research on reading and math skills has shown that

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• My Account Login
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Open access
• Published: 08 July 2014

The correlation between reading and mathematics ability at age twelve has a substantial genetic component

• Oliver S. P. Davis 1 , 2   na1 ,
• Gavin Band 3   na1 ,
• Matti Pirinen 3   na1 ,
• Claire M. A. Haworth 2 , 4 ,
• Emma L. Meaburn 5 ,
• Yulia Kovas 6 ,
• Nicole Harlaar 7 ,
• Sophia J. Docherty 2 ,
• Ken B. Hanscombe 2 ,
• Maciej Trzaskowski 2 ,
• Charles J. C. Curtis 2 ,
• Amy Strange 3 ,
• Colin Freeman 3 ,
• Céline Bellenguez 3 ,
• Zhan Su 3 ,
• Richard Pearson 3 ,
• Damjan Vukcevic 3 ,
• Cordelia Langford 8 ,
• Panos Deloukas 8 ,
• Sarah Hunt 8 ,
• Emma Gray 8 ,
• Serge Dronov 8 ,
• Simon C. Potter 8 ,
• Avazeh Tashakkori-Ghanbaria 8 ,
• Sarah Edkins 8 ,
• Suzannah J. Bumpstead 8 ,
• Jenefer M. Blackwell 9 , 10 ,
• Elvira Bramon 11 , 12 ,
• Matthew A. Brown 13 ,
• Juan P. Casas 14 , 15 ,
• Aiden Corvin 16 ,
• Audrey Duncanson 17 ,
• Janusz A. Z. Jankowski 18 , 19 , 20 ,
• Hugh S. Markus 21 ,
• Christopher G. Mathew 22 ,
• Colin N. A. Palmer 23 ,
• Anna Rautanen 3 ,
• Stephen J. Sawcer 24 ,
• Richard C. Trembath 22 ,
• Ananth C. Viswanathan 25 ,
• Nicholas W. Wood 26 ,
• Ines Barroso 8 ,
• Leena Peltonen 8 ,
• Philip S. Dale 27 ,
• Stephen A. Petrill 28 ,
• Leonard S. Schalkwyk 2 ,
• Ian W. Craig 2 ,
• Cathryn M. Lewis 2 ,
• Thomas S. Price 29 ,
• The Wellcome Trust Case Control Consortium ,
• Peter Donnelly 3 , 30 ,
• Robert Plomin 2   na2 &
• Chris C. A. Spencer 3   na2  

Nature Communications volume  5 , Article number:  4204 ( 2014 ) Cite this article

28k Accesses

61 Citations

564 Altmetric

Metrics details

• Cognitive neuroscience

Genome-wide association studies

• Learning and memory

Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.

Similar content being viewed by others

Computer programmers show distinct, expertise-dependent brain responses to violations in form and meaning when reading code

Chu-Hsuan Kuo & Chantel S. Prat

Emil Uffelmann, Qin Qin Huang, … Danielle Posthuma

Sleep quality, duration, and consistency are associated with better academic performance in college students

Kana Okano, Jakub R. Kaczmarzyk, … Jeffrey C. Grossman

Introduction

Understanding the aetiology of complex cognitive traits such as reading and mathematics ability is essential for helping children achieve their potential 1 . These traits are highly heritable 2 , 3 and have been shown to associate with quality of life including wealth and life expectancy 4 , 5 . In spite of their importance and well-established heritability, much remains to be understood about the genetic architecture of cognitive abilities and the genetic component to the correlation between them.

It has been shown 6 , 7 that population variation in cognitive abilities shares a substantial genetic component with learning difficulties such as dyslexia and dyscalculia (defined here as the low extreme of the distribution 8 ). These difficulties affect more than 10% of the population of English-speaking countries 9 , with undiagnosed problems costing economies billions of dollars per year, as well as the less well-documented human cost of missed opportunities. Dyslexia is by far the most frequently diagnosed form of learning difficulty in school-age children 10 , it shows strong stability across childhood and adolescence 10 , and frequently co-occurs with other childhood learning difficulties and psychopathologies 11 , 12 . Although much less is known about dyscalculia, numeracy is as much a requirement as literacy in our increasingly technological world 12 , 13 .

Dyslexia was one of the first traits studied using QTL sib-pair linkage analysis 14 , and although it has been proven to be difficult to identify the genes responsible for these linkages, several candidate genes are under scrutiny 14 , 15 . The first steps towards genome-wide association studies (GWAS) of reading and mathematics ability, using pooled DNA on microarrays, concluded that it is likely that no common genetic variants of large effect influence either trait 16 , 17 . Until recently 1 , 18 , 19 , no common variants associated with the normal range of cognitive traits have been discovered with compelling levels of evidence, although some candidates have been reported.

Here we conduct a GWAS of Reading and Mathematics abilities in a sample of ~3,000 twin pairs. We find no replicable loci with convincing levels of evidence for association, consistent with a substantially polygenic contribution of genetics to these traits. Using bivariate twin- and population-level models, we estimate the heritability and genetic correlation between the two traits. We find a high genetic correlation (around 70%), indicating substantial pleiotropy, and accounting for a large proportion of phenotypic correlation.

As part of the Wellcome Trust Case-Control Consortium 2 (WTCCC2), in collaboration with the Twins Early Development Study (TEDS), we performed a GWAS using 2,794 unrelated members of monozygotic (MZ) and dizygotic (DZ) twin pairs, measured for their reading and mathematics ability using a combination of web- and phone-based tests at age twelve. The scores were combined across tests and adjusted for age, while gender was used as a covariate in the analyses. Using genotype imputation we performed association analysis for 1,588,650 autosomal markers with reading and mathematics scores separately (see Methods). We followed up the strongest signals of association ( P GWAS <5 × 10 −5 ; reading, N =2,243; mathematics, N =2,772) in a further 2,153 individuals, some of whom were co-twins of individuals in the discovery data. One region on chromosome 19 (rs349045) achieved a P -value of 9.63 × 10 −9 (Merlin, N =6,061) for reading ability in the joint analysis of discovery and replication data. However, this association failed to replicate using a related phenotype (the Test of Word-Reading Efficiency (TOWRE)—one of four reading tests from the TEDS analysis) in the Avon Longitudinal Study of Parents and Children (ALSPAC, N =2,077). The results for the GWAS are shown in Supplementary Figs 1 and 2 and Supplementary Tables 1 and 2 . The results from loci previously reported to be associated with reading or mathematics ability or difficulties are reported in Supplementary Table 3 .

One explanation for the lack of compelling evidence for association at individual single-nucleotide polymorphisms (SNPs), despite large sample sizes and high heritability estimates, is that the traits studied here are substantially polygenic, with each variant having a small effect. Recent studies have demonstrated that the genetic variants that determine measures of intelligence early and late in life overlap 20 . In our data, standardised reading and mathematics scores show a high correlation, r =0.60. This is perhaps unsurprising given that many environmental influences (for example, parenting, schooling and socio-economic factors) will impact on both reading and mathematics ability. Twin studies have also identified a genetic contribution to the correlation 21 . Our data provide the opportunity to clarify the contribution of genetics to the strong correlation in these cognitive abilities using both twin and molecular data in the same sample.

To investigate the genetic contribution to the correlation, we first fit a bivariate version of the classical twin model using both MZ and DZ twin pairs for whom the reading and mathematics scores were available (Methods and Fig. 1 ). This method does not use the genotype data, but assumes that genetic relatedness at the variants that affect the traits follows average relatedness of twins (one half for DZ twins and one for MZ twins). The approach estimates the phenotypic covariance explained by additive genetic effects (narrow-sense heritability and correlation), shared environmental influences and non-shared environmental influences across traits. Our analysis estimated the narrow-sense heritability of reading at 0.66 (95% confidence interval (CI): 0.57–0.74), with shared and non-shared environmental contributions of 0.14 (0.06–0.22) and 0.20 (0.18–0.23), respectively. Heritability of mathematics was 0.51 (0.43–0.60), with shared and non-shared environmental estimates of 0.21 (0.14–0.28) and 0.27 (0.25–0.30), respectively. Using the bivariate approach we estimated that the genetic correlation (denoted ρ A ) between reading and mathematics is 0.64 (0.56–0.72), with shared and non-shared environmental correlations of 0.90 (0.67–1.00) and 0.30 (0.24–0.37), respectively.

Comparison of estimates of heritability and genetic correlation between reading and mathematics as estimated by twin and population-level models. ( a ) comparison of heritability estimates. A , C and E stand for additive genetic, shared environment and non-shared environment effects, respectively, and G denotes the population-level estimate of additive genetic effects. ( b ) comparison of estimates of genetic correlation in reading and mathematics ability from twin ( ρ A ) and population-level ( ρ G ) models. Bars indicate point estimates (twin model: N =2,794 twin pairs; population-level model: N =2,221 individuals) with solid black lines indicating 95% confidence intervals.

To exploit the genome-wide data collected as part of this study, we next applied a population-level variance component model to assess polygenic contribution to these traits (see Methods) that bases inference on small differences in allele sharing between individuals who are not closely related 22 . In this model, we estimate the proportion of the phenotypic variance that can be explained by the autosomal SNPs available in the genotyping array data (see Methods) using only the individuals from the GWAS discovery phase (with estimated identity by descent <5%). Using this approach, we estimated the proportion of variance accounted for by the available SNPs as 0.27 for reading (95% CI: 0.02–0.53) and 0.52 (0.20–0.82) for mathematics, with genetic correlation (denoted ρ G ) of 0.74 (0.32–1.00) ( Fig. 1 and Supplementary Table 4 ). By both simulation- and permutation-based approaches we confirmed that the estimated genetic correlation was significantly larger than zero (empirical P <0.02, N =2,221; see Supplementary Fig. 3 ).

As discussed elsewhere 23 , 24 , the difference between the twin and population-level models and their underlying assumptions complicates direct comparison of estimated parameters (see Methods). For example, unlike the twin model the population-level approach assumes that all environmental influences are independent among individuals. If there are geographically structured determinates of ability (for example, quality of teaching) that correlate with the genetic differences, then this can inflate population-based estimates of heritability 25 . To address potential confounding by population structure, we fit the model both with and without the leading principal components (PCs) of genetic structure as covariates with similar results ( Supplementary Table 4 ). The population-level approach is also influenced by the coverage of the SNPs used to estimate allele sharing; if a proportion of heritability is due to variants that are not in linkage disequilibrium with typed variants, the population-level model will underestimate heritability. Twin model estimates in principle capture all genetic variation but interpretation of the parameters depends on assumptions regarding the presence of dominance or interaction effects, correlation or interaction between genetics and environment, and putative genetic influences on the shared environmental component. We note that factors affecting additive genetic variance are likely to similarly affect genetic covariance between traits, so that estimates of genetic correlation may be more robust to these effects. The observation that the two different approaches, using different information in the data, estimate a substantial correlation in the genetic component of reading and mathematics ability strongly supports a shared genetic basis.

This observation can be interpreted in at least two ways. First, as a decomposition of the correlation in reading and mathematics ability (see Supplementary Methods ), where the twin model estimates that 62% of the observed phenotypic correlation is due to additive genetic factors, and the population-level model estimates that 47% of the observed phenotypic correlation is captured by the available SNPs. Second, by assuming that the genetic variants that affect these traits can be classified into either trait-specific or pleiotropic effects, with similar distribution of effect sizes (see Supplementary Methods ), we estimate that at least 10%, and probably around a half, of genetic variants that affect at least one of the traits contribute to both traits. These results suggest substantial pleiotropy, in line with the Generalist Genes Hypothesis 7 .

Our results support previous evidence that common learning abilities and their associated disabilities are unlikely to be affected by common genetic variants of large effect; even with a sample of thousands of individuals and 1,588,650 genetic variants, our most convincing signal of association failed to replicate in an independent sample (although it may still be of interest to future studies). However, we do find suggestive evidence in favour of some previously reported associations (see Supplementary Table 3 ) for reading ability, most notably rs807701 ( P GWAS =0.0084, N =2,243) in the DCDC2 gene, which has been implicated in neuronal development 26 , 27 , 28 . As is the case for other complex traits such as height 29 larger sample sizes and meta-analyses are needed to pinpoint individual genetic variants 19 . The comparison of our population-level and twin-based variance components analysis, conducted in the same cohort using identical phenotypes, shows that the GWAS data were able to explain a significant proportion of the variance in cognitive abilities ( Fig. 1 ). This is particularly true for mathematics, where the population-level model estimate of heritability is very close to the twin model estimate.

Importantly, our analyses show that a substantial proportion of the observed correlation in reading and mathematics abilities is due to genetics. If a large proportion of the genetic factors that affect these traits are pleiotropic, then the factors that lead to differences in an individual’s abilities (or disabilities) are relatively more likely to be environmental. Understanding the aetiology of these patterns increases our chances of developing effective learning environments that will help individuals attain the highest level of literacy and numeracy, increasingly important skills in the modern world.

Twins Early Development Study

TEDS recruited over 15,000 families of twins born in England and Wales 30 in 1994, 1995 and 1996 and the sample remains representative of the UK population 2 ( Supplementary Note 2 ). Ethical approval for TEDS has been provided by the Institute of Psychiatry ethics committee, reference number 05/Q0706/228. We excluded from the analyses children with severe current medical problems and children who had suffered severe problems at birth or whose mothers had suffered severe problems during pregnancy. We also excluded twins whose zygosity was unknown or uncertain, whose first language was other than English, and included only twins whose parents reported their ethnicity as ‘white’, which is 93% of this UK sample.

At age 12, the TEDS twins participated in web- and telephone-based testing, as described previously 31 . Four measures of reading ability were used: two measures of reading comprehension and a measure of reading fluency presented on the web, and a fourth measure (TOWRE) administered over the telephone. Mathematics ability was assessed using a web-based battery of tests that included questions from three components of mathematics, based on the UK national curriculum. Both the reading and mathematics phenotypes comprised an equally weighted combination of the quantile-normalized scales. For each phenotype, we regressed out the effect of age before further analyses. Further details are provided in Supplementary Note 2 .

Phenotypic measurements were available for 2,243 (reading) and 2,772 (maths) of these, with 2,794 samples having at least one measurement and 2,221 samples having both. The sample genotyped on the Immunochip ( N =2,432) included N =2,153 individuals with at least one phenotypic measurement, of which N =1,388 were DZ co-twins of individuals in the discovery sample. For analyses, taking into account family structure, we additionally included untyped MZ and DZ co-twins of individuals typed in the discovery or Immunochip phases ( N =1,737) for a combined sample of N =7,323. For twin analyses, to parallel the population-based variance estimates as closely as possible, we used a sub-sample of the full TEDS cohort: the 2,794 informative samples with genome-wide data plus their co-twins, for a sample size of N =2,794 twin pairs.

Avon Longitudinal Study of Parents and Children

ALSPAC recruited more than 14,000 pregnant women in the former Avon area of the UK (around Bristol and Bath), with estimated dates of delivery between April 1991 and December 1992 (ref. 32 ). Ethical approval for the study was obtained from the ALSPAC Ethics and Law Committee and the Local Research Ethics Committees. The ALSPAC study website contains details of all the data that are available through a fully searchable data dictionary ( http://www.bris.ac.uk/alspac/researchers/data-access/data-dictionary/ ). The sample used for replication here is a population-representative group of participants who were tested for word-reading efficiency (TOWRE) at the age of 12.5 years. After combining TOWRE scores across two subtests (see Supplementary Note 2 ) a total of N =2,140 samples were available for analysis.

GWAS genotyping and imputation

Samples were genotyped at the Affymetrix’s service laboratory on the Genome-Wide Human SNP Array 6.0. For all samples passing Affymetrix’s laboratory quality control, raw intensities (from the.CEL files) were renormalized within collections using CelQuantileNorm ( http://sourceforge.net/projects/outmodedbonsai/files/CelQuantileNorm/ ). These normalized intensities were used to call genotypes with an updated version of the Chiamo software 33 adapted for Affymetrix 6.0 SNP data.

As is the standard practice for GWAS studies, we excluded sets of individuals whose genome-wide patterns of diversity are outliers compared with the majority of those in the study 34 , and we excluded SNPs for which there is evidence that genotype calls do not provide precise estimates of genotype frequencies. Details of the quality control methods used are published elsewhere 34 , 35 . In total, 465 of 3,665 samples were excluded from the analyses by these criteria (see Supplementary Table 5 ). Genotypes and phenotypes from the discovery sample will be made available through the European Genome-Phenome Archive ( https://www.ebi.ac.uk/ega/ ).

To assess relatedness among study individuals, we compared each individual with the 100 individuals they were most closely related to (on the basis of genome-wide levels of allele sharing) and used a hidden Markov model (HMM) to decide, at each position in their genome, whether the two individuals shared 0, 1 or 2 chromosomes identical by descent. We obtained a set of ‘unrelated’ individuals with identity by descent <5% by iteratively removing the member of each pair of putatively related individuals with more missing genotypes. A total of 3,154 individuals were included in subsequent analyses.

In addition to standard SNP filters ( Supplementary Table 6 ), we considered a measure of the statistical information (the IMPUTE info measure) carried by the genotype calls for the underlying allele frequency 36 . SNPs were removed prior to imputation if this information measure was below 0.98 or if the estimated minor allele frequency was below 1%. In total 84,029 (9%) of SNPs were removed by these criteria.

We imputed additional genotypes from a combined reference panel of the 120 CEU trios in HapMap2 and HapMap3 and the common control group of WTCCC2. As an additional quality control step, prior to imputation we re-imputed each typed SNP using IMPUTE version 1 and removed any SNP where the concordance between typed and imputed genotypes was <0.965. We used this high-confidence subset of 736,939 SNPs from the array to impute additional genotypes using IMPUTE2 (refs 36 , 37 ).

IMPUTE2 adopts a two-stage approach using both a haploid reference panel and a diploid reference panel. For the haploid reference panel, we used HapMap2 and HapMap3 SNP data on the 120 unrelated CEU trios; and for the diploid reference, we used a merged set of genotype calls from Affymetrix 6.0 and Illumina 1.2 M genotyping chip typed on 5000 1958 Birth Cohort (58C) and National Blood Service (NBS) individuals forming the common control group of WTCCC2. For association testing we included SNPs with info measure of at least 0.98 (if imputed from HapMap) or 0.9 (if imputed from the WTCCC2 controls) and having an estimated minor allele frequency of at least 1%.

Immunochip genotyping

Replication samples were typed on the Illumina ‘Immunochip’, a custom chip designed by the Immunochip Consortium and WTCCC2, at the Wellcome Trust Sanger Institute. Bead intensity data were processed and normalized for each sample in BeadStudio. Data for successfully genotyped samples were extracted and genotypes were called using the Illuminus algorithm 38 . Samples and SNPs were subject to similar quality control procedures as described above.

