Research in Developmental Disabilities 33 (2012) 1128–1135

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Research in Developmental Disabilities

Mathematical problems in children with developmental coordinationdisorder

Stefanie Pieters a,*, Annemie Desoete a, Hilde Van Waelvelde b, Ruth Vanderswalmen c,Herbert Roeyers a

a Department of Experimental Clinical and Health Psychology, Ghent University, Belgiumb Rehabilitation Sciences and Physiotherapy, Ghent University, Belgiumc Department of Speech and Language Pathology, University college Arteveldehogeschool Ghent, Belgium

A R T I C L E I N F O

Article history:

Received 7 February 2012

Accepted 9 February 2012

Available online 7 March 2012

Keywords:

Developmental coordination disorder

Number fact retrieval

Procedural calculation

Co-morbidity

Developmental delay

A B S T R A C T

Developmental coordination disorder (DCD) is a heterogeneous disorder, which is often

co-morbid with learning disabilities. However, mathematical problems have rarely been

studied in DCD. The aim of this study was to investigate the mathematical problems in

children with various degrees of motor problems. Specifically, this study explored if the

development of mathematical skills in children with DCD is delayed or deficient. Children

with DCD performed significantly worse for number fact retrieval and procedural

calculation in comparison with age-matched control children. Moreover, children with

mild DCD differed significantly from children with severe DCD on both number fact

retrieval and procedural calculation. In addition, we found a developmental delay of 1 year

for number fact retrieval in children with mild DCD and a developmental delay of 2 years

in children with severe DCD. No evidence for a mathematical deficit was found. Diagnostic

implications are discussed.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Developmental coordination disorder (DCD) is defined in the Diagnostic and Statistical Manual of Mental Disorders(DSM-IV-TR; American Psychiatric Association [APA], 2000) as a significant impairment in the development of motorcoordination, which interferes with academic achievement or activities of daily living. A prevalence of 1.7% in school-agedchildren has been reported with a higher prevalence among boys than girls (Lingam, Hunt, Golding, Jongmans, & Emond,2009).

It is well-known that children with DCD often have co-morbid learning disabilities (Alloway & Archibald, 2008; Dewey,Kaplan, Crawford, & Wilson, 2002; Jongmans, Smits-Engelsman, & Schoemaker, 2003; Visser, 2003) including mathematicallearning disabilities. Whereas co-morbidity with reading and spelling problems has frequently been investigated (e.g.,Cheng, Chen, Tsai, Shen, & Cherng, 2011; Dewey et al., 2002; Fletcher-Flinn, Elmes, & Strugnell, 1997; Lingam et al., 2010),mathematical problems have only been studied indirectly in DCD (Alloway & Archibald, 2008). However, didacticalprinciples such as starting with the manipulation of concrete materials before asking to solve semi-concrete or abstract tasksin a number problem format, illustrate the importance of motor skills to develop mathematical skills. Moreover motoractivities such as seriation and classification (Nunes et al., 2007; Piaget & Inhelder, 1956; Stock, Desoete, & Roeyers, 2010)

* Corresponding author at: Department of Experimental Clinical and Health Psychology, Ghent, University, Henri Dunantlaan 2, 9000 Ghent, Belgium.

Tel.: +32 09 264 94 14, fax: +32 09 264 64 89.

E-mail address: Stefanie.Pieters@UGent.be (S. Pieters).

0891-4222/$ – see front matter � 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ridd.2012.02.007

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–1135 1129

and counting (Aunola, Leskinen, Lerkkanen, & Nurmi, 2004; Gersten, Jordan, & Flojo, 2005; Hannula, Rasanen, & Lehtinen,2007; Stock, Desoete, & Roeyers, 2009) seem necessary for early mathematics and the mental representation of numberconcepts. Mental representations lead to the understanding of simple operations such as additions and subtractions (Geary,1994; Luo, Jose, Huntsinger, & Pigott, 2007).

