Cognitive Dimensions of Learning in Children With Problems in Attention, Learning, and Memory

Abstract

A data-driven, transdiagnostic approach was used to identify the cognitive dimensions linked with learning in a mixed group of 805 children aged 5 to 18 years recognised as having problems in attention, learning and memory by a health or education practitioner. Assessments included phonological processing, information processing speed, short-term and working memory, and executive functions, and attainments in word reading, spelling, and maths. Data reduction methods identified three dimensions of phonological processing, processing speed and executive function for the sample as a whole. This model was comparable for children with and without ADHD. The severity of learning difficulties in literacy was linked with phonological processing skills, and in maths with executive control. Associations between cognition and learning were similar across younger and older children and individuals with and without ADHD, although stronger links between learning-related problems and both executive skills and processing speed were observed in children with ADHD. The results establish clear domain-specific cognitive pathways to learning that distinguish individuals in the heterogeneous population of children struggling to learn.

Several children in a typical classroom experience persistent learning difficulties that may reflect weaknesses in cognitive skills. Many education practitioners use areas of learning difficulty – such as reading or mathematics – as a guide to tailor their support. Researchers and other professionals in both education and health services use criteria-based diagnostic categories such as those outlined in the Diagnostic Statistical Manual-5 (DSM-5; American Psychiatric Association, 2013) to group children when examining phenotypic characteristics and underpinning mechanisms. While classification-based approaches have many pragmatic merits, they often fail to detect those with relatively mild problems, and the more complex needs of children with co-occurring problems can go unaddressed (Coghill & Sonuga-Barke, 2012). To capture the needs of the full range of struggling learners more effectively, this study adopted an alternative transdiagnostic approach to developmental disorders (Casey et al., 2014; Kushki et al., 2019; Sokolova et al., 2017). Putting disorder-based categories aside, the data themselves were used to identify cognitive dimensions and their links to learning in a large and highly heterogeneous sample that included children with and without diagnosed neurodevelopmental disorders recruited from education and health services. The study was preregistered (https://osf.io/jvm5t/).

Learning Problems

Unexplained learning difficulties are extremely common. Between 14 and 30% of school-aged children in the United Kingdom and the United States require additional support for learning (Department for Education, 2018; National Center for Education Statistics, 2019). The prevalence of reading difficulties is estimated at 16% (Catts et al., 2012), 7% of the school population are considered to be dyslexic (Peterson & Pennington, 2012), and 3% of children have reading comprehension problems (Lervåg & Aukrust, 2010; Snowling et al., 2009). Approximately 10% of children have a developmental language disorder (Laasonen et al., 2018) and mathematical difficulties are present in between 3 and 13% of children (Geary, 2013; Landerl & Moll, 2010). Long-term outcomes for individuals with learning problems include early disengagement from education (Balfanz et al., 2007), low rates of employment (Bynner et al., 2005; De Beer et al., 2014) and increased risks of mental health and behavioural problems (Emerson & Hatton, 2007). The need to minimise the risks of continued educational underachievement and the associated societal and economic costs is great: poor academic progress has many causes that can interact and cascade over time (e.g. Masten & Cicchetti, 2010).

Children often experience problems in multiple aspects of learning and behaviour. Co-occurring reading difficulties are present in between 17 and 70% of children with mathematical learning problems, and corresponding rates of mathematical difficulties in children identified with reading problems are 11 to 56% (Barbaresi et al., 2005; Dirks et al., 2008; Moll et al., 2014). Many children with learning difficulties also meet the diagnostic criteria for Attention Deficit and Hyperactivity Disorder (ADHD), a psychiatric disorder based on observations of elevated levels of inattention, hyperactivity and impulsivity (APA, 2013). In a US population study, 44% of children with ADHD had learning difficulties and 42% of those with a specific learning disability met criteria for ADHD (Pastor & Reuben, 2008). Learning difficulties are also common among individuals with Autism Spectrum Disorder (ASD), a term used to describe individuals with communication and social deficits, and restricted or repetitive interests and behaviours (APA, 2013). Prevalence rates of learning disorders among children with ASD range from 65-85% (Gillberg & Coleman, 2000).

Cognitive Origins of Learning Problems

There is a wealth of research examining links between cognition and learning in child populations, including those experiencing learning-related difficulties who are considered to have special educational needs, and clinically-recognised groups with neuropsychological disorders that include learning. This section provides an overview of some of the cognitive skills known to be closely related to children’s attainments in two key areas of academic learning, reading and mathematics. It should be noted that although the conventional labels for cognitive skills are used here, scores on each task draw on multiple and sometimes overlapping cognitive abilities. This can raise interpretational challenges, as the following three examples illustrate. Scores on conventional tests of phonological processing and verbal short-term memory (STM) are highly correlated. This could either reflect a common cognitive skill or sensitivity of both kinds of task to common as well as distinct processes (Gathercole, 2006; Melby-Lervåg, Lervåg, et al., 2012; Ramus et al., 2013). Working memory (WM) is widely investigated as distinct from executive function in the field of cognitive development and learning. However, it is often classified as a component of a multi-faceted executive system includes updating and inhibition in other fields (Miyake et al., 2000; St Clair-Thompson & Gathercole, 2006). The particular conditions under which cognitive abilities are measured can also influence the cognitive demands of a task. For example, simple measures of processing speed are often found to be linked to the higher-level abilities such as nonverbal reasoning (Fry & Hale, 1996; Jensen, 2006; Kievit et al., 2016; Sheppard & Vernon, 2008). The specific cognitive processes supporting the different tasks appear to be distinct. However, slower rates of processing impair performance on tasks are either time-based or time-limited (Salthouse, 1996).

Reading

Phonological Processing

Children with specific reading difficulties have deficits in a range of phonological skills including nonword reading, phonological awareness and rapid naming (Herrmann et al., 2006; Johnson & Goswami, 2010; Kudo et al., 2015; Melby-Lervåg, Lyster, et al., 2012; Metsala et al., 1998; Swanson & Jerman, 2006) This evidence provides the foundation for the hypothesis that reading difficulties arise from phonological processing limitations that interfere with the use of phonological representations to guide reading. These limitations include problems in phonological awareness, the ability to reflect on and manipulate covertly the constituent sounds of words. Limitations in phonological awareness are suggested to impair the acquisition and application of spelling-sound correspondences that are critical for decoding and spelling words (Bishop & Snowling, 2004; Clayton et al., 2020; Perfetti, 2007).

Although close links between phonological processing and reading development are evident, they are not yet fully understood. Phonological awareness contributes to reading development, but it also benefits from both reading instruction and exposure to text during reading acquisition (Huettig et al., 2018; Wagner et al., 1994). Recent evidence suggests that such reciprocal effects between cognitive abilities, as well as between cognitive abilities and school outcomes, are likely ubiquitous (Kievit et al., 2019; Peng & Kievit, 2019). Studies of formerly illiterate adults whose very low levels of phonological awareness at the beginning of reading instruction closely tracked their later success in learning to read support this (Morais, 1987; Morais & Kolinsky, 2005). However, it is also evident that phonological deficits cannot explain all forms of reading difficulties. Children with developmental surface dyslexia have no impairments in applying letter-sound correspondences to decode and spell words, but struggle in learning words with orthographically irregular sound patterns (Castles & Friedmann, 2014). Other children have no difficulties with single word reading but have impairments in the comprehension of written text (Cain et al., 2004; Nation, 1999).

Measures of verbal short-term memory (STM) such as digit span and nonword repetition are strongly associated with reading abilities (Gathercole et al., 2003; Kudo et al., 2015; Peng & Fuchs, 2016; Swanson et al., 2009). The causality of these links has been widely debated. One suggestion is that STM is critical for the maintenance and assembly of phonological segments in the process of word identification (Preßler et al., 2014). A discussed above, some have argued that there are no direct causal links between STM and reading and that their association is simply mediated by a common contribution of phonological processing skills (Melby-Lervåg, Lervåg, et al., 2012; Melby-Lervåg, Lyster, et al., 2012).

WM is a more complex cognitive system that combines short-term storage with the attentional capacity to integrate temporary representations of recently processed information with sources of long-term knowledge (Allen et al., 2012; Baddeley, 2010). Verbal measures of WM are highly correlated with reading. This has been proposed to reflect the role played by WM in integrating multiple sources of knowledge including phonological representations from STM and lexical-semantic knowledge from long-term memory (Cantor & Engle, 1993; Swanson & Ashbaker, 2000). Analyses of reading comprehension indicate that while WM is important, the abilities to draw inferences from text and monitor comprehension are also critical (Cain et al., 2004). The extent to which the link between WM and reading reflects a direct causal association has not gone without challenge. For example, findings from Nation (1999) suggest that verbal WM deficits are a consequence of, rather than a contributor to, the language processing problems of children with poor reading comprehension.

Executive Functions

Problems in the high-level control of cognitive resources tapped by executive function tasks have been reported in children with reading difficulties (Booth et al., 2010; Carretti et al., 2009; Yeniad et al., 2013). This is perhaps unsurprising: reading involves the coordination of multiple processes including attending to visual word forms, decoding words, retrieving semantic and lexical information, and integrating the syntactic and semantic context of a passage of text. Selective attention has been linked to the visual pattern recognition element of reading, while the flexible deployment of attention is thought to support the decoding of words and the extraction of their meaning (e.g., Cartwright, 2012). Inhibitory control has been proposed to be vital for the suppression of irrelevant word meanings and details when reading complex sentences containing words with multiple meanings (De Beni & Palladino, 2000; Kieffer et al., 2013). Both inhibitory control and the ability to switch attention have been associated with the development of reading skills, and in particular with the transition from early phonological to more advanced orthographic reading processes (Booth et al., 2010; Follmer, 2018).

Fluid Intelligence

Measures of nonverbal reasoning are widely considered to measure the general construct g that is common to cognitive tasks (Spearman, 1904). It is widely considered to reflect fluid intelligence, or more specifically, the flexible cognitive resources that an individual has to solve new problems (e.g., Duncan, 2013). While nonverbal reasoning is positively linked with reading ability (Peng et al., 2019), there is little evidence that it contributes directly to the phenotypic characteristics of reading disorders (Elliott & Grigorenko, 2014).

Processing Speed

Fluent reading requires rapid processing of incoming information (e.g., Cohen et al., 2008; Dehaene et al., 2005; Pastor & Reuben, 2008). Children with reading problems are relatively slow on rapid automated naming tasks used to measure the speed of verbal processing (Araújo et al., 2015). It has been suggested that rather than being central to reading difficulties (Kail & Hall, 1994), slow verbal processing speed may be a consequence of phonological processing difficulties (Bonifacci & Snowling, 2008; Patel et al., 2004). Nonverbal processing speed deficits are less common in reading difficulties (Bonifacci & Snowling, 2008; Gooch et al., 2012) and have been suggested to reflect co-occurring attentional problems (McGrath et al., 2011; Willcutt et al., 2010) or low IQ (Bonifacci & Snowling, 2008).

Mathematics

Phonological Processing

The phonological representation hypothesis proposes that solving calculation problems requires encoding and maintaining phonological representations in STM, and retrieving phonological codes from long-term memory (Hecht et al., 2001; Simmons & Singleton, 2008; Vukovic & Lesaux, 2013). However, the impact of phonological processing on mathematical development is not without debate. It has been suggested that the manipulation of phonological information influences mathematical achievement by supporting number-word sequence learning (Krajewski & Schneider, 2009) and that deficits in phonological processing are related to early calculation difficulties (Hecht et al., 2001). Other evidence indicates that phonological processing deficits are only present in children who have difficulties in both reading and mathematics because phonological processing problems are closely related to reading skills (Fuchs et al., 2005; Landerl & Moll, 2010).