ALSPAC genotyping

We obtained data for 194 SNPs from the region 48891732-49091732 (NCBI build 36) on chromosome 19 for ALSPAC participants by application to the ALSPAC executive. Details on ALSPAC genotyping and imputation are described elsewhere 39 . Samples were included in the analysis if they had attended the TOWRE test session and completed both parts of the test. N =63 individuals who were recorded as having scored zero on either part of the test were removed, leaving a total of N =2,077 individuals for analysis.

Genome-wide association analysis

After quality control, 1,588,650 SNPs were analyzed in the GWAS using SNPTEST ( https://mathgen.stats.ox.ac.uk/genetics_software/snptest/snptest.html ), fitting an additive linear model to the data, with sex as a covariate. We used the missing data likelihood score test implemented in SNPTEST to compute P -values, and refer to these as P GWAS above. SNPs with a P -value<5 × 10 −5 were further analyzed in a sample combining the GWAS and Immunochip participants, along with informative co-twins with phenotype data but no genotypes available ( N =1,737). To take account of the relatedness in the combined sample, we fitted the association model using Merlin software 40 , again with sex as a covariate. The Merlin software also infers the posterior probabilities of missing genotype information from available pedigree information to increase power. For the region on chromosome 19 we analyzed the ALSPAC data using SNPTEST again with sex as a covariate.

Variance component analysis

For twin and population-level analyses, we consider a general partitioning of a quantitative phenotype Y (either reading or mathematics ability in our study) into five components Y=A+D+I+C+E , where A , D and I correspond to additive, dominance and interaction genetic effects over the whole genome, respectively, and C and E are within-family and individual environmental effects, respectively. We assume that these components are defined to be uncorrelated with each other and thus the phenotypic variance is also partitioned into five components V Y = V A + V D + V I + V C + V E .

Bivariate twin analysis

We consider the traditional ACE twin model (see Supplementary Methods ) assuming that dominance and interaction effects are zero ( D = I =0). To extend the model to bivariate phenotype, we introduce three parameters ρ A , ρ C and ρ E to describe the correlation between additive genetic, shared environmental and individual environmental effects, respectively, between reading and mathematics abilities (see Supplementary Methods ). We use the model to estimate the variance components V A , V C , V E , and the three correlation parameters. The narrow-sense heritability is then defined as the ratio— V A / V Y .

For the twin analyses, standardized residuals correcting for age and sex were used because the age of twins is perfectly correlated across pairs, which means that, unless corrected, variation within each age group at the time of testing would contribute to the correlation between twins and be misrepresented as shared environmental influence. The same applies to the sex of the twins, since MZ twins are always of the same sex. The model was fitted using full information maximum likelihood analysis of raw data in the structural equation modelling R package OpenMx 41 , estimating the variance parameters for both phenotypes together with the correlation parameters.

Bivariate population-level analysis

As opposed to the twin model, the population-level model considers only individuals who are not closely related. The univariate version of this model was recently introduced to study human height 22 , 25 and subsequently further assessed 24 . The bivariate extension was also recently considered 20 , 42 .

This model decomposes the variance into an additive genetic component ( G ) that is due to the available panel of SNPs, and the residual component which in principle includes D , I , C and E as defined previously, together with the part of the additive component A that is not captured by G . Thus it can be used for estimating a lower bound for the variance and covariance (or correlation) between the additive genetic components of the two phenotypes ( Supplementary Methods ). A caveat of this model is that environmental effects that correlate with genetics can act as potential confounders.

As for the twin model, we extend the population-level model to the bivariate case by introducing parameters ρ G and ρ ε to describe the correlation between genetic and residual effects between phenotypes (see Supplementary Methods ). This model was previously used elsewhere 20 .

For population-level analysis, we included one member of each of those 2,221 twin pairs for which both the reading and the mathematics ability was measured. After quality control 686,458 autosomal SNPs from the Affymetrix array were included in the analysis. We used linear regression to adjust the phenotypes for age, sex and population structure (using 10 PCs) before the variance component analysis. We checked that the programme GCTA 22 gave very similar results for the variance parameters as our own implementation (see Supplementary Methods ).

We implemented a Metropolis-Hastings random walk algorithm to explore the posterior distribution on the parameters (here proportional to the likelihood due to the use of uniform priors, see Supplementary Figs 4 and 5 and Supplementary Methods ), and compute credible intervals. Finally, we computed a Bayes factor to quantify the evidence for this model relative to the model where ρ G =0, and used both permutations and simulations to obtain a P -value for this model comparison ( Supplementary Fig. 5 and Supplementary Methods ).

Interpretation of twin and population-level estimates

Although the twin and population models are similar in spirit, they differ in modelling assumptions and parameter interpretation. Here we list factors that could potentially lead to differences between the model estimates.

Population-level estimates of heritability and genetic correlation take into account only those genetic factors which are tagged by variants present on the genotyping platform. Consequently the population-level model gives a lower-bound estimate of heritability. In particular, we chose not to include genotypes of SNPs on the sex chromosomes in order to help simplify the model and its interpretation. In principle, twin model estimates capture all genetic factors which produce differences between trait values for siblings.

Twin model estimates of narrow-sense heritability may be biased upwards by the presence of dominance or interaction effects 23 . By contrast, because the population-level model employs only distantly related individuals, dominance and interaction effects are expected to be much less important effects.

Twin models take into account only those genetic factors which lead to differences in trait values between siblings: consider an unmeasured environmental variable S that depends only on the family (socio-economic status may be one such variable). If S is correlated with genetics—for example, through parental genotypes—its effect in the twin model, where S is unmodelled, will be to increase the estimated proportion of C 43 and so to act to deflate estimates of genetic contributions. However, since shared environment is not modelled in the population-level model, S potentially contributes to the estimated proportion of G . In principle, including PCs in the model may help control for this effect. We find little difference in the estimates between the model including and not including PCs ( Supplementary Table 4 ).

More complex effects, including interaction between genetic and environmental influences, could potentially have different effects on the two models. For example, twin model estimates of heritability may be affected by within-family (that is, shared) environmental effects that are more similar between MZ twins than DZ twins 44 , 45 . More generally, environmental effects that correlate or interact with genetics and other factors are not modelled directly 43 , 46 . However, several studies have shown that these assumptions of the twin model are usually reasonable in practice 44 , 46 . Population-level estimates appear to be remarkably robust to deviations from modelling assumptions 24 .

T he population-level model assumes a particular dependency between the minor allele frequency at a SNP and the size of the effect of that SNP on the phenotype (see Supplementary Methods ). Simulation studies 24 suggest the model is fairly robust to deviations from this assumption.

Additional information

How to cite this article: Davis O. S. P. et al. The correlation between reading and mathematics ability at age twelve has a substantial genetic component Nat. Commun. 5:4204 doi: 10.1038/ncomms5204 (2014).

Butterworth, B. & Kovas, Y. Understanding neurocognitive developmental disorders can improve education for all. Science 340 , 300–305 (2013).

Article   CAS   ADS   Google Scholar  

Kovas, Y., Haworth, C. M., Dale, P. S. & Plomin, R. The genetic and environmental origins of learning abilities and disabilities in the early school years. Monogr. Soc. Res. Child. Dev. 72 , vii1–144 (2007).

Google Scholar  

Davies, G. et al. Genome-wide association studies establish that human intelligence is highly heritable and polygenic. Mol. Psychiatry 16 , 996–1005 (2011).

Article   CAS   Google Scholar  

Ritchie, S. J. & Bates, T. C. Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychol. Sci. 24 , 1301–1308 (2013).

Article   Google Scholar  

Batty, G. D., Kivimaki, M. & Deary, I. J. Intelligence, education, and mortality. BMJ. 340 , c563 (2010).

Harlaar, N., Spinath, F. M., Dale, P. S. & Plomin, R. Genetic influences on early word recognition abilities and disabilities: a study of 7-year-old twins. J. Child. Psychol. Psychiatry 46 , 373–384 (2005).

Plomin, R. & Kovas, Y. Generalist genes and learning disabilities. Psychol. Bull. 131 , 592–617 (2005).

Stanovich, K. E. & Siegel, L. S. Phenotypic performance profile of children with reading disabilities—a regression-based test of the phonological-core variable-difference model. J. Educ. Psychol. 86 , 24–53 (1994).

Snowling, M., Bishop, D. V. & Stothard, S. E. Is preschool language impairment a risk factor for dyslexia in adolescence? J. Child. Psychol. Psychiatry 41 , 587–600 (2000).

Shaywitz, S. E. Dyslexia. New Engl. J. Med. 338 , 307–312 (1998).

Beitchman, J. H. & Young, A. R. Learning disorders with a special emphasis on reading disorders: a review of the past 10 years. J. Am. Acad. Child. Adolesc. Psychiatry. 36 , 1020–1032 (1997).

Gersten, R., Jordan, N. C. & Flojo, J. R. Early identification and interventions for students with mathematics difficulties. J. Learn. Disabil. 38 , 293–304 (2005).

Geary, D. C. Mathematics and learning disabilities. J. Learn. Disabil. 37 , 4–15 (2004).

Cardon, L. R. et al. Quantitative trait locus for reading disability on chromosome 6. Science 266 , 276–279 (1994).

Scerri, T. S. et al. DCDC2, KIAA0319 and CMIP are associated with reading-related traits. Biol. Psychiatry 70 , 237–245 (2011).

Meaburn, E. L., Harlaar, N., Craig, I. W., Schalkwyk, L. C. & Plomin, R. Quantitative trait locus association scan of early reading disability and ability using pooled DNA and 100K SNP microarrays in a sample of 5760 children. Mol. Psychiatry 13 , 729–740 (2008).

Docherty, S. J. et al. A genome-wide association study identifies multiple loci associated with mathematics ability and disability. Genes Brain Behav. 9 , 234–247 (2010).

Luciano, M. et al. A genome-wide association study for reading and language abilities in two population cohorts. Genes Brain Behav. 12 , 645–652 (2013).

Rietveld, C. A. et al. GWAS of 126,559 individuals identifies genetic variants associated with educational attainment. Science 340 , 1467–1471 (2013).

Deary, I. J. et al. Genetic contributions to stability and change in intelligence from childhood to old age. Nature 482 , 212–215 (2012).

Markowitz, E. M., Willemsen, G., Trumbetta, S. L., van Beijsterveldt, T. C. & Boomsma, D. I. The etiology of mathematical and reading (dis)ability covariation in a sample of Dutch twins. Twin Res. Hum. Genet. 8 , 585–593 (2005).

Yang, J., Lee, S. H., Goddard, M. E. & Visscher, P. M. GCTA: a tool for genome-wide complex trait analysis. Am. J. Hum. Genet. 88 , 76–82 (2011).

Zuk, O., Hechter, E., Sunyaev, S. R. & Lander, E. S. The mystery of missing heritability: genetic interactions create phantom heritability. Proc. Natl Acad. Sci. USA 109 , 1193–1198 (2012).

Zaitlen, N. & Kraft, P. Heritability in the genome-wide association era. Hum. Genet. 131 , 1655–1664 (2012).

Visscher, P. M., Yang, J. & Goddard, M. E. A commentary on 'common SNPs explain a large proportion of the heritability for human height' by Yang et al. (2010). Twin Res. Hum. Genet. 13 , 517–524 (2010).

Lind, P. A. et al. Dyslexia and DCDC2: normal variation in reading and spelling is associated with DCDC2 polymorphisms in an Australian population sample. Eur. J. Hum. Genet. 18 , 668–673 (2010).

Meng, H. et al. DCDC2 is associated with reading disability and modulates neuronal development in the brain. Proc. Natl Acad. Sci. USA 102 , 17053–17058 (2005).

Marino, C. et al. DCDC2 genetic variants and susceptibility to developmental dyslexia. Psychiatr. Genet. 22 , 25–30 (2012).

Lango Allen, H. et al. Hundreds of variants clustered in genomic loci and biological pathways affect human height. Nature 467 , 832–838 (2010).

Haworth, C. M., Davis, O. S. & Plomin, R. Twins Early Development Study (TEDS): a genetically sensitive investigation of cognitive and behavioral development from childhood to young adulthood. Twin Res. Hum. Genet. 16 , 117–125 (2013).

Haworth, C. M. et al. Internet cognitive testing of large samples needed in genetic research. Twin Res. Hum. Genet. 10 , 554–563 (2007).

Boyd, A. et al. Cohort profile: the 'children of the 90s'—the index offspring of the Avon Longitudinal Study of Parents and Children. Int. J. Epidemiol. 42 , 111–127 (2013).

Wellcome Trust Case Control Consortium. Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447 , 661–678 (2007).

Bellenguez, C., Strange, A., Freeman, C., Donnelly, P. & Spencer, C. C. A robust clustering algorithm for identifying problematic samples in genome-wide association studies. Bioinformatics 28 , 134–135 (2012).

Barrett, J. C. et al. Genome-wide association study of ulcerative colitis identifies three new susceptibility loci, including the HNF4A region. Nat. Genet. 41 , 1330–1334 (2009).

Howie, B. N., Donnelly, P. & Marchini, J. A flexible and accurate genotype imputation method for the next generation of genome-wide association studies. PLoS Genet. 5 , e1000529 (2009).

Howie, B., Marchini, J. & Stephens, M. Genotype imputation with thousands of genomes. G3 (Bethesda) 457–470 (2011).

Teo, Y. Y. et al. A genotype calling algorithm for the Illumina BeadArray platform. Bioinformatics 23 , 2741–2746 (2007).

Paternoster, L. et al. Adult height variants affect birth length and growth rate in children. Hum. Mol. Genet. 20 , 4069–4075 (2011).

Abecasis, G. R., Cherny, S. S., Cookson, W. O. & Cardon, L. R. Merlin—rapid analysis of dense genetic maps using sparse gene flow trees. Nat. Genet. 30 , 97–101 (2002).

Boker, S. et al. OpenMx: an open source extended structural equation modeling framework. Psychometrika 76 , 306–317 (2011).

Article   MathSciNet   Google Scholar  

Korte, A. et al. A mixed-model approach for genome-wide association studies of correlated traits in structured populations. Nat. Genet. 44 , 1066–1071 (2012).

Purcell, S. Variance components models for gene-environment interaction in twin analysis. Twin Res. 5 , 554–571 (2002).

Boomsma, D., Busjahn, A. & Peltonen, L. Classical twin studies and beyond. Nat. Rev. Genet. 3 , 872–882 (2002).

Martin, N., Boomsma, D. & Machin, G. A twin-pronged attack on complex traits. Nat. Genet. 17 , 387–392 (1997).

Keller, M. C., Medland, S. E. & Duncan, L. E. Are extended twin family designs worth the trouble? A comparison of the bias, precision, and accuracy of parameters estimated in four twin family models. Behav. Genet. 40 , 377–393 (2010).

Download references

Acknowledgements

Funding for this study was provided by the Wellcome Trust Case Control Consortium 2 project (085475/B/08/Z and 085475/Z/08/Z) and TEDS is supported by a program grant from the UK Medical Research Council (G0901245). The UK Medical Research Council and the Wellcome Trust (Grant ref: 092731) and the University of Bristol provide core support for ALSPAC. O.S.P. Davis was supported by a Sir Henry Wellcome Fellowship from the Wellcome Trust (WT088984). M. Pirinen is supported by the Academy of Finland (257654). C.M.A. Haworth was supported by a research fellowship from the British Academy. R. Plomin was supported by a research professorship from the UK Medical Research Council (G19/2) and a European Research Council Advanced Investigator Award (295366). P. Donnelly was supported in part by a Wolfson-Royal Society Merit Award. C.C.A. Spencer was supported by a Wellcome Trust Fellowship [097364/Z/11/Z], and work was supported in part by Wellcome Trust Centre for Human Genetics core grants 090532/Z/09/Z and 075491/Z/04/B. We acknowledge use of the British 1958 Birth Cohort DNA collection funded by the Medical Research Council (grant G0000934) and the Wellcome Trust (grant 068545/Z/02), and the UK National Blood Service controls funded by the Wellcome Trust. E Bramon holds a Medical Research Council new investigator award. We also thank the National Institutes of Health Research Biomedical Research Centre at Guy’s and St Thomas’ NHS Foundation Trust in partnership with King’s College London.

Author information

Oliver S. P. Davis, Gavin Band and Matti Pirinen: These authors contributed equally to this work

Robert Plomin and Chris C. A. Spencer: These authors jointly supervised this work

Authors and Affiliations

Department of Genetics, Evolution and Environment, UCL Genetics Institute, University College London, London, WC1E 6BT, UK

Oliver S. P. Davis

King’s College London, Social Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, London, SE5 8AF, UK

Oliver S. P. Davis, Claire M. A. Haworth, Sophia J. Docherty, Ken B. Hanscombe, Maciej Trzaskowski, Charles J. C. Curtis, Leonard S. Schalkwyk, Ian W. Craig, Cathryn M. Lewis & Robert Plomin

Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, OX3 7BN, UK

Gavin Band, Matti Pirinen, Amy Strange, Colin Freeman, Céline Bellenguez, Zhan Su, Richard Pearson, Damjan Vukcevic, Anna Rautanen, Peter Donnelly & Chris C. A. Spencer

Department of Psychology, University of Warwick, Coventry, CV4 7AL, UK

Claire M. A. Haworth

Department of Psychological Sciences, Birkbeck, University of London, London, WC1E 7HX, UK

• Emma L. Meaburn

Department of Psychology, Goldsmiths, University of London, London, SE14 6NW, UK

Yulia Kovas

Department of Psychology and Neuroscience, University of Colorado Boulder, Boulder, 80309-0345, Colorado, USA

Nicole Harlaar

Wellcome Trust Sanger Institute, Cambridge, CB10 1SA, UK

Cordelia Langford, Panos Deloukas, Sarah Hunt, Emma Gray, Serge Dronov, Simon C. Potter, Avazeh Tashakkori-Ghanbaria, Sarah Edkins, Suzannah J. Bumpstead, Ines Barroso & Leena Peltonen

Telethon Institute for Child Health Research, Centre for Child Health Research, University of Western Australia, Crawley, Western Australia, Australia

Jenefer M. Blackwell

Cambridge Institute for Medical Research, University of Cambridge School of Clinical Medicine, Cambridge, CB2 0XY, UK

UCL Institute of Cognitive Neuroscience, University College London, London, WC1N 3AR, UK

Elvira Bramon

UCL Mental Health Sciences Unit, University College London, London, W1W 7EJ, UK

University of Queensland Diamantia Institute, Translational Research Institute, Princess Alexandra Hospital, University of Queensland, Brisbane, QLD 4102, Queensland, Australia

Matthew A. Brown

Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, WC1E 7HT, UK

Juan P. Casas

Department of Epidemiology and Public Health, University College London, London, WC1E 6BT, UK

Neuropsychiatric Genetics Research Group, Institute of Molecular Medicine, Trinity College Dublin, Dublin 2, Ireland

Aiden Corvin

Molecular and Physiological Sciences, The Wellcome Trust, London, NW1 2BE, UK

Audrey Duncanson

Centre for Digestive Diseases, Blizard Institute, Queen Mary University of London, London, E1 2AT, UK

Janusz A. Z. Jankowski

Wolfson College, Linton Road, Oxford, OX2 6UD, UK

Peninsula School of Medicine and Dentistry, Associate Deans Office, John Bull Building, Plymouth, PL6 8BU, UK

Clinical Neurosciences, Saint George's University of London, London, SW17 0RE, UK

Hugh S. Markus

Department of Medical and Molecular Genetics, King’s College London, King’s Health Partners Guy’s Hospital, London, SE1 9RT, UK

Christopher G. Mathew & Richard C. Trembath

Biomedical Research Centre, Ninewells Hospital and Medical School, Dundee, DD1 9SY, UK

Colin N. A. Palmer

Department of Clinical Neurosciences, University of Cambridge, Addenbrooke’s Hospital, Cambridge, CB2 2QQ, UK

Stephen J. Sawcer

NIHR Biomedical Research Centre at Moorfields Eye Hospital NHSFT and UCL Institute of Ophthalmology, London, EC1V 2PD, UK

Ananth C. Viswanathan

Department of Molecular Neuroscience, Institute of Neurology, University College London, London, WC1N 3BG, UK

Nicholas W. Wood

Department of Speech and Hearing Sciences, University of New Mexico, Albuquerque, 87131, New Mexico, USA

Philip S. Dale

Department of Family Science, Institute for Population Research, The Ohio State University, Columbus, 43210, Ohio, USA

Stephen A. Petrill

Institute for Translational Medicine and Therapeutics, University of Pennsylvania School of Medicine, Philadelphia, 19104-5158, Pennsylvania, USA

Thomas S. Price

Department of Statistics, University of Oxford, Oxford, OX1 3TG, UK

Peter Donnelly

You can also search for this author in PubMed   Google Scholar

The Wellcome Trust Case Control Consortium

Contributions.

