearing loss with 3 years and 8 months, treated with extracorporeal hearing aids with good success. Hearing loss stabile upon regular audiometric controls. No past surgical history.

Clinical examination: High palate, prognatia secondary to persistent thumb sucking. Inward-strabism of the right eye. Mild persistent dorsal positioning of the fingers (’Bajonettstellung‘). On the inside of the left thigh: 3x1.5 cm depigmentation. Otherwise normal clinical examination.

Neurological examination: mild deficits in fine-motor coordination in upper and lower extremities on both sides. Normal reflex status of the upper extremities. Patellar

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Psychological status: Fully oriented and alert. Friendly and cooperative young girl. Repeated problems in understanding verbal instruction, constantly attempts to lip-read. Tendency to overplaying lacks in understanding. No other significant findings in psychological status.

EEG: Age-appropriately matured wave pattern. Suspected left-hemispheric lesion with regard to a overall reduction of amplitude and frequency on that side.

VEP: Physiologic latency periods with normal amplitude bilaterally.

AEP(assessed without hearing aid): Physiologic latency periods waves 3 through 5 bilaterally. Wave 1 markedly delayed bilaterally, indicating a peripheral impairment of perception.

cMRI: Two small hyperintensities, one located subependymal on the lateral side, right of the trigonum (see figure 10), the other on the medial, occipital aspect of the left posterior horn (see figure 11). Otherwise normal, age-appropriate cMRI.

4.3.4.2 Neuropsychological test results

Normal attention and perseverance as tested by the VDD.

Regular hand-lateralization towards right. Values in the average range for dynamic coordination. Accuracy and resting in the low average range.

Due to the hearing impairment especially verbal tasks had to be presented slowly, sometimes repeatedly. Upon persistent trouble with understanding, tasks were against standard procedure presented in a written form. The proband worked cooperative and diligent but markedly slow. Overall intelligence homogeneously notably below average, verbal and visual task performance approximately equal.

WISC-R-A-IQ=76. Subtest-scores (scores below average are in bold typeface):

V:6                A: 6                S: 5                DSp: 8        BD: 6                PA: 7.

Basic deficit in magnitude representation evident problems in the test of number processing and calculation abilities, with marked uncertainties and plural errors in more complex calculation tasks, such as operations with larger numbers, subtractions, and multi-step text problems.

NUCALC Test-profile (scores below average are in bold typeface):

CO         CB         NW         MA         MS         NR         EA         NCO         EM         JM         TP         NCW

72        107        112        112         81        113        36        102        72        87        73          75 .

In summary: Multiple findings indicative of a primarily left-hemispheric impaired cerebral function. Homogeneously decreased mental capacity with marked

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Fig. 10: cMRI of proband T.H. Note the hyperintensity located subependymal on the lateral side right of the trigonum. T1-weighted image on left, T2-weighted image on right side.

Fig. 11: cMRI of proband T.H. Note the hyperintensity located on the medial, occipital aspect of the left posterior horn. T1-weighted image on left, T2-weighted image on right side. 4.3.5.D.B.

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Sex: male, age: 9 years, 8 months, first language: German.

Screening test results: errors in DRT 3: 22; score in DRE 3: 6.

Teacher‘s evaluation: German: 2; mathematics: 4.

4.3.4.3 Clinico-neurological findings

Family history: No known neuropsychiatric disorders in the family. Proband is child from the mother‘s first marriage, the father reportedly has little emotional understanding for him. Mother reports difficulties with mathematics throughout her time at school, always had to study extensively for average grades in mathematics. Has today command only of basic calculations. No other family history of learning problems.

Past medical history: Normal pregnancy and delivery. Birth at term without perinatal complications. Normal early childhood development. Developmental milestones met within normal temporal limits. Sleep irregularities since early childhood, needs two hours to fall asleep, talks, moves and sweats frequently at night-time, feels unrested in spite of adequate sleeping times. In the past six months frequent complaints of gastrointestinal discomfort and headaches. Highly motivated for school, increasing difficulties and deficits in mathematics notwithstanding. No past surgical history.

Clinical examination: Left-convex facial skoliosis. Otherwise normal clinical examination.

Neurological examination: mild deficits in fine-motor coordination in upper and lower extremities pronounced on the left side. Normal reflex status both extremities bilaterally. Otherwise age-appropriately normal neurological examination.

Psychological status: Fully oriented and alert. Friendly, but withdrawn boy. Shy, internalizing personality. No other significant findings in psychological status.

EEG: Age-appropriately matured wave pattern. Minor right-hemispheric lesion in the posterior temporal region.

