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Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities

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Title: Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities
Language: English
Authors: Costa, H. M. (ORCID 0000-0002-3517-4292), Nicholson, B., Donlan, C., Van Herwegen, J. (ORCID 0000-0001-5316-1818)
Source: Journal of Intellectual Disability Research. Apr 2018 62(4):292-302.
Availability: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
Peer Reviewed: Y
Page Count: 11
Publication Date: 2018
Document Type: Journal Articles
Reports - Research
Descriptors: Preschool Children, Mathematics Skills, Low Achievement, Multivariate Analysis, Student Characteristics, Visual Perception, Spatial Ability, Academic Ability, Skill Development
DOI: 10.1111/jir.12465
ISSN: 0964-2633
Abstract: Background: Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain-specific and domain-general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub-types of LAs. Methods: 81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain-general and domain-specific tasks. Results: Cluster analysis revealed four subgroups of LAs in mathematics: (1) a weak processing sub-type; (2) a general mathematical LAs sub-type; (3) a mixed abilities sub-type; and (4) a visuo-spatial deficit sub-type. Whilst two of the groups showed specific domain-general difficulties, none showed only domain-specific difficulties. Conclusions: Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain-general factors for the development of mathematical abilities during the preschool years.
Abstractor: As Provided
Entry Date: 2018
Accession Number: EJ1172196
Database: ERIC
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  Value: <anid>AN0128440974;eul01apr.18;2018Mar14.12:18;v2.2.500</anid> <title id="AN0128440974-1">Low performance on mathematical tasks in preschoolers: the importance of domain‐general and domain‐specific abilities </title> <p>Abstract: Background: Different domain‐specific and domain‐general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school‐aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain‐specific and domain‐general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub‐types of LAs. Methods: 81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain‐general and domain‐specific tasks. Results: Cluster analysis revealed four subgroups of LAs in mathematics: (<reflink idref="bib1" id="ref1">1</reflink>) a weak processing sub‐type; (<reflink idref="bib2" id="ref2">2</reflink>) a general mathematical LAs sub‐type; (<reflink idref="bib3" id="ref3">3</reflink>) a mixed abilities sub‐type; and (<reflink idref="bib4" id="ref4">4</reflink>) a visuo‐spatial deficit sub‐type. Whilst two of the groups showed specific domain‐general difficulties, none showed only domain‐specific difficulties. Conclusions: Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain‐general factors for the development of mathematical abilities during the preschool years.</p> <p>domain‐general abilities; domain‐specific abilities; low performing; mathematics; preschoolers; sub‐types</p> <p>Studies show that between 5% and 10% of school‐aged children experience a substantial deficit in mathematics (Desoete et al. [<reflink idref="bib11" id="ref5">11</reflink>] ; Barbaresi et al. [<reflink idref="bib5" id="ref6">5</reflink>] ) and that mathematical achievement in school years correlates with educational and financial success later in life (Geary et al. [<reflink idref="bib15" id="ref7">15</reflink>] ; Parson & Bynner [<reflink idref="bib39" id="ref8">39</reflink>] ). This stresses the importance of investigating the cognitive characteristics of preschool children who are low achievers (LAs) on mathematical tasks, in order to promote early identification of children at risk for mathematical learning disabilities and implement appropriate early educational interventions.</p> <hd id="AN0128440974-2">Mathematical learning disabilities and low achievers</hd> <p>The term mathematical learning disabilities (MLD) is used to describe a developmental delay or deviance in the acquisition of one or more mathematical functions (Berch & Mazzocco [<reflink idref="bib7" id="ref9">7</reflink>] ). Recent studies have explored the cognitive characteristics of MLD children in primary education. Some of these studies used a top‐down approach, examining the cognitive profiles of MLD sub‐groups specified beforehand based on a‐priori assumptions (Jordan et al. [<reflink idref="bib24" id="ref10">24</reflink>] ; Murphy et al. [<reflink idref="bib36" id="ref11">36</reflink>] ). As a‐priori specified criteria may bias outcomes, other studies have used a data‐driven classification approach to describe the MLD profiles (Bartelet et al. [<reflink idref="bib6" id="ref12">6</reflink>] ; Von Aster [<reflink idref="bib53" id="ref13">53</reflink>] ). Both types of study emphasise the complexity of establishing the core deficits that constitute the MLD phenotype. In particular, previous data‐driven studies in primary schools (Bartelet et al. [<reflink idref="bib6" id="ref14">6</reflink>] ; Von Aster [<reflink idref="bib53" id="ref15">53</reflink>] ) support the notion that MLD is a heterogeneous disorder with a multifactorial origin. These studies identified sub‐types characterised by domain‐specific deficits, such as weak ANS skills or number‐line difficulties. In contrast, no clusters of primary school children were characterised by domain‐general cognitive deficits only.