Writing Group: O.S.P.D., G.B., M.P., P.D., R.P. and C.C.A.S. Data analysis: O.S.P.D., G.B., M.P., A.S., T.S.P., C.F., C.B., Z.S., R.P., D.V., P.D., C.C.A.S., K.B.H., M.T., L.S.S. and C.M.L. Sample preparation and genotyping: E.L.M., S.J.D., C.J.C.C., I.W.C., C.L., P.D., S.H., E.G., S.D., S.C.P., A.T.G., S.E. and S.J.B. Phenotype data planning and collection: C.M.A.H., Y.K., N.H., S.A.P. and P.S.D. WTCCC2 Management Committee: P.D., I.B., J.M.B., E.B., M.A.B., J.P.C., A.C., P.D., A.D., J.A.Z.J., H.S.M., C.G.M., C.N.A.P., R.P., A.R., S.J.S., R.C.T., A.C.V. and N.W.W.

Corresponding authors

Correspondence to Oliver S. P. Davis or Chris C. A. Spencer .

Ethics declarations

Competing interests.

The authors declare no competing financial interests.

A full list of members is provided in Supplementary Note 1 .

Supplementary information

Supplementary information.

Supplementary Figures 1-5, Supplementary Tables 1-6, Supplementary Notes 1-2, Supplementary Methods and Supplementary References (PDF 2054 kb)

Rights and permissions

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Reprints and permissions

About this article

Cite this article.

Davis, O., Band, G., Pirinen, M. et al. The correlation between reading and mathematics ability at age twelve has a substantial genetic component. Nat Commun 5 , 4204 (2014). https://doi.org/10.1038/ncomms5204

Download citation

Received : 04 September 2013

Accepted : 23 May 2014

Published : 08 July 2014

DOI : https://doi.org/10.1038/ncomms5204

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Dynamics between reading and math proficiency over time in secondary education – observational evidence from continuous time models.

• Christoph Jindra
• Karoline A. Sachse
• Martin Hecht

Large-scale Assessments in Education (2022)

Evidence for specificity of polygenic contributions to attainment in English, maths and science during adolescence

• Georgina Donati
• Iroise Dumontheil

Scientific Reports (2021)

The stability of educational achievement across school years is largely explained by genetic factors

• Kaili Rimfeld
• Margherita Malanchini
• Robert Plomin

npj Science of Learning (2018)

A genome-wide association study for extremely high intelligence

Molecular Psychiatry (2018)

A Genome-Wide Association Study Identifies Genetic Variants Associated with Mathematics Ability

• Xiao-hong Gu

Scientific Reports (2017)

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

An IERI – International Educational Research Institute Journal

• Open access
• Published: 09 December 2022

Dynamics between reading and math proficiency over time in secondary education – observational evidence from continuous time models

• Christoph Jindra   ORCID: orcid.org/0000-0002-9388-0443 1 ,
• Karoline A. Sachse 1 &
• Martin Hecht 2  

Large-scale Assessments in Education volume  10 , Article number:  22 ( 2022 ) Cite this article

3712 Accesses

1 Citations

Metrics details

Introduction

Reading and math proficiency are assumed to be crucial for the development of other academic skills. Further, different studies found reading and math development to be related. We contribute to the literature by looking at the relationship between reading and math using continuous time models. In contrast to previous studies, this allows us to (a) report estimates for autoregressive and cross-lagged effects for a range of possible time intervals while still only estimating one set of continuous time parameters and (b) identify peak effects for the relationship between the two. Using data from Starting Cohort 3 of the National Educational Panel Study, we find, in line with previous evidence, a larger effect of reading on math than the other way around. Furthermore, we identify peak standardized cross-lagged effects ( \({a}_{reading\to math}\approx 0.30\) , \({a}_{math\to reading}\approx 0.13\) ) for a time interval of approximately 6 months.

Reading and math proficiency are considered crucial for later development of other academic skills (e.g., Koponen et al., 2020 ). While the domains are often treated independently in practice, research frequently considers them alongside each other, recognizing that beyond their individual developmental trajectories there is interplay (e.g., Cameron et al., 2019 ; Koponen et al., 2020 ; Korpipää et al., 2017 ; Vanbinst et al., 2020 ; Bailey et al., 2020 ; Erbeli et al., 2021 ; Purpura et al., 2017 ). Learning about these developmental dynamics through appropriate models is crucial for improved prediction and identification of starting points for potential interventions.

The contribution of this study is twofold. First, we contribute to our knowledge on the relationship between math and reading by describing the interplay between the two over time using continuous time models. By doing so, we provide further evidence on potential reciprocal effects and the nature of such effects using a novel modeling technique. This allows us to answer questions such as; do we find further evidence that reading is the leading competency, whose effect on math is stronger than vice versa (e.g., Bailey et al., 2020 ; Erbeli et al., 2021 ) and for which time interval do we find peak effects? However, we can also assess each constructs’ persistence, that is, we can describe for which construct past deviations persist into the future for longer. Previous findings, for example, suggest that reading might be somewhat more persistent than math (Hecht et al., 2001 ; Korpipää et al., 2017 ). Furthermore, our application also demonstrates the potential of continuous time modeling for the analysis of the interplay between educational constructs in general and how these models increase comparability and thus facilitate the accumulation of knowledge. We do this by showcasing one of the main strengths of continuous time models, the ability to describe the entire dynamics between two constructs with one set of continuous time parameters, which can be used to calculate model implied discrete autoregressive and cross-lagged effects not just for the observed time interval but for a reasonable range.

The remainder of the paper is structured as follows. We firstly provide an overview over the current literature regarding the relationship between reading and math proficiency. Then, we discuss model requirements based on past evidence and data limitations, arguing for continuous time models as a solution for some of the issues. This section is followed by an introduction to continuous time models. Subsequently, we describe the data and measures. We then present the empirical results and conclude with a discussion of these as well as the limitations of our study.

Current evidence on the relationship between math and reading

Previous studies have frequently shown that proficiencies in math and reading are related (e.g., Cameron et al., 2019 , Bailey et al., 2020 , Erbeli et al., 2021 , Hübner et al., 2022 , Gnambs & Lockl, 2022 ). There are various possible reasons why we might observe an association: Footnote 1 (a) Reading skills could influence math skills, (b) math skills could influence reading skills, (c) both could be true, implying complex dynamics between the constructs, (d) the two constructs could share a set of time-constant and/or time-varying causes. Although previous empirical evidence is often based on vastly different types of empirical models which often lead to parameters that are not strictly comparable (e.g,. Orth et al., 2021 ), results are usually interpreted as providing evidence for one of the four mechanisms.

Thus, (a) reading proficiency could be important for math because language shapes the development of numbers concepts and learning rules of the number system is similar to mastering written language (as symbolic representational system) (LeFevre et al., 2010 ). Also, well developed phonological processing and fluency skills are a prerequisite for math. In line with this, Grimm ( 2008 ) found early reading skills to be a good predictor for success in mathematics and Jordan et al. ( 2002 ) reported that reading abilities influence children’s growth in mathematics. The inverse pathway, (b) math influencing reading proficiency, is also theoretically and empirically grounded. Early math proficiency, such as fluent counting, potentially shapes formation and retrieval skills of visual-verbal associations in long-term memory, which are crucial for reading fluency (Koponen et al., 2013). In line with this, Duncan et al. ( 2007 ) reported that early math skills have the greatest predictive power for later learning and that early math skills predicted reading better than reading predicted math. Further, Holenstein et al. ( 2020 ) found a transfer effect of mathematical literacy achievement on different school domains including reading for adolescents. Purpura et al. ( 2017 ) suggested mathematical language skills as a mediating mechanism for the effect of mathematical skills on later reading.

However, given that there exist studies that provide support for either (a) or (b), it seems difficult to exclude (c) as an option, and thus the possibility that there are complex dynamics between the variables. Thus the literature in (c) seems in most cases rather complementary than competitive to those cited in (a) and (b), unless a specific study explicitly seems to find support for one pathway only such as the one by Jordan et al. ( 2002 ), who find that in their case reading abilities do impact growth in math but not the other way around. On the other hand, Schmitt et al., ( 2017 ) for example reported a bidirectional relationship for certain time spans between kindergarten and preschool. Similarly, Cameron et al. ( 2019 ) concluded that proficiency in each domain contributes to the other in a reciprocal, supportive manner. Bailey et al. ( 2020 ) reported bidirectional effects between reading and math but found stronger effects for reading on math when using a cross-lagged panel model with random intercepts (RI-CLPM) compared to the simple cross-lagged panel model (CLPM). These results are somewhat in line with Erbeli et al., ( 2021 ) who found bidirectional effects with reading appearing to be a leading and math a lagging indicator. Hübner et al., ( 2022 ) also found a complex relationship between the constructs but concluded that reading skills might be particularly important for the development of math skills. Gnambs and Lockl ( 2022 ) on the other hand also demonstrated how sensitive results are towards modeling choices. While results from the CLPM and CLPM with lag 2 showed consistent positive bi-directional associations between the constructs, effects for the RI-CLPM changed over grades even turning negative for older students. However, one has to keep in mind that the methodological debate on the difficulties of comparing results from the different models is ongoing (for example Orth et al., 2021 ; Lucas, 2022 ). Recently, Lucas drew attention to the well-known problem that results from the CLPM are a potentially uninterpretable mix of between- and within-effects, whereas the RI-CLPM aims to disentangle both. This is why Bailey et al. ( 2020 ) argue that the observed reduction in their effect sizes, when using the RI-CLPM in contrast to the CLPM, is due to the former accounting for the effects of stable unmeasured factors, a source of between-effects, which leads to (d), confounders. It seems indisputable that both domains are likely to share a set of common causes. These could be a broadly defined g -factor, that is, general intelligence, as in the strata-theories (Carroll, 1993 ; Cattell, 1987 ; Horn, 1988 ). But also more specific common domain-general cognitive correlates were reported. Several studies discuss a variety of factors that seem to be correlated with both domains, such as working memory, attentive behavior, processing speed, listening comprehension, nonverbal reasoning, serial retrieval fluency, phonological awareness, processing speed, and numeral recognition (Fuchs et al., 2013 ; Korpipää et al., 2017 ; Koponen et al., 2020 ; Vanbinst et al., 2020 ; Cirino et al., 2018 ). Furthermore, there are likely other factors that cause the constructs to be related. Previous evidence, for example, suggests that there is a genetic component to the correlation between reading and mathematics ability (Davis et al., 2014 ). Additionally, standard confounders such as family or language background will lead to an empirical association between the variables unless accounted for. Thus, previous studies provide support for all the above stated reasons that could be behind the empirical association. However, depending on the underlying data generating process, different statistical strategies seem more appropriate, as will be discussed in the following section.

Methodological challenges in the study of reading-math dynamics

It is well known that panel data and standard panel methods can offer some protection against the threat of time-constant unobserved heterogeneity (Allison, 2009 ; Bell & Jones, 2015 ; Halaby, 2004 ; Zyphur et al., 2020 ). Footnote 2 Thus, while we have to observe time-varying confounders to be able to control for them, in the absence of a valid identification strategy, we can at least mitigate the risk of time-constant confounding with panel data. On the other hand, if researchers are interested in the effect of reading on math but cannot exclude the possibility that math influences reading as well, one would need to go beyond standard models when simultaneously aiming to control for time-constant confounding (Allison et al., 2017 ; Arellano & Bond, 1991 ; Moral-Benito, 2013 ). However, it can be argued that if (c) is true, the statistical approach should account for this and any dynamics should be modeled explicitly. Thus, given that previous evidence implies that we cannot rule out reciprocal effects between math and reading skills and given that it seems highly unlikely that the constructs do not share common time-constant causes (d), a convincing statistical model should aim to account for both.

Different statistical approaches offer potential solutions, such as the random intercept cross-lagged panel model (RI-CPLM, Hamaker, 2015 ) or the general cross-lagged panel model (GCLM, Zyphur et al., 2020 ). Both incorporate dynamics in the form of autoregressive and cross-lagged parameters. Furthermore, both include correlated random intercepts to account for stable elements. While these elements are sometimes referred to as traits in the RI-CLPM, the correlated random intercepts approach in the GCLM corresponds more closely to what social scientists call a fixed effects approach to control for stable unobserved confounders (Allison, 2009 ; Halaby, 2004 ; Wooldridge, 2010 ; Zyphur et al., 2020 ; Bollen & Brand, 2011 ). Footnote 3 While we are not aware of an application that uses the GCLM to understand the dynamics between reading and math, Bailey et al., ( 2020 ) as well as Gnambs & Lockl ( 2022 ) have shown that results from the CLPM and the RI-CLPM differ substantially. The former attribute the reduction in effect sizes to controlling for time-constant traits. Thus, a high correlation between the random intercepts might indicate support for the idea of a substantial overlap between these time-constant factors. Besides the CLPM and the RI-CLPM, other longitudinal models to examine reciprocal relations exists, for example, the the stable trait autoregressive trait and state model (STARTS; Kenny & Zautra, 2001 ; also known as the trait-state-error (TSE) model, Kenny & Zautra, 1995 ), the latent curve model with structured residuals (LCM-SR; Curran et al., 2014 ), the autoregressive latent trajectory model (ALT; Bollen & Curran 2004 ; Curran & Bollen, 2001 ), and the latent change score model (LCS; Hamagami & McArdle 2001 ; McArdle & Hamagami, 2001 ). Usami et al.,( 2019 ) provide a general framework to “facilitate the understanding of the strengths and weaknesses of these models” which “helps to clarify the conceptual and statistical differences” (p. 654). For longitudinal educational research, especially for large-scale assessment studies like PISA, Lohmann et al., ( 2022 ) discuss the advantages of the LCM-SR, one of which being that “systematic (linear) trends are disentangled from the autoregressive and cross-lagged parameters” (p. 8). In this vein, Curran and Bollen ( 2001 ) speak of the “best of both worlds” as linear growth and dynamics are combined into one model while retaining their typical interpretation. All these models share the property of being discrete-time models which is associated with some issues that we discuss next.

In practice, we observe a considerable amount of variation in the time intervals between measurements across studies. Codding et al. ( 2015 ), for example, analyze data from three measurement points distributed over a short time period, namely fall, winter, and spring of one academic year. Rinne et al. ( 2020 ) collect data for six measurement points distributed over three years, while Bailey et al. ( 2020 ) use data from four measurement points collected over four years. These variations represent a challenge for the interpretation and comparability of coefficients across studies, complicating the accumulation of knowledge as effects from standard discrete time models pertain to the specific time interval of the respective study only (Oud & Delsing, 2010 ). Furthermore, time intervals between measurements do not only vary between studies but frequently within studies as well. In large studies, such as the National Educational Panel Study (NEPS; Blossfeld et al., 2019), or the Early Childhood Longitudinal Study (ECLS; e.g., Tourangeau et al., 2018 ) this can already be due to the fact that field work is often taking place over a considerable amount of time (for examples in other fields see Steptoe et al., 2013 ; Sonnega et al., 2014 ). For the purpose of analyses, information on the exact timing of the measurements is sometimes discarded and measurements are subsumed under the year of the fieldwork for a specific wave. Similarly, studies often do not measure each construct across all waves, complicating the analysis as constructs are missing for some waves. While dynamic discrete time models struggle with these issues, continuous time models can handle different time intervals between and within studies (Oud & Delsing, 2010 ; Voelkle et al., 2012 , 2018 ; Hecht et al., 2019 ; Hecht & Zitzmann, 2020 ) and can help to explore the unfolding of effects over time (Hecht & Zitzmann, 2021 ). Given that these models are further able to model complex dynamics between constructs and are potentially able to account for time-constant unobserved heterogeneity, they are well suited for research questions such as the interplay between reading and math proficiencies over time.

The advantages of continuous-time models over discrete-time models have been excellently described and illustrated in other works (e.g., Voelkle et al., 2012 ; Ryan et al., 2018 ; Hecht et al., 2019 ; Hecht & Zitzmann, 2021 ; Lohmann et al., 2022 ; Hecht et al., 2022 ). To shortly reiterate: Continuous-time modeling conceptualizes longitudinal data as “snapshots” that inform the estimation of continuously evolving processes. Thus, data from all time points can be used for estimation. This lifts the usual spacing restrictions in discrete-time models and allows the usage of flexible longitudinal designs with intra- and interindividual varying spacing between measurement occasions. Once the continuous-time model is estimated, it can be used to calculate corresponding discrete-time model parameters for any desired time interval length. This helps to compare discrete-time model results from studies with differently spaced measurement occasions. For instance, if one programme uses 1-year intervals and another programme 3-year intervals, both programmes could estimate a continuous-time model, then calculate discrete-time parameters for the same time interval (e.g., 2 years or any other desired interval length) and hence arrive at comparable results. Another advantage of continuous-time models which is frequently discussed in the literature (and particularly highlighted by Hecht & Zitzmann, 2021 ) is that the unfolding and dissipation of dynamic effects can be explored. This is usually done by plotting the dynamic parameter of interest (y axis) against the discrete-time interval length (x axis). We use this technique later in the present work to identify for which time interval length the reciprocal relationship of students’ reading and math proficiencies is maximal (which could be termed “peak cross-lagged effects”, Hecht & Zitzmann, 2021 ). This exploration with the help of continuous-time modeling is interesting and relevant because researchers often (implicitly or explicitly) search for these effects, but might not be able to identify these effects when applying discrete-time models.