VEP and AEP: Physiologic latency periods with normal amplitude bilaterally.

cMRI: Circumscribed leukomalacia in the white matter right of the trigonum with slight enlargement of the trigonum proximate to the lesion (see figures 12 and 13). Otherwise normal, age-appropriate cMRI.

4.3.4.4 Neuropsychological test results

Normal attention and perseverance as tested by the VDD. Proband worked on the VDD with markedly slowed speed.

Regular hand-lateralization towards right. Values in the average range for dynamic coordination. Accuracy and resting in the low average range. Diadochokinesia at the

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Very heterogeneous test profile in WISC-R-A, with an IQ in the low-average range, better performance on verbal tasks. Logical thinking is developed in the high-average range, the proband has an average vocabulary, but a calculation performance approximately 2 standard deviations below average. Visual performance was in the low-average range. Test profile consistent with a visuo-spatial processing deficit.

WISC-R-A-IQ=88. Subtest-scores (scores below average are in bold typeface):

 V:11                A: 8                S: 13                DSp: 9           BD: 6                PA: 6.

Basic deficit in magnitude representation and numerosity with marked uncertainties and plural errors on more complex calculation tasks in the test of number processing and calculation abilities, suggesting a relation to the weak spatial abilities. Proband is unable to check for plausibility even on relatively simple calculations (e.g. 12 + 6 = 16). Frequent use of back-up strategies when faced with calculation tasks. Better performance on mathematical tasks with a strong verbal component.

NUCALC Test-profile (scores below average are in bold typeface):

CO         CB         NW         MA         MS         NR         EA         NCO         EM         JM         TP         NCW

104        107        109        64         81        43        86        110        103        110        95        106.

In summary: All findings indicate a indicative of a right-hemispherically impaired cerebral function. The discrepancy between the mathematical performance and the overall performance meets the ICD-10 criteria for a Specific disorder of arithmetical skills. In the light of the proband‘s internalizing personality it seems likely that his increasing somatic complaints have a strong psychosomatic foundation. Therapeutic intervention, both in the educational and medical realm are necessary to avoid a worsening of his situation.

Fig.12.: cMRI of proband D.B. Note the lesion in the white matter, right of the trigonum with slight enlargement of the trigonum proximate to the lesion. The lesion is hypointense in the T1-weighted image (left) and hyperintense in the T2-weighed image (right).

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Fig.13.: cMRI of proband D.B., coronar slices of T1-weighed images. Note the slight enlargement of the trigonum, proximate to the lesion in the white matter, right of the trigonum.

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4.4 Discussion of the clinical and neuropsychological validation process

We faced many problems with regard to the validation process, most of them laid out in chapter 4.1. A further problem was the low response rate, of 12 contacted probands only 5 (41.4 %) agreed to further testing. Even with repeated contact through the proband‘s teachers and the elucidation of the possible benefits of the examination process without any cost for the probands, we could not achieve a higher response. This is a common phenomenon and a well-known obstacle for research in Germany.

Considering these predicaments, our results were substantial. Only one of our probands (Y.Z.) had an altogether average performance on the test of number processing and calculation abilities (NUCALC). The other four probands performed below the average range on one or more of its subtests when compared to very recent standardization data from 1995.

In three probands (M.W., Y.Z., D.B.) the teachers rating corresponded well with the neuropsychological examination data. But in the two other probands (S.P., T.H.) we found remarkable discrepancies between the proband's results of their clinical and neuropsychological examination and the teacher's rating of their students of three years. Our data did not support the hypothesis of a previous publication of our group that the teachers are most likely to detect a Specific disorder of arithmetical skills in their students Rüdiger, 1994 .

To our knowledge there are no published data of imaging studies for children with a Specific disorder of arithmetical skills, although there has been a comprehensive debate about the hemispheric involvement in the disorder. We found two very similar lesions in two different probands with a mathematical performance markedly below average, pronounced in the domain of magnitude representation. Only further investigations will able to show whether this finding is accidental or reproducible.

All tests and assessment methods utilized by us in the validation process yielded significant data, producing distinctive profiles of the probands. We dissent with the proposition that calculation difficulties should be exclusively considered as educational problems as stated by some authors Grissemann, 1996 . We agree with Shalev and Gross-Tsur that the working diagnosis of a Specific disorder of arithmetical skills should lead to a clinical and neuropsychological validation process Shalev &Gross-Tsur, 1993 . We would argue that such a validation is not only justified but should rather be obligatory before establishing the diagnosis.

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