The existing research about mathematics in children with DCD mainly investigated working memory. These studiesestablished how working memory affects learning in DCD (e.g., mathematics) in comparison to children with otherdevelopmental disorders, such as learning disabilities or speech and language disabilities (Alloway, 2007; Alloway &Archibald, 2008; Alloway & Temple, 2007). They found that children with DCD had problems with both working memory aswell as short-term memory which was significantly associated with literacy and numeracy. Another approach to studylearning in DCD is to look at the automatization of children. The automatization deficit hypothesis states that deficits in thecerebellum could lead to general automatization and balance problems (Fawcett & Nicolson, 1992; Nicolson, Fawcett, &Dean, 2001). One might argue that the problems that children with DCD are confronted with, are due to deficits withautomatization (see Visser, 2003) explaining the co-morbidity between motor and mathematical problems. Automatizationproblems are also described in the semantic memory subtype of mathematical learning disabilities (MLD), focusing ondeficits in number fact retrieval (Geary, 1993, 2004). Besides the semantic memory subtype of MLD, there is also evidence fora procedural subtype in MLD (Geary, 1993, 2004; Temple, 1991; Wilson, Revkin, Cohen, Cohen, & Dehaene, 2006). Adifferentiation in mathematical skills between semantic memory skills (number fact retrieval) and procedural knowledge,seems indicated when exploring mathematical problems in children with DCD. Furthermore, some important similaritiesbetween the profile of children with MLD and younger children were described (Chan & Ho, 2010; Geary, 2004; Torbeyns,Verschaffel, & Ghesquiere, 2004). It might be interesting to investigate if this can be extended to children with DCD: are themathematical problems of children with DCD the result of a developmental delay or rather a deficit? To the best of ourknowledge, this has not yet been investigated.

Until recently, there was little consensus about the clinical cut-off scores to diagnose DCD. Recently, two differentrecommendations appeared, suggesting two different cut-off scores. Whereas the Leeds Consensus Statement (Sugden,Chambers, & Utley, 2006) proposed percentile 5 as the cut-off point, the European Academy of Childhood Disability (Blank,Smits-Engelsman, Polatajko, & Wilson, 2012) was less restrictive and recommended percentile 15. Given these differences,questions arise about whether the characteristics of DCD vary as a function of different performance criteria used byclinicians or researchers. As it concerns children with heterogeneous motor deficits, it might be that these children have adifferent cognitive profile. One might expect that children with mild DCD have better mathematical skills in comparison tochildren with severe DCD as previous research has been shown that (fine) motor skills predicts mathematics achievementover time (Luo et al., 2007; Pagani, Fitzpatrick, Archambault, & Janosz, 2010) and an increasing severity of motor problemsalso increases the range and severity of co-morbid problems (e.g., Jongmans et al., 2003; Rasmussen & Gillberg, 2000).However, we need to be careful with overgeneralization, as it might be that not all children with DCD, regardless of thedegree, have problems with mathematics. Therefore, analyses of group and individual differences will be conducted asrecommended by Geuze (2010) and Lachance and Mazzocco (2006).

To conclude, we aim to investigate whether (a) children with DCD have problems on the domains of number factretrieval and procedural calculation; (b) problems can be described as a deficit or as a mild/severe developmental delay; (c)there is a difference on mathematics between children with mild and severe DCD; (d) individual differences besides groupdifferences exist.

2. Methods

2.1. Participants

Forty-three 9-year-old children (14 girls) with DCD participated in this study. Children were recruited by purposefulsampling and reputational case selection through referral by psychologists, speech therapists and physicians inmultidisciplinary rehabilitation, special education and centres for developmental disorders and through newsletteradvertisements and letters to teachers and parents distributed in special education schools. Children were classified ashaving DCD if they met the four diagnostic criteria as described in the DSM-IV-TR (American Psychiatric Association [APA],2000). They all had poor motor coordination substantially below expected (criterion A) confirmed by testing with theMovement Assessment Battery for Children 2 (M-ABC 2; Henderson & Sugden, 2007; Smits-Engelsman, 2010). In some of thesubsequent analyses, the group of children with DCD was divided in two groups depending on their motor abilities. Childrenwith mild DCD (n = 17) scored between percentile 6 and 15 (i.e., having a total test score between 62 and 68) and childrenwith severe DCD (n = 26) scored �percentile 5 (i.e., having a total test score � 61) on the Movement Assessment Battery forChildren 2 (M-ABC 2; Henderson & Sugden, 2007). Functional impairment in daily life or in academic achievement (criterionB) was confirmed for both groups of children, since all of them received physiotherapy for their clumsiness or scored at orbelow percentile 15 for writing quality or writing speed on the Systematic Screening of Handwriting Difficulties (Smits-Engelsman et al., 2005). Moreover, the motor problems of the children with DCD were not due to a general medical conditionor epilepsy (criterion C), which was confirmed by a questionnaire filled out by the parents. Finally (criterion D), all childrenwere typically achieving on intelligence (IQ � 80) measured with the short version of the Wechsler Intelligence Scale forChildren (WISC-III; Kort et al., 2002; Wechsler, 1991).