• Continuous time modeling

We develop the main idea behind continuous time modeling following Voelkle et al. ( 2012 ), starting with a simple discrete time multivariate autoregressive model. We then move from an intuitive approach of dealing with variations in time intervals between studies in discrete time models to the continuous treatment of time. The starting point for our discussion is an autoregressive model of the following form:

All variables are assumed to be in deviation form, which allows us to ignore intercepts for now. In Eq. 1, \({x}_{j}\left(t\right)\) and \({x}_{j}(t- \varDelta t)\) each represent a \(K\times 1\) vector of the same \(K\) variables for individual j, once observed at discrete time point \(t\) and previously at time \(t-\varDelta t\) . Given that they appear on both sides of the equation, each variable can be an outcome and explanatory variable at the same time. The variables are linked to each other over time via the \(K\times K\) matrix \(A\left(\varDelta t\right)\) , containing the autoregressive parameters on its diagonal and cross-lagged effects on the off-diagonals. \({w}_{j}\left(\varDelta t\right)\) is a \(K\times 1\) vector of stochastic error terms, which are assumed to be uncorrelated over time. Both, \(A\left(\varDelta t\right)\) and \({w}_{j}\left(\varDelta t\right)\) , are a function of the time between measurements, indicated by \(\varDelta t\) . However, while they are a function of time, the underlying data generating process is nonetheless assumed to be constant over time. Hence, the equation just highlights that, while actual processes most often evolve continuously over time, our measurements are usually observed in discrete time intervals at specific time points and therefore, results based on discrete time methods will result in parameters that are a function of the study specific time intervals ( \(\varDelta t\) ). Consequently, they are not directly comparable.

An intuitive approach to make parameters from studies with varying time intervals comparable would be to predict normalized changes, \(({x}_{j}\left(t\right)-{x}_{j}\left(t-\varDelta t\right))/\varDelta t\) , instead of levels. Thus, ignoring error terms, we can relate the normalized changes to previous levels as follows:

Voelkle et al. ( 2012 ) call \({A}^{*}\) a crude approximation of the underlying continuous time process. It is important to note that \({A}^{*}\) is independent of the study specific time interval. However, the parameters are related and can be transformed into each other via the following equation:

Thus, once we have either \({A}^{*}\) or \(A\left(\varDelta t\right)\) and the time interval, we can easily move between the two. While simple and intuitive, Voelkle et al. ( 2012 ) highlight two main shortcomings of this approach. Firstly, while it represents an approximation of the underlying continuous process, it is just a crude approximation of the so-called drift matrix that represents the data generating process in continuous time modeling. Secondly, the approach can only be used if the time intervals between measurements are constant over time. Thus, while intuitive, the structure of some data prevents us from using this simple approach, which brings us to the exact approach. The intuitive approach still relies on a discrete understanding of time as we predict change between discrete measurement points. In continuous time models, change is still the dependent variable. However, given that time is treated as continuous variable, instead of predicting the normalized change between discrete measurement points, we now describe the relationship between \({x}_{j}\left(t\right)\) and the first derivative of \({x}_{j}\left(t\right)\) with respect to time:

Thus, the change in \({x}_{j}\left(t\right)\) over an infinitesimally small time interval, the first derivative, is a function of \({x}_{j}\left(t\right)\)  itself and all the relevant parameters describing this relationship are contained in drift matrix \(A\) . The solution of the differential equation from above is given by

where \({x}_{j}\left({t}_{0}\right)\) represents the value of the variables in the model at the initial time \({t}_{0}\) . Taking the first derivative of Eq. 5 with respect to time ( \(t\) ) yields Eq. 4. In order to distinguish parameters in \(A\)  from those in \(A\left(\varDelta t\right)\) , their naming conventions differ. Those on the diagonal are called auto -effects, while those off the diagonal are called cross -effects (in contrast to autoregressive and cross-lagged effects in the discrete time case; see Table  1 in the work of Hecht & Voelkle, 2021 , for an overview of discrete-time and continuous-time terms). Like in the case of the intuitive approach, parameters in  A can be transformed into discrete time parameters. Voelkle et al. ( 2012 ) show that the nonlinear relationship is given by the matrix exponential

Thus, as in the intuitive approach, we can move between discrete and continuous time parameters. However, unlike in the intuitive approach, the relationship in Eq. 6 represents the exact relationship between continuous and discrete time parameters, not just an approximation, and can be used to adequately describe the relationship between the variables over time.

Until now, we have ignored error terms, intercepts and time-constant unobserved heterogeneity in our discussion. Footnote 4 Including those leads to the following model

Briefly, \({W}_{j}\left(t\right)\) represents the continuous time error process, a so-called Wiener process or Brownian motion. \(d{W}_{j}\left(t\right)\) is the stochastic error term, an infinitesimally small increment of the Wiener process, while G represents the effect of the stochastic error term on the change in \({x}_{j}\left(t\right)\) . Together, these terms can be used to describe the noise in the continuous time process.

The random variables \({\xi }_{j }\) are assumed to follow a normal distribution with means \({\mu }_{\xi }\) and variance-covariance matrix \(\varPsi\) . Thus, the vector \({\mu }_{\xi }\) denotes the continuous time-intercepts and variance and covariances across subjects are contained in the matrix \(\varPsi\) . Together they account for nonzero mean trajectories. By modeling random intercepts for both domains, we allow individuals to deviate from the overall intercepts. More importantly, permitting a covariance between the random intercepts is argued to account for unobserved time-constant heterogeneity (compare Zyphur et al., 2020 ).

So far, our model is suitable for describing stable equilibrium processes, that is, processes that converge to final means over time. In educational research, such a model might be implausible, because development often occurs over sustained periods. To incorporate such trends, Lohmann et al. ( 2022 , in this same issue) developed the continuous-time latent change score model with structured residuals (CT-LCM-SR). The basic idea is to add an additional continuous-time process (for each variable) to the model that is specified in such a way that linear trends are captured. Thus, this model combines central components from both dynamic and descriptive models, the dynamics of the variables and the linear growth in the variables. As the focus of the present work is on the dynamics, we use ideas of the CT-LCM-SR to control for linear trends in the data so that the targeted dynamics can be properly estimated. An alternative option would be to detrend the data beforehand, but this might come with other disadvantages (e.g., the common problem of 2-step analyses of how to transfer the uncertainty of parameter estimates from the step-1 to the step-2 model). With respect to the interpretation of discrete-time dynamic effects, with controlling for the linear trends in the LCM-SR (or in its continuous-time version, the CT-LCM-SR) we fabricate an equivalent interpretation as in corresponding dynamic models that assume no trends, except that the reference line around which the state values fluctuate is the linear trend and not a flat line (which is, however, actually also just a linear trend with a zero slope).

We use data from the German NEPS study (Blossfeld & Roßbach, 2019 ). The study has a multicohort sequence design, consisting of several representative cohorts either defined by age or by specific points in the educational system. We analyse data from Starting Cohort 3 (SC3), a representative sample of students attending grade 5 in school year 2010/2011 who were subsequently followed over time. Students were selected using a stratified multistage sampling design (Skopek et al., 2012 ). Schools were sampled in the first stage, stratified by school type. Subsequently two classes in each school were selected in the second stage and all students in those classes were eligible for interviews. We use the five waves for which competency scores in math and reading are available (see Table  1 ). In waves 1 (grade 5), 3 (grade 7), and 9 (grade 12), students took tests in both math and reading. In wave 5 (grade 9), students took math tests only, while reading tests were administered around five months later, in wave 6 (grade 9). We include all students with at least one non-missing value on the competency scores in our analysis, leading to an effective sample size of 7,639 students. Footnote 5 Mean age at wave 1 wave is 10.5 ( SD  = 0.64, min. = 8, max. = 15), while mean age at wave 9 is 17.4 ( SD  = 0.59, min. = 16, max. = 19). The share of female students at wave 1 is 0.48.

As described above, time intervals vary between waves and furthermore within each wave, testing took place over a period of several months, resulting in unequal time intervals between measurement points (see Table  2 ). We use the month with the first observed competence score as our baseline ( t  = 0) and express subsequently elapsed time between measurements in years and months from baseline.

Competence scores

Reading (Gehrer et al., 2013 ) and mathematics proficiency (Neumann et al., 2013 ) were measured by the NEPS competence tests, which are constructed to adequately measure the respective construct in all age cohorts assessed. Students were tested by paper-based competence tests. The tests were scaled and linked based on IRT models. Individual scores (WLEs) based on the linked tests are available for different waves as described above and were placed on a common scale to facilitate meaningful mean-level comparisons across time. The first wave serves as a reference scale and values can thus be interpreted as developmental trajectories across measurement points (see Kutscher et al., 2020 , and Petersen et al., 2020 , for a detailed description). WLE reliabilities range between 0.721 and 0.812 across time and between domains.

Data analysis

The continuous time model is estimated via Structural Equation Modeling (Bollen, 1989 ) in R (R Core Team, 2021 ) by imposing restrictions on the relevant parameters (Oud & Delsing, 2010 ; Voelkle et al., 2012 ). Specifically, the R package ctsemOMX (Driver et al., 2021 ), which is based on OpenMX (Boker et al., 2021 ), was used for the analyses. In order to account for growth over time, we added a linear trend component to the continuous time model. In our case, growth intercepts and slopes are assumed to be “fixed”, that is, they do not vary over persons and thus have no random component. Random intercepts are however included in the models as trait variables to control for time-constant unobserved heterogeneity (Driver et al., 2017 ). The model specification can be found as a path diagram in Figure  S1 in the Supplementary Materials. The model is estimated using Full Information Maximum Likelihood (FIML), thus missing values are accounted for. Descriptive statistics were computed using Stata 16.1 SE (StataCorp, 2019 ). Growth curve models for validating the continuous time model trend component were estimated in Stata.

Descriptive statistics can be found in Table  3 . We report results for each domain by wave alongside the correlations between the domains across waves. Additionally, we provide summary statistics on the time between measurement points. All summary statistics are calculated using the maximum number of cases available for the specific statistic. Descriptive means show an increase of average proficiency in both domains over time in our sample. Correlations show strong associations between proficiency scores in the same domain across waves, though decreasing with increasing time intervals between measurement occasions. However, compared to reading, descriptive results show stronger correlations across waves for math. Furthermore, we also find strong correlations across domains with the similar pattern of decreasing associations for increasing time intervals.

Parameters from the continuous time model are displayed in Table  4 . The parameters accounting for a linear trend \((t{r}_{math}\) and \(t{r}_{reading})\) can be interpreted in a similar fashion to those in standard growth curve models. Both indicate, as expected, growth in each of the domains over time. A comparison of our estimates to those from growth curve models with random intercepts shows that estimates from the continuous time model are nearly identical to those from the simpler models (see Section S2 in the Supplementary Materials).

The main parameters of interest, describing the dynamics, the auto- and cross-effects, are all statistically significant at the 5% level against the null hypothesis that the respective parameter is equal to 0. Due to the complex nature of these parameters, we provide discrete-time equivalents for varying time intervals for interpretation in Fig.  1 . One way of interpreting Fig.  1 is that the plots show the autoregressive and cross-lagged effects we would expect based on our model for a range of plausible time intervals in hypothetical studies. For example, in case of the discrete-time cross-lagged parameters, a hypothetical study with a time-interval between measurements that approaches zero would provide us with estimates close to zero. This is a standard result as the effects would still have to develop.

Discrete-time autoregressive parameters for time intervals between zero and four years are shown in the upper panel of Fig.  1 . For our model, we find a strong decline in the size of the autoregressive parameters for reading (dashed line). In contrast, the decline in the effect size for the discrete-time autoregressive parameters for math is less rapid and it takes longer time intervals for the coefficients to go to zero (solid line). Thus, results for our data suggest that any deviations from mean math proficiency levels in earlier waves transmit to more distant later waves. Discrete-time versions of the cross-effects (i.e., cross-lagged effects), are displayed in the bottom panel of Fig.  1 . Effects of math on reading are displayed as a dashed line, while those for reading on math are displayed as a dotted line. The general shape of the relationship between time interval length and the discrete versions of the parameters is largely comparable, with effects peaking at a time interval of around six months ( \({a}_{reading\to math}\approx 0.30\) , \({a}_{math\to reading}\approx 0.13\) ), followed by a subsequent strong decline in effect sizes. Thus, our model suggests that studies with time-intervals of around six months between measurements would find the strongest effects for the cross-lagged parameters. For our data, the effect of reading on math is larger than the effect of math on reading for nearly all time intervals before finally converging and dissipating.

- Discrete-time autoregressive and cross-lagged parameters for varying time intervals

In the present article we investigated the dynamics between reading and mathematics achievement in 10- to 19-year-olds. Reading and math proficiency are important factors for successful participation in society and understanding their interplay allows prediction and identification of starting points for prevention and intervention. In order to understand the interplay of reading and mathematics development, we estimated a continuous time model including linear trend components. In this approach, central components from both, dynamic and descriptive models, are combined: the dynamics of the variables and the linear growth in the variables. The model provided us with a set of continuous-time coefficients that describe the underlying processes’ persistence and their cross-effects, controlled for linear trends and time-constant unobserved confounders.

Applying the model to the NEPS SC3 data revealed that the interplay between math and reading followed patterns that were similar to recently reported findings: We found evidence for both paths, effects of reading on math and effects of math on reading. The former appears to be somewhat stronger than the latter, which is in line with Erbeli et al. ( 2021 ), results from the RI-CLPM in the study by Bailey et al. ( 2020 ) as well as the conclusions in the study by Hübner et al. ( 2022 ). Further, math appeared to be the more persistent construct. However, our findings also extend previous research in several respects. First, our continuous time modeling strategy allows us to discretize our auto- and cross-effects for different time intervals and identify for which time intervals we expect peak effects between the domains. For example, Bailey et al. ( 2020 ) and Erbeli et al. ( 2021 ) reported effects for time intervals of one year, whereas Rinne et al. ( 2020 ) examined time intervals of approximately six months and Korpipää et al. ( 2017 ) of six years. Discretizing the continuous time parameters to these intervals (see Fig.  1 ) suggests that autoregressive effects of reading decrease rapidly, leveling off at an interval above six months. This does not hold for math, where, based on our results, we would expect to observe substantial effects of past changes even after two years. Thus, our results suggest that any deviations from mean reading levels (which may, e.g., be due to an intervention aimed at improving reading skills) might dissipate rather quickly. Similarly, for the cross-effects we estimated the maximum mutual influence of both constructs on each other at a time interval around six months. For all time intervals, we found the effect of reading on math to be stronger than the effect of math on reading. Thus, our results also suggest that interventions to improve reading skills might have larger positive spillover effects on math skills than the other way around. We would like to highlight some potential practical implications of our results. Firstly, any changes in one of the variables due to an exogenous one-off intervention targeted at one of the domains would, based on our model, not lead to long lasting effects as can be seen by the decreasing effects sizes for larger time-intervals. Secondly, any intervention targeted on reading would seem to have larger, potentially unintended, effects on math than the other way around. But, given that the effects disappear in our model, another implication would be that interventions might have to be sustained for long term effects. However, our approach does not have a valid identification strategy and we cannot claim to have identified any potential causal effects. Thus, until further research has confirmed our results, any implications need to be viewed with caution.

Second, we can compare our results to findings stemming from different analyses of different age groups. Very many studies examining the interplay of reading and math focus on children in primary school or preschoolers (e.g., Cameron et al., 2019 ; Koponen et al., 2020 ; Bailey et al., 2020 ; Erbeli et al., 2021 ; Purpura et al., 2017 ; Vukovic et al., 2013 ), whereas only a few studies examine development up to the end of lower secondary age, like Chen and Chalhoub-Deville ( 2016 ), Codding et al. ( 2015 ) and Grimm ( 2008 ) examining up to 14-year-olds or Korpipää et al. ( 2017 ) examining up to 15-year-olds. But none investigated the full secondary track age up to 18-year-olds as was the case in our sample.

There are several limitations to our study. NEPS has a complex survey design including unequal selection probabilities, clustering, stratification and a refreshment sample. Additionally, like in other panel studies, we observe non-response as well as attrition. While NEPS provides weights as a way to potentially account for some of these issues, the use of sampling weights is currently not implemented in the ctsemOMX package and hence we report results for the unweighted sample. Consequently, we cannot exclude bias in our estimates due to effect heterogeneity or endogenous sampling (Solon et al., 2015 ). On the other hand, given that the models are estimated using FIML, non-response as well as drop out should be accounted for. However, it is currently not possible to include auxiliary variables to improve the performance of FIML (Collins et al., 2001 ) for this type of model. Hence, the benefits of this approach might be somewhat limited in our case. Furthermore, not considering the complex survey design, including the clustering of students in schools, also implies that we are likely to underestimate the standard errors (Heeringa et al., 2010 ). However, accounting for complex survey designs in continuous time modeling is an ongoing area of research.

One of the major appeals of models such as the RI-CLPM, the GCLM and the continuous time model for applied research is the potential to control for time-constant confounding by including correlated random intercepts. There are, however, substantive differences between the approach in the RI-CLPM and the one implemented in ctsemOMX, the latter being more comparable to the GCLM. Given that recent research discusses scenarios under which the RI-CLPM might not perform as expected (Lüdtke & Robitzsch, 2021 ), further research might be necessary to fully understand the conditions under which the correlated random intercepts, as implemented in ctsemOMX, control for time-constant confounding. Crucially, we do not include any potential time-varying confounders, such as changes in classroom composition. Thus, independent of the methodological debate surrounding the effectiveness of the RI-CLPM approach to account for time-constant confounding, we cannot claim to have identified causal effects and the remaining effects might disappear when adding further controls. Thus, although we find significant cross-effects between the constructs which may indicate potential for interventions, our results alone are not sufficient to draw any strong recommendations for policies aimed at improving proficiencies. Similarly, we use a linear trend to account for changes over time. However, if the underlying change over time is non-linear our model would not account properly for this, which might affect the estimation of the parameters in our model. Future research using data with more measurement points should ideally explore if another model for the trend is more appropriate.

With the presented continuous-time model we were able to calculate discrete-time dynamic model parameters (autoregressive and cross-lagged effects) for any arbitrary time interval (and hence explore the dependency of these parameters on the length of the time interval, see Fig.  1 ), although the assessments were conducted with specific time interval lengths (of around one year, see Table  2 ). However, Voelkle et al.-( 2012 ) warn that one has to be careful when inter- or extrapolating to discrete time points that have not been observed empirically. In a similar fashion, Hecht and Zitzmann ( 2021 ) caution that peak cross-lagged effects might be located in regions with no or sparse data and that the quality of inter- or extrapolations into such regions might depend on design characteristics. These issues can be seen as providing some support for the call for potentially different survey designs that, instead of having repeated measures at equidistant intervals, maximise the potential to accurately estimate the effects for different time intervals by varying the length between measurements. Thus, further research should confirm our results by applying continuous time models to survey data with different time intervals than the ones observed in NEPS.

