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Persistence of developmental dyscalculia: What counts?
P
Persistence of developmental dyscalculia: What counts?
Results from a 3-year prospective follow-up study Ruth S. Shalev, MD, Orly Manor, PhD, Judith Auerbach, PhD, and Varda Gross-Tsur, MD
Objective: To study the natural history of developmental dyscalculia (DC), a specific learning disability affecting approximately 5% of the normal school age population and to identify factors that contribute to persistence.
Study design: Of a cohort of 3029 fourth-grade students, 185 children were classified as having DC; 140 participated in phase 1 in which they underwent IQ testing; arithmetic, reading, and writing evaluations; and an assessment for attention-deficit/hyperactivity disorder over a 3-year period. Three years later (phase 2), 88% of the children (123 of 140) were retested.
Results: The arithmetic scores of 95% of the 123 children with DC fell within the lowest quartile for their class. At phase 2, 47% (57 of 123) of the children were reclassified as having persistent DC, scoring in the lowest 5% for their age group (13 to 14 years old). Factors significantly associated with persistence of DC in a multivariate model were severity of the arithmetic disorder and arithmetic problems in siblings of the probands. Factors that were not associated with persistence included socioeconomic status, gender, the presence of another learning disability, and educational interventions. Conclusions: The outcome of DC is similar to that of other learning disabilities, with a persisting course in almost half of affected children; the remainder continue to perform poorly in arithmetic. The ultimate outcome of children with dyscalculia and the effect on education, employment, and psychologic wellbeing have yet to be determined. (J Pediatr 1998;133:358-62)
Learning disabilities affect an estimated 5% to 15% of children in the normal school population.1 The resources allocated to diagnose and alleviate the educational problems of these children are immense. Data regarding the etiology,
academic outcome, and utility of interventions are scarce. Developmental dyscalculia, a specific LD manifested by difficulty in acquiring arithmetic skills,2 is an example of an LD for which data on prognosis and usefulness of interventions
From the Neuropediatric Unit, Shaare Zedek Medical Center, Jerusalem, Israel; Braun School of Public Health and Community Medicine, Hebrew University-Hadassah, Jerusalem, Israel; and Department of Behavioral Sciences, Ben-Gurion University, Beer Sheva, Israel. Supported by the Israel Science Foundation. Submitted for publication July 16, 1997; revisions received Dec 19, 1997, and Mar 30, 1998; accepted Apr 7, 1998. Reprint requests: Ruth S. Shalev, MD, Neuropediatric Unit, Shaare Zedek Medical Center, POB 3235, Jerusalem, Israel 91031. Copyright © 1998 by Mosby, Inc. 0022-3476/98/$5.00 + 0 9/21/91051
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are lacking. Children with DC have arithmetic ability that falls below that expected for their age, IQ, and education and significantly affects activities of daily living.3 Studies have shown that DC affects approximately 2% to 6.5% of normal elementary school children,4-7 a prevalence sufficiently high to justify study.
See editorial, p. 320. There are indications that adequacy in arithmetic skills during childhood has an impact on future educational and professional achievement. There is a strong association between attainment of math skills at age 16 and the highest qualifications achieved by these children in adulthood,8 and a concomitant disability in arithmetic is one of the factors predicting poorer outcome in the academic, professional, and social spheres.9 ADHD CBCL DC LD
Attention-deficit/hyperactivity disorder Child Behavior Checklist Developmental dyscalulia Learning disability
The purposes of this study were to investigate the arithmetic ability and behavioral status of eighth-grade children diagnosed with DC in fifth grade and to determine the short-term persistence of DC and the factors that may contribute to persistence.
METHODS Phase 1 In a cohort of 3029 fourth-grade children attending mainstream city schools, 185 were classified as having DC, of
THE JOURNAL OF PEDIATRICS VOLUME 133, NUMBER 3 whom 140 were studied extensively.7 These children were identified by using a 2-stage screening process. In the first stage all fourth graders took an arithmetic achievement test assessing counting skills, knowledge of number facts, and ability to solve complex arithmetic exercises and word problems. Those scoring in the lowest 20% (n = 600) on this test entered the second stage; 555 of these children (45 could not be located), now in fifth grade (10 to 11 years old), received an individually administered arithmetic battery, standardized according to results of age-matched control subjects. A child was classified as having DC if his or her full-scale IQ was 80 or higher and if the score achieved on the second arithmetic test was equal to or less than the mean for normal children 2 grades lower (ie, third grade for our sample).2 The performance of at least 2 years below grade level coincided with the lowest 5th percentile of the scores for actual school grade. Among the 185 children classified as having DC, the parents of 140 consented to further testing including reading and writing evaluations, Wechsler Intelligence Scale for Children-Revised, neuropsychologic tests, and the Child Behavior Checklist7 and provided information regarding socioeconomic status.
Phase 2 At follow-up 3 years later, when the children were 13 to 14 years old, 123 members of the original cohort (88%) were restudied. The participating children underwent reevaluation of their arithmetic, reading, and spelling proficiency. Their parents completed the CBCL10 and a questionnaire to identify other family members with academic difficulty. The arithmetic battery used for both evaluations was based on a neurocognitive model developed by McCloskey et al.11 The test included questions on number comprehension, production, and calculation (number facts and complex arithmetic exercises) and is described in the Appendix. There were no word problems to avoid confusion with difficulties in reading comprehension. For eighth graders tested at phase 2, exercises on
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decimals and fractions were added to include material that was grade-appropriate for them. Otherwise, the tests were identical. Those eighth-grade children whose score on the arithmetic battery remained in the lowest 5th percentile of the normative group were identified as having persistent DC. Children with scores above the lowest 5th percentile were identified as having nonpersistent DC. Reading and spelling skills were retested to document the spectrum of learning problems affecting our population with DC. For the reading evaluation, the children read a paragraph aloud. The test was timed, and errors in word recognition were scored. The spelling test was a timed dictation of a short paragraph. The arithmetic, reading, and spelling evaluations were standardized on 77 normal eighth graders, who served as the control group for phase 2 of the study. The sampling method2 ensured representation of the populations’ various social and economic groups and school types. A score below the 5th percentile of control subjects was used to determine whether a child with dyscalculia also had reading or spelling problems.12 Reading problems were present in 7% of the children and spelling problems in 14%; 4% had a combination of both. Attention and other behavioral problems were reassessed in eighth grade on the basis of parental report (CBCL). Information from teachers was not available.