Table 1

Means of the four groups on descriptive and diagnostic measures.

Measure DCD (n = 43) Control children,

matched on age

(n = 41)

Control children, 1 year

younger (n = 56)

Control children,

2 years younger,

matched on manual

dexterity (n = 33)

F(3, 169)

M (SD) M (SD) M (SD) M (SD)

Age 112.16 a (5.07) 113.02 a (7.27) 102.17 b (4.03) 93.03 c (4.07) 121.99***

SESa 39.76 b (11.45) 48.94 a (8.46) 42.50 bc (10.16) 48.17 ac (8.02) 8.54***

IQ 96.02 b (11.26) 106.63 a (13.85) 103.37 a (12.52) 106.42 a (9.36) 6.98***

M-ABC 2 Total

standard score

4.81 b (1.76) 10.41 a (2.10) 11.44 a (1.89) 11.55 a (2.03) 117.90***

Note: Means with different letters are significantly different by post hoc tests with p < .05. DCD = developmental coordination disorder; SES = socio-

economic status; IQ = intelligence quotient.a Based on the Hollingshead index.

*** p < .001.

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–11351130

Control children were recruited through letters to parents distributed in mainstream schools. Parents reported noconcerns about their child’s level of motor skill and none of the children was reported to have an intellectual disability or amedical disorder. All 130 control children scored above the 15th percentile (i.e., a total test score � 71) on the M-ABC 2(Henderson & Sugden, 2007; Smits-Engelsman, 2010) and had an IQ � 80 based upon the short version of the WISC-III(Gregoire, 2000; Kort et al., 2002; Wechsler, 1991). To be able to investigate the developmental delay and deficit hypotheses,three different control groups with different ages (C1, C2 and C3) were included. The first control group (C1) included 41 (23girls) age-matched children (9 years). Fifty-six children (38 girls) were included in the second control group (C2) and were 1year younger (8 years). Finally, the third control group (C3) consisted of 33 children (15 girls) who were 2 years younger (7years) and who were matched on manual dexterity, as measured with the M-ABC 2, by means of recalculating the standardscores of the children with DCD as if they were 2 years younger, F(1, 74) = 2.93, p = .091.

The Hollingshead Index Score (Hollingshead, 1975) was calculated as a measure of socio-economic status (SES) whichwas obtained by questionnaires filled out by the parents. The mean social status in the total sample ranged from 17.5 to 64.5(M = 44.42, SD = 10.38). More detailed background information for all groups is presented in Table 1. Using one-way analysisof variance (ANOVA), significant differences in age, IQ and SES between children were found. When comparing the fourgroups on gender with a Pearson’s chi-square test, significant differences between groups were also found, x2(3) = 13.00,p = .005.

2.2. Tests and materials

2.2.1. Intelligence

To estimate IQ, four subtests of the Wechsler Intelligence Scale for Children (WISC-III; Kort et al., 2002; Wechsler, 1991),namely ‘similarities’, ‘picture arrangement’, ‘block design’ and ‘vocabulary’ were used. This abbreviated WISC-III has beenshown to have good psychometric qualities (Gregoire, 2000).

2.2.2. Mathematics

The Kortrijk Arithmetic Test Revision (Kortrijkse Rekentest-Revisie [KRT-R]; Baudonck et al., 2006) measures mentalcomputation (e.g., 456 + 99 = . . .) and number system knowledge (e.g., order the numbers from greatest to least and use theappropriate symbol: 625, 371, 890) without a time limit. The psychometric value has been demonstrated on a sample of3246 Dutch-speaking children (Baudonck et al., 2006).

The Arithmetic Number Fact Test (Tempo Test Rekenen [TTR]; De Vos, 1992) is a test consisting of arithmetic number factproblems (e.g., 2 + 5 = . . .; 9 � 2 = . . .). Children have to solve as many additions and subtractions as possible within 2 min.Standardization was done in Flanders on a sample of 10,059 children (Ghesquiere & Ruijssenaars, 1994).