One of the assumptions we have to make is that the nature of the process itself does not change over time. There is some recent evidence that this might not hold for our sample (Gnambs & Lockl, 2022 ). Hence, future research should look into the potential consequences for our model and ways of relaxing the assumption.

Continuous-time modeling provides a natural way of integrating longitudinal data with differently spaced measurement occasions. Alternatives might be the Mplus’ TSCORE option, which can, however, only be used to define growth models (Muthén & Muthén, 2017 , p. 614) or the “phantom variable approach”. Oud and Voelkle ( 2014 ) and Voelkle and Oud ( 2015 ) discuss this approach’s potential to account for unequal time intervals with the conclusion that it is rather limited. Instead, they argue for using continuous-time modeling.

In sum, this paper is the first to analyze the interplay of math and reading proficiency in a large representative sample of German students using continuous time models. We find evidence that math is the more persistent domain and further evidence math and reading are positively coupled over time with reading having a stronger effect on math than math on reading. The effects are most pronounced for a time interval of approximately six months.

Data Availability

This paper uses data from the National Educational Panel Study (NEPS): Starting Cohort 3–5th Grade, doi: https://doi.org/10.5157/NEPS:SC3:1.0.0 . From 2008 to 2013, NEPS data were collected as part of the Framework Programme for the Promotion of Empirical Educational Research funded by the German Federal Ministry of Education and Research (BMBF). As of 2014, the NEPS survey is carried out by the Leibniz Institute for Educational Trajectories (LIfBi) at the University of Bamberg in cooperation with a nationwide network. The anonymized data are available for the scientific community at https://www.neps-data.de .

The list is not exhaustive and we focus on simple mechanisms related to a potential causal understanding of the relationship between the constructs.

We use the term time-constant unobserved heterogeneity for confounding factors that are constant over time and potentially unobserved, in contrast to time-varying confounding which can change over time. While standard models usually assume time-constant effects for these factors, research highlights that this assumption can be relaxed using specific modeling strategies (Bollen & Brand, 2011 ; Zyphur et al., 2020 ).

There are substantive differences between the approaches. However, a full discussion is beyond the scope of the paper. One crucial difference is that the random-intercepts in the GCLM have indirect effects on future outcomes via autoregressive and cross-lagged paths, while the traits in the RI-CLPM only adjust the intercept of the observed variable at the time but do not allow for indirect effects (Usami, 2021 ).

Given that we do not include additional time-varying or time-constant predictors in our model, we do not further discuss these here. However, both types of predictors can be incorporated (see for example Oud and Delsing 2010 ; Driver et al. 2017 ).

As recommended by Skopek et al. ( 2012 ), we exclude the subsample of students with special education needs in our analyses.

Allison, P. D. (2009). Fixed effects regression models. Quantitative Applications in the Social Sciences (160 vol.). SAGE

Allison, P. D., Williams, R., & Moral-Benito, E. (2017). Maximum Likelihood for Cross-lagged Panel Models with Fixed Effects. Socius: Sociological Research for a Dynamic World, 3, 1–17. https://doi.org/10.1177/2378023117710578

Arellano, M., & Bond, S. (1991). Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. The Review of Economic Studies , 58 (2), 277. https://doi.org/10.2307/2297968

Article   Google Scholar  

Bailey, D. H., Oh, Y., Farkas, G., Morgan, P., & Hillemeier, M. (2020). Reciprocal effects of reading and mathematics? Beyond the cross-lagged panel model. Developmental Psychology , 56 (5), 912–921. https://doi.org/10.1037/dev0000902

Bell, A., & Jones, K. (2015). Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data. Political Science Research and Methods , 3 (01), 133–153. https://doi.org/10.1017/psrm.2014.7

Blossfeld, H. P., & Roßbach, H. G. (Eds.). (2019). Education as a lifelong process: The German National Educational Panel Study (NEPS). Edition ZfE (2nd ed.). Springer VS

Boker, S. M., Neale, M. C., Maes, H. H., Wilde, M. J., Spiegel, M., Brick, T. R., Estabrook, R., Bates, T. C., Mehta, P., von Oertzen, T., Gore, R. J., Hunter, M. D., Hackett, D. C., Karch, J., Brandmaier, A. M., Pritikin, J. N., Zahery, M., Kirkpatrick, R. M., Wang, Y., & Niesen, J. (2021). OpenMx: Extended Structural Equation Modelling (2.19.8) [Computer software]. https://CRAN.R-project.org/package=OpenMx

Bollen, K. A. (1989). Structural equations with latent variables. A Wiley-interscience publication . New York: Wiley

Google Scholar  

Bollen, K. A., & Brand, J. E. (2011). A General Panel Model with Random and Fixed Effects: A Structural Equations Approach. Social Forces , 89 (1), 1–34. https://doi.org/10.1353/sof.2010.0072

Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods & Research , 32 , 336–383. https://doi.org/10.1177/0049124103260222

Cameron, C. E., Kim, H., Duncan, R. J., Becker, D. R., & McClelland, M. M. (2019). Bidirectional and co-developing associations of cognitive, mathematics, and literacy skills during kindergarten. Journal of Applied Developmental Psychology , 62 , 135–144. https://doi.org/10.1016/j.appdev.2019.02.004

Carroll, J. B. (1993). Human Cognitive Abilities: A Survey of Factor-Analytic Studies . Cambridge University Press

Cattell, R. B. (1987). Intelligence: Its Structure, Growth and Action . Elsevier

Chen, F., & Chalhoub-Deville, M. (2016). Differential and long-term language impact on math. Language Testing , 33 (4), 577–605. https://doi.org/10.1177/0265532215594641

Cirino, P. T., Child, A. E., & Macdonald, K. T. (2018). Longitudinal predictors of the overlap between reading and math skills. Contemporary Educational Psychology , 54 , 99–111. https://doi.org/10.1016/j.cedpsych.2018.06.002

Codding, R. S., Petscher, Y., & Truckenmiller, A. (2015). CBM reading, mathematics, and written expression at the secondary level: Examining latent composite relations among indices and unique predictions with a state achievement test. Journal of Educational Psychology , 107 (2), 437–450. https://doi.org/10.1037/a0037520

Collins, L. M., Schafer, J. L., & Kam, C. M. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods , 6 (4), 330–351. https://doi.org/10.1037/1082-989x.6.4.330

Curran, P. J., & Bollen, K. A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 107–135). American Psychological Association. https://doi.org/10.1037/10409-004

Curran, P. J., Howard, A. L., Bainter, S. A., Lane, S. T., & McGinley, J. S. (2014). The separation of between-person and within-person components of individual change over time: A latent curve model with structured residuals. Journal of Consulting and Clinical Psychology , 82 , 879–894. https://doi.org/10.1037/a0035297

Davis, O., Band, G., Pirinen, M., et al. (2014). The correlation between reading and mathematics ability at age twelve has a substantial genetic component. Nature Communications , 5 , 4204. https://doi.org/10.1038/ncomms5204

Driver, C. C., Oud, J. H. L., & Voelkle, M. C. (2017). Continuous Time Structural Equation Modeling with R Package ctsem. Journal of Statistical Software , 77 (5), 1–35. https://doi.org/10.18637/jss.v077.i05

Driver, C., Voelkle, M., & Oud, H. (2021). ctsemOMX: Continuous Time SEM - „OpenMx“ Based Functions (1.0.4) [Computer software]. https://CRAN.R-project.org/package=ctsemOMX

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School Readiness and Later Achievement. Developmental Psychology , 43 (6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428

Erbeli, F., Shi, Q., Campbell, A. R., Hart, S. A., & Woltering, S. (2021). Developmental dynamics between reading and math in elementary school. Developmental Science , 24 (1), e13004. https://doi.org/10.1111/desc.13004

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Jordan, N. C., Siegler, R., Gersten, R., Changas, P., & Cirino, P. T. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology , 105 (3), 683–700. https://doi.org/10.1037/a0032446

Gehrer, K., Zimmermann, S., Artelt, C., & Weinert, S. (2013). NEPS framework for assessing reading competence and results from an adult pilot study. Journal for Educational Research Online , 5 (2), 50–79

Gnambs, T., & Lockl, K. (2022). Bidirectional effects between reading and mathematics development across secondary school. Zeitschrift für Erziehungswissenschaft . https://doi.org/10.1007

Grimm, K. J. (2008). Longitudinal Associations Between Reading and Mathematics Achievement. Developmental Neuropsychology , 33 (3), 410–426. https://doi.org/10.1080/87565640801982486

Halaby, C. N. (2004). Panel Models in Sociological Research: Theory into Practice. Annual Review of Sociology , 30 (1), 507–544. https://doi.org/10.1146/annurev.soc.30.012703.110629

Hamagami, F., & McArdle, J. J. (2001). Advanced studies of individual differences: Linear dynamic models for longitudinal data analysis. In G. A. Marcoulides, & R. E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 203–246). Psychology Press. https://doi.org/10.4324/9781410601858

Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods , 20 (1), 102–116. https://doi.org/10.1037/a0038889

Hecht, M., Hardt, K., Driver, C. C., & Voelkle, M. C. (2019). Bayesian continuous-time Rasch models. Psychological Methods , 24 , 516–537. https://doi.org/10.1037/met0000205

Hecht, M., Horstmann, K. T., Arnold, M., Sherman, R. A., & Voelkle, M. (2022). Modeling dynamic personality theories in a continuous-time framework: An illustration [Preprint]. PsyArXiv. https://doi.org/10.31234/osf.io/q97pz

Hecht, M., & Voelkle, M. C. (2021). Continuous-time modeling in prevention research: An illustration. International Journal of Behavioral Development , 45 (1), 19–27. https://doi.org/10.1177/0165025419885026

Hecht, M., & Zitzmann, S. (2020). A computationally more efficient Bayesian approach for estimating continuous-time models. Structural Equation Modeling: A Multidisciplinary Journal , 27 , 829–840. https://doi.org/10.1080/10705511.2020.1719107

Hecht, M., & Zitzmann, S. (2021). Exploring the unfolding of dynamic effects with continuous-time models: Recommendations concerning statistical power to detect peak cross-lagged effects. Structural Equation Modeling: A Multidisciplinary Journal , 1–9. https://doi.org/10.1080/10705511.2021.1914627

Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology , 79 (2), 192–227. https://doi.org/10.1006/jecp.2000.2586

Heeringa, S., West, B. T., & Berglund, P. A. (2010). Applied survey data analysis. Chapman & Hall / CRC statistics in the social and behavioral sciences series . Taylor & Francis. http://www.gbv.eblib.com/patron/FullRecord.aspx?p=555702

Holenstein, M., Bruckmaier, G., & Grob, A. (2020). Transfer effects of mathematical literacy: an integrative longitudinal study. European Journal of Psychology of Education , 1–27. https://doi.org/10.1007/s10212-020-00491-4

Horn, J. (1988). Thinking about Human Abilities. In J. R. Nesselroade & R. B. Cattell (Hrsg.), Handbook of Multivariate Experimental Psychology (pp. 645–685). Springer US. https://doi.org/10.1007/978-1-4613-0893-5_19

Hübner, N., Merrell, C., Cramman, H., Little, J., Bolden, D., & Nagengast, B. (2022). Reading to learn? The co-development of mathematics and reading during primary school. Child Development , 00 , 1–17. https://doi.org/10.1111/cdev.13817

Jordan, N. C., Kaplan, D., & Hanich, L. B. (2002). Achievement growth in children with learning difficulties in mathematics: findings of a two-year longitudinal study. Journal of Educational Psychology , 94 (3), 586–597. https://doi.org/10.1037//0022-0663.94.3.586

Kenny, D. A., & Zautra, A. (1995). The trait-state-error model for multiwave data. Journal of Consulting and Clinical Psychology , 63 , 52–59. https://doi.org/10.1037/0022-160

Kenny, D. A., & Zautra, A. (2001). Trait-state models for longitudinal data. In L. M. Collins, & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 243–263). American Psychological Association

Koponen, T., Eklund, K., Heikkilä, R., Salminen, J., Fuchs, L., Fuchs, D., & Aro, M. (2020). Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency. Child Development , 91 (4), 1063–1080. https://doi.org/10.1111/cdev.13287

Korpipää, H., Koponen, T., Aro, M., Tolvanen, A., Aunola, K., Poikkeus, A. M., Lerkkanen, M. K., & Nurmi, J. E. (2017). Covariation between reading and arithmetic skills from Grade 1 to Grade 7. Contemporary Educational Psychology , 51 , 131–140. https://doi.org/10.1016/j.cedpsych.2017.06.005

Kutscher, T., & Scharl, A. (2020). NEPS Technical Report for Reading: Scaling Results of Starting Cohort 3 for Grade 12. NEPS Survey Papers, volume 67. Leibniz Institute for Educational Trajectories, National Educational Panel Study, Bamberg, Germany

LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to Mathematics: Longitudinal Predictors of Performance. Child Development , 81 (6), 1753–1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x

Lohmann, J. F., Zitzmann, S., Voelkle, M. C., & Hecht, M. (2022). A primer on continuous-time modeling in educational research: An exemplary application of a continuous-time latent curve model with structured residuals (CT-LCM-SR) to PISA data. Large-Scale Assessments in Education , 10 , 1–32. https://doi.org/10.1186/s40536-022-00126-8

Lüdtke, O., & Robitzsch, A. (2021). A critique of the random intercept cross-lagged panel model. https://doi.org/10.31234/osf.io/6f85c

Lucas, R. E. (2022, February 14). It’s Time To Abandon The Cross-Lagged Panel Model. https://doi.org/10.31234/osf.io/pkec7

McArdle, J. J., & Hamagami, F. (2001). Latent difference score structural models for linear dynamic analyses with incomplete longitudinal data. In L. M. Collins, & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 137–175). American Psychological Association

Moral-Benito, E. (2013). Likelihood-based estimation of dynamic panels with predetermined regressors. Journal of Business and Economic Statistics , 31 (4), 451–472. https://doi.org/10.1080/07350015.2013.818003

Muthén, L. K., & Muthén, B. O. (2017). Mplus User’s Guide: 8th Edition (Version 8, April 2017) . Los Angeles, CA: Muthen & Muthen. https://www.statmodel.com/download/MplusUserGuideVer_8.pdf

Neumann, I., Duchhardt, C., Grüßing, M., Heinze, A., Knopp, E., & Ehmke, T. (2013). Modeling and assessing mathematical competence over the lifespan. Journal for Educational Research Online , 5 (2), 80–109

Orth, U., Clark, D. A., Donnellan, M. B., & Robins, R. W. (2021). Testing prospective effects in longitudinal research: Comparing seven competing cross-lagged models. Journal of Personality and Social Psychology , 120 , 1013–1034. https://doi.org/10.1037/pspp0000358

Oud, J. H. L., & Delsing, M. J. M. H. (2010). Continuous Time Modeling of Panel Data by means of SEM. In K. Montfort, J. H. L. Oud, & A. Satorra (Eds.), Longitudinal Research with Latent Variables (pp. 201–244). Springer

Oud, J. H. L., & Voelkle, M. C. (2014). Do missing values exist? Incomplete data handling in cross-national longitudinal studies by means of continuous time modeling. Quality & Quantity , 48 , 3271–3288. https://doi.org/10.1007/s11135-013-9955-9

Petersen, L. A., Litteck, K., & Rohenroth, D. (2020). NEPS Technical Report for Mathematics: Scaling Results of Starting Cohort 3 for Grade 12. NEPS Survey Paper, Volume 75. Leibniz Institute for Educational Trajectories, National Educational Panel Study, Bamberg, Germany

Purpura, D. J., Logan, J. A. R., Hassinger-Das, B., & Napoli, A. R. (2017). Why do early mathematics skills predict later reading? The role of mathematical language. Developmental Psychology , 53 (9), 1633–1642. https://psycnet.apa.org/buy/2017-32731-001

R Core Team. (2021). R: A language and environment for statistical computing . R Foundation for Statistical Computing. https://www.R-project.org

Rinne, L. F., Ye, A., & Jordan, N. C. (2020). Development of arithmetic fluency: A direct effect of reading fluency? Journal of Educational Psychology , 112 (1), 110–130. https://doi.org/10.1037/edu0000362

Ryan, O., Kuiper, R. M., & Hamaker, E. L. (2018). A continuous time approach to intensive longitudinal data: What, why and how? In K. van Montfort, J. H. L. Oud, & M. C. Voelkle (Eds.), Continuous time modeling in the behavioral and related sciences (pp. 27–57). Springer International Publishing. https://doi.org/10.1007/978-3-319-77219-6

Schmitt, S. A., Geldhof, G. J., Purpura, D. J., Duncan, R., & McClelland, M. M. (2017). Examining the relations between executive function, math, and literacy during the transition to kindergarten: A multi-analytic approach. Journal of Educational Psychology , 109 (8), 1120–1140. https://doi.org/10.1037/edu0000193

Skopek, J. S., Pink, & Bela, D. (2012). Data Manual. Starting Cohort 3 – From Lower to Upper Secondary School. NEPS SC3 1.0.0. NEPS Research Data Paper . University of Bamberg

Solon, G., Haider, S. J., & Wooldridge, J. M. (2015). What Are We Weighting For? The Journal of Human Resources , 50 (2), 301–316. http://www.jstor.org/stable/24735988

Sonnega, A., Faul, J. D., Ofstedal, M. B., Langa, K. M., Phillips, J. W. R., & Weir, D. R. (2014). Cohort Profile: the Health and Retirement Study (HRS). International Journal of Epidemiology , 43 (2), 576–585. https://doi.org/10.1093/ije/dyu067

Steptoe, A., Breeze, E., Banks, J., & Nazroo, J. (2013). Cohort Profile: The English Longitudinal Study of Ageing. International Journal of Epidemiology , 42 , 1640–1648. https://doi.org/10.1093/ije/dys168

StataCorp. (2019). Stata Statistical Software: Release 16. College Station . TX: StataCorp LLC

Tourangeau, K., Nord, C., Le, T., Wallner-Allen, K., Vaden-Kiernan, N., Blaker, L., & Najarian, M. (2018). User’s manual for the ECLS-K: 2011 kindergarten-third grade data file and electronic codebook, public version . Washington, DC: National Center for Education Statistics

Usami, S., Murayama, K., & Hamaker, E. L. (2019). A unified framework of longitudinal models to examine reciprocal relations. Psychological Methods, 24, 637–657 . https://doi.org/10.1037/met0000210

Usami, S. (2021). On the Differences between General Cross-Lagged Panel Model and Random-Intercept Cross-Lagged Panel Model: Interpretation of Cross-Lagged Parameters and Model Choice. Structural Equation Modeling: A Multidisciplinary Journal , 28 (3), 331–344. DOI: https://doi.org/10.1080/10705511.2020.1821690

Vanbinst, K., van Bergen, E., Ghesquière, P., & De Smedt, B. (2020). Cross-domain associations of key cognitive correlates of early reading and early arithmetic in 5-year-olds. Early Childhood Research Quarterly , 51 , 144–152. https://doi.org/10.1016/j.ecresq.2019.10.009

Voelkle, M. C., Gische, C., Driver, C. C., & Lindenberger, U. (2018). The Role of Time in the Quest for Understanding Psychological Mechanisms. Multivariate Behavioral Research , 53 (6), 782–805. https://doi.org/10.1080/00273171.2018.1496813

Voelkle, M. C., Oud, J. H. L., Davidov, E., & Schmidt, P. (2012). An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia. Psychological Methods , 17 (2), 176–192. https://doi.org/10.1037/a0027543

Voelkle, M. C., & Oud, J. H. L. (2015). Relating latent change score and continuous time models. Structural Equation Modeling: A Multidisciplinary Journal , 22 , 366–381. https://doi.org/10.1080/10705511.2014.935918

Vukovic, R. K., & Lesaux, N. K. (2013). The language of mathematics: Investigating the ways language counts for children’s mathematical development. Journal of Experimental Child Psychology , 115 (2), 227–244. https://doi.org/10.1016/j.jecp.2013.02.002

Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). The MIT Press

Zyphur, M. J., Allison, P. D., Tay, L., Voelkle, M. C., Preacher, K. J., Zhang, Z., Hamaker, E. L., Shamsollahi, A., Pierides, D. C., Koval, P., & Diener, E. (2020). From Data to Causes I: Building A General Cross-Lagged Panel Model (GCLM). Organizational Research Methods , 23 (4), 651–687

Download references

Acknowledgements

Dynamics between reading and math proficiency over time in secondary education – Observational evidence from continuous time models.