Statistical Analysis Comparisons among children with persistent DC, those with nonpersistent DC, and control subjects were carried out on the arithmetic scores by using analysis of variance. Tukey’s method was used for multiple pairwise comparisons, and the Kruskal-Wallis test was used when the distribution was skewed.18 Two-tailed t tests were used on the differences in IQ and behavioral measures between children with persistent and those with nonpersistent DC. Adjustment for multiple comparisons was made.14 Comparisons on categorical variables were carried out by chi square tests or Fisher’s exact test in cases of small numbers.15 The association between a series of predicting variables and
the presence or absence of persistent DC was assessed by a logistic regression model.16 The explained variation for logistic regression was measured by the squared correlation between the observed and predicted values.17
RESULTS We found that 47% (n = 58) of the 123 children diagnosed with DC in fifth grade had persistent DC in eighth grade (Table). The remaining 65 scored above the 5th percentile, no longer fulfilling criteria for DC; they were classified as having nonpersistent DC. The overall performance of all the 123 children was poor; 95% of them scored within the lowest quartile of normal control subjects. All 3 groups (persistent DC, nonpersistent DC, and control) performed on a similar level for number facts and complex exercises in addition. For almost all other measures of arithmetic, children with persistent DC had the poorest performance, followed by that of children with nonpersistent DC, and both groups were generally inferior to the control group. An example of the difference in performance was in division, of which 56% of control subjects had achieved mastery as compared with 11% of children with nonpersistent DC and none (0%) of the children with persistent DC (P < .001). Only 22% of children with persistent DC had mastered complex subtraction compared with 54% of those with nonpersistent DC and 75% of control subjects (P < .001). However, for mastery of addition, the differences were smaller: 83% of children with persistent DC, 94% of those with nonpersistent DC, and 97% of control children (P < .01). For the persistent DC group, the score in the arithmetic battery at time of diagnosis 3 years earlier was 71.5 ± 7.2, whereas that of the nonpersistent DC group was 74.2 ± 6.4 (P = .03). Parents of children in whom persistent DC ultimately developed reported significantly more attention problems on the CBCL (6.32 ± 4.32) than parents of children with nonpersistent DC (4.49 ± 3.60, P < .05). The same pattern was seen for anxiety problems (5.59 ± 4.84 vs 4.00 ± 359
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Table. Arithmetic scores (mean number of errors) of children with persistent DC, children with nonpersistent DC, and normal control subjects
Arithmetic score Number facts† Addition (5) Subtraction (5) Multiplication (5) Division (5) Complex arithmetic† Addition (10) Subtraction (9) Multiplication (10) Division (11) Decimals† Addition (5) Fractions† Addition (5) Subtraction (2) Multiplication (3) Division (1)
Children with PDC (n = 57)
Children with NPDC (n = 66)
Control subjects (n = 77)
P value*
Pairwise comparison
0.09 ± 0.28 0.36 ± 0.58 1.71 ± 1.15 1.33 ± 0.94
0.11 ± 0.31 0.20 ± 0.44 0.74 ± 0.73 0.45 ± 0.64
0.04 ± 0.19 0.14 ± 0.39 0.26 ± 0.52 0.35 ± 0.70
NS <.05‡ <.001‡ <.001‡
P=N=C P>C P>N>C P > N, C
1.47 ± 2.11 2.72 ± 1.80 6.55 ± 2.47 9.48 ± 1.56
0.97 ± 1.40 1.35 ± 1.46 3.91 ± 3.01 6.83 ± 2.81
0.99 ± 1.59 0.70 ± 1.04 2.34 ± 2.67 3.09 ± 3.22
NS <.001‡ <.001‡ <.001‡
P=N=C P>N>C P>N>C P>N>C
2.57 ± 1.17
1.34 ± 1.16
0.87 ± 1.23
<.001‡
P > N, C
4.38 ± 1.11 2.00 ± 0.00 2.26 ± 0.89 0.64 ± 0.48
2.28 ± 1.85 1.51 ± 0.79 1.58 ± 1.03 0.60 ± 0.49
0.73 ± 1.34 0.61 ± 0.85 0.94 ± 1.09 0.26 ± 0.44
<.001‡ <.001‡ <.001‡ <.001‡
P>N>C P>N>C P>N>C P, N > C
PDC, Persistent DC; NPDC, nonpersistent DC; P, persistent; N, nonpersistent; C, control; NS, not significant. *P values for comparisons between the 3 groups. †Maximum score. ‡After adjustment for multiple comparison for all statistical tests carried out within each arithmetic domain (eg, number facts, complex arithmetic, etc), the results remained significant at the 5% level.