STM and WM

It has been suggested that skills in these temporary storage systems may support the storage of problem information and both the storage and retrieval of partial results for simple and complex mathematical tasks (De Smedt et al., 2009; Passolunghi et al., 2008; Peng et al., 2016). Geary (1993, 2003) proposed that these memory systems enable children to remember number bonds to commit to a network of arithmetic facts in long-term memory. Mathematical abilities are typically more closely associated with visuo-spatial than verbal aspects of STM and WM (Holmes et al., 2008; Li & Geary, 2013; Meyer et al., 2010). The specificity of this deficit is most evident in children with specific impairments in mathematics but not in reading (Child et al., 2019; Cirino et al., 2018; Szucs et al., 2013; Willcutt et al., 2013).

Executive Functions

Mathematical abilities are associated with many aspects of executive functioning in typically-developing individuals and are often impaired in those with mathematical difficulties (Friso-van den Bos et al., 2013; Johnson & Goswami, 2010; Peng et al., 2018; Peng & Fuchs, 2016; Swanson & Jerman, 2006; Yeniad et al., 2013). Inhibitory control and attentional switching are two areas of deficit common in groups with mathematical problems (Bull & Scerif, 2001; Landerl & Kölle, 2009; Rotzer et al., 2009; Szucs et al., 2013). These skills have been suggested to play important roles in supporting the selection of solution strategies and the suppression of non-optimal approaches (Bull & Lee, 2014).

Fluid Intelligence

Nonverbal reasoning ability is more strongly associated with attainments in mathematics than reading (Peng et al., 2019). This may reflect the high cognitive loads involved in learning and acquiring increasingly complex concepts and sets of rules as mathematical education progresses, and also the greater reliance on abilities to represent and manipulate information in the nonverbal domain at multiple stages of mathematical learning (Peng et al., 2018; Peng & Kievit, 2019; Young et al., 2018).

Processing Speed

Geary (1993) and Gersten et al. (2005) have suggested that processing speed supports fluent counting, which in turn allows problems and answers to be bound in WM before entering long-term memory. This binding of problems and answers supports the development of a network of basic arithmetic facts in long-term memory that can be used to rapidly retrieve answers as mathematical skills develop (Hamann & Ashcraft, 1985; Kaye, 1986). Consistent with this, children with mathematical difficulties are less likely to use direct memory retrieval to solve arithmetic questions (Bull & Johnston, 1997; Geary et al., 1991; Mussolin & Noel, 2008), count more slowly and inaccurately than children with age-appropriate maths abilities (Bull & Johnston, 1997; Geary et al., 1992), and have weak or incomplete networks of number facts in long-term memory (Geary et al., 1991; Hitch & McAuley, 1991). Faster processing speed may also help prevent the decay and loss of task-critical information such as the arithmetic problem the child is attempting to solve, or the interim calculations that are necessary steps in more complex mathematical calculations (Holloway & Ansari, 2008).

A New Approach to Learning Problems

The majority of studies of children with specific learning difficulties employ relatively small numbers of participants grouped according to the presence or absence of one or more disorders such as ADHD and reading difficulties (Marzocchi et al., 2008; Rucklidge & Tannock, 2002; Willcutt et al., 2001). Participant selection is widely based on inclusionary and exclusionary criteria applied in recruitment from either clinical or school populations (Geurts et al., 2006; Jordan et al., 2003; McLean & Hitch, 1999).

Group-based studies such as these have shaped our understanding of the cognitive deficits underlying specific learning difficulties, but the approach has its limitations. Participants are often recruited according to stringent criteria that are arbitrarily set and inconsistently applied across studies (Stuebing et al., 2012; Tolar et al., 2014). For example, selection criteria for children with reading difficulties ranges from reading scores of -1 standard deviation (SD) to -2.5 SD below the population mean (Barbot et al., 2016; Catts et al., 2006). As a consequence, children included in one study may be excluded from others, yielding evidence that may not be generalizable to the broad, mixed population of children with learning-related difficulties (Coghill & Sonuga-Barke, 2012; Kotov et al., 2017). Within-group heterogeneity is often disregarded and undetected, with analysis focussing on differences at the group level that mask the high levels of variability found in the cognitive characteristics of children within each group. This is evident in the high degrees of variability in executive function skills in children with ADHD (Castellanos et al., 2005; Nigg et al., 2005) and in the variable cognitive profiles of children with reading difficulties (Nation et al., 2002). Group designs also obscure cross-disorder commonalities in symptoms across different conditions. WM problems, for example, are common across children with difficulties in reading and mathematics, as well as those with ADHD and ASD (Duinmeijer et al., 2012; Gathercole & Alloway, 2008; Holmes et al., 2008; Loe & Feldman, 2007; Rommelse et al., 2011).

The same issues of high levels of symptom heterogeneity, cross-disorder homogeneity and comorbidity in adult psychopathology has led to a shift towards using symptom dimensions rather than singular diagnostic labels to understand these complex conditions (Cuthbert & Insel, 2013; Owen, 2014). This transdiagnostic approach opens up the possibility of tailoring interventions to the constellation of needs of the individual rather than to a single and potentially ill-fitting diagnostic label, with promising applications of this approach in the areas of depression, anxiety and psychosis (e.g., Newby et al., 2015; Mercier et al., 2018; Reininghaus et al., 2019; Sakiris & Berle, 2019; Titov et al., 2011).

Although the value of extending this approach to neurodevelopmental disorders has been widely recognised (Casey et al., 2014; Sonuga-Barke et al., 2016; Sonuga-Barke & Coghill, 2014; Zhao & Castellanos, 2016), the majority of studies espousing this approach over the past decade have compared cognitive or behavioural symptoms across groups of children with conventionally-defined disorders such as reading difficulties, maths difficulties, ADHD or ASD with typically-developing individuals (de Jong et al., 2009; Hobson, 2014; Karalunas et al., 2014; Mercier et al., 2018; Willcutt et al., 2013).

This situation looks set to change with the recent emergence of studies using data-driven analyses of symptom-level data as an alternative to diagnostic categories to understand developmental disorders present in the population at large. Applying this approach to a mixed sample of children with ASD, ADHD and OCD, as well as typically-developing children, Kushki et al.(2019) identified ten clusters with shared cognitive, behavioural and neurobiological phenotypes. Most clusters included children from multiple diagnostic groups and the authors concluded that they may be best understood as reflecting two key dimensions – the behavioural features of ASD and inattention – that extend across both typical and atypical populations. Sokolova et al. (2017) took an even more direct dimensional approach to multiple diagnosed neurodevelopmental conditions. Combining large samples of children with ADHD and ASD, as well as affected and unaffected siblings and controls, they identified common pathways relating to hyperactivity/ repetitive behaviour, impulsivity/ social understanding and inattention/ social understanding that bridged the two disorders. By this approach, conditions usually considered as comorbid are simply emergent properties of the multiple and sometimes common dimensions of impairment present in different diagnosed conditions.

The Present Study

This study is to our knowledge the first to apply a fully data-driven transdiagnostic approach to a large, mixed sample of children experiencing learning-related problems. Its aim was to identify the dimensions of cognitive impairment that characterize children across the spectrum of severity of learning-related difficulties. The sample included children with relatively mild problems considered by educational practitioners to be compromising their academic progress, who would likely not meet diagnostic thresholds for specific learning disorders, in addition to many children whose more marked problems definitely would. A considerable proportion of the sample had a primary diagnosis of ADHD, a neurodevelopmental disorder characterised by inattention and hyperactivity and high rates of co-occurring learning disorders (Holmes et al., 2014; Willcutt et al., 2010).

A critical step in meeting the goals of any study is establishing a suitable sampling frame (Cuthbert & Insel, 2013). The goal in this study was to recruit a highly heterogeneous sample of children varying in both the severity and nature of their learning-related problems, and in whom other co-occurring conditions were neither inclusionary nor exclusionary criteria. This could not be achieved using the recruitment methods usually applied in this field. It was not possible to not depend exclusively on recruiting children with recognised disorders through specialist clinics, as this would exclude children with milder learning-related difficulties who are unlikely to meet referral thresholds for these centres. Routine school-wide screening to identify these children with milder problems through schools (who represent approximately 15% of the school population) was not feasible to achieve the target sample size of 800 children needed for a latent variable study with large numbers of assessments. Moreover, a central tenet of the approach adopted here was to represent the full spectrum and complexity of children with learning-related problems, avoiding selection criteria involving arbitrary cut points for population-referenced learning scores that themselves have limited sensitivity to a child’s true abilities.

To address these issues, we adopted the following sampling frame. Referrals were requested of children aged between 5 and 18 years with difficulties related to attention, learning, and/ or memory from a large network of head teachers, specialist and special educational needs teachers, educational and clinical psychologists, speech and language therapists and paediatricians. Referrers were advised that children with other known psychological, psychiatric or health problems should not be excluded from the study. To ensure the difficulties faced by those recruited fell broadly within the categories of attention, learning and / memory, a member of the research team contacted the referring practitioner for a brief description of child’s problems upon receipt of an expression of interest form from a family. The children were therefore selected on the basis of functional problems related to cognition and learning that had been identified by experienced professionals. To ensure that children with attentional problems were well-represented in the sample, children exhibiting high levels of ADHD symptoms were recruited. Many had been diagnosed with ADHD and others had a diagnosis of possible ADHD from a specialist ADHD nurse. A research clinic for the children was established as part of the larger Centre for Attention Learning and Memory (CALM) project (Holmes et al., 2019). Study exclusionary criteria were uncorrected sensory problems, known neurological or genetic disorders, non-native English speaker and referrer descriptions that did not conform to the recruitment rubric. Data from 805 children attending the clinic were analysed to identify the main dimensions of cognitive skills and to chart links between these cognitive dimensions and learning. Of the sample, 484 had no diagnosis, 321 had been diagnosed with one or more disorders related to learning, behaviour or mental health. Of those with a diagnosis, 255 had been diagnosed with ADHD, or were identified as probably having ADHD following assessment by a specialist nurse practitioner but were awaiting a final diagnosis (see Table 1).

Table 1. Diagnostic Status of all Children in the CALM Sample.

Diagnosis	N (female)
ADHD or possible ADHD	255 (61)
Dyslexia	47 (15)
Dyspraxia	21 (7)
Dysgraphia	1 (0)
Dyscalculia	2 (2)
FASD	6 (4)
Global delay	10 (5)
Depression	4 (3)
Anxiety (inc. social anxiety)	9 (4)
Autism	57 (7)
PDA	1 (1)
Tourettes	5 (1)
DAMP	4 (1)
OCD	5 (4)
Sensory processing disorder	3 (1)
Language disorder (inc. SLI)	2 (1)
Conduct disorder	1 (0)
ODD	3 (1)
Epilepsy	3 (2)
Anorexia	1 (1)
Speech & language therapy	163 (50)
No diagnosis	484 (166)

Note. Total N is higher than the sample size as some children had multiple diagnoses.

