The authors have declared that no competing interests exist.
Conceived and designed the experiments: LA JC MJ DA. Analyzed the data: LA. Wrote the manuscript: LA. Manuscript review: JC MJ DA.
Dyscalculia, dyslexia, and specific language impairment (SLI) are relatively specific developmental learning disabilities in math, reading, and oral language, respectively, that occur in the context of average intellectual capacity and adequate environmental opportunities. Past research has been dominated by studies focused on single impairments despite the widespread recognition that overlapping and comorbid deficits are common. The present study took an epidemiological approach to study the learning profiles of a large school age sample in language, reading, and math. Both general learning profiles reflecting good or poor performance across measures and specific learning profiles involving either weak language, weak reading, weak math, or weak math and reading were observed. These latter four profiles characterized 70% of children with some evidence of a learning disability. Low scores in phonological short-term memory characterized clusters with a language-based weakness whereas low or variable phonological awareness was associated with the reading (but not language-based) weaknesses. The low math only group did not show these phonological deficits. These findings may suggest different etiologies for language-based deficits in language, reading, and math, reading-related impairments in reading and math, and isolated math disabilities.
Specific learning disabilities are a category of developmental disabilities characterized by difficulty learning in one or more areas despite otherwise typical neurological, physical, and emotional development, and adequate experiential and educational opportunities. Specific language impairment (SLI), dyslexia, and dyscalculia are childhood learning disabilities distinguished by the domain of the disability. SLI refers to a delay in the onset or development of oral language while dyslexia and dyscalculia refer to reading and math difficulties, respectively.
Relevant findings reveal considerable heterogeneity within each disorder [
Traditionally, SLI, dyslexia, and dyscalculia have been described as relatively specific deficits in respective areas. Children with SLI typically have impaired lexical skills (word knowledge) including late development of first words [
While pure forms of SLI, dyslexia, and dyscalculia occur, children identified with one of these learning disabilities often present with other co-morbid conditions. For example, SLI has been associated with high rates of speech production deficits [
These three childhood learning difficulties also tend to co-occur with each other, although appreciably less is known about such comorbidities. The co-occurrence of SLI and dyslexia has received considerable attention. In a review of studies, McArthur, Hogben, Edwards, Heath, and Mengler [
Observations of the qualitative differences between SLI and dyslexic groups have led to the suggestion that both phonological and nonphonological dimensions of language must be considered in order to account for variations in language and reading development [
Generally high rates of comorbidity have been reported for dyslexia and dyscalculia ranging from 17% [
Nevertheless, some researchers have reported qualitative differences between groups with dyscalculia with or without dyslexia. Fuchs and Fuchs [
The high rate of comorbidity between dyslexia and dyscalculia may appear to undermine a strictly separable but co-occurring account of these disorders. An alternative view is that verbally based deficits may give rise to both reading and math impairments whereas a more domain-specific impairment related to number processing may underpin pure dyscalculia. Rourke and colleagues [
To our knowledge, no studies have investigated the comorbidity of dyscalculia and SLI. Nevertheless, a relationship may be expected. According to Dehaene et al.’s [
The findings reviewed above provide strong evidence for the presence of important relationships between SLI, dyslexia, and dyscalculia. Nevertheless, work in this area has been hindered by inconsistencies in the criteria applied to define each learning disability, and in the tasks and analyses employed to investigate group differences. In addition, most studies have investigated the overlap between these disorders by focusing on small groups exhibiting only one or two of these disabilities. While informative, these studies cannot describe the overall pattern of variance and covariance in learning language, reading, and mathematics present in children generally, and in those struggling to learn specifically. It was the purpose of the present study to provide this crucial population perspective concerning SLI, dyslexia, and dyscalculia. In particular, this study is the first to consider learning patterns and challenges in language, reading, and math within subjects in a large developmental sample. The emerging patterns from this work can then form the basis for future research questions aimed at understanding corresponding deficits.