3.67, respectively; P < .05). In eighth grade the only behavioral domain that remained significant at the 5% level after adjustment for multiple comparison was attention. Although the performance IQ was similar for both children with persistent DC (100.4 ± 12.2) and those with nonpersistent DC (104.2 ± 11.0), the fullscale IQ was significantly lower in the persistent DC group (95.9 ± 9.5 compared with 100.3 ± 9.3, P < .01), possibly because of the lower score achieved on the verbal IQ (92.8 ± 8.9 compared with 96.9 ± 11.4). To determine whether the lower verbal IQ in the persistent DC group was just a reflection of a more profound arithmetic disorder seen in their lower score on the WISC-R arithmetic subtest (7.3 ± 2.0 for persistent DC and 7.9 ± 2.0 for nonpersistent DC), we recalculated the IQ scores without the arithmetic subtest. According to these adjusted IQ scores, the differences for the verbal IQ became nonsignificant, and for the full-scale IQ, the 360
difference was borderline (0.06), indicating the relative contribution of the arithmetic disability to the lower IQ values. (A complete data set is available from the authors.) Children with persistent DC tended to receive more educational interventions than those with nonpersistent DC. This was reflected by the number of children receiving special education in school and those receiving any type of arithmetic assistance. Forty-seven percent (n = 27) of children with persistent DC had received some arithmetic intervention, whereas only 17% (n = 17) of the children with nonpersistent DC had (P < .05). Fortysix percent (n = 25) of siblings of children with persistent DC had received arithmetic tutorials compared with 28% (n = 17) of siblings of children with nonpersistent DC (P < .05). Socioeconomic status, gender, and the presence or absence of an associated problem in reading or spelling did not differentiate between persistent DC and nonpersistent DC. However, only a relatively small
percentage of the children with DC had a reading or spelling disability (7% and 14%, respectively; 4% both) as determined by screening procedures. Logistic regression analysis was used to assess the strength of the associations with those variables significantly correlated with persistence of DC. A model including 2 variables, the arithmetic score on diagnosis and siblings who received arithmetic tutorials, indicated that both variables were significantly associated with the persistence or nonpersistence of DC. To control for the effect of IQ (ie, adjusted full-scale without arithmetic subtest), we used a second model in which the separate effects of the variables arithmetic score on diagnosis and siblings who received arithmetic tutorials were examined, and both remained significant. However, in this model the effect of IQ became nonsignificant (P > .10). A final model including all 4 variables shown to have significant association with persistent or nonpersistent DC (siblings who received arithmetic tutori-
THE JOURNAL OF PEDIATRICS VOLUME 133, NUMBER 3 als, arithmetic score on diagnosis, adjusted full-scale IQ, and attention problems) showed that only the arithmetic score on diagnosis and siblings receiving arithmetic tutorials had significant and equivalent contribution in the model, and the contribution of both accounted for about 10% of the variation. Specifically, the odds of a study child with siblings receiving arithmetic tutorials to have persistent DC were 2.5 times that of a child with siblings who had not received such tutorials; the odds of a child with a given score on the arithmetic test to have persistent DC were 1.9 times that of a child with a score 10 points greater (of a total of 100 points).
DISCUSSION This study is a prospective, longitudinal follow-up of DC. The methodological criteria we used were faithful to those recommended for a follow-up assessment in the field of LD.18,19 Because there are no other longitudinal studies of DC, we compared our results with developmental dyslexia, another developmental disorder. Rutter et al,20 in the Isle of Wight study, found that the majority of 9-year-old children with dyslexia were poor readers 5 years later. In contrast, a study by Shaywitz et al21 has shown that less than 20% of children identified as having developmental dyslexia in first grade would be dyslexic 4 years later. Perhaps the difference in outcome between the 2 studies may be the age at which the children are diagnosed as having a learning problem. For children just beginning elementary school, as in the study by Shaywitz et al,21 the pace at which learning skills are acquired may be secondary to the variability of normal development. For older children, as in the study by Rutter et al,20 the normal range of variability in reading is more restricted, and therefore dyslexia assessed at this age represents a true LD. Our children with DC, who are in the same age range as those in the study by Rutter et al,20 demonstrated a similar degree of persistence of their LD, possibly reflecting the more restricted range of normal variability at this age.
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We found that difficulty with arithmetic in siblings of probands with DC was a significant risk factor for persistent DC. Longitudinal studies on attentiondeficit/hyperactivity disorder have likewise documented the importance of familial factors, whether genetic or environmental, in the persistence of ADHD.22,23 In this group of children with DC, behavioral dysfunction was more prominent in those children with persistent DC. The only behavioral domain that was significantly different from the normative sample across DC groups and assessment periods was the domain of attention problems. In both assessment periods, attention problems were more severe in children with persistent DC as compared with children with nonpersistent DC. The co-occurrence of attention problems and LDs, including DC, has been well documented.24,25 Although pathophysiologic mechanisms may be operative for both the behavioral and cognitive disorders, particularly for those children who are more severely impaired, the negative effect of prolonged school failure on behavior must also be considered. Recognition of DC as an LD, awareness of its prevalence, stability over time, and association with other developmental problems is important to the pediatrician. Often, it is the pediatrician who is called on to diagnose and confirm the presence of cognitive problems, discuss the implications with the family, and manage or oversee the overall treatment—pharmacologic, educational, and behavioral. Because arithmetic disorders are no less frequent than reading disabilities, often interacting with behavioral problems, appropriate testing should be part of the developmental-cognitive-behavioral assessment. Certain reservations need to be emphasized when evaluating our results. First, although the results are based on a large sample of 123 children, 12% of the cohort could not be reexamined at the end of the 3-year follow-up period. Second, for reasons of consistency, we continued to use the lowest 5th percentile of the normative group to determine the presence of DC.33,12,26 We realize that
the 5% cutoff excludes children who could be considered learning disabled by virtue of the gap between a high intellectual potential and mediocre arithmetic ability.27 Another weakness relates to the limited assessments of reading, writing, and ADHD; our interest in these domains was secondary because arithmetic ability was the main focus of the study. DC, at least over the short term, is a stable cognitive disability, which may have a heritable biologic etiology, a finding that has recently received support from a twin study of DC.28 Clearly, other genetic-familial studies are necessary to delineate the relative contribution of biologic factors, if any, to the etiology of DC and those that may be derived from adverse social circumstances.