The wide age range of children in the study provided the opportunity not only to investigate the broad links between dimensions of cognitive skill and learning across the sample as a whole, but also to detect possible changes in the dynamic nature of cognition-learning relationships across the course of development. Phonological processes have long since been considered important for early reading development, supporting word decoding (e.g., de Jong & van der Leij, 1999; Heath et al., 2014; Torgesen et al., 1994). Executive skills are more typically linked to advanced aspects of reading such as text comprehension (De Beni & Palladino, 2000; Follmer, 2018; Pimperton & Nation, 2012). However, both skills independently account for age-related changes in reading in typically developing children (Swanson & Howell, 2001). Early maths development relies on learning arithmetic facts, which has been linked to phonological proficiency (e.g., Bull & Johnston, 1997). Learning to align and mentally represent numerical values have both been linked to visuo-spatial skills (Geary, 1993; Holmes & Adams, 2007; McKenzie et al., 2003). Evidence suggests a greater role for executive abilities in more complex mathematics problem-solving as children get older (Swanson, 2006), and for selecting and switching between different solution strategies (Bull & Lee, 2014). Consistent with this, growth in executive skills is the strongest determinant of mathematical problem-solving skills over developmental time (Bull et al., 2008; Swanson, 2006; Van der Ven et al., 2012; Viterbori et al., 2015). In this study we were able examine whether corresponding changes in the concurrent links between broad cognitive dimensions and learning are also present in children with learning-related problems.

A latent variable approach was adopted to identify the primary cognitive dimensions of the sample, in line with data-driven approaches recently adopted in other transdiagnostic, dimensional studies (e.g., Kotov et al., 2017; Mercier et al., 2018; Reininghaus et al., 2019; Sokolova et al., 2017). This approach side-steps debates about which of two different measures sharing common variance represents the core deficit (e.g., phonological processing or verbal STM in reading difficulties). It simply identifies the major sources of variance across all measures in a dataset: in this case, the broad dimensions of cognitive skills that may or may not contribute to learning. Using this approach, we set out to answer two primary questions.

1. What are the broad cognitive dimensions underpinning individual cognitive abilities within this sample?

The choice of the cognitive assessments included was guided by measures identified in previous research as showing robust links to learning. The majority of assessments were age-standardised tests that spanned across the full age range of the sample. This made it possible to measure performance relative to the typically developing population at each age and also yielded comparable scores across age groups for the analyses. The test battery assessed six aspects of cognition: phonological processing, processing speed, STM, WM, executive functions, and nonverbal reasoning. It was anticipated that the dimensional structure of the data might take one of three possible forms. First, the tasks might fit neatly within the conventional neuropsychological taxonomy of cognitive assessments, with dimensions corresponding to phonological processing, STM, WM, executive functions, and fluid intelligence. Second, the dimensions might crosscut these task-based dimensions and instead fractionate according to domain (verbal vs visuo-spatial). Third, a hybrid model might emerge that combines domain-specific factors with a domain-general factor spanning all tasks requiring higher-level cognitive control.

2. How are the cognitive dimensions linked with learning?

Reading abilities both in the general population and in groups of typical and atypical learners are closely associated with phonological skills (e.g., Bishop & Snowling, 2004; Melby-Lervåg & Hulme, 2010). In contrast, mathematical abilities are more strongly linked with visuo-spatial skills and executive functions (Peng et al., 2018), particularly when children with comorbid reading difficulties are excluded (e.g., Szucs et al., 2013). Whether the same dimensions differentiate a large mixed sample of children with learning-related difficulties is unknown. If the same factors influence learning as in other typical and atypical populations, it would be expected that reading abilities would be strongly linked with phonological processing and verbal aspects of STM and WM, while mathematical abilities would show the strongest links with tasks requiring executive control.

Method

Participants

This study includes all children attending the CALM clinic between February 2014 and December 2018. The children were referred by a network of practitioners in education (teachers, special needs coordinators, specialist teachers, educational psychologists, health (paediatricians, child psychiatrists and psychologists, ADHD nurses), and speech and language therapists. Figure 1 shows the number of children and number of girls referred from each category of referrer. The age of children referred from education was, M= 9.28, SD=2.13 (boys M=9.25, SD=2.09; girls M=9.34, SD=2.20), from health was, M=9.93, SD=2.74 (boys M=9.74, SD=2.67; girls M=10.49, SD=2.87), and from speech and language therapy was M=8.93, SD=2.59 (boys M=8.87 SD=2.66; girls M=9.03 SD=2.56). A UK-based Index of Multiple Deprivation (IMD) was used to classify the socio-economic status of the sample (English Indices of Deprivation, 2019). Scores for different local areas in the UK range from 1^st to 32844^th (most to least deprived). The average and range of IMD for the (M=20487, range 155-32803), indicated participants came from areas with varying degrees of deprivation, with an average ranking above the national median.

Figure 1. Consort Diagram Showing CALM Study Referral Routes.

Note. n (female). M and SD are ages in years. CAMHS = Child and Adolescent Mental Health Services. SLT = Speech and Language Therapists.

Children were eligible to take part if they were aged between 5 and 18 years (M = 9.48, SD = 2.38) and had been recognised by a referrer as having problems in one or more of the following areas: attention, memory, language, maths, and / or literacy. Exclusion criteria were significant uncorrected visual or hearing problems, pre-existing genetic or neurological conditions for which cognitive difficulties are known possible symptoms, and not being a native English speaker.

Referrers passed a study information pack to families with children who they judged in their professional opinion to have problems in the areas of attention, learning and / or memory. Families then sent an expression of interest form to CALM if they wanted to participate. The research team then contacted the referrer to discuss the child’s problems and diagnostic status, and to check their eligibility for the study. If the child met the inclusion criteria, the family was sent an appointment letter to attend the clinic for an assessment. Families were reminded of their appointment by telephone the day before the assessment, and at this time, they were asked whether their child had any diagnosed conditions.

The number of children referred to CALM was 914 (291 females). Twenty-five families did not attend their clinic appointment and a further 77 children did not meet the inclusion criteria. A total of 812 (255 females) were assessed, with data excluded for three children who were non-native English speakers, three children who refused to complete the majority of the tests, and one child with a neurological condition that prevented completion of the assessments (see Figure 1). Reports of diagnosed disorders from the referrer and family at the time of referral are summarised in Table 1. The percentage of children with ADHD (or probable ADHD) was 31.7%, and with ASD was 7.1%. These are higher than average prevalence rates reported for a UK population representative school sample (e.g., ADHD, 1.4%; ASD, 1.7%, Russell et al., 2014). Of the sample, 5.8% had a diagnosis of dyslexia, lower than the 7% reported for school populations (Peterson & Pennington, 2012), and 20.3% had a diagnosed language problem or had sought help from a speech and language therapist, which is higher than recently reported prevalence rates of diagnosed developmental language disorders (10%, Laasonen et al., 2018). The total number of children with ADHD included children with a diagnosis of ADHD (n=198; 107 of whom were taking medication) and those who had seen a specialist ADHD nurse and were awaiting the final diagnostic consultation (probable ADHD, n=57). Children with diagnoses of ADHD had been diagnosed by a clinician (child psychiatrist) prior to their referral to the study according to standard practice in the UK. This includes a psychosocial assessment, clinical and parent observer reports and a formal clinical assessment of the child’s mental state by a child psychiatrist. Those with probable diagnoses had been referred to child psychiatric services by their General Practitioner for concerns related to possible ADHD, had been assessed by a specialist ADHD nurse working in psychiatric services, and based on the nurses assessment had been referred for a final formal clinical appointment with a child psychiatrist to confirm their diagnosis.

The final sample for analysis includes 805 children (253 female), yielding power of .999/0.992 to detect a correlation of .2 with α = .05 and .001, respectively. Data from a subset of approximately 600 participants aged 8 years and over (8+) were analysed separately in a second set of analyses. Power for this subgroup was .998/ .951 to detect a .2 correlation with α=.05 and .001, respectively.

Materials and Procedures

Parents or caregivers completed questionnaires regarding the child’s behaviour, communication skills, family history, and mental health. Children participated in a four-hour assessment of cognitive and learning skills on a one-to-one basis. They were invited to provide an optional saliva sample for later genetic analysis and to attend a separate session for an optional MRI brain scan. A report summarising performance on the cognitive and behavioural tasks was sent to the referrer to guide ongoing support for the child. A full description of assessments administered in the CALM clinic is provided in the study protocol paper (Holmes et al., 2019). Analysis in the present study was performed on the cognitive and learning measures. All tests were presented in a fixed order to participants and had moderate to good reliability for use with the sample (see Table 2). The internal consistency and test re-test estimates for individual tasks ranges from .5 to .97. Some of these values are moderate rather than good, but using factor analytic methods means no single task is used as an indicator of performance in any particular cognitive domain. In the factor models (see Results, page 21) tasks with moderate reliability group with measures with high reliability, and the overall reliability of the factors, as measured omega is excellent, ω =0.83.

Table 2. Reliability Estimates for all Cognitive and Learning Tasks.

Measurement	Subtest	Internal Consistency α/ Average Split-Half Reliability	Average Test-Retest Reliability r
PhAB (6-14yrs)	Alliteration	0.86	-
Rapid Naming		0.89	-
CNRep		0.66	0.77
AWMA
	Digit Recall	-	0.89
	Backward Digit Recall	-	0.86
	Dot Matrix	-	0.85
	Mr X	-	0.84
CMS (5-16yrs)	Delayed Recall	0.75	-
TEA-CH 2 Junior (5-7yrs)	Cancellation (Balloon Hunt)	0.9	0.70
	Barking	0.58	0.37
	Simple Reaction Time	0.72	0.70
TEA-CH 2 Adult (8-15yrs)	Cancellation (Hector)	0.96	0.84
	Vigil	0.55	0.52
	Simple Reaction Time	0.91	0.81
	Reds Blues Bags Shoes	0.78	0.70
WASI-R (6-16yrs)	Matrix Reasoning	0.87	0.79
DKEFS (8-19yrs)
	Visual Scanning	-	0.5
	Number Sequencing	-	0.77
	Letter Sequencing	-	0.57
	Switching	0.77	0.78
	Motor Speed	-	0.82
	Tower - Total Achievement	0.61	0.51
WIAT-II	Word Reading	0.97	0.98
	Numerical Operations	0.91	0.92
	Spelling	0.94	0.96

Note. α = Cronbach’s alpha; r = correlation coefficient; test-retest reliability reported from time 1.

Cognition

Phonological Processing

Two subtests from the Phonological Assessment Battery (PhAB; Frederickson et al., 1997) were administered: Rapid Naming and Alliteration. Raw scores from both subtests were converted to standard scores (M = 100, SD = 15). The Children’s Test of Nonword Repetition (CNRep; Gathercole & Baddeley, 1996) was also administered: raw scores were converted to standard scores. Closest-age matching was used to derive standardised scores for children outside the age-normed reference frame (e.g., for those aged 11 and over, norms for 11 year olds were used). Analyses testing the appropriateness of these tasks for children for whom this scoring method was are reported in Supplementary Figures 5, 6 and 7. The CNRep was introduced after the first 300 children to attend the clinic had been tested.

Processing Speed

The Motor Speed and Visual Scanning subtests of the Delis Kaplan Executive Function System (DK-EFS; Delis et al., 2001) were administered. Completion times were converted to scaled scores (M=10, SD=3). The Simple Reaction Time subtest of the Test of Everyday Attention for Children 2 (TEA-Ch2; Manly et al., 2016) was also administered. Reaction time in seconds was recorded and converted to a scaled score.