2.2.3. Motor skills

The Movement Assessment Battery for Children 2 (M-ABC 2; Henderson & Sugden, 2007) provides an assessment of theeveryday motor competence of children between the ages of 3 and 16 years. As items change with age, the appropriate ageband (7–10 years) was applied in this study. The test includes eight subtests across three different domains: ‘manualdexterity’ (placing pegs, threading a lace and drawing trail), ‘aiming and catching’ (catching with two hands and throwingbeanbag onto mat) and ‘balance’ (one-board balance, walking heel-to-toe forwards and hopping on mats) and generates anoverall motor impairment score besides a score for the separate domains. The M-ABC 2 has good reliability and validity(Henderson & Sugden, 2007). In this study, the Dutch norms were used (Smits-Engelsman, 2010).

The Systematic Screening of Handwriting Difficulties (in Dutch: Systematische opsporing van schrijfmotorischeproblemen [SOS]) measures quality and speed of handwriting by copying a standard text within 5 min on an unruled paper(Smits-Engelsman et al., 2005). Handwriting quality is evaluated on six domains: fluency in letter formation; fluency in

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–1135 1131

connections between letters; letter height; regularity of letter height; space between words and straightness or regularity ofthe sentence. Handwriting speed is determined by counting the number of letters written in 5 min. Dutch norms were usedin this study, which are based upon a reference group of 860 children. The SOS has good test–retest, inter- and intra-raterreliability (Van Waelvelde, Hellinckx, Peersman, & Smits-Engelsman, in press).

2.3. Procedure

Ethical approval for this study was provided by the Ethical Committee of Ghent University. After written parental consentwas obtained, each child was evaluated individually for several hours by one examiner who was blind to group division. Themeasures were part of a longer battery of cognitive and achievement tests which were always conducted in the same order. Ifnecessary, breaks were provided.

3. Results

Pearson correlation coefficients were calculated to explore a possible relationship between IQ, SES and gender and thedependent measures. A significant correlation was found between IQ on the one hand and the TTR (r = .30, p < .001) andthe KRT-R total score (r = .45, p < .001) on the other hand. SES correlated also significantly with the TTR (r = .38, p < .001)and the KRT-R total score (r = .39, p < .001). As a result, analyses of the dependent measures were also conducted with IQand SES as covariates in the analyses. Gender will not be taken into account as no significant correlations with any of thedomains within mathematics were found.

3.1. Mathematical problems in DCD? Is this a mild/severe developmental delay or a deficit?

An ANOVA was conducted with the raw score for addition and subtraction on the TTR as a dependent variable and groupmembership (DCD, C1, C2 or C3) as an independent variable. Children with DCD performed significantly lower in comparisonto age-matched control children and control children of 1 year younger, but equal to control children of 2 years younger.Means and standard deviations for the performance of the four groups on the TTR with post hoc tests are displayed in Table 2.Furthermore, as the TTR has a time limit, we also covaried for writing speed as measured with the SOS. When covarying forwriting speed, IQ and SES, group differences remained significant and post hoc analyses did not change significantly. Thecovariates writing speed, F(1, 168) = 18.27, p < .001, h2

P ¼ :10, and SES, F(1, 167) = 9.08, p = .003, h2P ¼ :05, were significant

while IQ was not, F(1, 167) = 2.82, p = .095.For the KRT-R, it was only possible to investigate probable differences between DCD and age-matched control children as

different versions were applied, depending on the age of the child and the time period in which the test was conducted.Different ANOVA’s were conducted with the percentile score for number system knowledge, mental computation and totalscore as dependent variables and group membership (DCD or C1) as an independent variable. Means and standard deviationsfor the performance of both groups on the KRT-R and a summary of the ANOVA’s are displayed in Table 2. For the KRT-R, weonly covaried for SES and IQ. It was not necessary to covary for writing speed as this test has no time limit. The covariates SESand IQ were significant in all the analyses (for KRT-R total; respectively, F(1, 80) = 13.11, p = .001, h2

P ¼ :14 and F(1,80) = 13.04, p = .001, h2

P ¼ :14). For the KRT-R there were some violations of normality, but the results of the nonparametrictests confirmed those of the parametric tests.