REFERENCES 1. Nass R, Koch D. Innate specialization of emotion: temperament differences in children with early left versus right brain damage. In: Amir N, Rapin I, Branski D, editors. Pediatric neurology: behavior and cognition of the child with brain dysfunction. Basel: Karger; 1991. p. 1-17. 2. Shalev RS, Manor O, Amir N, GrossTsur V. Acquisition of arithmetic in normal children: assessment by a cognitive model of dyscalculia. Dev Med Child Neurol 1993;35:593-601. 3. American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 4th ed. Washington (DC): American Psychiatric Association; 1994. p. 37-121. 4. Badian NA. Arithmetic and nonverbal learning. In: Myklebust HR, editor. Progress in learning disabilities, Vol 5. New York: Grune and Stratton; 1983. p. 253-64. 5. Lewis C, Hitch GJ, Walker P. The prevalence of specific arithmetic difficulties and specific reading difficulties in 9 to 10 year old boys and girls. J Child Psychol Psychiatry 1994;35:283-92. 6. von Aster M. Developmental dyscalculia in children: review of the literature and clinical validation. Acta Paedopsychiatrica 1994;56:169-78. 7. Gross-Tsur V, Manor O, Shalev RS. Developmental dyscalculia: prevalence and demographic features. Dev Med Child Neurol 1996;38:25-33. 8. Fogelman K. Growing up in Great Britain. London: Macmillan; 1983. p. 88-95. 9. Hartzell HE, Compton C. Learning disabilities: 10 year follow up. Pediatrics 1984;74:1058-64.
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10. Achenbach TM. Manual for the Child Behavior Checklist/4-18 and 1991 Profile. Burlington (VT): University of Vermont Department of Psychiatry, 1991. 11. McCloskey M, Caramazza A, Basili A. Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain Cognition 1985;4:171-96. 12. Reynolds CR. Critical measurement issues in learning disabilities. J Special Ed 1984;18:451-76. 13. Miller RG Jr. Beyond ANOVA. New York: Wiley; 1986. p. 71-3. 14. Hommel G. A stage wise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 1988;75:383-6. 15. Fleiss JL. Statistical analysis of rates and proportions. New York: Wiley; 1981. p. 24. 16. Hosmer DW, Lemeshow SL. Applied logistic regression. New York: Wiley; 1989. p. 25-30. 17. Mittlbock M, Schemper M. Explained variation for logistic regression. Stat Med 1996;15:1987-97. 18. Schonhaut S, Satz P. Prognosis for children with learning disabilities: a review of follow-up studies. In: Rutter M, editor. Developmental neuropsychology. New York: Guilford Press; 1983. p. 542-63. 19. Horn WF, O’Donnell JP, Vitulano LA. Long-term follow-up studies of learningdisabled persons. J Learn Dis 1983;16: 542-55. 20. Rutter M, Tizard J, Yule W, Graham P, Whitmore K. Research report: Isle of Wight studies 1964-1974. Pyschol Med 1976;6:313-32. 21. Shaywitz SE, Escobar MD, Shaywitz BA, Fletcher JM, Mackuck R. Evidence that dyslexia may represent the lower tail of a normal distribution of reading ability. N Engl J Med 1992;324:145-50. 22. Biederman J, Faraone S, Milberger S, Curtis S, Chen L, Marrs A, et al. Predictors of persistence and remission of ADHD into adolescence: results from a four-year prospective follow-up study. J Am Acad Child Adolesc Psychiatry 1996;35:343-51. 23. Biederman J, Faraone S, Mick E, Spencer T, Wilens T, Kiely K, et al. High risk for attention deficit hyperactivity
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24.
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disorder among children of parents with childhood onset of the disorder: a pilot study. Am J Psychiatry 1995;152:431-5. Shalev RS, Auerbach J, Gross-Tsur V. Developmental dyscalculia: attentional and behavioral aspects. J Child Psychol Psychiatry 1995;35:1261-8. Harris JC. Learning disorders. In: Developmental neuropsychiatry. Vol II. Assessment, diagnosis, and treatment of developmental disorders. Oxford: Oxford University Press; 1995. p. 142-80. Gordon HW. The effect of “right brain/left brain” cognitive profiles on school achievement. In: Molfese DL, Segalowitz SJ, editors. Brain lateralization in children. New York: Guilford Press; 1988. p. 237-55. Hammill DD. On defining learning disabilities: an emerging consensus. J Learn Dis 1990;23:74-85. Alarcon M, DeFries JC, Light JC, Pennington BF. A twin study of mathematics disability. J Learn Dis 1997;30:617-23.
APPENDIX Arithmetic Battery Part 1: Number Comprehension and Production Tests devised primarily for number comprehension A. Matching written Arabic numerals to quantities. In a multiple-choice task, the children matched the appropriate quantity of drawn stimuli (dots, dashes, and triangles) to a single written Arabic numeral. There were 5 such tasks, and the numbers ranged from 3 to 12. B. Comprehension of quantities. Two groups of nonnumerical stimuli of different shapes (dots, dashes, etc) were drawn on 5 cards. The number of stimuli on each card ranged from 2 to 7. The children were asked to indicate whether a partic-
ular group had more, fewer, or the same number of stimuli. C. Comprehension of numerical values. The children were presented with 5 pairs of written Arabic numerals, and for each pair they had to identify which number was higher or which was lower. D. Serial order. Children were presented with a sequence of written numbers, which they had to put in order, from highest to lowest. Tasks designed for number production A. Counting. The children were asked to count aloud numbers of stimuli (dots, dashes, etc) appearing in rows or groups. The number of stimuli ranged from 5 to 14. There were 5 such tasks. B. Production (writing) of numbers. The children were instructed to copy and read 5 numbers, between 1 and 4 digits long, and write 5 other 1- to 4-digit numbers to dictation. Part 2: Calculation: Number Facts The children were required to do 20 simple addition, subtraction, multiplication, and division exercises. Part 3: Calculation: Complex Exercises The children had to compute complex written arithmetic problems (addition, subtraction, multiplication, and division). The first 8 exercises were addition and subtraction, and the remaining 8 were multiplication and division. Part 4: Decimals and Fractions There were 2 complex addition and 2 complex subtraction exercises requiring knowledge of decimals. There were 10 simple exercises with fractions: 5 addition, 2 subtraction, 3 addition, and 1 division. In 7 of the exercises, a common denominator had to be determined to solve the problem.