Author information

Authors and affiliations.

Institute for Educational Quality Improvement, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

Christoph Jindra & Karoline A. Sachse

Department of Psychology, Helmut Schmidt University, Holstenhofweg 85, 22043, Hamburg, Germany

Martin Hecht

You can also search for this author in PubMed   Google Scholar

Contributions

Conceptualization, C.J, and K.S.; data acquisition, C.J., methodology, C.J., K.S. and M.H.; formal analysis, K.S. and C.J.; data curation, K.S. & C.J.; writing—original draft preparation, C.J. and K.S.; writing—review and editing, C.J., K.S. and M.H.; visualization, M.H. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Christoph Jindra .

Ethics declarations

Competing interests, additional information, publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary Material 1

Rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Jindra, C., Sachse, K.A. & Hecht, M. Dynamics between reading and math proficiency over time in secondary education – observational evidence from continuous time models. Large-scale Assess Educ 10 , 22 (2022). https://doi.org/10.1186/s40536-022-00136-6

Download citation

Received : 28 February 2022

Accepted : 06 October 2022

Published : 09 December 2022

DOI : https://doi.org/10.1186/s40536-022-00136-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Mathematics
• Proficiency development

Read to succeed -- in math; study shows how reading skill shapes more than just reading

A University at Buffalo researcher's recent work on dyslexia has unexpectedly produced a startling discovery which clearly demonstrates how the cooperative areas of the brain responsible for reading skill are also at work during apparently unrelated activities, such as multiplication.

Though the division between literacy and math is commonly reflected in the division between the arts and sciences, the findings suggest that reading, writing and arithmetic, the foundational skills informally identified as the three Rs, might actually overlap in ways not previously imagined, let alone experimentally validated.

"These findings floored me," said Christopher McNorgan, PhD, the paper's author and an assistant professor in UB's Department of Psychology. "They elevate the value and importance of literacy by showing how reading proficiency reaches across domains, guiding how we approach other tasks and solve other problems.

"Reading is everything, and saying so is more than an inspirational slogan. It's now a definitive research conclusion."

And it's a conclusion that was not originally part of McNorgan's design. He planned to exclusively explore if it was possible to identify children with dyslexia on the basis of how the brain was wired for reading.

"It seemed plausible given the work I had recently finished, which identified a biomarker for ADHD," said McNorgan, an expert in neuroimaging and computational modeling.

Like that previous study, a novel deep learning approach that makes multiple simultaneous classifications is at the core of McNorgan's current paper, which appears in the journal Frontiers in Computational Neuroscience.

Deep learning networks are ideal for uncovering conditional, non-linear relationships.

Where linear relationships involve one variable directly influencing another, a non-linear relationship can be slippery because changes in one area do not necessarily proportionally influence another area. But what's challenging for traditional methods is easily handled through deep learning.

McNorgan identified dyslexia with 94% accuracy when he finished with his first data set, consisting of functional connectivity from 14 good readers and 14 poor readers engaged in a language task.

But he needed another data set to determine if his findings could be generalized. So McNorgan chose a math study, which relied on a mental multiplication task, and measured functional connectivity from the fMRI information in that second data set.

Functional connectivity, unlike what the name might imply, is a dynamic description of how the brain is virtually wired from moment to moment. Don't think in terms of the physical wires used in a network, but instead of how those wires are used throughout the day. When you're working, your laptop is sending a document to your printer. Later in the day, your laptop might be streaming a movie to your television. How those wires are used depends on whether you're working or relaxing. Functional connectivity changes according to the immediate task.

The brain dynamically rewires itself according to the task all the time. Imagine reading a list of restaurant specials while standing only a few steps away from the menu board nailed to the wall. The visual cortex is working whenever you're looking at something, but because you're reading, the visual cortex works with, or is wired to, at least for the moment, the auditory cortex.

Pointing to one of the items on the board, you accidentally knock it from the wall. When you reach out to catch it, your brain wiring changes. You're no longer reading, but trying to catch a falling object, and your visual cortex now works with the pre-motor cortex to guide your hand.

Different tasks, different wiring; or, as McNorgan explains, different functional networks.

In the two data sets McNorgan used, participants were engaged in different tasks: language and math. Yet in each case, the connectivity fingerprint was the same, and he was able to identify dyslexia with 94% accuracy whether testing against the reading group or the math group.

It was a whim, he said, to see how well his model distinguished good readers from poor readers -- or from participants who weren't reading at all. Seeing the accuracy, and the similarity, changed the direction of the paper McNorgan intended.

Yes, he could identify dyslexia. But it became obvious that the brain's wiring for reading was also present for math.

Different task. Same functional networks.

"The brain should be dynamically wiring itself in a way that's specifically relevant to doing math because of the multiplication problem in the second data set, but there's clear evidence of the dynamic configuration of the reading network showing up in the math task," McNorgan says.

He says it's the sort of finding that strengthens the already strong case for supporting literacy.

"These results show that the way our brain is wired for reading is actually influencing how the brain functions for math," he said. "That says your reading skill is going to affect how you tackle problems in other domains, and helps us better understand children with learning difficulties in both reading and math."

As the line between cognitive domains becomes more blurred, McNorgan wonders what other domains the reading network is actually guiding.

"I've looked at two domains which couldn't be farther afield," he said. "If the brain is showing that its wiring for reading is showing up in mental multiplication, what else might it be contributing toward?"

That's an open question, for now, according to McNorgan.

"What I do know because of this research is that an educational emphasis on reading means much more than improving reading skill," he said. "These findings suggest that learning how to read shapes so much more."

• Learning Disorders
• Mathematics
• Computer Modeling
• Educational Technology
• Neural Interfaces
• Learning disability
• Encephalopathy
• Human brain
• Social psychology
• Sudden infant death syndrome
• Anchoring bias in decision-making
• Left-handed

Story Source:

Materials provided by University at Buffalo . Original written by Bert Gambini. Note: Content may be edited for style and length.

Journal Reference :

• Chris McNorgan. The Connectivity Fingerprints of Highly-Skilled and Disordered Reading Persist Across Cognitive Domains . Frontiers in Computational Neuroscience , 2021; 15 DOI: 10.3389/fncom.2021.590093

Cite This Page :

Explore More

• Next-Gen Solar Cells: Perovskite Semiconductors
• When Faces Appear Distorted: Rare Condition
• End of Planet Formation
• Enormous Ice Loss from Greenland Glacier
• Signs of Life Detectable in Single Ice Grain
• Tudor Era Horse Cemetery
• When Do Babies Become Conscious?
• Secrets of the Van Allen Belt Revealed
• Robotic Prostheses, Exoskeletons
• Bronze Age Families: Clothing, Recipes, Pets

Trending Topics

Strange & offbeat.

ORIGINAL RESEARCH article

Do reading and arithmetic fluency share the same cognitive base.

• 1 Department of Educational Psychology, University of Alberta, Edmonton, AB, Canada
• 2 Department of Psychology, The Chinese University of Hong Kong, Hong Kong, China
• 3 School of Education, Macquarie University, Sydney, NSW, Australia

We examined the role of different cognitive-linguistic skills in reading and arithmetic fluency, and whether the effects of these skills are mediated by reading and arithmetic accuracy. One hundred twenty-six English-speaking Grade 1 children (67 females, 59 males; M age = 6.41 years) were followed from the beginning of Grade 1 (Time 1) to the end of Grade 1 (Time 2). At Time 1, they were assessed on measures of non-verbal IQ, speed of processing, working memory, phonological awareness, rapid automatized naming (RAN), and number sense. At Time 2, they were assessed on measures of reading and arithmetic accuracy as well as on measures of reading and arithmetic fluency. Results of path analysis showed first that when reading and arithmetic fluency were included in the model as separate outcomes, RAN was predictive of both and that speed of processing and working memory were predictive of only arithmetic fluency. Second, RAN, speed of processing, and working memory had both direct and indirect effects ( via reading and arithmetic accuracy) on the covariation of reading and arithmetic fluency. Irrespective of how reading and arithmetic fluency were treated in the analyses, the effects of non-verbal IQ, phonological awareness, and number sense were all indirect. Taken together, these findings suggest that reading and arithmetic fluency draw on a broader network of cognitive-linguistic skills, whose effects can sometimes be indirect through reading and arithmetic accuracy.

Introduction

For decades, research on the predictors of reading and mathematics skills has focused on each academic skill separately. Cognitive skills such as phonological awareness (the ability to identify and manipulate the speech sounds) and rapid automatized naming (RAN; the ability to name as fast as possible highly familiar stimuli) have been described as fundamental for learning to read (e.g., Hulme and Snowling, 2015 ). Likewise, number sense (an intuitive understanding of numbers, their magnitude, and relations) and counting have been viewed as critical for the development of mathematics skills (e.g., Geary, 2011 ). However, recent cross-domain research has revealed that there is considerable overlap in the predictors of reading and mathematics skills (e.g., Koponen et al., 2007 , 2016 , 2020 ; Korpipää et al., 2017 ; Purpura et al., 2017 ; Cirino et al., 2018 ). For example, in one of the pioneering studies, Koponen et al. (2007) showed that counting (assessed in kindergarten) and RAN (assessed in Grade 4) were significant predictors of both reading and arithmetic fluency in Grade 4.

Despite the recent proliferation of cross-domain studies examining the role of different cognitive predictors of reading and mathematics skills, several issues remain unclear. First, only a handful of studies have examined the predictors of the shared variance (i.e., covariation) between reading and mathematics skills, they have all been conducted in Finnish (a transparent alphabetic orthography), and have focused on fluency (e.g., Koponen et al., 2013 , 2020 ; Korpipää et al., 2017 ). Given the possible impact of orthographic transparency on reading development and its predictors (e.g., Georgiou et al., 2008 ; Moll et al., 2014 ), their findings need to be replicated in orthographies that are less transparent than Finnish. Second, to our knowledge, none of the previous studies that examined the role of different cognitive skills in the covariation of reading and arithmetic fluency have examined if the effects of these predictors are mediated by reading and mathematics accuracy. Finally, with one exception (see Koponen et al., 2020 ), all previous studies that examined the predictors of the covariation of reading and mathematics skills have focused on counting as a math-related skill (e.g., Koponen et al., 2007 , 2013 , 2016 ; Korpipää et al., 2017 ). Thus, we do not know if other basic number skills (e.g., number sense) are also important. To address these shortcomings, we aimed to examine if reading-related skills (phonological awareness and RAN), math-related skills (number sense), and general cognitive abilities (non-verbal IQ, speed of processing, and working memory) account for the covariance between reading and arithmetic fluency in English, an opaque alphabetic orthography, and if the effects of these skills are mediated by the effects of reading and arithmetic accuracy.

The Predictors of the Covariation Between Reading and Arithmetic

Several studies have shown that reading and mathematics are highly correlated (e.g., Koponen et al., 2007 ; Landerl and Moll, 2010 ; Codding et al., 2015 ; Balhinez and Shaul, 2019 ; Erbeli et al., 2020 ), and that comorbid disabilities occur far more often than isolated reading, and mathematics disabilities (e.g., Dirks et al., 2008 ; Willcutt et al., 2013 ; Koponen et al., 2018 ). Researchers have also argued that the observed covariation of reading and mathematics skills may be partly due to the fact that the development of both academic skills relies on similar cognitive processes (e.g., Koponen et al., 2007 , 2020 ; Zoccolotti et al., 2020 ). Thus, examining the predictors of the covariation can reveal important information about the cognitive base of reading and mathematics acquisition.

Two slightly different approaches have been used to examine the unique and shared predictors of reading and mathematics skills. First, some researchers have created a latent factor to represent the shared variance between reading and mathematics skills and then regressed that factor on different predictors ( Koponen et al., 2007 , 2013 , 2016 , 2020 ; Korpipää et al., 2017 ). This makes sense if we are looking at what cognitive processes underlie what is common between reading and mathematics, but, at the same time, it does not allow us to say what processes are unique predictors of each academic skill. For example, it is possible that a cognitive process might be a significant predictor of reading, but not of what is shared between reading and mathematics. The second approach might be considered a mirror image of the first. Researchers have included both reading and mathematics tasks as dependent variables in the same model (allowing them to co-vary), and then used several predictors to examine which ones predict both outcomes and which ones predict only reading or mathematics (e.g., Slot et al., 2016 ; Hornung et al., 2017 ; Peterson et al., 2017 ; Yang et al., 2021 ). Even though this approach can show us what cognitive processes predict each outcome measure, it does not tell us if they predict the covariation between the two outcomes. For this reason, we employed both approaches in our study.

Obviously, an important question in this line of research is what cognitive processing skills are included as predictors. Previous studies have considered three kinds of skills: linguistic skills (e.g., Cirino et al., 2018 ; Zhang and Lin, 2018 ; de Megalhães et al., 2021 ), basic number skills (e.g., Koponen et al., 2016 , 2020 ; Cirino et al., 2018 ), and general cognitive abilities (e.g., Cattell, 1987 ; Gathercole et al., 2004 ; Alloway and Alloway, 2010 ; Georgiou et al., 2015 ). In regard to the linguistic skills, researchers have focused mostly on the role of phonological awareness and RAN, both of which are considered components of phonological processing (e.g., Wagner and Torgesen, 1987 ). Phonological awareness is important for learning to read because it is involved in matching the letters (i.e., graphemes) in words to their corresponding sounds (i.e., phonemes) and supports the blending of the sounds in word recognition. Likewise, it is important in mathematics because some mathematics tasks (e.g., counting) involve processing of verbal codes (see triple-code model of numerical cognition; Dehaene, 1992 ; Dehaene et al., 2003 ; see also De Smedt et al., 2010 ). More specifically, when asked to solve a mathematics problem, children may convert the terms, operators, and quantities into sound-based codes and unimpaired access to these codes can support the execution of the problems. However, evidence from previous studies is mixed. Whereas, some cross-domain studies have reported significant effects of phonological awareness in both reading and mathematics (e.g., Slot et al., 2016 ; Cirino et al., 2018 ; Zhang and Lin, 2018 ; de Megalhães et al., 2021 ), others have reported significant effects only on reading (e.g., Durand et al., 2005 ; Peterson et al., 2017 ) or no significant effects on either academic skill (e.g., Yang et al., 2021 ). Studies on the predictors of the shared variance between reading and mathematics skills have also reported mixed findings. Whereas, Korpipää et al. (2017) found that phonological awareness (measured with an initial sound identification task at the Fall of Kindergarten) was not a significant predictor of the time-invariant covariation between reading and arithmetic fluency, 1 Koponen et al. (2020) found that phonological awareness (measured with a syllable and phoneme deletion task at the Spring of Grade 1) was a significant predictor of the covariation between reading and arithmetic fluency at the Fall of Grade 2.

Beyond phonological awareness, researchers have also examined the role of RAN in both reading and mathematics skills (particularly arithmetic fact fluency; e.g., Koponen et al., 2007 , 2013 , 2016 , 2020 ; Georgiou et al., 2013 ; Hornung et al., 2017 ; Balhinez and Shaul, 2019 ). For example, in a longitudinal study with Finnish children followed from kindergarten to Grade 3, Koponen et al. (2016) found that RAN was a significant predictor of both reading and arithmetic fluency, even after controlling for the effects of phonological awareness, verbal short-term memory, vocabulary, counting, and mother's education.

Examining the relation between RAN and reading/mathematics skills in the same study is interesting in light of theoretical accounts that have been put forward to explain their relation. For example, (e.g., Wagner and Torgesen, 1987 ; Torgesen et al., 1994 , 1997 ) have argued that RAN reflects the speed of access to, and retrieval of, phonological representations from long-term memory. If phonological representations are of low quality, this will interfere with the retrieval, manipulation, and retention of phonological codes, which, in turn, will impede reading development. However, researchers have also argued that if phonological representations for number words and number facts in long-term memory are weak, this will affect how quickly they can be retrieved from long-term memory, which, in turn, will impact mathematics development (e.g., Simmons and Singleton, 2008 ; De Smedt et al., 2010 ). To the extent the conceptualization of RAN as an index of children's ability to access and retrieve phonological representations from long-term memory is correct, RAN should predict the covariation of reading and mathematics skills (at least of tasks such as word reading fluency and addition fluency that rely on quick access to phonological representations in long-term memory). Koponen et al. (2016 , 2020) findings are in line with this prediction.

Examining the role of RAN in the covariation of reading and mathematics skills is also interesting because some math researchers have used RAN tasks as measures of speed of processing (e.g., Berg, 2008 ; Chan and Ho, 2010 ; Vanbinst et al., 2015 ). Kail and colleagues ( Kail and Hall, 1994 ; Kail et al., 1999 ) have also argued that speed of processing is per se important in tasks such as reading and mathematics that require timely integration of information within and between cognitive sub-processes. If RAN is a measure of speed of processing, then it should predict the shared variance between reading and arithmetic fluency tasks because both outcomes are speeded. If this is the case, then RAN's effects on the covariation should also disappear after controlling for other measures of speed of processing. Existing research has shown that controlling for speed of processing accounts for only a small part of the RAN-reading relation (e.g., Bowey et al., 2005 ; Georgiou et al., 2016 ); if RAN specifically captures access to the phonological representations for number words and facts, the same should be true for arithmetic fluency. This, however, may not be the case: in a study with Greek-speaking children, Georgiou et al. (2013) showed that speed of processing was enough to eliminate RAN's effects on arithmetic fluency, but not on reading fluency, suggesting that different mechanisms account for RAN-reading and RAN-arithmetic fluency connections.