Short-term (STM) and Working Memory (WM)

Four span tasks from the Automated Working Memory Assessment (AWMA; Alloway, 2007) were administered: Digit Recall (verbal STM), Dot Matrix (visuo-spatial STM), Backward Digit Recall (verbal WM), and Mr X (visuo-spatial WM). Trials correct were converted to standard scores for each task (M=100, SD=15). A following instructions task (Gathercole et al., 2008; Jaroslawska et al., 2016) was also administered. This experimental task required children to follow increasingly long instruction sequences. Total raw scores were tallied. To account for age, a regression analysis was conducted predicting raw scores from age. Residual scores therefore represent the difference between each participant’s observed and age-predicted score and were used for the purpose of the reported analyses.

Episodic Memory

The Stories subtest of the Children’s Memory Scale (Cohen, 1997) was used to assess verbal episodic memory. Children listened to two stories. After each story the child was asked to retell the story in as much detail as possible to provide an index of immediate recall. Following a short delay, the child was asked to retell the two stories again (delayed recall). The measure of delayed recall was used: raw scores were converted to scaled scores (M=10, SD=3).

Executive Function

The Tower and Trail Making subtests of the DKEFS (Delis et al., 2001) were administered to children aged 8 years and above to measure planning and switching abilities respectively. For the Tower task, total achievement scores were converted to scaled scores (M=10, SD=3); for the Trails Number-Letter Sequencing task completion times were converted to scaled scores (M=10, SD=3). The DKEFS subtests were not administered to the first 60 children attending the CALM clinic.

Three tests from the Test of Everyday Attention for Children Version 2 J (TEA-Ch2 J; Manly et al., 2016) were completed by children younger than 8 years. Those aged 8 and above completed the Test of Everyday Attention for Children Version 2 A (TEA-Ch2 A; Manly et al., 2016) that includes more difficult adaptations of the same tasks, in addition to a switching task. Sustained attention was measured using the Vigil (8 years +) and Barking (<8 years) subtests. Visual selective attention was assessed using the Hector Cancellation (8 years+) and Balloon Hunt (<8years) subtests. Raw scores were converted to scaled scores (M=10, SD=3). The switching task, Reds, Blues, Bags and Shoes (RBBS), was administered only to those aged 8 years and over. Reaction times on switch trials were converted to scaled scores (M=10, SD=3).

Nonverbal Reasoning

The Matrix Reasoning subtest of the Wechsler Abbreviated Scales of Intelligence II (WASI-II; Wechsler, 2011) was used to index general reasoning. Trials correct were converted to T-scores (M=50, SD=10).

Learning

Spelling, Word Reading and Maths

The Spelling, Word Reading and Numerical Operations subtests of the Wechsler Individual Achievement Test II (WIAT II; Wechsler, 2005) were given. Raw scores for all subtests were converted to standard scores (M=100, SD=15). The Maths Fluency subtest of the Woodcock Johnson III Test of Achievement (WJ-III; Woodcock et al., 2007) was administered to the first 64 children attending the clinic. Children had to respond accurately to as many simple maths problems as possible in three minutes. It was substituted for the WIAT II Numerical Operations test due to consistently low scores. To ensure these low scores reflected maths ability and were not caused by the time constraint in the WJ-III, the WIAT II subtest was introduced. A small number of children completed both maths assessments and there were no significant differences in performance across the tests (Holmes et al., 2019).

Results

Analysis Plan

A statistical analysis plan for this study was pre-registered on the Open Science Framework (https://osf.io/jvm5t/). Two datasets were analysed separately. The first consists of all children (N=805) referred to CALM, and the second of a subset of children that includes all children aged 8+ years (N=566). This additional set of analyses for the older children was necessary because several of the executive function measures were not administered to the younger children due to age restrictions of the tests. The analyses were conducted on both datasets using R version 3.5.1 (R Core Team, 2020).

Exploratory factor analysis (EFA) was used to estimate the number of cognitive factors using R’s Psych package (version 1.8.12; Revelle, 2018). The results from the EFA were used to fit confirmatory factor analyses (CFA) to the optimal model with the R Lavaan package (version 0.6-3; Rosseel, 2012). Cross-loadings were dropped in the CFA to simplify the model. Links between cognition and learning were explored through correlational analysis. Path model analyses with each learning outcome as the dependent variable and simultaneous entry of the cognitive factors were conducted to identify unique links with learning outcomes.

The pre-registered analysis plan states that measurement invariance will be used to determine whether the winning cognitive dimensions model fits subgroups within the sample. The original plan was to test whether the winning model fitted: a) children with and without an ADHD diagnosis; b) children with standard scores <86 on the learning measures compared to those with scores >86 (poor vs typical learners; c) children with and without an ADHD diagnosis within the subgroup of poor learners. On re-consideration the decision was made prior to the commencement of analysis to remove the comparisons made with poor learners in steps b) and c) from the manuscript. There were several reasons for this decision. First, on reflection it is not appropriate to use a criterion score to define individuals as poor learners when the entire sample was referred for learning-related cognitive difficulties. Second, any model derived from the whole sample would anyway consist predominantly of children who would be meet the criteria of being poor learners (N = 601 poor learners, N = 204 typical learners). Its composition would therefore be strongly biased towards the poor learners. It also makes comparison c) of children with and without ADHD in the poor learner subgroup redundant, as this sample contains the majority of the whole sample for whom the results will have already been reported. However, for completeness, transparency and commitment to our preregistration, all analyses as originally outlined have been performed and are reported in the supplementary materials (Supplementary Tables 16-23).

Measurement invariance (e.g., van de Schoot et al., 2013) was used to determine whether the optimal model of the cognitive dimensions derived for the whole sample fitted subgroups with and without ADHD. While the primary transdiagnostic dimensional approach adopted in this study is entirely neutral to diagnostic status, the inclusion of a large, clinically-assessed subgroup with potentially distinct characteristics inevitably raises the question of whether the cognitive dimensions and their links to learning are representative of the sample as whole or reflect in part at least the inclusion of this subgroup. To answer this specific question of representativeness, the data from both the ADHD and no ADHD subgroups will be compared directly with cognitive model derived for the sample as a whole. Additional exploratory moderation analyses, not stated in the pre-registration, will be conducted to explore whether ADHD group (ADHD or no ADHD) moderates the relationship between the emergent cognitive factors and learning outcomes.

Measurement invariance was tested across a number of steps, including manual modification of the model syntax as well as the measurementInvariance function as part of the semTools package (version 0.5.1; Jorgensen et al., 2018). Violations of metric /weak invariance were examined (i.e. equal factor loadings), as metric invariance is required to compare links between cognition and learning across groups. Where necessary, parameters were freed to meet metric invariance, guided by modification indices and as discussed in van de Schoot et al. (2013) and Steenkamp & Baumgartner (1998). Equality-constrained path models were used to test whether the hypothesized effects of cognitive performance on learning outcomes differed between children with and without ADHD.

Additional exploratory analyses were conducted to explore whether the links between cognition and learning differed according to age. The sample were split into age bins with sufficient numbers for regression analyses (5-6; 7-8; 9-10; 11+ years). For each age group the links between the cognitive dimensions derived for the whole sample and each learning outcome were explored using multiple regression analyses.

Descriptive Statistics

Performance on the cognitive and learning measures is reported for the whole sample and the 8 + group in Table 3. All scores were in the low average range (i.e., approximately 1 SD below age-typical scores) except for Mr X, and Cancellation, where scores were within the age-typical range. Correlations between all measures for both groups are shown in Supplementary Tables 1 and 8.

Table 3. Descriptive Statistics for All Children and Children 8 Years and Older.

Measurement	Group
	All Ages						8 years +
	n	min	max	M	SD	SE	n	min	max	M	SD	SE
Phonological Processing
Alliteration	788	69	107	91.31	10.12	0.36	559	70	101	92.63	9.51	0.4
Rapid Naming	786	0	131	88.68	15.14	0.54	554	0	131	90.6	14.7	0.62
Nonword Repetition	481	45	125	82.41	20.62	0.94	351	45	123	80.55	21.6	1.15
Processing Speed
Visual Scanning	-	-	-	-	-	-	478	1	16	9.32	3.41	0.16
Motor Speed	-	-	-	-	-	-	473	1	14	10.11	2.78	0.13
Simple Reaction Time	739	1	19	7.8	4.06	0.15	524	1	19	8.11	4.18	0.18
WM/STM
Digit Recall	801	60	149	92.63	15.41	0.54	564	60	149	91.64	15.62	0.66
Dot Matrix	799	47	141.2	90.63	14.98	0.53	564	47	141.2	90.01	15.62	0.66
Backward Digit Recall	780	58	137	91.53	12.62	0.45	562	58	137	91.44	11.48	0.48
Mr X	795	61	148	97.38	15.35	0.54	563	61.7	144	95.9	14.46	0.61
Following Instructions	750	9.6	18.58	0	3.64	0.13	530	-9.19	18.95	0	3.71	0.16
Episodic Memory
Delayed Recall	775	1	19	7.88	3.3	0.12	550	1	18	7.7	3.23	0.14
Executive Function
Vigil/Barking	748	3	19	8.01	3.29	0.12	528	3	19	8.26	3.3	0.14
Cancellation	771	1	19	10.17	3.31	0.12	552	1	19	10.32	3.26	0.14
Switching (RBBS)	-	-	-	-	-	-	516	1	19	7.72	3.49	0.15
Planning	-	-	-	-	-	-	441	1	19	9.43	2.52	0.12
Number Letter Switching	-	-	-	-	-	-	423	1	15	6.28	3.87	0.19
Nonverbal Reasoning
Matrix Reasoning	804	20	80	43.04	9.56	0.34	566	20	80	42.41	10.07	0.42
Learning Measures
Reading	785	40	140	87	16.87	0.6	556	40	129	87.26	16.54	0.7
Spelling	778	32	131	84.17	14.01	0.5	553	46	131	83.72	14.01	0.6
Maths	789	42	156	84.9	16.43	0.58	555	45	156	84.13	17.06	0.72

Note. Residual scores were calculated for the following instructions task. WM= Working Memory; STM = Short-term Memory; RBBS = Reds, Blues, Bags and Shoes.

Cognitive Dimensions for the Whole Sample

Exploratory Factor Analysis (EFA)

A parallel analysis was conducted using the R Psych package (version 1.8.12) to determine the number of factors underlying performance on the cognitive measures. This uses a simulation of data with properties similar to the true data to compare the estimated number of factors to a permuted baseline. An oblimin (oblique) rotation, allowing the factors to be correlated, was used. For the subsequent confirmatory factor models fit indices outlined by Schermelleh-Engel et al.(2003) were used. These included the root mean square error of approximation (RMSEA) and its confidence interval, the comparative fit index (CFI), and the standardized root mean squared residuals (SRMR). The χ² test and its corresponding p value were also reported. A good model fit was defined as RMSEA <0.05, CFI > 0.95, SRMR <0.05, and an acceptable fit was defined as RMSEA 0.05-0.08, CFI 0.90-0.95, SRMR 0.05-.10.