Persistence of developmental dyscalculia: What counts?
Results from a 3-year prospective follow-up study Ruth S. Shalev, MD, Orly Manor, PhD, Judith Auerbach, PhD, and Varda Gross-Tsur, MD
Objective: To study the natural history of developmental dyscalculia (DC), a specific learning disability affecting approximately 5% of the normal school age population and to identify factors that contribute to persistence.
Study design: Of a cohort of 3029 fourth-grade students, 185 children were classified as having DC; 140 participated in phase 1 in which they underwent IQ testing; arithmetic, reading, and writing evaluations; and an assessment for attention-deficit/hyperactivity disorder over a 3-year period. Three years later (phase 2), 88% of the children (123 of 140) were retested.
Results: The arithmetic scores of 95% of the 123 children with DC fell within the lowest quartile for their class. At phase 2, 47% (57 of 123) of the children were reclassified as having persistent DC, scoring in the lowest 5% for their age group (13 to 14 years old). Factors significantly associated with persistence of DC in a multivariate model were severity of the arithmetic disorder and arithmetic problems in siblings of the probands. Factors that were not associated with persistence included socioeconomic status, gender, the presence of another learning disability, and educational interventions. Conclusions: The outcome of DC is similar to that of other learning disabilities, with a persisting course in almost half of affected children; the remainder continue to perform poorly in arithmetic. The ultimate outcome of children with dyscalculia and the effect on education, employment, and psychologic wellbeing have yet to be determined. (J Pediatr 1998;133:358-62)
Learning disabilities affect an estimated 5% to 15% of children in the normal school population.1 The resources allocated to diagnose and alleviate the educational problems of these children are immense. Data regarding the etiology,
academic outcome, and utility of interventions are scarce. Developmental dyscalculia, a specific LD manifested by difficulty in acquiring arithmetic skills,2 is an example of an LD for which data on prognosis and usefulness of interventions
From the Neuropediatric Unit, Shaare Zedek Medical Center, Jerusalem, Israel; Braun School of Public Health and Community Medicine, Hebrew University-Hadassah, Jerusalem, Israel; and Department of Behavioral Sciences, Ben-Gurion University, Beer Sheva, Israel. Supported by the Israel Science Foundation. Submitted for publication July 16, 1997; revisions received Dec 19, 1997, and Mar 30, 1998; accepted Apr 7, 1998. Reprint requests: Ruth S. Shalev, MD, Neuropediatric Unit, Shaare Zedek Medical Center, POB 3235, Jerusalem, Israel 91031. Copyright © 1998 by Mosby, Inc. 0022-3476/98/$5.00 + 0 9/21/91051
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are lacking. Children with DC have arithmetic ability that falls below that expected for their age, IQ, and education and significantly affects activities of daily living.3 Studies have shown that DC affects approximately 2% to 6.5% of normal elementary school children,4-7 a prevalence sufficiently high to justify study.
See editorial, p. 320. There are indications that adequacy in arithmetic skills during childhood has an impact on future educational and professional achievement. There is a strong association between attainment of math skills at age 16 and the highest qualifications achieved by these children in adulthood,8 and a concomitant disability in arithmetic is one of the factors predicting poorer outcome in the academic, professional, and social spheres.9 ADHD CBCL DC LD
Attention-deficit/hyperactivity disorder Child Behavior Checklist Developmental dyscalulia Learning disability
The purposes of this study were to investigate the arithmetic ability and behavioral status of eighth-grade children diagnosed with DC in fifth grade and to determine the short-term persistence of DC and the factors that may contribute to persistence.
METHODS Phase 1 In a cohort of 3029 fourth-grade children attending mainstream city schools, 185 were classified as having DC, of
THE JOURNAL OF PEDIATRICS VOLUME 133, NUMBER 3 whom 140 were studied extensively.7 These children were identified by using a 2-stage screening process. In the first stage all fourth graders took an arithmetic achievement test assessing counting skills, knowledge of number facts, and ability to solve complex arithmetic exercises and word problems. Those scoring in the lowest 20% (n = 600) on this test entered the second stage; 555 of these children (45 could not be located), now in fifth grade (10 to 11 years old), received an individually administered arithmetic battery, standardized according to results of age-matched control subjects. A child was classified as having DC if his or her full-scale IQ was 80 or higher and if the score achieved on the second arithmetic test was equal to or less than the mean for normal children 2 grades lower (ie, third grade for our sample).2 The performance of at least 2 years below grade level coincided with the lowest 5th percentile of the scores for actual school grade. Among the 185 children classified as having DC, the parents of 140 consented to further testing including reading and writing evaluations, Wechsler Intelligence Scale for Children-Revised, neuropsychologic tests, and the Child Behavior Checklist7 and provided information regarding socioeconomic status.