A large, unselected group of school age children completed measures of language, reading, and math. One aim of the study was to examine the patterns of performance across measures using cluster analysis in which sets of observations are created using the dimensions of interest such that sets are more similar to each other within clusters than between clusters. We anticipated that general ability (i.e., performance across all tasks of interest) would yield several clusters reflecting ability levels (e.g., clusters identifying children who generally score in the low, average and high ranges across all tasks). Nevertheless, we were interested in differentiating patterns of performance, and so the analysis aimed to reveal additional clusters with unique profiles if they do in fact exist. Findings of clusters identifying solely language, reading or math weaknesses would be suggestive of specific and separable underlying mechanisms with comorbidity due to artifacts in the data. The presence of clusters with weaknesses in multiple areas would be reflective of potentially meaningful comorbidity perhaps suggesting a different pattern of core deficits. We also examined whether the same pattern of learning profiles would be found for those performing at the low end of the distribution. Findings of similar distributions would suggest that our cluster rates might be applicable to learning disabilities.
A second goal of the study was to provide a preliminary validation of our clusters, and to explore cognitive performance differences across clusters using data available for a subset of the large, unselected sample. Findings that a particular cognitive profile characterizes both unitary and comorbid clusters would implicate similar underlying processes whereas different cognitive deficits for unitary and comorbid clusters might suggest separate underlying cognitive constraints.
The Nonmedical Research Ethics Board at The University of Western Ontario approved all procedures in this study.
A total of 34 schools (including 5 rural schools) in the southwest region of Ontario, Canada were recruited to the study. All children in senior kindergarten through grade 4 in each of the schools were invited to participate in October of the school year, corresponding to an age range of 4 years;10 months to 10;10. Approximately 5967 consent forms were distributed of which 1605 were returned, signed by parents. Of these, 1387 children participated in the study (the remainder were either outside the age range,
All participants in the Epidemiological Sample completed a 10-minute screening protocol consisting of four tasks,
All participants completed the screening measures described below.
The sentences were taken from Redmond [
The
The
The Standardized Test Subsample was comprised of monolingual English speakers, and was selected based on criteria motivated by other studies focusing on children with impairments and on practical constraints. Briefly, standard score cutoffs equivalent to -1.3
The Standardized Test Subsample comprised all low performers, that is, all who scored below the cutoffs and who could be tested (186/255), and children who scored within the average range on all screening tasks and attended the same schools as the low performers (
Each child in the Standardized Test Subsample completed the four core subtests appropriate for the child’s age for the Composite Language Score (CLS) from the Clinical Evaluation of Language Fundamentals IV (CELF-IV; [
Two subtests from the WJ III [
In the
The children completed the four subtests of the Wechsler Abbreviated Scale of Intelligence (WASI; [
Eight subtests from the Automated Working Memory Assessment (AWMA; [
In order to compare performance across our screening tasks, we created our own normative scores based on our large, unselected Epidemiological Sample. To do this, raw scores from the screening measures were converted to z-scores within four age bands (6;0-6;11; 7;0-7;11; 8;0-8;11; 9;0-9;11) and then transformed to a standard score scale with a mean of 100 and a
In order to explore the patterns of unique learning profiles in our Epidemiological Sample, we completed a two-step cluster analysis appropriate for large samples (SPSS v. 17). The cluster analysis technique groups cases of observations into discrete subgroups based on their similarity across a set of chosen dimensions. The clustering procedure proceeds hierarchically so that smaller subgroups (clusters) are merged iteratively into increasingly larger clusters. We planned to explore the number of unique learning profiles by systematically increasing the number of clusters to be found by the solution until no further unique learning profiles were established. Additional tests available for the Standardized Test Subsample allowed us to examine performance on related cognitive measures for each profile group.
The four screening variables, Sentence Recall, Math Fluency, Sight Word Efficiency, and Phonemic Decoding Efficiency, were entered into a two-step cluster analysis with noise handling set to the 25% default and using the log-likelihood distance measure. The autoclustering statistics include the Schwarz’s Bayesian Information Criterion (BIC), BIC changes, ratio of BIC changes, and ratio of distance measures. Smaller BICs and BIC changes reflect better models and are used to find an initial estimation for the number of clusters. The initial estimate is refined by taking into account the ratio of distance measure, which reflects the greatest change in distance between the two closest clusters in each hierarchical clustering stage (SPSS, 2001). In the current analysis, the absolute value of the BIC declined to five clusters although the ratio of distance measures indicated that the complexity beyond three clusters is not necessary. Given our interest in identifying the largest number of unique clusters that would fit our data, we repeated the two-step cluster analysis requesting increasing numbers of clusters from three until profiles were duplicated. It should be noted that the order of case entry can influence cluster formation in these analyses. We validated our clustering by repeating the analyses with four additional uniquely randomized case orders and found no additional unique profiles.