Beyond the linguistic skills, basic number skills (e.g., counting, number sense) may be associated with the covariation of reading and mathematics skills. Most previous studies have focused on counting ( Koponen et al., 2007 , 2016 , 2020 ; Korpipää et al., 2017 ). Koponen et al. (2007) , for example, showed that counting (measured in kindergarten) was a significant predictor of the covariation of single-digit calculation and text reading in Grade 4 over and above the effects of letter knowledge and RAN. Koponen et al. (2020) further showed that a latent factor consisting of counting and RAN in Grade 1 (called “serial retrieval fluency”) was a significant predictor of the covariation of reading and arithmetic fluency in Grade 2 over and above the effects of letter knowledge, phonological awareness, number comparison, and number writing. Interestingly, number comparison and number writing also predicted the covariation. To our knowledge, no studies have examined the role of number sense in the covariation of reading and mathematics skills. However, in a cross-domain study with 130 Grade 1–5 Dutch children, Slot et al. (2016) found that number sense was predictive of only mathematics skills. Thus, in this study we aimed to replicate this finding.

Finally, general cognitive abilities, such as non-verbal IQ, speed of processing, and working memory may predict the covariation of reading and mathematics skills. In regard to non-verbal IQ, several studies have shown that it is associated with both academic skills (e.g., Deary et al., 2007 ; Roth et al., 2015 ; Peng et al., 2019 ). For example, in their meta-analysis, Peng et al. (2019) estimated the average correlation between non-verbal IQ (fluid intelligence) with reading and mathematics to be 0.38 and 0.41, respectively. Korpipää et al. (2017) also showed that non-verbal IQ was a significant predictor of the time-invariant covariation of reading and arithmetic fluency; a finding that needs replication. In regard to working memory, researchers have argued that it is particularly important for reading comprehension ( Kendeou et al., 2014 ) because children must retain information in their short-term memory while processing other parts of text. However, it may also contribute to word recognition because young children may hold the sound of individual letters in their memory while visually processing the upcoming letters within a word before blending of the individual sounds takes place. Likewise, it is needed when solving different mathematics problems [e.g., (3 + 6) * 6 = ?] because individuals need to first hold part of the solution in their memory (e.g., the result of 3 + 6) before executing another operation (e.g., multiplying by 6). However, evidence on the role of working memory in reading and mathematics skills is mixed (e.g., Alloway and Alloway, 2010 ; Peterson et al., 2017 ; Balhinez and Shaul, 2019 ; de Megalhães et al., 2021 ; Yang et al., 2021 ). For example, Balhinez and Shaul (2019) showed that working memory was a significant predictor of both reading and arithmetic fluency in Grades 1 and 2. In turn, working with a sample of Grade 5 and 5 children, de Megalhães et al. (2021) showed that working memory was a significant predictor of arithmetic accuracy and fluency, but not of reading accuracy and fluency. Finally, Yang et al. (2021) showed that working memory was not a significant predictor of either reading or mathematics skills in Grade 1. Clearly, more research is needed on the role of working memory in the covariation of reading and mathematics skills.

To summarize, even though a few studies have examined the role of different cognitive processes in reading and mathematics skills in the same study (e.g., Hornung et al., 2017 ; Peterson et al., 2017 ; Cirino et al., 2018 ; Balhinez and Shaul, 2019 ; Yang et al., 2021 ), very few have examined the predictors of the covariation of reading and mathematics skills ( Koponen et al., 2007 , 2016 , 2020 ; Korpipää et al., 2017 ). Given that both the dependent variables and the predictors are measured with complex, multifaceted tasks, failing to take the covariance between reading and mathematics skills into account does not allow us to draw firm conclusions on the shared cognitive base of these academic skills.

The Present Study

The present study aimed to answer the following two research questions:

1) To what extent do linguistic skills (phonological awareness and RAN), number skills (number sense), and general cognitive abilities (non-verbal IQ, speed of processing, and working memory) predict reading and arithmetic fluency, and their covariation? Based on the findings of previous studies (e.g., Koponen et al., 2007 , 2020 ; Korpipää et al., 2017 ), we expected that RAN would be a significant predictor of both academic skills as well as of their covariation. Because previous studies have provided mixed findings for the rest of the predictors, we did not formulate any specific hypotheses for them.

2) To what extent the effects of the linguistic skills, number skills, and general cognitive abilities on the covariation of reading and arithmetic fluency will be mediated by the effects of reading and arithmetic accuracy? We did not formulate any specific hypotheses here because no previous studies have examined the role of reading/arithmetic accuracy in these relations.

The findings of this study are expected to contribute to the literature in two important ways. First, as mentioned above, findings on the predictors of the covariation of reading and arithmetic fluency need to be replicated in a language with a less transparent orthography. This not only allows us to validate the previous findings, but also to examine the possible mediating role of reading and mathematics accuracy. Because reading accuracy reaches ceiling by the end of Grade 1 in Finland ( Seymour et al., 2003 ), this may have prevented Koponen et al. (2007 , 2016 , 2020) and Korpipää et al. (2017) from testing the mediating role of reading accuracy. Given that RAN and number sense are related to reading and arithmetic accuracy (e.g., Leppänen et al., 2004 ; Slot et al., 2016 ; Zhang and Lin, 2018 ) and reading and arithmetic accuracy are significant predictors of reading and arithmetic fluency (e.g., Nunes et al., 2012 ; Fuchs et al., 2016 ), it is possible that the effects of RAN and number sense on the covariation of reading and arithmetic fluency are mediated. Second, to our knowledge, this is the first study to examine the role of number sense in the covariation of reading and arithmetic fluency. All previous studies had examined the role of counting ( Koponen et al., 2007 , 2016 , 2020 ; Korpipää et al., 2017 ).

Participants

Our sample consisted of 126 English-speaking children (67 females, 59 males; M age = 6.41 years, SD = 0.45) followed from the beginning of Grade 1 (October/November, Time 1) to the end of Grade 1 (May/June, Time 2). They were recruited on a voluntary basis (155 children attending Grade 1 in the participating schools were initially invited to participate in the study) from six public elementary schools in Edmonton, Canada. The schools were located in different parts of the city in order to increase the representation of different demographics in our study. Ninety percent of the children were White, 4% East Asian, and 4% Middle Eastern, and 2% Indigenous. None of the children were experiencing any intellectual, emotional, or sensory difficulties (based on school records). Parental and school consent was obtained prior to testing. Ethics approval was also obtained from the University of Alberta (Pro00065133).

Non-verbal IQ

Non-verbal Matrices from the Cognitive Assessment System-2 (CAS-2; Naglieri et al., 2014 ) was administered to assess non-verbal IQ. Children were presented with a page containing a pattern of shapes/geometric designs that was missing a piece and were asked to choose among five or six alternatives the piece that would accurately complete the pattern. There were 44 items arranged in terms of increasing difficulty and the test was discontinued after four consecutive errors. A participant's score was the total number correct. Cronbach's alpha reliability in our sample was 0.94.

Working Memory

The Backward Digit Span task from Wechsler Intelligence Scale for Children-III ( Wechsler, 2002 ) was used to assess working memory. Children were asked to repeat a sequence of digits in the reverse order. The strings started with only two digits and one digit was added at each difficulty level (the maximum length was seven digits). The task was discontinued when participants failed both trials of a given length. A participant's score was the total number of correctly recalled trials. Cronbach's alpha reliability in our sample was 0.78.

Speed of Processing

To assess speed of processing we administered the Matching Numbers task from the CAS-2 ( Naglieri et al., 2014 ). Children were presented with four pages, each consisting of eight rows of numbers with six numbers in each row. The numbers ranged in length from one to six digits. Children were asked to find and underline the two numbers in each row that were the same within a time limit (e.g., 18 22 25 17 33 22 ). Naglieri et al. (2014) reported test-retest reliability to be 0.75.

Phonological Awareness

To assess phonological awareness, we administered the Elision task from the Comprehensive Test of Phonological Processing-2 ( Wagner et al., 2013 ). Children were asked to first listen to a word and then say the word without saying one of its sounds (e.g., Say the word bold without saying the/b/sound). The task was discontinued after three consecutive errors and a participant's score was the total number correct (max = 33). Cronbach's alpha reliability in our sample was 0.92.

Rapid Automatized Naming

To assess RAN we administered Digit Naming from the RAN/RAS test battery ( Wolf and Denckla, 2005 ). Children were asked to name as fast as possible five digits (2, 4, 5, 7, 9) that were repeated 10 times each and arranged semi-randomly in five rows of ten. Prior to beginning the timed naming, the children were asked to name the digits in a practice trial to ensure familiarity. The time to name all digits was the participant's score. The score was multiplied by −1 to ease the interpretation of our results (a higher score means better performance). Only a few naming errors occurred (mean number of errors was <1) and for this reason they were not considered further. Wolf and Denckla (2005) reported test-retest reliability for Digit Naming to be 0.92.

Number Sense

To assess number sense, we administered the Number Sets task ( Geary et al., 2009 ). Children were presented with four pages and each page included a target number at the top (e.g., 5) and sets indicated by two or three linked boxes with Arabic numerals (e.g., 2) and concrete objects (e.g., ▴▴▴). Children were asked to circle all the sets that can be put together to match the target number. The target number of the first two pages was 5 and the time limit was 60 secs per page. The target number of the last two pages was 9 and the time limit was 90 s per page. Signal detection method was used to calculate each child's sensitivity ( d ') in detecting the correct sets based on the number of hits and the number of false alarms (see Geary et al., 2009 , for details). Cronbach's alpha reliability in our sample was 0.90.

Reading Accuracy

The Word Identification task (Form H) from the Woodcock Reading Mastery Tests—Revised ( Woodcock, 1998 ) was used to assess reading accuracy. Children were asked to read out loud a list of words of increasing difficulty. The task was discontinued after six consecutive errors and a participant's score was the total number correct (max = 104). Cronbach's alpha reliability in our sample was 0.94.

Reading Fluency

To assess reading fluency, we administered two tasks: Sight Word Efficiency (SWE; Form A) from the Test of Word Reading Efficiency ( Torgesen et al., 2011 ) and CBM-Maze ( Deno, 1985 ). In SWE, children were presented with a list of 108 words, divided into four columns of 27 words each, and asked to read them as fast as possible. An 8-word practice list was presented first to ensure familiarity with the task demands. The number of words read correctly within a 45 s time limit was the participant's score. Torgesen et al. (2011) reported test–retest reliability of 0.93 for ages 6 to 7. In CBM-Maze, children were exposed to a 96-word passage in which every seventh word was replaced by three options (with the exception of the first sentence that remained intact). The passage was deemed by a group of Grade 1 teachers to be appropriate for this grade level. Children were asked to circle the option that was correctly completing the meaning of each sentence. A participant's score was the number of correct answers minus the number of incorrect answers within a 3 min time limit. Cronbach's alpha reliability in our sample was 0.90. CBM-Maze correlated 0.80 with SWE in our sample. A composite score for reading fluency was subsequently created by averaging the z -scores of SWE and CBM-Maze and used in the analyses.

Arithmetic Accuracy

The Mathematics Reasoning task from WIAT-III ( Wechsler, 2009 ) was used to assess arithmetic accuracy. The Mathematics Reasoning task is a verbal problem-solving task that measures children's ability to count, identify geometric shapes, and solve single- and multistep word problems. The task was discontinued after four consecutive errors and a participant's score was the total number correct (max = 67). Cronbach's alpha reliability in our sample was 0.88.

Arithmetic Fluency

To assess arithmetic fluency, we administered three tasks: Addition Fluency and Subtraction Fluency from WIAT-III ( Wechsler, 2009 ) and Missing Number ( Clarke and Shinn, 2004 ). In Addition and Subtraction Fluency, children were asked to solve as many additions or subtractions as possible within a 1-min time limit by writing their response in the space provided beside each problem. Each subtest included two pages (24 items on each page for a total of 48 problems). A participant's score was the total correct number of additions and subtractions completed within the time limit. Wechsler (2009) has reported test-retest reliability for Addition and Subtraction fluency to be 0.76 and 0.90, respectively. The Missing Number task consisted of three pages of 21 boxes each, arranged in seven rows of three. Each box contained a sequence of four numbers (three numbers and a blank; e.g., 2 3 _ 5). Children were asked to say out loud what number goes in the blank in each box. A participant's score was the total number correct within a 1-min time limit (max = 63). Clarke and Shinn (2004) reported test-retest reliability to be 0.79. Missing Number correlated 0.58 with Addition Fluency and 0.57 with Subtraction Fluency. A composite score for arithmetic fluency was subsequently created by averaging the z -scores of these three tasks and used in the analyses.

At Time 1, children were assessed on measures of non-verbal IQ, speed of processing, working memory, phonological awareness, RAN, and number sense. At Time 2, they were assessed on measures of reading/arithmetic accuracy and fluency. At both times, testing was conducted in a quiet room at children's school during school hours by graduate students who received extensive training on test administration and scoring. At both times, testing was completed in one sitting and the order of task administration was fixed across participants. At Time 1, testing lasted ~40 min and at Time 2~30 min.

Statistical Analyses

To examine the unique contributions of the cognitive skills to reading fluency, arithmetic fluency, and the covariation of the two, we constructed the following two sets of models. First, a path model for the predictors of reading fluency and arithmetic fluency was constructed ( Figure 1 ). Reading accuracy and arithmetic accuracy were included in the model to test their mediating roles in the relations between the cognitive skills and reading/arithmetic fluency. Non-significant paths were eliminated one at a time from the initial model to evaluate a more parsimonious model with fewer paths. Second, a latent variable model for the covariation of reading fluency and arithmetic fluency was constructed ( Figure 2 ). Additionally, to examine the indirect effect of the cognitive skills on reading fluency, arithmetic fluency, and the covariance factor of fluency through reading accuracy and arithmetic accuracy, we performed a series of mediation analyses using these models. A bias-corrected bootstrapping technique ( Hayes and Scharkow, 2013 ) with 5,000 resamples was used to establish confidence intervals for the indirect effects ( Preacher and Hayes, 2008 ).

Figure 1 . Path model for reading fluency and arithmetic fluency. Non-significant paths are not shown for clarity purposes. * p < 0.05, ** p < 0.01, *** p < 0.001.

Figure 2 . Latent variable model for the covariation of reading fluency and arithmetic fluency. Non-significant paths are not shown for clarity purposes. * p < 0.05, ** p < 0.01, *** p < 0.001.

All analyses were conducted using Mplus 8.6 ( Muthén and Muthén, 1998–2017 ). Little's Missing Completely at Random test ( Little, 1988 ) showed that our missing data (either due to attrition or to children's decision to discontinue a task) were missing completely at random (χ 2 = 16.32, df = 18, p = 0.57), and thus were handled by the full information maximum likelihood estimation. The model fit of each model was assessed using the chi-square value and a set of fit indices: the comparative fit index (CFI), the Tucker-Lewis index (TLI), the root-mean-square error of approximation (RMSEA), and the standardized root-mean-square residual (SRMR). A non-significant chi-square value, CFI and TLI values above 0.95, an RMSEA value below 0.06, and an SRMR value below 0.08 indicate a good model fit ( Kline, 2015 ).

Descriptive Statistics and Correlations

The descriptive statistics for the measures used in the study are presented in Table 1 . Before conducting any further analyses, we examined the distributional properties of the measures. RAN at Time 1 was positively skewed and log transformation was performed to normalize its distribution. The transformed scores were used in subsequent analyses. In addition, outliers on some measures (defined as more than 3 SD above/below the mean) were winsorized to the next non-outlier's score ±1 to avoid overemphasizing their effects on the results ( Tabachnick and Fidell, 2012 ).

Table 1 . Descriptive statistics for the measures used in the study.

The zero-order correlations among all of the variables are presented in Table 2 . The correlations with the linguistic/number skills (i.e., phonological awareness, RAN, and number sense) ranged from 0.30 to 0.53 for reading fluency and from 0.32 to 0.62 for arithmetic fluency. RAN showed the strongest association with both reading and arithmetic fluency. Additionally, in all instances, the cognitive measures correlated more strongly with arithmetic fluency than reading fluency.

Table 2 . Correlations between the variables.

Structural Models and Mediational Analyses

The path model for reading fluency and arithmetic fluency is shown in Figure 1 . The model showed an excellent fit, χ 2 (6) = 4.62, p = 0.59, CFI = 1.00, TLI = 1.00, RMSEA = 0, 90%CI [0, 0.10], SRMR = 0.03. The results showed that RAN predicted both reading fluency (β = 0.09) and arithmetic fluency (β = 0.30) even when the effects of reading accuracy and arithmetic accuracy were controlled. Additionally, speed of processing (β = 0.23), and working memory (β = 0.12) had a direct effect on arithmetic fluency.

The model for the cognitive predictors of the covariation of reading fluency and arithmetic fluency is shown in Figure 2 . In order to have a well-fitting model, we had to allow the residuals of reading accuracy and reading fluency to covary. The model fit the data very well (χ 2 = 15.51, df = 12, p = 0.24, CFI = 0.99, TLI = 0.98, RMSEA = 0.05, 90%CI [0, 0.11], SRMR = 0.04), and the results showed that RAN (β = 0.38), speed of processing (β = 0.26), and working memory (β = 0.10) predicted the covariance factor of fluency over and above the significant effects of reading and arithmetic accuracy. Importantly, the predictor variables accounted for a large amount of variance in the covariance factor (99%).

Finally, the results of the mediation analyses are shown in Table 3 . The results showed that speed of processing and phonological awareness had indirect effects on reading fluency, arithmetic fluency, and the covariance of fluency via both reading and arithmetic accuracy. RAN also had indirect effects on the same outcome variables via reading accuracy, while those of non-verbal IQ and number sense were mediated by arithmetic accuracy. Moreover, working memory had indirect effects on reading and arithmetic fluency via arithmetic accuracy, and it also had indirect effects on the covariance of fluency via reading and arithmetic accuracy. To summarize, these results indicate that speed of processing and RAN predict reading and arithmetic fluency and the covariation of the two both directly and indirectly through reading and arithmetic accuracy (except the direct effect of speed of processing on reading fluency). Additionally, working memory had direct effects on arithmetic fluency and the covariance factor of fluency over and above its indirect effects via reading and arithmetic accuracy. In contrast, phonological awareness and number sense predict reading fluency, arithmetic fluency, and the covariance factor of fluency only indirectly through the accuracy measures.

Table 3 . Indirect effects of the cognitive predictors on reading fluency, arithmetic fluency, and the covariance of fluency.

The purpose of this study was to examine the shared and unique predictors of reading and arithmetic fluency and whether their effects are mediated by reading and mathematics accuracy. To this end, we used two slightly different approaches: First, we used reading and arithmetic fluency as separate outcomes in the same model. Our findings showed that only RAN Digits predicts both outcomes over and above the effects of reading and mathematics accuracy. Speed of processing and working memory predicted only arithmetic fluency. In regard to RAN Digits, our finding replicates those of previous studies ( Koponen et al., 2007 , 2013 , 2016 ; Hornung et al., 2017 ) and suggests that word reading fluency and arithmetic fact retrieval rely on how quickly one could access the phonological representations of words or numbers. Notably, this is independent of the effects of speed of processing. The unique effect of RAN Digits on reading and arithmetic fluency over and above the effects of speed of processing has already been documented (e.g., Georgiou et al., 2009 ; however, see also Georgiou et al., 2013 ; Cui et al., 2017 ). The fact that processing speed and working memory predicted only arithmetic fluency may be due to the strong effects of reading accuracy on reading fluency that left very little room for other variables to make any significant contributions. In fact, when we reran our analyses without reading accuracy, both speed of processing and working memory predicted reading fluency. However, this finding may also reflect the fact that both speed of processing and working memory tasks involved processing of numbers and this brought them closer to arithmetic fluency.