Phase 2 At follow-up 3 years later, when the children were 13 to 14 years old, 123 members of the original cohort (88%) were restudied. The participating children underwent reevaluation of their arithmetic, reading, and spelling proficiency. Their parents completed the CBCL10 and a questionnaire to identify other family members with academic difficulty. The arithmetic battery used for both evaluations was based on a neurocognitive model developed by McCloskey et al.11 The test included questions on number comprehension, production, and calculation (number facts and complex arithmetic exercises) and is described in the Appendix. There were no word problems to avoid confusion with difficulties in reading comprehension. For eighth graders tested at phase 2, exercises on
SHALEV ET AL
decimals and fractions were added to include material that was grade-appropriate for them. Otherwise, the tests were identical. Those eighth-grade children whose score on the arithmetic battery remained in the lowest 5th percentile of the normative group were identified as having persistent DC. Children with scores above the lowest 5th percentile were identified as having nonpersistent DC. Reading and spelling skills were retested to document the spectrum of learning problems affecting our population with DC. For the reading evaluation, the children read a paragraph aloud. The test was timed, and errors in word recognition were scored. The spelling test was a timed dictation of a short paragraph. The arithmetic, reading, and spelling evaluations were standardized on 77 normal eighth graders, who served as the control group for phase 2 of the study. The sampling method2 ensured representation of the populations’ various social and economic groups and school types. A score below the 5th percentile of control subjects was used to determine whether a child with dyscalculia also had reading or spelling problems.12 Reading problems were present in 7% of the children and spelling problems in 14%; 4% had a combination of both. Attention and other behavioral problems were reassessed in eighth grade on the basis of parental report (CBCL). Information from teachers was not available.
Statistical Analysis Comparisons among children with persistent DC, those with nonpersistent DC, and control subjects were carried out on the arithmetic scores by using analysis of variance. Tukey’s method was used for multiple pairwise comparisons, and the Kruskal-Wallis test was used when the distribution was skewed.18 Two-tailed t tests were used on the differences in IQ and behavioral measures between children with persistent and those with nonpersistent DC. Adjustment for multiple comparisons was made.14 Comparisons on categorical variables were carried out by chi square tests or Fisher’s exact test in cases of small numbers.15 The association between a series of predicting variables and
the presence or absence of persistent DC was assessed by a logistic regression model.16 The explained variation for logistic regression was measured by the squared correlation between the observed and predicted values.17
RESULTS We found that 47% (n = 58) of the 123 children diagnosed with DC in fifth grade had persistent DC in eighth grade (Table). The remaining 65 scored above the 5th percentile, no longer fulfilling criteria for DC; they were classified as having nonpersistent DC. The overall performance of all the 123 children was poor; 95% of them scored within the lowest quartile of normal control subjects. All 3 groups (persistent DC, nonpersistent DC, and control) performed on a similar level for number facts and complex exercises in addition. For almost all other measures of arithmetic, children with persistent DC had the poorest performance, followed by that of children with nonpersistent DC, and both groups were generally inferior to the control group. An example of the difference in performance was in division, of which 56% of control subjects had achieved mastery as compared with 11% of children with nonpersistent DC and none (0%) of the children with persistent DC (P < .001). Only 22% of children with persistent DC had mastered complex subtraction compared with 54% of those with nonpersistent DC and 75% of control subjects (P < .001). However, for mastery of addition, the differences were smaller: 83% of children with persistent DC, 94% of those with nonpersistent DC, and 97% of control children (P < .01). For the persistent DC group, the score in the arithmetic battery at time of diagnosis 3 years earlier was 71.5 ± 7.2, whereas that of the nonpersistent DC group was 74.2 ± 6.4 (P = .03). Parents of children in whom persistent DC ultimately developed reported significantly more attention problems on the CBCL (6.32 ± 4.32) than parents of children with nonpersistent DC (4.49 ± 3.60, P < .05). The same pattern was seen for anxiety problems (5.59 ± 4.84 vs 4.00 ± 359
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Table. Arithmetic scores (mean number of errors) of children with persistent DC, children with nonpersistent DC, and normal control subjects
Arithmetic score Number facts† Addition (5) Subtraction (5) Multiplication (5) Division (5) Complex arithmetic† Addition (10) Subtraction (9) Multiplication (10) Division (11) Decimals† Addition (5) Fractions† Addition (5) Subtraction (2) Multiplication (3) Division (1)
Children with PDC (n = 57)
Children with NPDC (n = 66)
Control subjects (n = 77)
P value*
Pairwise comparison
0.09 ± 0.28 0.36 ± 0.58 1.71 ± 1.15 1.33 ± 0.94
0.11 ± 0.31 0.20 ± 0.44 0.74 ± 0.73 0.45 ± 0.64
0.04 ± 0.19 0.14 ± 0.39 0.26 ± 0.52 0.35 ± 0.70
NS <.05‡ <.001‡ <.001‡
P=N=C P>C P>N>C P > N, C
1.47 ± 2.11 2.72 ± 1.80 6.55 ± 2.47 9.48 ± 1.56
0.97 ± 1.40 1.35 ± 1.46 3.91 ± 3.01 6.83 ± 2.81
0.99 ± 1.59 0.70 ± 1.04 2.34 ± 2.67 3.09 ± 3.22
NS <.001‡ <.001‡ <.001‡
P=N=C P>N>C P>N>C P>N>C
2.57 ± 1.17
1.34 ± 1.16
0.87 ± 1.23
<.001‡
P > N, C
4.38 ± 1.11 2.00 ± 0.00 2.26 ± 0.89 0.64 ± 0.48
2.28 ± 1.85 1.51 ± 0.79 1.58 ± 1.03 0.60 ± 0.49
0.73 ± 1.34 0.61 ± 0.85 0.94 ± 1.09 0.26 ± 0.44
<.001‡ <.001‡ <.001‡ <.001‡
P>N>C P>N>C P>N>C P, N > C
PDC, Persistent DC; NPDC, nonpersistent DC; P, persistent; N, nonpersistent; C, control; NS, not significant. *P values for comparisons between the 3 groups. †Maximum score. ‡After adjustment for multiple comparison for all statistical tests carried out within each arithmetic domain (eg, number facts, complex arithmetic, etc), the results remained significant at the 5% level.