</p> <p>Although previous studies have examined mathematical difficulties in primary school children with MLD, little is known about the rate of mathematical difficulties in preschoolers. There is currently some debate about what abilities drive mathematical competencies in typically developing preschool children, and it has been suggested that different abilities may be important at different developmental stages.</p> <hd id="AN0128440974-3">Domain‐specific and domain‐general precursors of mathematical learning</hd> <p>Research studies show that both domain‐specific and domain‐general abilities predict successful mathematical achievement outcomes in later life (Mazzocco & Thompson [<reflink idref="bib33" id="ref16">33</reflink>] ; Passolunghi & Lanfranchi [<reflink idref="bib41" id="ref17">41</reflink>] ). However, the role played by these cognitive abilities in mathematical cognition most likely varies with expertise and development.</p> <p>Domain‐specific abilities that relate to mathematics include both verbal and non‐verbal number‐specific cognitive processes. Counting ability, and especially knowledge of the number word sequence, seems to be one of the most discriminating and efficient precursors of early mathematical learning (Passolunghi et al. [<reflink idref="bib43" id="ref18">43</reflink>] ; Krajewski & Schneider [<reflink idref="bib25" id="ref19">25</reflink>] ). A child who has achieved the cardinality principle (Gelman & Gallistel [<reflink idref="bib19" id="ref20">19</reflink>] ) understands that the last word spoken in counting indicates the cardinality of the whole set. Studies focusing on preschool children indicate that understanding the cardinality principle is important for creating the link between non‐symbolic skills and number symbols (Ansari et al. [<reflink idref="bib3" id="ref21">3</reflink>] ; Le Corre & Carey [<reflink idref="bib28" id="ref22">28</reflink>] ). Another building block for the development of mathematics is the non‐verbal ability to discriminate approximate large numerosities, supported by the Approximate Number System (ANS) (Halberda et al. [<reflink idref="bib23" id="ref23">23</reflink>] ). Specifically, some researchers propose that the acquisition of the meaning of symbolic numerals is done by mapping number words and Arabic digits onto the pre‐existing approximate number representations (Dehaene [<reflink idref="bib10" id="ref24">10</reflink>] ; Piazza [<reflink idref="bib44" id="ref25">44</reflink>] ). Research has found a relationship between ANS and mathematical abilities in primary school and preschool children (Libertus et al. [<reflink idref="bib29" id="ref26">29</reflink>] ; Mussolin et al. [<reflink idref="bib38" id="ref27">38</reflink>] ). Moreover, longitudinal studies have shown that ANS abilities at age three predict general mathematical achievement in 6 year olds (Mazzocco et al. [<reflink idref="bib31" id="ref28">31</reflink>] ). A core hypothesis regarding MLD is that it originates from a core deficit in the innate ANS (Dehaene [<reflink idref="bib10" id="ref29">10</reflink>] ). In line with this hypothesis, research on MLD has shown that impaired acuity of the ANS contributes to lower calculation skills and MLD in general (Mussolin et al. [<reflink idref="bib37" id="ref30">37</reflink>] ; Mazzocco et al. [<reflink idref="bib32" id="ref31">32</reflink>] ). Still, other studies have failed to find a relationship between non‐verbal ANS abilities and mathematical performance (Lyons et al. [<reflink idref="bib30" id="ref32">30</reflink>] ; Passolunghi et al. [<reflink idref="bib42" id="ref33">42</reflink>] ; Szücs et al. [<reflink idref="bib49" id="ref34">49</reflink>] ; Vanbinst et al. [<reflink idref="bib51" id="ref35">51</reflink>] ).</p> <p>Domain‐general precursors also play an important role in the development of mathematical abilities. This is especially so during the preschool years, with the importance of domain‐general abilities usually diminishing as a consequence of a greater influence of domain‐specific abilities during primary school education (Passolunghi & Lanfranchi [<reflink idref="bib41" id="ref36">41</reflink>] ). The domain‐general cognitive deficit hypothesis of MLD proposes that general cognitive impairments affect the development of mathematical skills (Geary & Hoard [<reflink idref="bib16" id="ref37">16</reflink>] ). Amongst general cognitive skills, working memory (WM) is considered a key domain‐general predictor of mathematical learning. WM refers to a temporary memory system that allows short‐term storage and manipulation of verbal and visuo‐spatial information (Baddeley [<reflink idref="bib4" id="ref38">4</reflink>] ). WM abilities and short‐term memory (STM) skills are related both to early numeracy skills in preschool years and to later mathematical skills (Alloway & Alloway [<reflink idref="bib1" id="ref39">1</reflink>] ; Friso‐van den Bos et al. [<reflink idref="bib14" id="ref40">14</reflink>] ). Visuo‐spatial memory skills are especially strongly related to early numeracy ability in young children (Ansari et al. [<reflink idref="bib3" id="ref41">3</reflink>] ; Kyttälä et al. [<reflink idref="bib26" id="ref42">26</reflink>] ), while verbal WM abilities support mathematical performance to a greater extent from the age of seven onwards (Rasmussen & Bisanz [<reflink idref="bib45" id="ref43">45</reflink>] ). Speed of processing (SP), being the efficiency and speed with which cognitive tasks are executed (see Case [<reflink idref="bib9" id="ref44">9</reflink>] ), is another domain‐general cognitive precursor important for the development of mathematics (Gersten et al. [<reflink idref="bib20" id="ref45">20</reflink>] ). A number of studies have shown children with poor mathematical abilities to have poor SP performance compared with typically developing peers (Bull & Johnston [<reflink idref="bib8" id="ref46">8</reflink>] ; Geary et al. [<reflink idref="bib18" id="ref47">18</reflink>] ).