Results of the cluster analyses are displayed in
Dashed lines represent critical
Cluster | n | No. males | Age (mths) | SR | SWE | PDE | MF | Cluster Descriptor |
---|---|---|---|---|---|---|---|---|
1 | 111 | 63 | 93.3 (12.4) | 73.3 (11.4) | 81.0 (10.9) | 83.1 (7.8) | 83.2 (9.7) | Below average overall |
2 | 188 | 102 | 93.7 (13.9) | 86.1 (10.2) | 96.6 (7.2) | 95.0 (7.9) | 98.3 (11.3) | Below average sentence recall |
3 | 202 | 108 | 94.1 (14.4) | 109.6 (6.0) | 95.7 (5.9) | 93.0 (5.8) | 99.0 (10.6) | Below average reading efficiency |
4 | 120 | 74 | 95.0 (13.6) | 102.8 (7.3) | 79.1 (9.9) | 82.7 (7.7) | 89.6 (9.7) | Below average math and reading |
5 | 186 | 83 | 98.3 (12.7) | 104.5 (9.6) | 108.5 (6.4) | 107.4 (6.9) | 94.0 (7.8) | Below average math fluency |
6 | 313 | 179 | 96.7 (12.3) | 108.3 (9.4) | 115.1 (8.1) | 116.1 (11.0) | 115.1 (11.3) | Above average overall |
The boxplot presented in
Solid line marks standard score of 100, and dashed line marks standard score of 85.
In order to validate our clusters, the same pattern of performance across clusters would need to be demonstrated for additional measures of language, reading, and math such as those available for our Standardized Test Subsample. Thus, we compared the standardized test performance of our Standardized Test Subsample in a multivariate ANOVA with the Composite Language Score (language), reading fluency, and calculations scores entered as multivariates. The between group factor in this ANOVA was the cluster (6 levels) to which each child had been assigned in our cluster analysis. All effects were significant,
Cluster | Cluster Descriptor | n | CLS | Reading Fluency | Calculations | Significant differences across clusters | Validation Descriptor | Matches model? |
---|---|---|---|---|---|---|---|---|
1 | Below average overall | 69 | 83.4 (11.3) | 87.1 (10.7) | 80.1 (18.2) | CLS < all others; RF & Calc < all but cluster 4 | Below average overall | ✓ |
2 | Below average sentence recall | 63 | 93.8 (11.7) | 102.4 (9.5) | 95.5 (19.4) | CLS >1 & < 3, 5, 6; RF > 1, 4 & < 6 | Lower language than reading | ✓ |
3 | Below average reading efficiency | 70 | 104.0 (10.8) | 101.6 (9.5) | 95.9 (15.0) | CLS > 1, 2, 4 & < 6; RF > 1, 4 & < 6 | Average overall | ✗ |
4 | Below average math and reading | 38 | 93.8 (11.9) | 88.3 (15.7) | 88.0 (18.0) | CLS > 1 & < 3, 5, 6; RF < 2, 3, 5, 6; Calc < 6 | Below average reading (and math) | ✓ |
5 | Below average math fluency | 44 | 104.8 (10.8) | 106.2 (8.3) | 96.7 (14.8) | CLS > 1, 2, 4; RF > 1, 4 | Above average language & reading (not math) | ? |
6 | Above average overall | 38 | 107.2 (11.0) | 109.3 (10.3) | 101.4 (10.8) | CLS & RF > 1, 2, 3, 4; Calc > 1, 4 | Above average overall | ✓ |
Given the reasonable validation of our clusters in the Standardized Test Subsample as described above, we next explored differences in performance on our cognitive measures across clusters. To do this, we completed a multivariate ANOVA with cluster (6 levels) as the between group factor, and the data related to short-term memory, working memory, intelligence, and phonological awareness from our Standardized Test Subsample entered as multivariates. All effects were significant,
Cluster / Validation Descriptor | Ph. STM | vssp STM | Working Memory | Peformance IQ | Ph. awareness | Summary of consistent differences relative to 3 or more other clusters | |
---|---|---|---|---|---|---|---|
1 | Below average overall / Below average overall | 85.5bcde (11.9) | 96.4ab (17.7) | 88.1abcd (10.9) | 91.4abcd (9.7) | 8.0abcd (2.6) | phonological STM, working memory, performance IQ, phonological awareness significantly lower |
2 | Below average sentence recall / Lower language than reading | 88.1fghi (9.8) | 101.5c (15.3) | 94.8fa (9.4) | 99.6aef (11.8) | 10.8a (2.4) | phonological STM significantly lower |
3 | Below average reading efficiency / Average overall | 98.7bf (12.4) | 103.4 (15.0) | 97.7b (9.3) | 101.4bg (12.8) | 11.6be (6.5) | |
4 | Below average math and reading / Below average reading (and math) | 96.7cg (13.5) | 99.5d (18.3) | 95.4c (8.9) | 98.3hi (12.7) | 9.1efg (2.5) | phonological awareness significantly lower (with average phonological STM) |
5 | Below average math fluency / Above average language & reading | 101.6dh (14.5) | 111.8acd (15.3) | 101.4df (10.1) | 108.6ceh (16.8) | 11.8cf (2.6) | PIQ, visuospatial (vssp) short term memory significantly higher |
6 | Above average overall / Above average overall | 103.4ei (11.8) | 107.3b (13.5) | 100.6e (9.0) | 109.9dfg (13.4) | 12.1dg (2.3) | PIQ significantly higher |