3.67, respectively; P < .05). In eighth grade the only behavioral domain that remained significant at the 5% level after adjustment for multiple comparison was attention. Although the performance IQ was similar for both children with persistent DC (100.4 ± 12.2) and those with nonpersistent DC (104.2 ± 11.0), the fullscale IQ was significantly lower in the persistent DC group (95.9 ± 9.5 compared with 100.3 ± 9.3, P < .01), possibly because of the lower score achieved on the verbal IQ (92.8 ± 8.9 compared with 96.9 ± 11.4). To determine whether the lower verbal IQ in the persistent DC group was just a reflection of a more profound arithmetic disorder seen in their lower score on the WISC-R arithmetic subtest (7.3 ± 2.0 for persistent DC and 7.9 ± 2.0 for nonpersistent DC), we recalculated the IQ scores without the arithmetic subtest. According to these adjusted IQ scores, the differences for the verbal IQ became nonsignificant, and for the full-scale IQ, the 360
difference was borderline (0.06), indicating the relative contribution of the arithmetic disability to the lower IQ values. (A complete data set is available from the authors.) Children with persistent DC tended to receive more educational interventions than those with nonpersistent DC. This was reflected by the number of children receiving special education in school and those receiving any type of arithmetic assistance. Forty-seven percent (n = 27) of children with persistent DC had received some arithmetic intervention, whereas only 17% (n = 17) of the children with nonpersistent DC had (P < .05). Fortysix percent (n = 25) of siblings of children with persistent DC had received arithmetic tutorials compared with 28% (n = 17) of siblings of children with nonpersistent DC (P < .05). Socioeconomic status, gender, and the presence or absence of an associated problem in reading or spelling did not differentiate between persistent DC and nonpersistent DC. However, only a relatively small
percentage of the children with DC had a reading or spelling disability (7% and 14%, respectively; 4% both) as determined by screening procedures. Logistic regression analysis was used to assess the strength of the associations with those variables significantly correlated with persistence of DC. A model including 2 variables, the arithmetic score on diagnosis and siblings who received arithmetic tutorials, indicated that both variables were significantly associated with the persistence or nonpersistence of DC. To control for the effect of IQ (ie, adjusted full-scale without arithmetic subtest), we used a second model in which the separate effects of the variables arithmetic score on diagnosis and siblings who received arithmetic tutorials were examined, and both remained significant. However, in this model the effect of IQ became nonsignificant (P > .10). A final model including all 4 variables shown to have significant association with persistent or nonpersistent DC (siblings who received arithmetic tutori-
THE JOURNAL OF PEDIATRICS VOLUME 133, NUMBER 3 als, arithmetic score on diagnosis, adjusted full-scale IQ, and attention problems) showed that only the arithmetic score on diagnosis and siblings receiving arithmetic tutorials had significant and equivalent contribution in the model, and the contribution of both accounted for about 10% of the variation. Specifically, the odds of a study child with siblings receiving arithmetic tutorials to have persistent DC were 2.5 times that of a child with siblings who had not received such tutorials; the odds of a child with a given score on the arithmetic test to have persistent DC were 1.9 times that of a child with a score 10 points greater (of a total of 100 points).
DISCUSSION This study is a prospective, longitudinal follow-up of DC. The methodological criteria we used were faithful to those recommended for a follow-up assessment in the field of LD.18,19 Because there are no other longitudinal studies of DC, we compared our results with developmental dyslexia, another developmental disorder. Rutter et al,20 in the Isle of Wight study, found that the majority of 9-year-old children with dyslexia were poor readers 5 years later. In contrast, a study by Shaywitz et al21 has shown that less than 20% of children identified as having developmental dyslexia in first grade would be dyslexic 4 years later. Perhaps the difference in outcome between the 2 studies may be the age at which the children are diagnosed as having a learning problem. For children just beginning elementary school, as in the study by Shaywitz et al,21 the pace at which learning skills are acquired may be secondary to the variability of normal development. For older children, as in the study by Rutter et al,20 the normal range of variability in reading is more restricted, and therefore dyslexia assessed at this age represents a true LD. Our children with DC, who are in the same age range as those in the study by Rutter et al,20 demonstrated a similar degree of persistence of their LD, possibly reflecting the more restricted range of normal variability at this age.
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We found that difficulty with arithmetic in siblings of probands with DC was a significant risk factor for persistent DC. Longitudinal studies on attentiondeficit/hyperactivity disorder have likewise documented the importance of familial factors, whether genetic or environmental, in the persistence of ADHD.22,23 In this group of children with DC, behavioral dysfunction was more prominent in those children with persistent DC. The only behavioral domain that was significantly different from the normative sample across DC groups and assessment periods was the domain of attention problems. In both assessment periods, attention problems were more severe in children with persistent DC as compared with children with nonpersistent DC. The co-occurrence of attention problems and LDs, including DC, has been well documented.24,25 Although pathophysiologic mechanisms may be operative for both the behavioral and cognitive disorders, particularly for those children who are more severely impaired, the negative effect of prolonged school failure on behavior must also be considered. Recognition of DC as an LD, awareness of its prevalence, stability over time, and association with other developmental problems is important to the pediatrician. Often, it is the pediatrician who is called on to diagnose and confirm the presence of cognitive problems, discuss the implications with the family, and manage or oversee the overall treatment—pharmacologic, educational, and behavioral. Because arithmetic disorders are no less frequent than reading disabilities, often interacting with behavioral problems, appropriate testing should be part of the developmental-cognitive-behavioral assessment. Certain reservations need to be emphasized when evaluating our results. First, although the results are based on a large sample of 123 children, 12% of the cohort could not be reexamined at the end of the 3-year follow-up period. Second, for reasons of consistency, we continued to use the lowest 5th percentile of the normative group to determine the presence of DC.33,12,26 We realize that
the 5% cutoff excludes children who could be considered learning disabled by virtue of the gap between a high intellectual potential and mediocre arithmetic ability.27 Another weakness relates to the limited assessments of reading, writing, and ADHD; our interest in these domains was secondary because arithmetic ability was the main focus of the study. DC, at least over the short term, is a stable cognitive disability, which may have a heritable biologic etiology, a finding that has recently received support from a twin study of DC.28 Clearly, other genetic-familial studies are necessary to delineate the relative contribution of biologic factors, if any, to the etiology of DC and those that may be derived from adverse social circumstances.