</p> <hd id="AN0128440974-4">The present study</hd> <p>Although previous studies have examined which cognitive abilities relate to mathematical difficulties in primary school children with MLD (Bartelet et al. [<reflink idref="bib6" id="ref48">6</reflink>] ; Von Aster [<reflink idref="bib53" id="ref49">53</reflink>] ), to our knowledge, no study has explored the cognitive sub‐types of preschool children who show mathematical difficulties using a data‐driven approach. As the developmental process needs to be considered, and it cannot be assumed that the deficit observed in older children is the same deficit in younger children (Ansari [<reflink idref="bib2" id="ref50">2</reflink>] ), further studies are needed to identify potential different cognitive profiles in low achieving preschool children. The identification of these cognitive patterns is of great importance for the early identification and remediation of mathematical difficulties.</p> <p>In the present study, we examined the cognitive characteristics of a sample of preschoolers with low mathematical abilities and identified sub‐types of LAs using cluster analysis. Based on the literature discussed earlier (e.g. Bartelet et al. [<reflink idref="bib6" id="ref51">6</reflink>] ; Geary et al. [<reflink idref="bib18" id="ref52">18</reflink>] ; Kyttälä et al. [<reflink idref="bib26" id="ref53">26</reflink>] ; Le Corre & Carey [<reflink idref="bib28" id="ref54">28</reflink>] ; Mazzocco et al. [<reflink idref="bib31" id="ref55">31</reflink>] ), four cognitive factors were considered in the clustering process, two domain‐specific (cardinality and ANS) and two domain‐general (visuo‐spatial memory and SP). This allowed greater insight into whether mathematical difficulties can be contributed to domain‐general or domain‐specific deficiencies in preschoolers.</p> <hd id="AN0128440974-5">Method</hd> <hd id="AN0128440974-6">Participants</hd> <p>To identify LAs in mathematics, 283 preschool children aged 3 to 5 years old (M<subs>age</subs> = 45.45 months, SD = 5.26, 141 girls) attending 14 preschool settings in London and Greater London were included in the screening phase. All children were screened using a standardised assessment of mathematical abilities (Test of Early Mathematics Ability – Third Edition; Ginsburg & Baroody [<reflink idref="bib22" id="ref56">22</reflink>] ) and on the Picture Similarities subtest of the British Ability Scales (BAS‐3; Eliot & Smith [<reflink idref="bib13" id="ref57">13</reflink>] ). Children were considered as LAs if they performed at or below the 35<sups>th</sups> percentile on the Test of Early Mathematics Ability (TEMA‐3). All children spoke English at home or performed within the normal range on the Verbal Comprehension subtest of the BAS (T score > 37). Parents did not report any developmental delays or hearing and vision disabilities. Ten children were excluded from the screening sample as they failed to complete the assessment battery due to opting out (N = 2) and illness or long absence (N = 8).</p> <p>81 children were identified as LAs (M<subs>age</subs> = 44.38 months, SD = 5.47, 44 girls; M<subs>TEMA percentile</subs> = 22.39, SD = 9.10). A control group of 56 (M<subs>age</subs> 45.96 months, SD = 4.88, 31 girls; M<subs>TEMA percentile</subs> = 71.21, SD = 17.45) children who obtained TEMA‐3 scores at or above the 50<sups>th</sups> percentile was also identified. These children were randomly chosen from each preschool setting.</p> <p>Socio‐economic status (SES) was established using mothers' highest level of education, as parental education is considered to be one of the most stable aspects of SES (Sirin [<reflink idref="bib48" id="ref58">48</reflink>] ).</p> <hd id="AN0128440974-7">Materials</hd> <hd id="AN0128440974-8">Mathematical screening measure</hd> <p>Test of Early Mathematics Ability – Third Edition (TEMA‐3) is normed for use with children aged 3 to 8 years old. TEMA‐3 items assess both symbolic and non‐symbolic knowledge and facts. Test–retest reliability is .93. Our variable of interest was the percentile score to identify children as LAs, and raw scores were used to compare the different groups (see footnote 1 for a discussion).</p> <hd id="AN0128440974-9">Reasoning</hd> <p>The Picture Similarities non‐verbal subtest of the BAS‐3 was administered as a measure of general reasoning abilities. This task requires the child to match a sample card to one of four possible target pictures on the basis of perceptual similarities or semantic associations between items.</p> <hd id="AN0128440974-10">Approximate Number System (ANS)</hd> <p>In this ANS task, children were asked to identify which side of the screen showed more dots. They responded using a touch screen. There were 48 randomised trials of 0.5, 0.6, 0.7 and 0.8 ratios. The number of dots in each array ranged from 5 to 20, and both congruent and incongruent trials were used to control for continuous quantity variables (see Simms et al. [<reflink idref="bib47" id="ref59">47</reflink>] ). In each of the experimental trials, children saw a fixation point followed by presentation of the stimuli for 1500 ms. The ANS task was preceded by instructions and practice trials with dot displays of the ratio 1:3. A score of 1 was given for every trial performed correctly. The minimum score was 0, and the maximum was 48. Cronbach's α based on average inter‐item correlation = .867.