Repeated measures ANOVA showed that both children with DCD as well as typically achieving children performedsignificantly worse for subtraction than for addition (on the TTR, number fact retrieval) and significantly worse for mental

Table 2

Comparison of the children with DCD with control children matched on age, 1 year younger and 2 years younger on the TTR and the KRT-R.

Test DCD (n = 43) Control children,

matched on age

(n = 41)

Control children,

1 year younger

(n = 56)

Control children,

2 years younger,

matched on manual

dexterity (n = 33)

F h2P

M (SD) M (SD) M (SD) M (SD)

TTR number fact

retrievala

29.19 c (8.48) 43.34 a (6.97) 35.86 b (8.40) 29.09 c (7.89) F(3, 169) = 28.49*** .34

KRT-R number

system knowledgeb

14.88 (23.44) 56.15 (31.28) – – – – F(1, 82) = 47.10*** .37

KRT-R mental

computationb

8.81 (12.73) 49.56 (28.25) – – – – F(1, 82) = 73.79*** .47

KRT-R total scoreb 10.84 (17.69) 52.88 (30.05) – – – – F(1, 82) = 61.74*** .43

Note: Means with different letters are significantly different by post hoc tests with p < .05. DCD = developmental coordination disorder; TTR = Arithmetic

Number Fact Test; KRT-R = Kortrijk Arithmetic Test Revision.a Raw scores: solved simple additions and subtractions on 2 min.b Different versions and therefore percentile scores.

*** p < .001.

Table 3

Repeated measures comparing addition and subtraction (TTR) and number system knowledge and mental computation (KRT-R) in children with DCD and

typically achieving children.

Test Mathematical domain DCD (n = 43) Typically achieving

(n = 130)

F h2P

M (SD) M (SD)

TTR Additiona 15.35 (4.26) 18.80 (4.97) F(1, 171) = 20.28*** .11

Subtractiona 13.84 (4.72) 17.70 (5.09)

KRT-R Number system knowledgeb 14.88 (23.44) 58.97 (26.82) F(1, 171) = 14.71*** .08

Mental computationb 8.81 (12.73) 50.98 (28.91)

Note: DCD = developmental coordination disorder; TTR = Arithmetic Number Fact Test; KRT-R = Kortrijk Arithmetic Test Revision.a Based upon raw scores.b Different versions and therefore percentile scores.

*** p < .001.

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–11351132

computation than for number system knowledge (on the KRT-R, procedural calculation). This difference was similar for bothgroups, because the interaction effect Number fact retrieval x Group was not significant, F(1, 171) = 0.50, p = .479, and theinteraction effect Procedural calculation � Group was not significant, F(1, 171) = 0.27, p = .602. For repeated measures, meansand standard deviations, we refer to Table 3.

3.2. Difference on mathematics between children with severe and mild DCD?

ANOVA’s revealed no significant differences between children with severe DCD and children with mild DCD in age, F(1,41) = 0.25, p = .618, in IQ, F(1, 41) = 0.01, p = .987, or in SES, F(1, 41) = 0.03, p = .876. The only significant difference betweenthese groups was the M-ABC 2 total standard score, F(1, 41) = 50.11, p < .001, h2

P ¼ :55.Children with severe DCD performed significantly lower in comparison to children with mild DCD on raw score for

addition and subtraction on the TTR, but there was no significant difference between the two groups when controlled forwriting speed, F(1, 40) = 1.69, p = .201. The effect of the covariate writing speed was significant, F(1, 40) = 10.35, p = .003,h2

P ¼ :21. ANOVA’s also revealed that children with severe DCD performed significantly worse in comparison to children withmild DCD on KRT-R number system knowledge, KRT-R mental computation and KRT-R total score. For the KRT-R, there weresome violations of normality, but the results of the nonparametric tests confirmed those of the parametric tests. ANOVA’s,means and standard deviations for the performance of both groups on the TTR and the KRT-R are displayed in Table 4.

An ANOVA revealed that the profile of children with severe DCD on the TTR (M = 26.92, SD = 7.56) was comparable tochildren of 2 years younger (M = 29.09, SD = 7.89), as no significant differences were found, F(1, 57) = 1.14, p = .290. Childrenwith mild DCD (M = 32.65, SD = 8.87) had a profile on the TTR which was comparable to children of 1 year younger (M = 35.86,SD = 8.40), as no significant differences between those two groups were found, F(1, 71) = 1.86, p = .177.