REFERENCES 1. Nass R, Koch D. Innate specialization of emotion: temperament differences in children with early left versus right brain damage. In: Amir N, Rapin I, Branski D, editors. Pediatric neurology: behavior and cognition of the child with brain dysfunction. Basel: Karger; 1991. p. 1-17. 2. Shalev RS, Manor O, Amir N, GrossTsur V. Acquisition of arithmetic in normal children: assessment by a cognitive model of dyscalculia. Dev Med Child Neurol 1993;35:593-601. 3. American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 4th ed. Washington (DC): American Psychiatric Association; 1994. p. 37-121. 4. Badian NA. Arithmetic and nonverbal learning. In: Myklebust HR, editor. Progress in learning disabilities, Vol 5. New York: Grune and Stratton; 1983. p. 253-64. 5. Lewis C, Hitch GJ, Walker P. The prevalence of specific arithmetic difficulties and specific reading difficulties in 9 to 10 year old boys and girls. J Child Psychol Psychiatry 1994;35:283-92. 6. von Aster M. Developmental dyscalculia in children: review of the literature and clinical validation. Acta Paedopsychiatrica 1994;56:169-78. 7. Gross-Tsur V, Manor O, Shalev RS. Developmental dyscalculia: prevalence and demographic features. Dev Med Child Neurol 1996;38:25-33. 8. Fogelman K. Growing up in Great Britain. London: Macmillan; 1983. p. 88-95. 9. Hartzell HE, Compton C. Learning disabilities: 10 year follow up. Pediatrics 1984;74:1058-64.
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10. Achenbach TM. Manual for the Child Behavior Checklist/4-18 and 1991 Profile. Burlington (VT): University of Vermont Department of Psychiatry, 1991. 11. McCloskey M, Caramazza A, Basili A. Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain Cognition 1985;4:171-96. 12. Reynolds CR. Critical measurement issues in learning disabilities. J Special Ed 1984;18:451-76. 13. Miller RG Jr. Beyond ANOVA. New York: Wiley; 1986. p. 71-3. 14. Hommel G. A stage wise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 1988;75:383-6. 15. Fleiss JL. Statistical analysis of rates and proportions. New York: Wiley; 1981. p. 24. 16. Hosmer DW, Lemeshow SL. Applied logistic regression. New York: Wiley; 1989. p. 25-30. 17. Mittlbock M, Schemper M. Explained variation for logistic regression. Stat Med 1996;15:1987-97. 18. Schonhaut S, Satz P. Prognosis for children with learning disabilities: a review of follow-up studies. In: Rutter M, editor. Developmental neuropsychology. New York: Guilford Press; 1983. p. 542-63. 19. Horn WF, O’Donnell JP, Vitulano LA. Long-term follow-up studies of learningdisabled persons. J Learn Dis 1983;16: 542-55. 20. Rutter M, Tizard J, Yule W, Graham P, Whitmore K. Research report: Isle of Wight studies 1964-1974. Pyschol Med 1976;6:313-32. 21. Shaywitz SE, Escobar MD, Shaywitz BA, Fletcher JM, Mackuck R. Evidence that dyslexia may represent the lower tail of a normal distribution of reading ability. N Engl J Med 1992;324:145-50. 22. Biederman J, Faraone S, Milberger S, Curtis S, Chen L, Marrs A, et al. Predictors of persistence and remission of ADHD into adolescence: results from a four-year prospective follow-up study. J Am Acad Child Adolesc Psychiatry 1996;35:343-51. 23. Biederman J, Faraone S, Mick E, Spencer T, Wilens T, Kiely K, et al. High risk for attention deficit hyperactivity
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APPENDIX Arithmetic Battery Part 1: Number Comprehension and Production Tests devised primarily for number comprehension A. Matching written Arabic numerals to quantities. In a multiple-choice task, the children matched the appropriate quantity of drawn stimuli (dots, dashes, and triangles) to a single written Arabic numeral. There were 5 such tasks, and the numbers ranged from 3 to 12. B. Comprehension of quantities. Two groups of nonnumerical stimuli of different shapes (dots, dashes, etc) were drawn on 5 cards. The number of stimuli on each card ranged from 2 to 7. The children were asked to indicate whether a partic-
ular group had more, fewer, or the same number of stimuli. C. Comprehension of numerical values. The children were presented with 5 pairs of written Arabic numerals, and for each pair they had to identify which number was higher or which was lower. D. Serial order. Children were presented with a sequence of written numbers, which they had to put in order, from highest to lowest. Tasks designed for number production A. Counting. The children were asked to count aloud numbers of stimuli (dots, dashes, etc) appearing in rows or groups. The number of stimuli ranged from 5 to 14. There were 5 such tasks. B. Production (writing) of numbers. The children were instructed to copy and read 5 numbers, between 1 and 4 digits long, and write 5 other 1- to 4-digit numbers to dictation. Part 2: Calculation: Number Facts The children were required to do 20 simple addition, subtraction, multiplication, and division exercises. Part 3: Calculation: Complex Exercises The children had to compute complex written arithmetic problems (addition, subtraction, multiplication, and division). The first 8 exercises were addition and subtraction, and the remaining 8 were multiplication and division. Part 4: Decimals and Fractions There were 2 complex addition and 2 complex subtraction exercises requiring knowledge of decimals. There were 10 simple exercises with fractions: 5 addition, 2 subtraction, 3 addition, and 1 division. In 7 of the exercises, a common denominator had to be determined to solve the problem.