</p> <hd id="AN0128440974-11">Visuo‐spatial short‐term memory</hd> <p>The Pathway Recall task (Lanfranchi et al. [<reflink idref="bib27" id="ref60">27</reflink>] ) was used to assess visuo‐spatial STM abilities. The child was shown a path taken by a small toy frog on a 3 × 3 or 4 × 4 grid. The child had to recall the pathway immediately after the presentation by moving the frog from square to square, reproducing the experimenter's moves. The task is composed of eight trials and had four levels of difficulty, depending on the number of steps in the frog's path and dimensions of the chessboard (3 × 3 in the first level with two steps and 4 × 4 in the other levels with two, three and four steps, respectively). Two trials for each difficulty level were presented. A score of 1 was given for every trial performed correctly. The minimum score was 0, and the maximum was 8. The test–retest reliability for this task is .70 (Passolunghi & Costa [<reflink idref="bib40" id="ref61">40</reflink>] ).</p> <hd id="AN0128440974-12">Speed of processing (SP)</hd> <p>The Naming Speed sub‐test from the Phonological Assessment Battery 2 (PhAB2; Gibbs & Bodman [<reflink idref="bib21" id="ref62">21</reflink>] ) was used to assess SP. A total of 50 stimuli were presented on one page, and the child was asked to name the stimuli (pictured objects) as quickly as possible without making errors. Non‐standardised total response time measure was obtained. The reliability of this test is adequate with internal consistency alpha coefficients above .80.</p> <hd id="AN0128440974-13">Cardinality</hd> <p>To assess cardinality abilities, children were assessed on a Give‐a‐Number task (Wynn [<reflink idref="bib54" id="ref63">54</reflink>] ). In this task, children were asked to give the experimenter exactly 1, 2, 3, 4 and 5 beads from a pile. The child was asked to provide each number three times in randomised order. A score of 1 was given for every trial performed correctly. The minimum score was 0 ,and the maximum was 15. Cronbach's alpha for reliability was .865.</p> <hd id="AN0128440974-14">Procedure</hd> <p>After the head teacher or manager had provided consent, parental written consent was obtained for all children as well as children's verbal assent before the start of the study. Trained research assistants carried out the assessments. Each child was assessed individually in a quiet area within the preschool setting. In order to encourage children and keep them motivated, they received stickers at the end of each session.</p> <p>This study was assessed by the Ethics Committee for the Faculty of Arts and Social Sciences at Kingston University and allowed to proceed.</p> <hd id="AN0128440974-15">Data analyses</hd> <p>We examined the existence of sub‐groups within the group of LAs using cluster analysis. Cluster analysis is a descriptive, multivariate statistical technique that aims to group individuals that are close together. Performance on the ANS, SP, cardinality and visuo‐spatial STM tasks were entered as variables of interest in the cluster analysis. Standardisation into z scores was performed prior to the cluster analysis to ensure that differences in measurement scale did not influence the results. The variable scores entered in the analysis were standardised relative to the sample of LAs. Thus, the profile description represents performance relative to the average performance of the LAs group, not relative to the norm.</p> <p>First, we used an agglomerative hierarchical clustering approach (Ward's method) to determine the number of optimal clusters. This approach combines the cases into clusters such that the variance within a cluster is minimised. To do so, clusters whose merger increases the overall within‐cluster variance to the smallest possible degree are merged (Mooi & Sarstedt [<reflink idref="bib35" id="ref64">35</reflink>] ). The result can be described with a dendogram (see Fig. ) and a plot of the agglomeration coefficients. To establish the initial clusters, the percentage change in the agglomeration coefficients was evaluated, and a screen‐plot was used to detect a point of inflection. Following the interpretation of the height of the different nodes in the dendogram, a four‐cluster solution was judged as the optimal one for producing subgroups in LAs. As suggested by Milligan ([<reflink idref="bib34" id="ref65">34</reflink>] ), after the number of clusters and the cluster centroids has been determined with the hierarchical method, a K‐means cluster analysis was used in order to reduce the overall within‐cluster variation and optimise the results.</p> <p>To further describe the sub‐types identified, we compared performance scores for the different clusters to a group of control children on the variables of interest entered in the cluster analysis, as well as age, mathematical abilities (TEMA‐3) and reasoning abilities (Picture Similarities). For this purpose, univariate ANOVAs on the unstandardised scores for each of the clustering variables were used to describe differences between the clusters. The Bonferroni procedure was used for post‐hoc comparisons of the means.