A four-factor solution was indicated by the parallel analysis (see Supplementary Table 2), with a good fit to the data, χ² (32) = 53.39, RMSEA = 0.029 (90% confidence interval [CI] = 0.014, 0.042), CFI =0.989, RMSR = 0.02. The measures loading most heavily on Factor 1 were Nonword Repetition and Digit Recall, both of which tap both phonological processing and verbal short-term memory. Measures of visuo-spatial STM and WM (Dot Matrix and Mr X), verbal WM (Backward Digit Recall), visual selective attention (Cancellation), and Matrix Reasoning loaded most highly on Factor 2. These tasks have a common executive component. Less optimal features were that only a single variable loaded on Factor 3 (Rapid Naming) and that Factor 4 was difficult to interpret with reference to standard cognitive theory. A measure of sustained attention (Vigil), a processing speed measure (simple reaction time (SRT), phonological measure (Alliteration) and two measures of memory, episodic (Delayed Recall) and working (Following Instructions) memory, loaded on to this factor, and they have little in common.

A likely explanation for the interpretational challenges of the four-factor model is that it overfits the data due to using the full sample for both the exploratory and confirmatory step (a decision made to maximize the data available, but with known risks of overfitting). We therefore also tested a three-factor solution (Supplementary Table 2). This model was a good fit, χ² (42) = 113.56, RMSEA = 0.046 (90% confidence interval [CI] = 0.036, 0.056), CFI = 0.965, RMSR = 0.03. Factor 1 included three variables that rely on processing verbal material: Nonword Repetition, Digit Recall and Delayed Recall. The measures loading most highly on Factor 2 were either speeded tasks (scores derived from RTs: SRT, Rapid Naming, Vigil) or completed under time constraints (Cancellation). The loading of the Alliteration and Following Instructions tasks was unexpected, and is discussed below. The remaining measures known to draw on executive resources (Dot Matrix, Mr X, Matrix Reasoning, and Backward Digit Recall) loaded on the final factor.

For practical purposes these factors have been labelled phonological processing, processing speed, and executive function, respectively. These labels are indicative only and are based on a cognitive analysis of highest-loading variables on each latent construct. Labelling factor 2 as processing speed does not imply that either the Alliteration or Following Instructions tasks are measures of processing speed. The naming of this factor reflects the larger constellation of tasks loading on that factor with a speeded component.

The three-factor solution yielded a better fit based on measures that more substantially penalize complexity such as the BIC (ΔBIC = -6.742 for the 4 vs 3 factor model), and the CFA comparison (below) suggested an only marginal preference for the simplified (cross-loadings removed) 4 factor versus 3 factor model Δχ² =6.30, Δdf=2, p=.043) despite the large sample. Most importantly, the factors and factor loadings were more theoretically interpretable in terms of cognitive theory. For these reasons, the three-factor model was taken forward for reasons of parsimony, theoretical interpretability and generalizability to other samples. Reliability estimates for some individual tasks were moderate rather than good, but the overall factor structure shows measures with moderate reliability grouping with measures with high reliability, and the overall reliability of the factors, as measured omega is excellent, ω =0.83.

Confirmatory Factor Analysis (CFA)

A CFA was used to test the fit of the three-factor solution derived through the EFA. Fit statistics indicated that the three-factor model (Figure 2) was an acceptable fit to the data, χ²(62) = 247.76, p < .0001; RMSEA =0.061; CFI = 0.90; SRMR = 0.047. Resulting factor scores were extracted and saved using the Predict function in Lavaan to allow links between the cognitive dimensions and learning to be explored in a separate analysis (although a one-step analysis can be preferable, a two stage analysis was chosen for simplicity).

Figure 2. Three-Factor Confirmatory Factor Analysis Model for the Whole CALM sample (All Ages).

Note. Latent variables phonological processing (phono), speed, and executive functions (exec) are represented in ovals. Cognitive measures are shown as observed variables in squares. Variable names are: CNrep = Nonword Repetition, DR = Digit Recall, CMS = Delayed Recall, SRT = Simple Reaction Time, Allit = Alliteration, RAN = Rapid Automatic Naming, FI = Following Instructions, Can= Cancellation, MR= Matrix Reasoning, DM = Dot Matrix, BDR = Backward Digit Recall, MrX = Mr X. Parameter estimates are fully standardized. Residual variances are freely estimated but not shown for visual clarity.

Links between Cognition and Learning for the Whole Sample

To explore links between cognition and learning, scores for the three cognitive factors were correlated with each of the learning outcomes (see Supplementary Table 3 and Supplementary Figure 1). All measures of learning were significantly correlated to each of the cognitive dimensions (p<.05 in each case). Measures of reading and spelling were most strongly related to phonological processing and mathematics was linked more closely to executive function. Links between the cognitive factors and learning measures were explored further in multi-group path models in which the cognitive factor scores were entered simultaneously (see Supplementary Table 4 and Figure 3).

Table 4. Multiple Regression Models Showing the Links between Cognition and Learning Across Age Groups.

	Reading
	5-6yrs	7-8yrs	9-10yrs	11+yrs
	B (SE)	B (SE)	B (SE)	B (SE)
Phonological	0.48* (0.18)	0.22* (0.11)	0.40*** (0.11)	0.66*** (0.15)
Speed	0.38 (0.20)	0.65*** (0.12)	0.40** (0.13)	-0.01 (0.15)
Executive	-0.17 (0.25)	-0.27 (0.15)	-0.19 (0.16)	-0.04 (0.19)
R 2	0.45	0.35	0.34	0.38
Adjusted R2	0.43	0.34	0.33	0.37
	Spelling
	5-6yrs	7-8yrs	9-10yrs	11+yrs
	B (SE)	B (SE)	B (SE)	B (SE)
Phonological	0.74*** (0.20)	-0.05 (0.12)	0.25* (0.12)	0.55*** (0.16)
Speed	0.08 (0.22)	0.41** (0.13)	0.28* (0.14)	0.05 (0.17)
Executive	-0.24 (0.27)	0.10 (0.16)	0.01 (0.17)	-0.08 (0.21)
R 2	0.36	0.21	0.26	0.28
Adjusted R2	0.34	0.20	0.25	0.27
	Maths
	5-6yrs	7-8yrs	9-10yrs	11+yrs
	B (SE)	B (SE)	B (SE)	B (SE)
Phonological	0.17 (0.18)	-0.02 (0.10)	0.08 (0.11)	-0.28* (0.14)
Speed	0.30 (0.20)	0.41*** (0.11)	0.13 (0.12)	0.15 (0.15)
Executive	0.23 (0.25)	0.26 (0.14)	0.46** (0.15)	0.76*** (0.19)
R 2	0.46	0.40	0.42	0.42
Adjusted R2	0.45	0.39	0.41	0.41
N	104	278	236	187

Note. Phonological = Phonological Processing

^*p<0.05;

^**p<0.01;

^***p<0.001

Figure 3. Path Models Predicting Learning from Cognitive Factors for the Whole Sample, All Ages.

Note. N=805; Learning outcomes (reading, spelling, and maths) are regressed on phonological processing, speed, and executive factors. Parameter estimates are fully standardized. Factor loadings and covariances are not shown for simplicity. Variable names are: CNrep = Nonword Repetition, DR = Digit Recall, CMS = Delayed Recall, SRT = Simple Reaction Time, Allit = Alliteration, RAN = Rapid Automatic Naming, FI = Following Instructions, Can= Cancellation, MR= Matrix Reasoning, DM = Dot Matrix, BDR = Backward Digit Recall, MrX = Mr X. Residual variances are freely estimated but not shown for visual clarity.

In combination, the phonological, speed, and executive factors accounted for approximately 35% of the variance in reading, 24% in spelling, and 39% in maths scores. Reading and spelling were most strongly predicted by the phonological processing factor (p <.001, in all cases). Reading performance was also significantly predicted by the speed factor (p <.001). Mathematics scores were predicted solely by the executive function factor (p <.001).

Additional exploratory analyses that were not included in the study pre-registration were conducted to discover whether the associations between the cognitive factors and learning reported for the whole sample varied according to the age. A series of regression models were conducted for four age groups with sufficient numbers of children in each group for these analyses: 5-6yrs (n=104); 7-8yrs (n=278); 9-10yrs (n=236); 11yrs+ (n=187). Separate models were conducted for each group and for each learning outcome (reading, spelling and maths) with the factor scores for the three factors (phonological, speed and executive) entered as predictors. The outcomes are reported in Table 4.

Phonological processing skills significantly predicted reading outcomes across all age groups, and spelling in all age groups except 7-8 year olds. Processing speed predicted reading and spelling in children aged 7-10 years, and maths in the 7-8 year olds. Executive function abilities predicted maths outcomes for children aged 9 and over.

Children With and Without ADHD

To examine whether the three-factor structure of the cognitive variables derived for the whole sample generalizes to possible subgroups, a series of measurement invariance tests were conducted. These enable us to test whether the factor structure identified in the sample of 805 children is present, and similar, in identifiable subgroups within the sample. A two-step approach was used to determine whether the cognitive dimensions underlying individual cognitive abilities in the whole sample apply to children with ADHD (N = 255; 107 medicated) and without ADHD (N = 550), and to test whether the pathways to learning are the same or different between groups. Descriptive statistics for these groups are provided in Table 5. Both groups performed similarly across all cognitive tasks; scores were below average on all tasks for both groups, with the exception of the Cancellation task and a test of visuo-spatial WM where scores were in the age-typical range for both groups. Children with ADHD scored significantly higher on Cancellation, Matrix Reasoning, and the reading and spelling tasks.

Table 5. Descriptive Statistics for Children with and without ADHD, All Ages.

Measurement	Group												Group Comparisons
	Children without ADHD (N=550)						Children with ADHD (N=255)
	n	min	max	M	SD	SE	n	min	max	M	SD	SE	t	p	d
Phonological Processing
Alliteration	539	69	107	90.91	10.33	0.45	249	70	103	92.20	9.61	0.45	-1.66	.096	-0.13
Rapid Naming	541	69	131	88.00	14.78	0.64	245	0	131	90.18	15.84	0.64	-1.87	.061	-0.14
Nonword Repetition	263	45	125	81.35	19.6	1.21	218	45	123	83.7	21.76	1.21	-1.25	.213	-0.11
Processing Speed
Simple Reaction Time	509	1	19	7.77	4.01	0.18	230	1	19	7.85	4.19	0.28	-0.25	.804	-0.02
WM/STM
Digit Recall	547	60	139	93.05	15.35	0.66	254	60	149	91.72	15.54	0.97	1.14	.256	0.08
Dot Matrix	545	47	141.2	91.20	14.70	0.63	254	56	135	89.4	15.53	0.97	1.58	.114	0.12
Backward Digit Recall	530	58	135	91.62	12.58	0.55	250	64	137	91.35	12.72	0.8	0.28	.783	0.02
Mr X	543	61.7	148	97.74	15.54	0.67	252	61	134	96.6	14.93	0.94	0.98	.330	0.07
Following Instructions	507	-9.6	16.23	-0.14	3.54	0.16	243	-9.11	18.58	0.28	3.83	0.25	-1.48	.140	-0.12
Episodic Memory
Delayed Recall	532	1	19	7.98	3.34	0.14	243	1	17	7.66	3.21	0.21	1.25	.212	0.10
Executive Function
Vigil/Barking	517	3	19	7.94	3.25	0.14	231	3	16	8.16	3.39	0.22	-0.84	.403	-0.07
Cancellation	523	1	19	9.95	3.19	0.14	248	1	19	10.62	3.5	0.22	-2.66	.008**	-0.21
Nonverbal Reasoning
Matrix Reasoning	549	20	80	42.51	9.21	0.39	255	23	73	44.18	10.21	0.64	-2.33	.021*	-0.17
Learning Measures
Reading	539	40	140	85.97	16.72	0.72	246	49	134	89.26	17.01	1.08	-2.54	.011*	-0.20
Spelling	530	32	123	83.38	13.53	0.59	248	48	131	85.88	14.85	0.94	-2.33	.020*	-0.18
Maths	537	46	153	84.18	15.36	0.66	252	42	156	86.46	18.44	1.16	-1.82	.068	-0.14

Note. WM= Working Memory; STM = Short-term Memory. Residual scores were calculated for the following instructions task.