3.3. Individual differences?

Not all children with mild/severe DCD had problems with mathematics, as can be seen in Table 5. Although there aredifferences in means, there is wide variation within each group as children have scores within all ranges: clinical, subclinicaland average scores. The proportion of children with severe DCD scoring in the clinical range (pc 1–5) on the TTR number factretrieval test (x2(1) = 4.80; p = .030) and on the KRT-total score (x2(1) = 7.09; p = .010), was significantly higher incomparison with the proportion of clinical scores in children with mild DCD. Severe number fact retrieval problems (pc 1–5)were found in 56% of the total sample of children with DCD and severe problems for procedural calculation (pc 1–5) werefound in 65% of the children with DCD.

Table 4

Comparison of the children with mild DCD and severe DCD on the TTR and the KRT-R.

Test Mild DCD (n = 17) Severe DCD (n = 26) F(1, 41) h2P

M (SD) M (SD)

TTR number fact retrievala 32.65 (8.87) 26.92 (7.56) 5.14* .11

KRT-R number system knowledgeb 23.59 (27.62) 9.19 (18.70) 4.17* .09

KRT-R mental computationb 15.88 (15.46) 4.19 (7.95) 10.66** .21

KRT-R total scoreb 19.41 (22.12) 5.23 (11.41) 7.65** .16

Note: DCD = developmental coordination disorder; TTR = Arithmetic Number Fact Test; KRT-R = Kortrijk Arithmetic Test Revision.a Based upon raw scores for addition and subtraction.b Different versions and therefore percentile scores.

* p < .05.

** p < .01.

Table 5

The distribution of mathematical scores in children with mild DCD and severe DCD.

Measure Mild DCD (n = 17) Severe DCD (n = 26)

pc 1–5 pc 6–16 pc 17–25 pc > 25 pc 1–5 pc 6–16 pc 17–25 pc > 25

n % n % n % n % n % n % n % n %

TTR number fact retrieval 6 35.3 4 23.5 2 11.8 5 29.4 18 69.3 3 11.5 2 7.7 3 11.5

KRT-R number system

knowledge

6 35.3 4 23.5 2 11.8 5 29.4 17 65.4 5 19.2 1 3.8 3 11.5

KRT-R mental computation 7 41.2 1 5.9 4 23.5 5 29.4 22 84.6 2 7.7 1 3.8 1 3.8

KRT-R total score 7 41.2 3 17.6 3 17.6 4 23.5 21 80.8 3 11.5 1 3.8 1 3.8

Note: DCD = developmental coordination disorder; TTR = Arithmetic Number Fact Test; KRT-R = Kortrijk Arithmetic Test Revision.

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–1135 1133

4. Discussion

The present study was designed to expand upon the knowledge about mathematics in children with DCD. As such, wesought to add to the existing literature in four ways.

The first aim of the present study was to investigate if children with DCD have problems on the domain of number factretrieval and procedural calculation. The study revealed that children with DCD have problems on both domains. Researchabout reading and spelling in children with DCD (e.g., Fletcher-Flinn et al., 1997; Lingam et al., 2010) found that children withDCD also have problems in both domains. From our data, it can be concluded that the scholastic problems they areconfronted with, can be extended to the domain of mathematics. More in detail, we found problems in both number factretrieval and procedural calculation (involving both number system knowledge and mental computation). Children withDCD seem to have problems with both arithmetic facts that are ‘easy problems’ (e.g., 4 + 5 = . . .) as well as with more difficultproblems, such as mental computation. These more difficult problems require more complex procedural knowledge andother psychological functions, such as attention and working memory, to perform sequential execution of algorithms(Ashcraft, 1992; McCloskey, 1992). Due to our cross-sectional design, it was impossible to draw conclusions about cause andeffect. Automatization problems might be a possible explanation as stressed by Visser (2003). However, the finding thatthese children also have problems with number system knowledge might assume that there is more than only anautomatization problem. More research is definitely needed.

A second main goal of this study was to determine if problems could be described as a deficit or as a mild/severedevelopmental delay. We found evidence that children with DCD have a developmental delay for number fact retrieval astheir profile is similar to that of children who are 2 years younger. Moreover, we found that children with DCD have moreproblems with subtraction than addition and more problems with mental computation than number system knowledge,which was exactly the same profile in comparison to typically achieving children without motor problems. Although bothbehavioural findings are in favour of the developmental delay hypothesis, more experimental research might be interesting.