</p> <hd id="AN0128440974-16">Results</hd> <hd id="AN0128440974-17">Description of the clusters</hd> <p>Analyses revealed four clusters (Fig. ):</p> <p>Cluster 1 (n = 13) included LAs characterised by average performance in the visuo‐spatial STM task (M z score = .00, SD = .72), low‐average performance on cardinality (M z score = −.87, SD = 1.10) and ANS (M z score = −.88, SD = .97), and weak performance on the SP task (M z score = −1.71, SD = .93). On the basis of the described profile, this group was assigned the label weak processing sub‐type.</p> <p>Cluster 2 (n = 37) is the larger subgroup of LAs and consisted of children characterised by average performance on all tasks: visuo‐spatial STM M z score = .26, SD = .61; cardinality M z score = .12. SD = .65; ANS M z score = −.09, SD = .68; SP M z score = −.38, SD = .53. As it is not possible to identify a specific cognitive strength of weaknesses in this group compared with the other LAs, this group was labelled general mathematical LAs sub‐type.</p> <p>Cluster 3 (n = 15) included LAs with average performance on the SP task (M z score = −.55, SD = .59) and above average performance on the visuo‐spatial STM task (M z score = .97, SD = .60). This group is characterised by strong performance on the domain‐specific mathematical tasks considered in this study (cardinality: M z score = 1.17, SD = .59; ANS: M z score = 1.25, SD = .60) and was therefore labelled mixed abilities sub‐type.</p> <p>Cluster 4 (n = 16) comprised LAs with impaired visuo‐spatial STM skills (M z score = −1.51. SD = .37) but average performance on the other tasks: cardinality M z score = −.66. SD = .70, ANS M z score = −.26. SD .88, SP M z score = .01. SD = .75. Scoring specifically low on the visuo‐spatial STM tasks, this group was assigned the label visuo‐spatial deficit sub‐type.</p> <hd id="AN0128440974-18">Group comparisons</hd> <p>The descriptive statistics for age and performance scores for each task for the LAs sub‐types and the control group are presented in Tables  and .</p> <p>Chronological age in months and performance scores for reasoning ability (picture similarities), mathematical abilities (TEMA‐3), non‐symbolic comparison (ANS), speed of processing, visuo‐spatial STM and cardinality</p> <p> <ephtml> <table border="1" cellpadding="11"><tr><th /><th>Cluster 1N = 13(10 females)</th><th>Cluster 2N = 37(19 females)</th><th>Cluster 3N = 15(8 females)</th><th>Cluster 4N = 16(7 females)</th><th>Control groupN = 56(31 females)</th></tr><tr><th /><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th></tr><tr><td>Chronological age</td><td>42.77</td><td>5.31</td><td>44.49</td><td>5.04</td><td>47.47</td><td>5.21</td><td>42.56</td><td>5.93</td><td>45.96</td><td>4.88</td></tr><tr><td>Picture similarities</td><td>46.85</td><td>6.89</td><td>44.59</td><td>8.38</td><td>45.33</td><td>6.23</td><td>43.63</td><td>5.80</td><td>47.09</td><td>10.25</td></tr><tr><td>TEMA‐3</td><td>2.85</td><td>1.77</td><td>4.38</td><td>1.66</td><td>6.00</td><td>2.67</td><td>3.25</td><td>1.73</td><td>13.21</td><td>5.64</td></tr><tr><td>ANS</td><td>23.77</td><td>5.07</td><td>27.89</td><td>3.56</td><td>34.87</td><td>3.11</td><td>27.00</td><td>4.59</td><td>32.80</td><td>5.23</td></tr><tr><td>Speed of processing</td><td>227.46</td><td>49.36</td><td>116.16</td><td>28.26</td><td>107.20</td><td>26.07</td><td>136.94</td><td>39.87</td><td>95.68</td><td>23.40</td></tr><tr><td>Visuo‐spatial STM</td><td>2.77</td><td>1.17</td><td>3.19</td><td>1.00</td><td>4.33</td><td>.98</td><td>.31</td><td>.60</td><td>4.34</td><td>1.82</td></tr><tr><td>Cardinality</td><td>4.69</td><td>4.23</td><td>8.51</td><td>2.50</td><td>12.53</td><td>2.26</td><td>5.50</td><td>2.71</td><td>13.32</td><td>3.05</td></tr></table> </ephtml> </p> <p>2 Note: Cluster 1 = weak processing sub‐type; Cluster 2 = general mathematical LAs sub‐type; Cluster 3 = mixed abilities sub‐type, Cluster 4 = visuo‐spatial deficit sub‐type.</p> <p>Overview of socio‐economic status (SES) per group as a percentage</p> <p> <ephtml> <table border="1" cellpadding="7"><tr><th /><th>No formal qualification</th><th>Finished secondary school</th><th>Vocational degree</th><th>Undergraduate degree</th><th>Post‐graduate degree</th><th>Missing data</th></tr><tr><td>Group</td><td /><td /><td /><td /><td /><td /></tr><tr><td>Cluster 1</td><td>14.3%</td><td>28.6%</td><td>42.9%</td><td>14.3%</td><td>0.0%</td><td>42.9%</td></tr><tr><td>Cluster 2</td><td>16.7%</td><td>10.0%</td><td>16.7%</td><td>56.7%</td><td>0.0%</td><td>10.0%</td></tr><tr><td>Cluster 3</td><td>0.0%</td><td>20.0%</td><td>20.0%</td><td>40.0%</td><td>20.0%</td><td>20.0%</td></tr><tr><td>Cluster 4</td><td>50.0%</td><td>0.0%</td><td>20.0%</td><td>20.0%</td><td>10.0.%</td><td>40.0%</td></tr><tr><td>Control</td><td>8.9%</td><td>11.1%</td><td>11.1%</td><td>35.6%</td><td>33.3%</td><td>4.4%</td></tr></table> </ephtml> </p> <p>3 Note: Cluster 1 = weak processing sub‐type; Cluster 2 = general mathematical LA sub‐type; Cluster 3 = mixed abilities sub‐type, Cluster 4 = visuo‐spatial deficit sub‐type.</p> <p>An ANOVA for T‐scores on the Picture Similarities subtest revealed no significant difference between the five groups, F<subs>4.132</subs> = .80, p = .53, η<sups>2</sups><subs>p</subs> = .02. Group comparisons revealed a significant effect for chronological age, F<subs>4.132</subs> = 2.971, p = .022, η<sups>2</sups><subs>p</subs> = .083, and thus age was included as a covariate in subsequent analyses.