^*p < .05.

^**p < .01.

Tests of measurement invariance were conducted to determine whether the best-fitting three factor cognitive model identified for the whole sample showed similar model fit in children with and without ADHD. The parameters of the group level model were constrained in the following order. First, factor loadings were constrained to test for weak / metric invariance. If the models were invariant for the subgroups, the factors could be assumed to measure the same construct and links between these and learning outcomes could be compared between groups. Measurement invariance tests were evaluated using the χ² likelihood ratio test and associated p values to determine whether the application of increasing constraints worsened model fit (Putnick & Bornstein, 2016). Where necessary, modification indices and fit indices from the measurementInvariance function (e.g., Δχ² and ΔCFI) were used to indicate which parameters needed to be freed to meet partial metric / weak invariance, which had to be established for the pathways to learning to be compared between groups.

Configural invariance indices indicated that the 3-factor model was an acceptable fit for both groups, with exception of the CFI (see Supplementary Table 5). Tests of metric invariance revealed that a model which assumed identical factor loadings across groups did not worsen fit, Δχ2 = 7.33, Δdf = 10, p = .694, indicating that metric invariance was met between the ADHD and non-ADHD groups.

The ADHD group included both children with a diagnosis of ADHD (n=198) and those who had seen a specialist ADHD nurse and were awaiting the final diagnostic consultation (n=57). Test scores were compared for these two subgroups. Descriptive statistics are provided in Supplementary Table 6. Both groups performed similarly across the cognitive and learning tasks, with the exception of Matrix Reasoning, reading and maths (see Supplementary Figure 2). In these cases, children with diagnosed ADHD performed significantly more poorly. To test whether including only children with a confirmed diagnosis affected the fit of the three-factor model to both ADHD and non-ADHD groups, metric invariance was tested again including only those with a diagnosis in the ADHD group. The models were still invariant, Δχ2 =8.74, Δdf = 10, p = .557 (see Supplementary Table 7). Having established metric invariance between those with and without ADHD irrespective of whether the ADHD group included only those with a confirmed diagnosis or those with possible ADHD, all subsequent analyses were conducted including both those with confirmed and possible ADHD in the ADHD group.

The relationships between the three cognitive dimensions of phonological processing, executive function and processing speed and each of the learning outcomes were compared between the ADHD and non-ADHD groups. The cognitive dimensions were entered as predictors of reading, spelling, and maths in three separate equality-constrained path models (standardized coefficients of paths estimated in the model between cognition and learning were compared for children with and without ADHD). These models, in which the effect of cognition on learning are treated as equal across groups, were compared to models in which the effects of cognition on learning are estimated individually. Interpretation of these comparisons are as follows. If the relationships are equal or highly similar across groups, the equality constrained models will fit the data better than freely estimated models due to greater parsimony. However, if the cognitive factors predict learning differentially across groups, the freely estimated models will provide a better fit to the data than the constrained models. The outcomes of these comparisons are shown in Table 6.

Table 6. Path Models for Cognitive Factors Predicting Learning Outcomes in Children with and without ADHD, All Ages.

	Group
	Children without ADHD (n=550)					Children with ADHD (n=255)
Estimates - Free Models	Estimate	SE	z	p	Fully Standardized Estimate	Estimate	SE	z	p	Fully Standardized Estimate
Reading
Reading ~ Phono	0.909	0.142	6.38	<.001**	0.517	0.574	0.183	3.132	.002**	0.329
Reading ~ Speed	0.463	0.256	1.81	.071	0.152	1.823	0.362	5.038	<.001**	0.571
Reading ~ Executive	-0.154	0.246	-0.624	.533	-0.07	-0.546	0.331	-1.652	.098	-0.246
R2	0.338					0.400
Maths
Maths ~ Phono	0.085	0.125	0.675	.499	0.052	-0.118	0.160	-0.738	.460	-0.063
Maths ~ Speed	0.221	0.236	0.936	.350	0.079	0.427	0.363	1.177	.239	0.124
Maths ~ Executive	0.961	0.229	4.198	<.001**	0.476	1.503	0.346	4.347	<.001**	0.629
R2	0.359					0.473
Estimates - Constrained Models	Estimate	SE	z	p	Fully Standardized Estimate	Estimate	SE	z	p	Fully Standardized Estimate
Spelling
Spelling ~ Phono	0.458	0.108	4.232	<.001**	0.313	0.458	0.108	4.232	<.001**	0.318
Spelling ~ Speed	0.286	0.182	1.569	.117	0.113	0.286	0.182	1.569	.117	0.108
Spelling ~ Executive	0.159	0.181	0.877	.380	0.087	0.159	0.181	0.877	.380	0.086
R2	0.242					0.241

Note. Phono= Phonological Processing.

^*p < .05.

^**p < .01.

The freely estimated models for reading and maths provided a better fit than models in which the effects of cognitive factors on educational outcomes were assumed to be identical across groups (reading, Δχ2 (3) = 11.85, p =.008, mathematics, Δχ2 (3) = 12.31, p =.006). This indicates that the relationship between cognition and reading and maths differed in children with and without ADHD. For both groups, phonological processing significantly predicted reading (ADHD, p = .002, no ADHD, p <.001), but for children without ADHD this prediction was stronger (ADHD, standardized beta: 0.329; no ADHD, standardized beta: 0.517; see Supplementary Figure 3). In contrast, processing speed predicted reading more strongly in children with ADHD (standardized beta: 0.571) than in children without ADHD (standardized beta: 0.152; see Supplementary Figure 3). Finally, executive functions predicted mathematics more strongly so in children with ADHD (standardized beta= 0.629) than in those without ADHD (standardized beta= 0.476; see Supplementary Figure 3). The model for spelling did not differ significantly across groups (spelling, Δχ2 = 7.03, p =.071). Spelling was most strongly associated with phonological processing in children with and without ADHD (Spelling: ADHD, standardized beta: 0.318; no ADHD, standardized beta: 0.313).

Additional exploratory analyses, not listed in the pre-registration, were conducted to test whether ADHD group moderated the relationship between cognition and learning. Moderation analyses were conducted for links identified as significantly different across groups based on the path models (see Table 6). The extent to which the effect of executive skills on maths; and phonological processing and processing speed on reading were moderated by ADHD group was tested using regression analyses. Small but significant moderation effects of ADHD status on the relationship between executive function and maths (F (3, 785) = 176.3, p <.001, standardized coefficient =.12, p = .0006) and processing speed and reading (F (3,781) = 112.4, p <.001, standardized coefficient = .07, p = .046) were revealed. Consistent with the outcomes of the path models, the links between the executive factor and maths and the processing speed factor and reading were stronger for children with ADHD. ADHD status did not significantly moderate the relationship between phonological processing and reading (standardized coefficient =-.01, p = 0.75).

In summary, the three-factor structure derived for the whole sample is an adequate fit for both children with and without ADHD, and irrespective of whether the ADHD group was comprised of those with a confirmed diagnosis or possible diagnosis. For both those with and without ADHD, executive skills predicted maths and phonological processing skills predicted reading and spelling. The effect of executive function on maths was stronger for children with ADHD than those without ADHD. Speed was additionally linked to reading in children with ADHD and the link between phonological processing and reading was weaker in these children than those without ADHD. However, when moderation analyses were used to test for the effects of an ADHD diagnosis on the relationship between cognition and learning, ADHD status had a small but significant moderating effect on the relationships between executive skills and maths and processing speed and reading. Consistent with the regression analyses, these relationships were stronger for children in the ADHD group.

Cognitive Dimensions for Children Aged 8 Years and Above

Children aged eight years and over (N=566) completed an additional set of executive function measures including two tests of switching (Trails and RBBS) and a measure of planning (Towers). Subtests of the Trails task included measures of visual scanning (cross out task) and motor speed (connecting dots as quickly as possible), increasing the number of speeded tasks included in these analyses. Data from the 8+ group were analysed in order to establish how the broader set of executive function measures administered to this age group fit the dimensional structure of the data. The analyses completed for the whole sample were replicated on the 8+ data. Each step of the analyses and the outcomes are reported in full in the Supplementary materials (see Supplementary Tables 8-9). For clarity, only the final models and outcomes are reported here.

Outcomes from the parallel analyses and EFA identified that a three-factor solution consisting of phonological processing, processing speed and executive factors was the best fit to the 8+ data. A CFA was performed on the three-factor solution identified by the EFA (Figure 4). For diagrammatic purposes, the factors have been positioned in the same order as those for the whole sample. Fit indices revealed that this model was an acceptable fit to the data, χ²(101) = 258.84, RMSEA=0.053 (90% confidence interval [CI] = 0.045,0.060), CFI =0.910, SRMR = 0.053. These factor scores were saved and entered into path models to explore links with learning.

Figure 4. Three-Factor Confirmatory Factor Analysis for Children Aged 8 Years and Older.

Note. Latent variables executive functions (exec), processing speed (speed), and phonological processing (phono) are represented in ovals. Cognitive measures are shown as observed variables in squares. DM = Dot matrix, BDR = Backward Digit Recall, MrX = Mr X, FI = Following Instructions, CMS = Delayed Recall, Plan = planning, MR= Matrix Reasoning, RAN = Rapid Automatic Naming,VS = Visual Scanning, Spd = Motor Speed, SWT = Number-Letter Switching, Can= Cancellation, RBBS= Reds, Blues, Bags and Shoes Switching, Allit = Alliteration, CNrep = Nonword Repetition, DR = Digit Recall. Parameter estimates are fully standardized. Residual variances are freely estimated but not shown for visual clarity.

The three dimensions identified for the 8+ data were consistent with those identified for the whole sample: both had factors corresponding to phonological processing, processing speed and executive function. This was despite additional measures being entered into the model for the 8+ group, and the sample including fewer children. Some measures included in the whole sample analysis shifted factors in the 8+ model (e.g., alliteration loaded on the speed factor in the whole sample analysis and the phonological factor in the analysis of the 8+ data), and some had weak loadings so were not included in the final CFA model for the 8+ group (e.g., SRT and Vigil).

To test whether the original model derived for the whole sample fit the smaller 8+ sample when exactly the same measures were included (i.e., excluding the additional measures of executive function administered only to the 8+ children), tests of measurement invariance were conducted comparing children aged 5-7 years to those aged 8+. These confirmed that the original three-factor structure identified for the whole sample was an acceptable fit for both groups (Supplementary Table 10). When factor loadings were constrained, metric invariance was violated, Δχ2 = 40.96, Δdf = 10, p <.001. Inspection of factor loadings and modification indices showed the largest discrepancy occurred for Backward Digit Recall (children 5-7 years: 0.783, children 8+ years: 0.675), and when this parameter was allowed to vary between groups, partial metric invariance was achieved such that equality constraining the other nine factor loadings did not adversely affect fit, Δχ2 = 10.15, Δdf = 9, p =.339.