Note: Same superscript indicates significantly different pairs; verbal STM – digit recall; vssp STM – block recall; Phonological (Ph.) awareness – elision (scaled score:
The distribution of cluster membership across the epidemiological sample is shown in
Cluster Descriptor / Validation Descriptora | Epidemiological Sample | Children with potential LDb | |
---|---|---|---|
1 | Below av. Overall | 10% | 27% |
2 | Below av. sentence recall / Lower language than reading | 17% | 24% |
3 | Below av. reading efficiency / Av. Overall | 18% | 12% |
4 | Below av. math and reading / Below av. reading (and math) | 11% | 27% |
5 | Below av. math fluency / Above av. language and reading | 16% | 7% |
6 | Above av. Overall | 28% | 3% |
A final descriptive analysis considered whether the learning profile distributions of children with a potential learning disability differed from that of the Epidemiological Sample. To do this, we compared the cluster membership distribution (see
In a large epidemiological sample, we identified clusters of children differing in patterns of relative strengths and weaknesses in language, reading, and math. In addition to finding profiles of children who had globally above or below average abilities across all three academic skills, we found separable profiles of children who had relative weaknesses specific only to language, reading efficiency, math fluency, or reading and math combined. Using independent measures available for a subsample of the original participant group, we validated all profiles except that involving relative weaknesses in reading efficiency. Examination of the learning profiles of the subset of the epidemiological group for whom there was some evidence of a learning disability (i.e., below average performance on one or more screening measures) revealed higher proportions of relatively specific deficits in language, or reading and math. Importantly, we discovered that these unique learning profiles could be further distinguished by differing abilities in underlying cognitive processes including immediate memory, intelligence, and phonological awareness. Perhaps not surprisingly, the overall below average group was weak across all of these cognitive processes, and higher nonverbal intelligence scores characterized the above average overall group. Of interest, limitations in phonological short-term memory characterized the group with a relative weakness in language, whereas limitations in phonological awareness were observed in the group with dual reading and math weaknesses.
The present findings clearly establish that there are patterns in children’s learning that go beyond a simple below average, average, above average grouping. Using a novel cluster analysis approach, we identified children with both general and specific learning profiles. Over one third of our large epidemiological sample had a general learning profile characterized by either consistently above or below average performance across all measures. These groups with generally enhanced or depressed learning were further distinguished by significantly higher or lower nonverbal intelligence, respectively, a finding consistent with the well-established relationship between general intellectual ability and academic performance (e.g., [
Of greater interest are the four specific learning profiles we observed characterized by below average scores on one of language, reading and math, reading only, or math only. Our validation analysis using independent measures in a subset of the original sample confirmed the first two profiles, and was numerically consistent for the group with a specific math learning difficulty. There was less evidence for a specific reading difficulty in that this profile was not confirmed in our validation analysis using an additional reading fluency measure that involved reading short sentences. Nevertheless, it may be that the reading fluency task was not as sensitive to individual differences in reading as the single word and nonword reading measures employed in our cluster analysis. The results of this validation analysis must be interpreted with caution because the subsample on which it was based differed in composition from the original epidemiological sample. Nevertheless, the considerable consistency in the learning characteristics between the two independent sets of measures suggests that the learning profiles identified in our cluster analysis warrant further attention.