</p> <p>As predicted, the ANCOVA for TEMA‐3 raw scores revealed a significant difference between groups, F<subs>4.131</subs> = 45.10, p < .001, η<sups>2</sups><subs>p</subs> = .58. Post‐hoc Bonferroni analyses showed that all four LAs sub‐types differed significantly from the control group (all ps < .001) but not from one another (all ps = n.s.).</p> <p>The ANCOVA for performance scores on the ANS task revealed a significant difference between groups; F<subs>4.131</subs> = 16.20, p < .001, η<subs>p</subs><sups>2</sups> = .33. Bonferroni‐adjusted post‐hoc pairwise comparisons indicated that the performance of three of the sub‐types of LAs was significantly lower compared with the control group (all ps < .001). However, children in Cluster 3 (mixed abilities sub‐type) showed higher average ANS scores compared with the controls (M<subs>diff</subs> = 1.83, p = .99) as well as all the other sub‐types (all ps < .001). There were no significant differences between the other three LAs sub‐types (all ps = n.s.).</p> <p>There was a significant difference between the groups for SP performance: F<subs>4.111</subs> = 48.16, p < .001, η<subs>p</subs><sups>2</sups> = .59. Bonferroni‐adjusted post‐hoc pairwise comparisons indicated that the control group performed significantly better compared with all LAs sub‐types (Cluster 1: p < .001; Cluster 2: p = .030; Cluster 4: p = .001), except for Cluster 3 (mixed abilities sub‐type) (M<subs>diff</subs> = 12.50, p = .999). Considering the difference between the LAs sub‐types, performance for children in Cluster 1 (weak processing sub‐type) was significantly slower for the SP task compared with all the LAs sub‐types (all ps < .001), but there were no significant differences between the other LAs sub‐types (all ps = n.s.).</p> <p>There was a significant difference between the groups for performance on the visuo‐spatial STM task F<subs>4.111</subs> = 25.80, p < .001, η<subs>p</subs><sups>2</sups> = .44. Bonferroni‐adjusted post‐hoc pairwise comparisons indicated that the control group performed significantly better compared with all the LAs sub‐types (Cluster 1: p = .008; Cluster 2: p < .002; Cluster 4: p < .001), except for the Cluster 3 (mixed abilities sub‐type) (M<subs>diff</subs> = .04, p = .999). Comparisons between the LAs sub‐types showed that children in Cluster 4 (visuo‐spatial deficit sub‐type) performed significantly lower on the visuo‐spatial STM task compared with all the other LAs groups (all ps < .001) and that there were no differences between the remaining LAs sub‐types (all ps = n.s.).</p> <p>The ANCOVA for the cardinality scores revealed a significant difference between the groups, F<subs>4.111</subs> = 37.99, p < .001, η<subs>p</subs><sups>2</sups> = .54. Bonferroni‐adjusted post‐hoc pairwise comparisons indicated that the control group performed significantly better compared with all the LAs sub‐types (all ps < .001), except for the Cluster 3 (mixed abilities sub‐type) (Mdiff = 1.08, p = .999). Considering the difference between the LAs sub‐types on cardinality scores, children in Cluster 3 (mixed abilities sub‐type) outperformed those in all other clusters (Cluster 1: p < .001; Cluster 2: p = .001; Cluster 4: p < .001). Cluster 2 (general mathematical LAs sub‐type) performed better on the cardinality task compared with Cluster 1 (weak processing sub‐type) (M<subs>diff</subs> = 3.45, p = .002) and Cluster 4 (visuo‐spatial deficit sub‐type) (M<subs>diff</subs> = 2.64, p = .019). There was no significant difference between Clusters 1 and 4, which both have the lowest cardinality scores (respectively M = 4.69 and M = 5.50, p = .999).</p> <hd id="AN0128440974-19">Discussion</hd> <p>The current study builds on previous findings of mathematical abilities relying on a wide range of domain‐specific and domain‐general abilities. We examined the cognitive characteristics of a sample of preschool children with low mathematical abilities, identifying different sub‐types of LAs using a data‐driven approach. The analyses identified four different cognitive profiles: a general mathematical LAs sub‐type, a weak processing sub‐type, a visuo‐spatial deficit sub‐type and a mixed abilities sub‐type.</p> <p>Within the sub‐types identified, two LAs groups were characterised by particularly weak domain‐general abilities, supporting the domain‐general cognitive deficit MLD hypothesis (Geary & Hoard [<reflink idref="bib16" id="ref66">16</reflink>] ). Children in the visuo‐spatial deficit sub‐type showed impaired performance on visuo‐spatial abilities compared with the other LAs and the control group. Importantly, there were no differences in visuo‐spatial skills between the other LAs sub‐types, suggesting that mathematical difficulties in the visuo‐spatial deficit sub‐type could be driven by a specific deficit in this area. This finding is in line with Bartelet et al. ([<reflink idref="bib6" id="ref67">6</reflink>] ) who found a sub‐group of primary school children with MLD that had spatial difficulties. Moreover, research has generally shown visuo‐spatial memory skills to be strongly related to preschooler's mathematical skills (Kyttälä et al. [<reflink idref="bib26" id="ref68">26</reflink>] ). Children in the weak processing sub‐type were characterised by impaired SP compared with all other sub‐types and the control group. Again, there were no differences between the other LA sub‐types. Children in the weak processing sub‐type process information more slowly, which may explain their low mathematical performance. This result is in line with previous studies showing that SP is an important domain‐general cognitive precursor for the development of mathematics (Bull & Johnston [<reflink idref="bib8" id="ref69">8</reflink>] ; Geary et al. [<reflink idref="bib17" id="ref70">17</reflink>] ).