Links Between Cognition and Learning for Children Aged Eight and Above

Cognitive factor scores derived from the 8+ CFA were used in the following analyses. The cognitive and learning measures were all positively and significantly correlated (Supplementary Table 11 and Supplementary Figure 4). Mathematics was most strongly associated with the executive factor (r=.63), and reading and spelling with the phonological factor (r=.60 and r=.50, respectively). Multi-group path analyses established that phonological processing predicted reading and spelling, ps <.001. Mathematics was significantly predicted by executive function, p <.001 (see Supplementary Table 12 and Figure 5).

Figure 5. Path Models Predicting Learning from Cognitive Factors for Children 8 Years and Older.

Note. N=566; Learning outcomes (reading, spelling, and maths) are regressed on phonological processing, speed, and executive factors. Parameter estimates are fully standardized. Factor loadings are not shown for simplicity.

Children Aged Eight and Above, With and Without ADHD

Mirroring the analyses on the whole sample, the fit of the cognitive dimensions and their links with learning were compared between those with (N = 192) and without ADHD (N=374). Descriptive statistics are provided in Table 7.

Table 7. Descriptive Statistics for Children with and without ADHD, 8 years and Older.

	Group												Group Comparisons
	Children without ADHD (n=374)						Children with ADHD (n=192)
Measurement	n	min	max	M	SD	SE	n	min	max	M	SD	SE	t	p	d
Phonological Processing
Alliteration	372	70	101	92.50	9.51	0.49	187	70	101	92.89	9.53	0.70	-0.46	.642	-0.04
Rapid Naming	370	69	131	89.98	14.28	0.74	184	0	131	91.85	15.47	1.14	-1.41	.160	-0.12
Nonword Repetition	185	45	119	79.88	20.53	1.51	166	45	123	81.30	22.77	1.77	-0.61	.540	-0.07
Processing Speed
Visual Scanning	303	1	15	9.45	3.21	0.18	175	1	16	9.11	3.72	0.28	1.05	.293	0.10
Motor Speed	298	1	14	9.89	2.84	0.16	175	1	14	10.49	2.64	0.20	-2.27	.023*	-0.21
Simple Reaction Time	353	1	19	8.09	4.11	0.22	171	1	19	8.13	4.31	0.33	-0.11	.916	-0.01
WM/STM
Digit Recall	372	60	139	92.06	15.46	0.8	192	60	149	90.82	15.92	1.15	0.89	.373	0.08
Dot Matrix	372	47	141.2	90.36	15.36	0.80	192	56	135	89.34	16.11	1.16	0.74	.462	0.06
Backward Digit Recall	371	58	132	91.32	11.4	0.59	191	70	137	91.67	11.67	0.84	-0.34	.737	-0.03
Mr X	372	61.7	144	95.98	14.39	0.75	191	62	134	95.74	14.64	1.06	0.19	.851	0.02
Following Instructions	346	-9.19	16.25	-0.17	3.55	0.19	184	-8.81	18.95	0.32	3.98	0.29	-1.45	.148	-0.13
Episodic Memory
Delayed Recall	366	1	18	7.80	3.22	0.17	184	1	17	7.52	3.26	0.24	0.94	.350	0.08
Executive Function
Vigil/Barking	354	3	19	8.14	3.23	0.17	174	3	16	8.50	3.44	0.26	-1.17	.244	-0.10
Cancellation	365	1	19	10.10	3.09	0.16	187	1	19	10.75	3.54	0.26	-2.25	.024*	-0.19
Switching (RBBS)	344	1	19	7.53	3.49	0.19	172	1	16	8.09	3.49	0.27	-1.74	.082	-0.15
Planning	270	1	19	9.32	2.45	0.15	171	3	16	9.59	2.62	0.20	-1.09	.273	-0.10
Number Letter Switching	265	1	15	5.92	3.84	0.24	158	1	15	6.88	3.85	0.31	-2.49	.013*	-0.24
Planning	270	1	19	9.32	2.45	0.15	171	3	16	9.59	2.62	0.20	-1.09	.273	-0.10
Nonverbal Reasoning
Matrix Reasoning	374	20	80	41.92	9.78	0.51	192	23	73	43.38	10.56	0.76	-1.63	.104	-0.14
Learning Measures
Reading	370	40	121	85.95	16.63	0.86	186	49	129	89.88	16.08	1.18	-2.66	.008**	-0.23
Spelling	367	46	119	82.77	13.38	0.7	186	48	131	85.58	15.04	1.10	-2.23	.026*	-0.19
Maths	366	46	153	83.17	16.05	0.84	189	45	156	85.99	18.77	1.37	-1.85	.064	-0.16

Note. WM= Working Memory; STM = Short-term Memory; RBBS = Reds, Blues, Bags and Shoes.

^*p <.05;

^**p <.01.

The groups performed similarly on the cognitive and learning measures, but those with ADHD had significantly higher scores on the Motor Speed, Cancellation, Number-Letter Switching, reading and spelling tasks than those without ADHD. The children in the ADHD group with a confirmed diagnosis scored significantly more poorly on the Mr X and Matrix Reasoning tasks, and all the learning measures, relative to those with a possible ADHD diagnosis (see Supplementary Table 13). Tests of measurement invariance revealed that the three factor cognitive model met metric invariance (see Supplementary Table 14 for details), indicating it was an acceptable fit for both groups, even when children with possible ADHD were removed from the analysis (see Supplementary Table 15). There were no differences in the pathways between cognition and learning for those with and without ADHD (see Table 8). For both groups, phonological processing was significantly associated with reading and spelling, and executive function with maths.

Table 8. Path Models Predicting Learning from Cognition in Children with and without ADHD, 8 Years and Older.

	Group
	Children without ADHD (n=374)					Children with ADHD (n=192)
Estimates – Constrained Models	Estimate	SE	z	p	Fully Standardized Estimate	Estimate	SE	z	p	Fully Standardized Estimate
Reading
Reading ~ Phono	0.761	0.095	7.989	<.001**	0.590	0.761	0.095	7.989	<.001**	0.626
Reading ~ Speed	0.597	0.528	1.13	.259	0.065	0.597	0.528	1.13	.259	0.072
Reading ~ Executive	-0.073	0.188	-0.386	.700	-0.037	-0.073	0.188	-0.386	.700	-0.039
R 2	.353					.400
Spelling
Spelling ~ Phono	0.514	0.087	5.878	<.001**	0.479	0.514	0.087	5.878	<.001**	0.477
Spelling ~ Speed	0.374	0.498	0.750	.453	0.049	0.374	0.498	0.750	.453	0.051
Spelling ~ Executive	-0.014	0.178	-0.081	.935	-0.009	-0.014	0.178	-0.081	.935	-0.009
R 2	.249					.248
Maths
Maths ~ Phono	0.046	0.092	0.499	.618	0.035	0.046	0.092	0.499	.618	0.035
Maths ~ Speed	-0.019	0.567	-0.034	.973	-0.002	-0.019	0.567	-0.034	.973	-0.002
Maths ~ Executive	1.189	0.202	5.903	<.001**	0.597	1.189	0.202	5.903	<.001**	0.596
R 2	.392					.390

Note. Estimates are from the constrained models. In all cases, constraining the paths did not significantly degrade the model fit.

Phono = Phonological Processing.

^*p <.05;

^**p <.01

In summary, a three-factor latent model with factors of phonological processing, speed and executive function provided the best fit to the 8+ data, and was structurally and metrically invariant across those with and without ADHD. The phonological processing factor shared the strongest links with reading and spelling outcomes, and the executive function factor with maths.

Discussion

This study used a data-driven approach to identify the cognitive dimensions linked to learning in a large mixed sample of children aged 5 to 18 years with problems in attention, learning and memory. The following questions were addressed in the analyses.

1. What are the Broad Dimensions of Cognitive Skills in this Population?

A primary aim of the study was to discover the cognitive dimensions that characterized this sample of children with learning-related cognitive problems. Three dimensions of cognitive skill were identified for the whole sample using exploratory and confirmatory factor analysis. This model also fitted children with ADHD and those without ADHD. The composition of the corresponding three-factor model for an older subgroup tested on an expanded set of executive function assessments was broadly similar. The three factors in both cases were associated with measures that were largely phonological or verbal, spatial or executive and speed-dependent in nature. In the interests of simplicity these factors have been labelled phonological, processing speed and executive. While these terms broadly capture the cognitive composition of the factors, some of the variable loadings do not align fully with this reductive nomenclature.

Consider first the phonological factor. There is extensive evidence that the digit span and nonword repetition measures loading highly on this factor are closely linked with both phonological processing skills (Hulme & Snowling, 2016; Melby-Lervåg, Lyster, et al., 2012; Ramus et al., 2013) and verbal STM (Gathercole, 2006). There was a more moderate loading on this factor of Delayed Recall. This is an episodic memory task for which less is known about its specific cognitive mechanisms, but which undoubtedly involves substantial verbal processing. The alliteration task – a classic measure of phonological awareness - loaded on this factor only in the older age subgroup. In the whole sample alliteration scores loaded on a third factor discussed below, which has been termed processing speed.

The second factor was closely linked with nonverbal reasoning, planning (assessed in the children aged 8 and over only), visuo-spatial STM, visuo-spatial WM, and verbal WM. Although four of these measures involve visuo-spatial mental activities, this factor has been labelled executive because each loading measure is known to be supported by the flexible, high-level control of cognitive processes. Nonverbal reasoning is widely interpreted as an index of fluid intelligence (Duncan et al., 1996). Performance on tests of visuo-spatial STM and WM depends substantially on domain-general attentional capacity (Alloway et al., 2006; Kane et al., 2004; Morey & Miron, 2016; Pearson et al., 2014; St Clair-Thompson & Gathercole, 2006). Backward digit span is a test of verbal WM that is known to place high demands on strategic control within WM (Byrne et al., 2019; Norris et al., 2019; Oberauer et al., 2000). The Tower Test of spatial planning is also widely considered to be a measure of executive control (Pennington & Ozonoff, 1994).

The final factor was largely related to tasks that tap the speed of processing. Three of the measures loading on this factor required speeded responses, although their cognitive demands otherwise had little in common: rapid naming required the retrieval of the phonological structure corresponding to a printed word, Cancellation involved a rapid visual search for a target digit in display of mixed digits, and Simple Reaction Time required a speeded button response to a target. Other measures administered only to older children that loaded on this factor included another speeded visual search cancellation task, a motor speed task, and two switching tasks in which performance was scored based on speed and accuracy. Alliteration and an instruction-following task loaded on this factor in the model generated for the whole sample, but this does not imply they are measures of processing speed. Rather, the labelling of this factor reflects the larger constellation of tasks loading on this construct with a speeded component. Overall, this processing speed factor appears to be domain-general in nature, specific neither to the more cognitive characteristics of the task nor its representational domain (Kail & Salthouse, 1994; Moll et al., 2016).