Our analysis of children who performed poorly on the screening measures provided unique information about the learning profiles of children with possible learning disabilities. Just over one quarter (27%) of these children exhibited a general pattern of poor scores across measures, compared to 10% in the entire sample. Importantly, 70% presented with a relatively specific learning impairment. These data are the first to suggest that specific patterns in learning strengths and weaknesses characterize the majority of children with learning disabilities.
What does the observed comorbidity tell us about potential underlying factors? Consider first the pattern observed in the present results for the oral language measure, sentence recall. Poor language coupled with somewhat higher and similar scores on reading and math occurred across three clusters and characterized 45% of the entire sample. Low language scores never occurred entirely in isolation. They occurred either with below average reading only (relative to the sample), or, in more severe cases, both below average reading and math (i.e., a general below average profile). Thus, poor language was associated with below average reading consistently, but was linked to low math scores only when language scores were markedly poor. These language-based clusters were differentiated in our analysis of related cognitive measures by low phonological short-term memory, a finding consistent with previous research demonstrating strong links between phonological short-term memory and vocabulary development [
Reduced efficiencies in reading occurred either with a language deficit, with a math deficit, or with no other deficits. The two comorbid clusters (i.e., weaknesses in reading and language, or in reading and math) were differentiated by their cognitive profile: the below average reading and language cluster was associated with poor phonological short-term memory, whereas the below average math and reading cluster had low phonological awareness. These differing cognitive profiles may suggest different underlying causes, the language impairment in the case of the below average reading and language cluster with low phonological short-term memory, and a deficit specific to another aspect of phonological processing for the below average reading and math cluster. Although less clear, the results for the reduced reading efficiency cluster revealed high variability in phonological awareness potentially indicating some phonological processing weakness in this group as well. The common cognitive profile of low/variable phonological awareness in the low reading only and low reading and math clusters suggests a possible common etiology to this reading impairment that is distinct from the mechanism involved in the below average language and reading cluster. Certainly, the finding of a specific association between phonological awareness and reading is consistent with many previous studies of typical reading development [
For math fluency, below average scores occurred in relative isolation, with below average reading efficiency, or with a general below average profile (including markedly low language). The comorbid clusters with math were differentiated by their cognitive profiles with the below average reading and math cluster having a phonological awareness deficit, and the general below average group having multiple deficits. Importantly, the cognitive profile of the general below average cluster had an impairment in common with the other clusters involving below average language, phonological short-term memory. Once again, these results suggest distinct etiologies for these two comorbid deficits, one possibly language-based in the general below average profile, and one related to reading but not language. Unfortunately, our measures did not capture any cognitive deficits in our below average math fluency cluster. The only indication of a difference between our below average math only vs. below average math and reading clusters was that the below average math and reading cluster had a phonological awareness deficit while the below average math fluency group did not. It may be that differences in these groups would have been revealed had additional cognitive measures been included. In future, studies of this nature should include measures specific to the cognitive mechanisms thought to support math skills such as estimating the number of objects in a group [
While it is interesting to speculate on the patterns observed in the present study, it is clear that caution is warranted in interpreting the observed comorbidity. For one, the 3-cluster solution adequately explained the data. It may be that a general factor can capture a considerable proportion of the variation characterizing young children’s learning. Indeed, our reading and math measures were timed placing demands on processing speed, which has been suggested as a common deficit in reading disorder and ADHD [
The present study examined learning profiles on language, reading, and math screening measures across a large epidemiological sample of school age children. Three primary clusters reflective of below average, largely average, and above average performance across measures were sufficient to describe the sample. More detailed analyses identified overall above and below average profiles, as well as unique learning profiles involving weaknesses in language, reading, math, or reading and math. These latter four specific profiles characterized 70% of those with a potential learning disability as evidenced by below average performance on at least one screening measure. As well, differences in cognitive profiles characterized several of the clusters including associations between poor phonological short-term memory and language-based weaknesses, and between poor phonological awareness and reading weaknesses. The results have implications for the study of learning disabilities that warrant further investigation and replication. Specifically, distinct specific and cormorbid subtypes of learning profiles were identified and were common among those with potential learning disabilities. As well, the findings suggest different etiologies for language-based deficits across domains, reading-related impairments in reading and math, and isolated math disabilities.