</p> <p>The larger subgroup consisted of the general mathematical LAs sub‐type and included children characterised by average performance on all tasks compared with the other LAs groups and impaired performance on all tasks compared with the control group. The sub‐type did not differ from the other groups in terms of general reasoning abilities. These children are not characterised by a specific deficit in one area, but their performance is generally low on both domain‐general and domain‐specific precursors. This result supports the idea of MLD as heterogeneous disorder with a multifactorial origin (Traff et al. [<reflink idref="bib50" id="ref71">50</reflink>] ). Indeed, some children with mathematical difficulties might not have a single deficit but rather have multiple small deficits on different domains (Dowker [<reflink idref="bib12" id="ref72">12</reflink>] ; Rubinsten & Henik [<reflink idref="bib46" id="ref73">46</reflink>] ; Von Aster & Shalev [<reflink idref="bib52" id="ref74">52</reflink>] ).</p> <p>Finally, children in the mixed abilities sub‐type outperformed the other LAs groups on all tasks but TEMA‐3. This group did not differ from controls in terms of domain‐general and domain‐specific abilities, despite their low performance on TEMA‐3. Interestingly, they demonstrated above‐average performance on the ANS task compared with controls. Thus, the difficulties in this group are likely caused by other cognitive or behavioural difficulties (e.g. anxiety) not currently measured. The current finding that one group of children did not show any numerical deficits, despite low performance on the TEMA‐3, is in line with the ‘no numerical cognitive deficit’ group in the study by Bartelet et al. ([<reflink idref="bib6" id="ref75">6</reflink>] ).</p> <p>In our study, three of the sub‐types (65% of the LAs children) showed lower performance on all four of the variables considered (i.e. ANS, cardinality, SP and WM) compared with the control group. In contrast to previous studies of primary school children (Bartelet et al. [<reflink idref="bib6" id="ref76">6</reflink>] ; Von Aster [<reflink idref="bib53" id="ref77">53</reflink>] ), we did not find any groups that showed numerical deficits (ANS or cardinality) only. Instead, nearly half of the LAs preschool children included in the study are characterised by domain‐general cognitive deficits. This suggests that in preschoolers, WM and SP deficits may impair performance on tasks assessing mathematical abilities (Geary & Hoard [<reflink idref="bib16" id="ref78">16</reflink>] ). This result has important implications for the early prevention of MLD and suggests the possibility to work on the improvement of domain‐general abilities in preschool years (Passolunghi & Costa [<reflink idref="bib40" id="ref79">40</reflink>] ).</p> <p>Some limitations of the current study include that, due to their young age, children were not assessed on all aspects of mathematical ability or domain‐general abilities. Given the importance of domain‐general abilities that emerged in this study, future studies should consider including an assessment of all components of WM, to further examine what sub‐components are important precursors of mathematical learning. The inclusion of more variables could provide valuable insight into why some children in the mixed abilities sub‐type performed low on TEMA‐3. In addition, we did not examine the effects of SES in detail. Further research using larger samples is required to see how low SES affects the different LAs sub‐types so that effective educational programmes can be developed.</p> <p>Overall, our findings show that mathematical difficulties are associated with different patterns of cognitive abilities in preschool years compared with primary school age children, and that young low‐achieving children may struggle with mathematics for different reasons. In contrast to previous studies with older children, we found two groups characterised by severe weaknesses in domain‐general precursors, while no groups were characterised by domain‐specific weaknesses only. This is in line with previous studies that highlight the importance of domain‐general abilities in preschool years, and suggest that domain‐specific abilities become more important during primary school (Passolunghi & Lanfranchi [<reflink idref="bib41" id="ref80">41</reflink>] ). Yet, longitudinal studies are required to investigate the stability of the LAs sub‐types identified in this study as well as to examine which children obtain a formal diagnosis for MLD later on (Ansari [<reflink idref="bib2" id="ref81">2</reflink>] ).</p> <p>The present study has practical implications for early identification and prevention of mathematical difficulties and disabilities. The identification of four different sub‐types suggests that intervention programmes for low‐achieving preschoolers need to be specific, based on children's cognitive profiles and focussed on domain‐general abilities as well as domain‐specific number skills.