Three differences in the factor composition between the sample as a whole and the older subgroup of children aged 8 years and over are worthy of note. The Delayed Recall measure of verbal episodic memory loaded on the phonological processing factor in the whole sample and the executive factor in the older children. Also, the Following Instructions task usually considered a measure of WM (e.g., Jaroslawska et al., 2016) was associated with the processing speed factor in the whole sample and the executive factor in the 8+ group. Finally, the Alliteration task loaded on the processing speed factor in the whole sample, and on the phonological processing factor in the 8+ group. This task typically thought to measure of phonological processing abilities (e.g., Carroll & Snowling, 2001). The task loadings for the 8+ group align with what might be expected based on typical assumptions about the skills tapped by each of these measures, but the data should not be over-interpreted. The 8+ group were included in the model derived for whole sample, and the shifts in loadings seen in the analyses may well be a consequence of adding additional measures, and therefore variance, in this subgroup of older children. To test whether the model derived for the whole sample for the core set of tests administered across all ages was different for older and younger children within the sample, formal measurement invariance testing was used (e.g., Steenkamp & Baumgartner, 1998). The likelihood ratio test, as well as information criteria, suggested the differences in measurement properties did not exceed what would be expected by chance. As such, interpreting nominal differences is not appropriate.

All three core factors were strongly associated with one another, a ubiquitous finding in individual differences studies that has been suggested to reflect the ‘positive manifold’ of intelligence arising from mutually beneficial interactions between cognitive processes during development (Kievit et al., 2017; Van Der Maas et al., 2006). The composition of the three factors provides important new information about the dimensions that differentiate individuals within a large mixed sample of children with learning-related problems.

Executive skills, phonological processing and processing speed are familiar constructs within the fields of psychological assessment of both children and adults. The standard neuropsychological taxonomy would identify five aspects of cognition tapped by the test battery employed in the study: phonological processing, STM and WM, executive functions, processing speed, and fluid intelligence. The factor structure deviates most markedly from this in the absence of one or more distinct dimensions corresponding to STM and WM. Instead, there is a domain-specific migration of the verbal STM task into a broader dimension of phonological processing, while the verbal WM and visuospatial STM and WM tasks load together on the executive factor with other tasks in the two models. Although this factor appears to be predominantly WM-loaded in the whole sample, the additional loading of the fluid reasoning task suggests it is tapping something broader. This is reinforced by the loadings of a range of other measures that require flexible, high-level control of cognitive processes on the same factor in the older children.

STM and WM nonetheless remain meaningful constructs for understanding developmental disorders of learning. Whereas experimental designs permit fine-grained analysis of the cognitive system, the granularity of constructs that can be identified using latent construct methods is coarse, lacking the resolution to specify or test precise cognitive models of individual tasks. Over 10 000 data points have been boiled down to just three correlated factors in this study. Factor reduction methods simply identify sources of shared variance across a particular set of tests, which in the present study was selected to reflect skills likely to influence learning. The present findings establish that there is substantial overlap - but not equivalence - between the cognitive processes supporting phonological awareness, verbal STM, and verbal WM on the one hand, and those involved in visuo-spatial STM, visuo-spatial WM, nonverbal reasoning and planning.

2. How are the Cognitive Dimensions Linked with Learning?

A second study aim was to examine how the core cognitive dimensions relate to children’s learning outcomes. As expected, the sample performed more poorly on tests of single-word reading, spelling and maths than would be expected by their age. Individual variation in these learning scores was closely linked to the cognitive dimensions. Word reading and spelling abilities were both strongly associated with phonological processing skills, in line with a large body of evidence from study designs including individual differences studies of typically developing children and group studies of children with and without specific reading difficulties (Bishop & Snowling, 2004; Melby-Lervåg & Hulme, 2010). Reading achievement was also significantly, although more weakly, linked with processing speed, again in line with a broader body of evidence (Araújo et al., 2015). In contrast, mathematical abilities were linked strongly and solely with executive skills.

While the individual pathways between cognition and learning pathways in the unique mixed population of children with learning-related difficulties are consistent with findings from a range of other developmental populations as discussed above, the distinctiveness of the cognitive contributors to the different areas of learning in the present sample is more unusual. Deficits in phonological skills are widely reported in children with mathematical difficulties (Fuchs et al., 2005; Hecht et al., 2001; Landerl & Moll, 2010; Swanson & Sachse-Lee, 2001), as are executive impairments in children with reading difficulties in studies of mixed samples of typically-developing children (Booth et al., 2010; Carretti et al., 2009; Yeniad et al., 2013). However, many of these children have problems that extend across both reading and maths, potentially obscuring the specificity of cognitive pathways to these two aspects of learning. The same is true of the current sample, with 34% of the children scoring more that 1SD below the population mean in both reading and maths. In contrast, the smaller number of studies that have distinguished children with difficulties that are restricted to either maths or reading have yielded evidence of specific deficits in phonological skills in groups with reading difficulties (Moll et al., 2015) and of spatial executive skills in those with difficulties restricted to maths (Szucs et al., 2013). A major strength of the current approach of using latent factor structures to track pathways to learning in a large sample with heterogeneous profiles of learning-related difficulties is its capacity to detect the same highly specific links without having to apply arbitrary cut points to partition children into distinct subgroups.

In addition to investigating the broad links between dimensions of cognitive skill and learning across the sample as a whole, age-related changes in the dynamic nature of cognition-learning relationships were explored. Phonological skills were linked to word reading and spelling across the full age range of the sample, with the exception of spelling in 7 and 8 year olds. Finding strong links between reading and phonological processing abilities in our sample with reading impairments is consistent with the idea that phonological processing difficulties can, and do, persist and limit reading skills throughout development (e.g., Stothard et al., 1998). Executive skills predict age-related changes in reading in typically developing groups (e.g., Swanson & Howell, 2001). No links between executive abilities and reading were found for any age group in our sample. However, reading was measured using a test of single word reading. Associations with executive skills may have been found if more complex measures of literacy, including tests of listening and reading comprehension, had been used. Executive skills were uniquely significantly associated with maths abilities in children aged 9 and over. This is consistent with the idea that growth in executive skills determines mathematical problem-solving skills as children get older (e.g., Swanson, 2006).

The purpose of the present study was to apply a data-driven, dimensional approach to characterise a sample of struggling learners, rather using the more traditional group-based approach that compares children with different kinds of disorder. However, there was one notable categorical distinction in the sample: approximately a third of the children had either a diagnosis of ADHD or high levels of ADHD symptoms and were awaiting a final diagnostic assessment. This raises the possibility that the characteristics of the sample may have been distorted by the inclusion of this group. Although not a primary aim of the study, comparisons of cognitive and learning skills and of their links were conducted to test whether this was the case, in line with the study pre-registration (https://osf.io/jvm5t/). The outcomes were clear. First, those with and without ADHD differed neither in their cognitive skills nor their learning scores, despite their distinct recruitment pathways which were primarily from education (those without ADHD) and health services (those with diagnosed and probable ADHD). Second, executive skills were linked to maths and phonological skills to reading and spelling in both groups, but the strengths of these associations varied by group. In the children with diagnosed or probable ADHD, links were stronger between executive skills and maths, weaker between phonological skills and reading, and the positive association between processing speed and reading was present only in the ADHD group. Of these, further analysis established that the ADHD status of the child only moderated the links between executive skills and maths and processing speed and reading, with stronger associations between the two in children with ADHD. Evidence from population studies also suggest that the severity of ADHD symptoms predicts achievements in both mathematics and reading (Gremillion & Martel, 2012; McGrath et al., 2011). Together, these findings indicate that understanding differences in pathways to learning in children with elevated symptoms of hyperactivity and inattention may be valuable for providing effective support both for those with ADHD and those with high levels of behavioural symptoms who do not have a diagnosis.

Limitations and Strengths

The sampling frame adopted in this study differed markedly from the standard approach of applying stringent inclusionary and exclusionary criteria to select and compare children with specific learning problems to typically-developing children. It was guided neither by diagnostic status nor by quantitative inclusion criteria. The characteristic common to all of the children was that practitioners in either education or health services considered them to have problems in either attention, learning or memory. The absence of strict exclusion criteria made it possible to recruit a large mixed sample of children experiencing a wide range of common developmental problems, some of whom had diagnosed neurodevelopmental disorders.

While critical to addressing the study goals, this functionally-defined recruitment approach clearly has its risks. It is an open question whether the findings will generalize to samples recruited using different selection criteria. Within the limited context of the current sample, though, the outcomes are largely robust across different subgroups. The same three-dimensional cognitive structure derived for children across the ranges of ages from 5 to 18 years fitted children aged under and over 8 years, and a similar three-factor model emerged for those aged 8 and older when more tasks were included. The model was also a good fit both for children with and without ADHD. The cognitive links with learning conform closely to those of more conventionally-defined samples. Specific associations were found between both phonological processing and processing speed and reading ability, and between executive skills and mathematics abilities. This novel sampling strategy demonstrates that the same core skills differentiate the broad population of struggling learners as in the typically-developing population and in children recruited according to stringent and often arbitrary recruitment criteria.

A shortcoming of the study is that the assessment of literacy was limited by constraints on clinic time. Tests were limited to single word reading and single word spelling, lacking a measure reading comprehension that would tap understanding and fluency with larger sections of text. Relatedly, measures of language ability were not included. These limitations have been addressed in a four-year longitudinal follow-up of the sample, which is now underway.

In the interests of clarity of communication, and reflecting standard practice in the field, labels were assigned to latent variables identified in the exploratory and confirmatory analyses (phonological, speed, and executive). These labels capture a concise summary of the hypothesized dimension underlying differences in performance across tasks based on the constellation of tasks with the highest loadings, but do not represent a rigid mapping of tasks on factors. Differences in factor structure can occur across ages (Simpson-Kent et al., 2020) and cohorts (Wicherts et al., 2004) dependent on the sample size and number of tasks included. Even within a sample, differences in task demand can affect the correlations between tasks, and thus the factor structure. For example, fluid intelligence under time pressure becomes isomorphic with WM, but is only moderately correlated with WM if the time constraints are modest or absent (Chuderski, 2013). These issues create challenges in the clear and consistent labelling and interpretation of latent factors, but do not limit the usefulness of having theory-guided labels to summarise populations and patterns of factor loadings for convenience and interpretability.

The dimensional perspective adopted in this study represents just one example of how a transdiagnostic approach can be used both to understand cognition and learning in children with mixed cognitive problems and to identify the kinds of support needed by the individual child. Other data-driven methods are also now being used to great effect to test the adequacy of conventional diagnostic systems for different developmental populations. Sokolova et al. (2017) combined a causal modelling approach with mediation analysis to understand the comorbidity between ADHD and ASD. In a separate analysis of these two disorders alongside Obsessive-Compulsive Disorder, Kushki et al. (2019) used machine learning to identify the optimal clusters of children based both on cortical thickness and phenotypic data.

Within the CALM dataset, machine learning methods have been used to identify novel subgroups with complex and distinct cognitive, learning and behavioural profiles (Astle et al., 2019; Bathelt et al., 2018) and using a network analysis approach, inter-related behavioural and cognitive symptoms have been detected that are not captured by traditional diagnostic criteria (Mareva & Holmes, 2019). The insights gained from the application of these methods to transdiagnostic samples are distinctive and complementary. They are, however, consistent in one important respect: in each case, they demonstrate that the complexity of neurodevelopmental disorders is not well served by conventional diagnostic systems.

Educational Impact and Implications Statement.

Understanding how cognitive skills relate to learning can inform educational practice. Links between cognition and learning were explored in a group of children who represent the substantial majority of poor learners, including those with relatively mild problems through to those with complex and co-occurring needs. The ability to process the sound structure of words (phonological processing) was linked to the severity of word reading problems, while the high-level cognitive control of processes such as problem-solving was related to mathematical difficulties. Understanding these specific associations may be useful in guiding support for children who are struggling at school.