Investigating whether there is a difference on mathematics between children with severe and mild DCD, was the thirdaim of the present study. We found significant differences between both groups on both procedural calculation as well asnumber fact retrieval, except when we covaried for writing speed. This last finding suggests that a small part of themathematical problems can for some children be explained by difficulties to write down their results. However, the effectsize when covarying for writing speed was small (h2

P ¼ :04) Besides the difference between those two groups, we also lookedat their profile in comparison to the different control groups. Whereas children with severe DCD had a developmental delayof 2 years for number fact retrieval, the fact retrieval delay in children with mild DCD was smaller (1 year). We cannotcompare our study with others, as to the best of our knowledge mathematical problems in children with different degrees ofmotor problems has not been investigated yet. However, there are some studies investigating reading differences betweenchildren with mild and severe DCD and they found no significant differences between these two groups (Dewey et al., 2002;Kadesjo & Gillberg, 1999) except for writing (i.e., proofreading, punctuation and capitalization and word usage) (Dewey et al.,2002). One possible explanation for these different results could be that mathematics is not comparable to reading (andwriting). Mathematics is mainly based upon number fact retrieval and the use of procedures, while reading and spelling ismainly a connection between phonemes and graphemes. Another possible explanation could be the use of different criteria,which makes studies difficult to compare. For instance, in the study from Dewey et al. (2002) a lower IQ and a less stringentcut-off in the motor assessment for the mild and severe DCD group was used and it was not verified if children had difficultiesin daily life.

The fourth research question explored the heterogeneity or the existence of individual differences besides groupdifferences. Our data revealed that children with DCD are a rather heterogeneous group concerning their mathematicalskills. Problems with mathematics occur in some, but not all, children with DCD. However, most children with DCD havemathematical problems. Children with severe mathematical problems may have a co-morbid mathematical learningdisability, if they meet all diagnostic criteria. Especially the criterion of resistance to instruction will be important to considerin these children (Fuchs et al., 2007; Geary, 2011) in order to determine if they have a mathematical learning disability aswell or if this is not the case.

S. Pieters et al. / Research in Developmental Disabilities 33 (2012) 1128–11351134

This study has limitations. We acknowledge that this study was conducted with a clinical and not with a populationsample, which increases the chance for a potential bias towards a higher severity of co-morbid mathematical problems.Furthermore, in this study a considerable amount of children with DCD were attending special education (56%). Furtherresearch should certainly elaborate on children with DCD in regular schools. A third shortcoming in this study was the factthat children with DCD were not matched on IQ with the typically achieving children. This was not surprising, as twosubtests of the WISC-III also include a motor component (namely block design and picture arrangement) and for instance,block design has been shown to be a good discriminator of children with DCD from typically achieving children (Alloway,2007).

Further longitudinal and neuropsychological research is necessary to reveal underlying processes to gain insight intothe co-morbidity between DCD and MLD. Besides looking at the developmental delay in mathematics in children with DCDon a behavioural level (based upon mathematical assessment), it might also be interesting to investigate this at aneuropsychological level.

This study also has some clinical implications. It seems that co-morbidity is rather the rule than the exception (Kaplan,Wilson, Dewey, & Crawford, 1998; Pieters et al., 2012) and this suggests that a multidisciplinary diagnostic evaluation shouldalso include a mathematical assessment. Therapists should be aware that the mathematical development in children withDCD may be delayed by 2 years. Furthermore, our findings underscore the need for clear cut-off criteria, as the cognitiveprofile is quite different between children with mild and severe DCD with respect to mathematics. It is recommended to usecut-off scores cautiously, in research as well as in diagnostic assessment and therapy, and to be aware that the chosen cut-offcriteria can have (indirect) implications on prevalence but also on possible co-morbid conditions.

5. Conclusions

To conclude, a substantial proportion of children with DCD have problems with mathematics (number fact retrieval andprocedural calculation). Both children with mild as well as children with severe motor disabilities have problems on thedomain of mathematics, but this is more obvious in the group of children with severe DCD who demonstrated adevelopmental delay of 2 years for number fact retrieval.

Acknowledgements

This article was written as a part of the first author’s doctoral work. This research was supported by grants from the GhentUniversity Special Research Fund. The authors gratefully thank all children and their parents for their cooperation.

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