</p> <hd id="AN0128440974-20">Acknowledgments</hd> <p>We would like to thank all families, children and preschool settings that have taken part in this research. This project was funded by the Nuffield foundation, but the views expressed are those of the authors and not necessarily those of the foundation.</p> <ref id="AN0128440974-21"> <title>References</title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext>Alloway T. P. & Alloway R. G. (2010) Investigating the predictive roles of working memory and IQ in academic attainment. 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Cognitive Psychology 24, 220–251. https://doi.org/10.1016/0010‐0285(92)90008‐P. </bibtext> </blist> </ref> <p>PHOTO (COLOR): Dendogram plot of the agglomerative hierarchical clustering approach (Ward's method).</p> <p>PHOTO (COLOR): Mean z scores on the domain‐general and domain‐specific precursors included in the cluster analyses for each of the four LAs sub‐types. [Colour figure can be viewed at wileyonlinelibrary.com]</p> <aug> <p>By H. M. Costa; B. Nicholson; C. Donlan and J. Van Herwegen</p> </aug>
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  Data: Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities
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  Data: English
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  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Costa%2C+H%2E+M%2E%22">Costa, H. M.</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-3517-4292">0000-0002-3517-4292</externalLink>)<br /><searchLink fieldCode="AR" term="%22Nicholson%2C+B%2E%22">Nicholson, B.</searchLink><br /><searchLink fieldCode="AR" term="%22Donlan%2C+C%2E%22">Donlan, C.</searchLink><br /><searchLink fieldCode="AR" term="%22Van+Herwegen%2C+J%2E%22">Van Herwegen, J.</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-5316-1818">0000-0001-5316-1818</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Intellectual+Disability+Research%22"><i>Journal of Intellectual Disability Research</i></searchLink>. Apr 2018 62(4):292-302.
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  Data: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
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  Data: Y
– Name: Pages
  Label: Page Count
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  Data: 11
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  Label: Publication Date
  Group: Date
  Data: 2018
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  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Preschool+Children%22">Preschool Children</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Low+Achievement%22">Low Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Multivariate+Analysis%22">Multivariate Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Characteristics%22">Student Characteristics</searchLink><br /><searchLink fieldCode="DE" term="%22Visual+Perception%22">Visual Perception</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+Ability%22">Spatial Ability</searchLink><br /><searchLink fieldCode="DE" term="%22Academic+Ability%22">Academic Ability</searchLink><br /><searchLink fieldCode="DE" term="%22Skill+Development%22">Skill Development</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/jir.12465
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0964-2633
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Background: Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain-specific and domain-general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub-types of LAs. Methods: 81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain-general and domain-specific tasks. Results: Cluster analysis revealed four subgroups of LAs in mathematics: (1) a weak processing sub-type; (2) a general mathematical LAs sub-type; (3) a mixed abilities sub-type; and (4) a visuo-spatial deficit sub-type. Whilst two of the groups showed specific domain-general difficulties, none showed only domain-specific difficulties. Conclusions: Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain-general factors for the development of mathematical abilities during the preschool years.
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  Data: 2018
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  Label: Accession Number
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  Data: EJ1172196
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        Value: 10.1111/jir.12465
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      – Text: English
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        PageCount: 11
        StartPage: 292
    Subjects:
      – SubjectFull: Preschool Children
        Type: general
      – SubjectFull: Mathematics Skills
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      – SubjectFull: Low Achievement
        Type: general
      – SubjectFull: Multivariate Analysis
        Type: general
      – SubjectFull: Student Characteristics
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      – SubjectFull: Visual Perception
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      – SubjectFull: Spatial Ability
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      – SubjectFull: Academic Ability
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      – SubjectFull: Skill Development
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      – TitleFull: Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities
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            – TitleFull: Journal of Intellectual Disability Research
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