Second, we tested a model in which the cognitive-linguistic skills were used as predictors of the covariation of reading and arithmetic fluency. This approach allows us to examine what skills predict what is shared between reading and arithmetic fluency. For example, if these two are related because they both require speeded responses, then speed of processing should predict their covariation. Our findings were slightly different than those of the first approach. More specifically, RAN, speed of processing, and working memory were unique predictors of the covariation of reading and arithmetic fluency. This suggests first that the cognitive base of reading and arithmetic fluency consists of multiple cognitive processes. Obviously, both outcomes require speeded responses (hence the effects of speed of processing). However, on top of that, they also require quick access and retrieval of phonological representations stored in long-term memory (hence the effects of RAN and working memory). Second, it shows that some cognitive processes (i.e., speed of processing and working memory) might be related more to what reading and arithmetic share than what is unique to them (see Figure 1 ), when it is used as a separate outcome in the analyses. This implies that depending on the approach used researchers may draw slightly different conclusions.

Phonological awareness and number sense contributed to the covariance of reading and arithmetic fluency indirectly through the effects of reading and mathematics accuracy. The strong connection between phonological awareness and reading accuracy is not surprising and has been reported in several previous studies (see e.g., Melby-Lervåg et al., 2012 ; Ruan et al., 2018 , for evidence from meta-analyses). Successful decoding relies on children's ability to blend the sounds in words. However, perhaps less expected is the significant effect of phonological awareness on mathematics accuracy. Previous studies on the relation between phonological awareness and mathematics skills provided mixed findings (for significant effects see Cirino et al., 2018 ; Zhang and Lin, 2018 ; Yang and McBride, 2020 for non-significant effects see Durand et al., 2005 ; Koponen et al., 2016 ; Peterson et al., 2017 ; Yang et al., 2021 ). An explanation for the mixed findings may relate to the type of mathematics task used as an outcome in different studies. According to the triple-code model ( Dehaene, 1992 ; Dehaene et al., 2003 ), three types of codes are used in numerical processing: a visual code, a verbal code, and an analog magnitude code. Phonological awareness may be predictive of mathematics tasks like Mathematic Reasoning that include more items requiring processing of verbal codes than some other tasks. This explanation is independent of the complexity of the mathematics problems and whether the solution to a given problem can be retrieved directly from memory. For example, De Smedt et al. (2010) showed that phonological awareness was a significant predictor of only arithmetic problems with a small problem size and concluded that this is likely due to the fact that these problems can be solved by rapid retrieval of the problem's solution from long-term memory. This explanation is problematic as it has also been used to explain why RAN predicts more strongly arithmetic fluency tasks such as addition and multiplication fluency (but not subtraction or division fluency) that involve rapid retrieval of an answer from memory (e.g., Georgiou et al., 2013 , 2020 ; Cui et al., 2017 ). In our study, phonological awareness predicted arithmetic accuracy but not fluency. This suggests that it is not the rapid access but the integrity/quality of the accessed phonological codes that matters in this case.

In contrast to phonological awareness, number sense appears to have a more domain specific contribution as it predicted only mathematics accuracy (see Jordan et al., 2010 ; Slot et al., 2016 , for a similar finding) and through the effects of mathematics accuracy the covariance of reading and arithmetic fluency. This suggests that in the early phases of reading and mathematics development, there is a set of skills such as non-verbal IQ and number sense that may exert domain specific rather than domain general effects.

Some limitations of the present study should be reported. First, we used single measures of each predictor variable. Obviously, administering more tasks would strengthen each construct, but given the time restrictions associated with assessing young children, we had to make a tough choice between covering more constructs with a single task and assessing fewer constructs with more measures. We opted for the former. Second, our study included Grade 1 children and our findings may not generalize to other grade levels. This is important to note because the effects of some cognitive-linguistic skills (e.g., RAN) on reading and mathematics may vary across grade levels (e.g., Araújo et al., 2015 ). Third, we did not include counting in our study. A pilot study we ran prior to collecting these data produced ceiling effects in counting and for this reason we did not assess it. This does not allow us to compare our findings to those of previous studies that assessed counting ( Koponen et al., 2007 , 2016 ; Korpipää et al.,2017 ). Fourth, we did not administer a measure of vocabulary. Finally, our RAN, speed of processing, and working memory tasks involved numbers and this may have inflated their relation with mathematics accuracy and fluency. A future study should replicate our findings using also neutral RAN, speed of processing, and working memory tasks.

Do reading and arithmetic fluency share a similar cognitive base? Our findings add to those of previous studies (e.g., Koponen et al., 2007 , 2020 ; Korpipää et al., 2017 ; Cirino et al., 2018 ; Balhinez and Shaul, 2019 ) and show that the answer is not straightforward. On the one hand, there was a set of cognitive skills (i.e., RAN, speed of processing, and working memory) that exerted both a direct and an indirect effect on the covariance of reading and arithmetic fluency. For these processing skills we can say with some confidence that they are part of a cognitive base that supports both reading and arithmetic fluency. On the other hand, there was a second set of processing skills (i.e., non-verbal IQ, phonological awareness, and number sense) that predicted the covariation of reading and arithmetic fluency through the effects of reading and mathematics accuracy. In fact, number sense and non-verbal IQ predicted only mathematics accuracy, which suggests that some processing skills might be uniquely associated with mathematics (see Slot et al., 2016 ; de Megalhães et al., 2021 ; for a similar finding). Taken together, these findings suggest that reading and arithmetic fluency do not rely on a single cognitive process, but rather on a broader network of linguistic and general cognitive abilities. Future studies should replicate our findings following the same children over a longer period of time and in different languages.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Ethics Statement

The studies involving human participants were reviewed and approved by Ethics Board of the University of Alberta. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Author Contributions

GG and RP designed the study. GG prepared the data for the analysis and wrote the introduction, method, and discussion sections of the manuscript. TI ran the analyses and wrote the results section of the manuscript. All authors interpreted the data and discussed the results.

This study was supported by a grant from the Social Sciences and Humanities Research Council of Canada (RES0029061) to GG.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Acknowledgments

We would like to thank Professor David Geary for sharing with us his Number Sets task and the teachers/principals of the participating schools for facilitating our research.

1. ^ Because they assessed reading and arithmetic fluency in both Grades 1 and 7, they created both a time-specific covariance factor and a time-invariant covariance factor of reading and arithmetic fluency across the two grades.

Alloway, T. P., and Alloway, R. G. (2010). Investigating the predictive roles of working memory and IQ in academic attainment. J. Exp. Child Psychol. 106, 20–29. doi: 10.1016/j.jecp.2009.11.003

PubMed Abstract | CrossRef Full Text | Google Scholar

Araújo, S., Reis, A., Petersson, K. M., and Faísca, L. (2015). Rapid automatized naming and reading performance: a meta-analysis. J. Educ. Psychol. 107, 868–883. doi: 10.1037/edu0000006

CrossRef Full Text | Google Scholar

Balhinez, R., and Shaul, S. (2019). The relationship between reading fluency and arithmetic fact fluency and their shared cognitive skills: a developmental perspective. Front. Psychol. 10:1281. doi: 10.3389/fpsyg.2019.01281

Berg, D. H. (2008). Working memory and arithmetic calculation in children: the contributory roles of processing speed, short-term memory, and reading. J. Exp. Child Psychol. 99, 288–308. doi: 10.1016/j.jecp.2007.12.002

Bowey, J. A., McGuigan, M., and Ruschena, A. (2005). On the association between serial naming speed for letters and digits and word-reading skill: towards a developmental account. J. Res. Read. 28, 400–422. doi: 10.1111/j.1467-9817.2005.00278.x

Cattell, R. B. (1987). Intelligence: Its structure, Growth, and Action . Amsterdam: Elsevier.

Google Scholar

Chan, B. M., and Ho, C. S. (2010). The cognitive profile of Chinese children with mathematics difficulties. J. Exp. Child Psychol. 107, 260–279. doi: 10.1016/j.jecp.2010.04.016

Cirino, P. T., Child, A. E., and Macdonald, K. T. (2018). Longitudinal predictors of the overlap between reading and math skills. Contemp. Educ. Psychol. 54, 99–111. doi: 10.1016/j.cedpsych.2018.06.002

Clarke, B., and Shinn, M. R. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psych. Rev. 33, 234–248. doi: 10.1080/02796015.2004.12086245

Codding, R. S., Petscher, Y., and Truckenmiller, A. (2015). CBM reading, mathematics, and written expression at the secondary level: examining latent composite relations among indices and unique predictions with a state achievement test. J. Educ. Psychol. 107, 437–450. doi: 10.1037/a0037520

Cui, J., Georgiou, G. K., Zhang, Y., Li, Y., Shu, H., and Zhou, X. (2017). Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children. J. Exp. Child Psychol. 154, 146–163. doi: 10.1016/j.jecp.2016.10.008

de Megalhães, C. G., Mervis, C. B., and Cardoso-Martins, C. (2021). Cognitive predictors of arithmetic, reading, and spelling in Brazilian-Portuguese children. Read. Writ. 34, 171–198. doi: 10.1007/s11145-020-10062-0

De Smedt, B., Taylor, J., Archibald, L., and Ansari, D. (2010). How is phonological processing related to individual differences in children's arithmetic skills? Dev. Sci. 13, 508–520. doi: 10.1111/j.1467-7687.2009.00897.x

Deary, I. J., Strand, S., Smith, P., and Fernandes, C. (2007). Intelligence and educational achievement. Intelligence 35, 13–21. doi: 10.1016/j.intell.2006.02.001

Dehaene, S. (1992). Varieties of numerical abilities. Cogn. Int. J. Cogn. Sci. 44, 1–42. doi: 10.1016/0010-0277(92)90049-N

Dehaene, S., Piazza, M., Pinel, P., and Cohen, L. (2003). Three parietal circuits for number processing. Cogn. Neuropsychol. 20, 487–506. doi: 10.1080/02643290244000239

Deno, S. L. (1985). Curriculum-based measurement: the emerging alternative. Except. Child. 52, 219–232. doi: 10.1177/001440298505200303

Dirks, E., Spyer, G., van Lieshout, E. C. D. M., and de Sonneville, L. (2008). Prevalence of combined reading and arithmetic disabilities. J. Learn. Disabil. 41, 460–473. doi: 10.1177/0022219408321128

Durand, M., Hulme, C., Larkin, R., and Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7-to 10-year-olds. J. Exp. Child Psychol. 91, 113–136. doi: 10.1016/j.jecp.2005.01.003

Erbeli, F., Shi, Q., Campbell, A. R., Hart, S. A., and Woltering, S. (2020). Developmental dynamics between reading and math in elementary school. Dev. Sci. 56, 912–914. doi: 10.1111/desc.13004

Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., and Hamlett, C. L. (2016). Pathways to third-grade calculation versus word-reading competence: are they more alike or different? Child Dev. 87, 558–567. doi: 10.1111/cdev.12474

Gathercole, S. E., Pickering, S. J., Knight, C., and Stegmann, Z. (2004). Working memory skills and educational attainment: evidence from national curriculum assessments at 7 and 14 years of age. Appl. Cogn. Psychol. 18, 1–16. doi: 10.1002/acp.934

Geary, D. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Dev. Psychol. 47, 1539–1552. doi: 10.1037/a0025510

Geary, D. C., Bailey, D. H., Littlefield, A., Wood, P., Hoard, M. K., and Nugent, L. (2009). First-grade predictors of mathematical learning disability: a latent class trajectory analysis. Cogn. Dev. 24, 411–429. doi: 10.1016/j.cogdev.2009.10.001

Georgiou, G., Aro, M., Liao, C.-H., and Parrila, R. (2016). Modeling the relationship between rapid automatized naming and literacy skills across languages varying in orthographic consistency. J. Exp. Child Psychol. 143, 48–64. doi: 10.1016/j.jecp.2015.10.017

Georgiou, G., Parrila, R., and Kirby, J. (2009). RAN components and reading development from Grade 3 to Grade 5: what underlies their relationship? Sci. Stud. Read. 13, 508–534. doi: 10.1080/10888430903034796

Georgiou, G., Parrila, R., and Papadopoulos, T. (2008). Predictors of word decoding and reading fluency in English and Greek: a cross-linguistic comparison. J. Educ. Psychol. 100, 566–580. doi: 10.1037/0022-0663.100.3.566

CrossRef Full Text

Georgiou, G., Wei, W., Inoue, T., and Deng, C. (2020). Are the relations of rapid automatized naming with reading and mathematics accuracy and fluency bidirectional? Evidence from a 5-year longitudinal study with Chinese children. J. Educ. Psychol. 112, 1506–1520. doi: 10.1037/edu0000452

Georgiou, G. K., Manolitsis, G., and Tziraki, N. (2015). “Is intelligence relevant in reading “μ?να” and in calculating “3+5”?” in Cognition, Intelligence and Achievement , eds T. C., Papadopoulos, R. Parrila, and J. R. Kirby (Cambridge, MA: Academic Press), 225–243.

Georgiou, G. K., Tziraki, N., Manolitsis, G., and Fella, A. (2013). Is rapid automatized naming related to reading and mathematics for the same reason(s)? a follow-up study from kindergarten to Grade 1. J. Exp. Child Psychol. 115, 481–496. doi: 10.1016/j.jecp.2013.01.004

Hayes, A. F., and Scharkow, M. (2013). The relative trustworthiness of inferential tests of the indirect effect in statistical mediation analysis: does method really matter? Psychol. Sci. 24, 1918–1927. doi: 10.1177/0956797613480187

Hornung, C., Martin, R., and Fayol, M. (2017). General and specific contributions of RAN to reading and arithmetic fluency in first graders: a longitudinal latent variable approach. Front. Psychol. 8:1746. doi: 10.3389/fpsyg.2017.01746

Hulme, C., and Snowling, M. J. (2015). Learning to read: What we know and what we need to understand better. Child Dev. Perspect. 7, 1–5. doi: 10.1111/cdep.12005

Jordan, N. C., Glutting, J., and Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learn. Individ. Differ. 20, 82–88. doi: 10.1016/j.lindif.2009.07.004

Kail, R., and Hall, L. K. (1994). Speed of processing, naming speed, and reading. Dev. Psychol. 30, 949–954. doi: 10.1037/0012-1649.30.6.949

Kail, R., Hall, L. K., and Caskey, B. J. (1999). Processing speed, exposure to print, and naming speed. Appl. Psycholinguist 20, 303–314. doi: 10.1017/S0142716499002076

Kendeou, P., van den Broek, P., Helder, A., and Karlsson, J. (2014). A cognitive view of reading comprehension: implications for reading difficulties. Learn. Disabil. Res. Pract. 29, 10–16. doi: 10.1111/ldrp.12025

Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling, 4th edn . New York, NY: Guilford Press.

Koponen, T., Aro, M., Poikkeus, A.-M., Niemi, P., Lerkkanen, M.-K., Ahonen, T., et al. (2018). Comorbid fluency difficulties in reading and math: longitudinal stability across early grades. Except. Child. 84, 298–311. doi: 10.1177/0014402918756269

Koponen, T., Aunola, K., Ahonen, T., and Nurmi, J. E. (2007). Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill. J. Exp. Child Psychol. 97, 220–241. doi: 10.1016/j.jecp.2007.03.001

Koponen, T., Eklund, K., Heikkil,ä, R., Salminen, J., Fuchs, L., Fuchs, D., et al. (2020). Cognitive correlates of the covariance in reading and arithmetic fluency: importance of serial retrieval fluency. Child Develop. 91, 1063–1080. doi: 10.1111/cdev.13287

Koponen, T., Salmi, P., Eklund, K., and Aro, T. (2013). Counting and RAN: predictors of arithmetic calculation and reading fluency. J. Educ. Psychol. 105, 162–175. doi: 10.1037/a0029285

Koponen, T., Salmi, P., Torppa, M., Eklund, K., Aro, T., Aro, M., et al. (2016). Counting and rapid naming predict the fluency of arithmetic and reading skills. Contemp. Educ. Psychol. 44, 83–94. doi: 10.1016/j.cedpsych.2016.02.004

Korpipää, H., Koponen, T., Aro, M., Tolvanen, A., Aunola, K., Poikkeus, A.-M., et al. (2017). Covariation between reading and arithmetic skills from grade 1 to grade 7. Contemp. Educ. Psychol. 5, 131–140. doi: 10.1016/j.cedpsych.2017.06.005

Landerl, K., and Moll, K. (2010). Comorbidity of learning disorders: prevalence and familial transmission. J. Child Psychol. Psychiatry 51, 287–294. doi: 10.1111/j.1469-7610.2009.02164.x

Leppänen, U., Niemi, P., Aunola, K., and Nurmi, J.-E. (2004). Development of reading skills among preschool and primary school pupils. Read. Res. Q. 39, 72–93. doi: 10.1598/RRQ.39.1.5

Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. J. Am. Stat. Assoc. 83, 1198–1202. doi: 10.1080/01621459.1988.10478722

Melby-Lervåg, M., Lyster, S.-A., and Hulme, C. (2012). Phonological skills and their role in learning to read: a meta-analytic review. Psychol. Bull. 138, 322–352. doi: 10.1037/a0026744

Moll, K., Ramus, F., Bartling, J., Bruder, J., Kunze, S., Neuhoff, N., et al. (2014). Cognitive mechanisms underlying reading and spelling development in five European orthographies. Learn. Instruc. 29, 65–77. doi: 10.1016/j.learninstruc.2013.09.003

Muthén, L. K., and Muthén, B. O. (1998–2017). Mplus User's Guide, 8th Edn , Muthén and Muthén.

Naglieri, J. A., Das, J. P., and Goldstein, S. (2014). Cognitive Assessment System, 2nd Edn, Austin, Texas: Brief. PRO-ED.

Nunes, T., Bryant, P., and Barros, R. (2012). The development of word recognition and its significance for comprehension and fluency. J. Educ. Psychol. 104, 959–973. doi: 10.1037/a0027412

Peng, P., Wang, T. F., Wang, C. C., and Lin, X. (2019). A meta-analysis on the relation between fluid intelligence and reading/mathematics: effects of tasks, age, and social economics status. Psychol. Bull. 145, 189–236. doi: 10.1037/bul0000182

Peterson, R. L., Boada, R., McGrath, L. M., Willcutt, E. G., Olson, R. K., and Pennington, B. F. (2017). Cognitive prediction of reading, math, and attention: shared and unique influences. J. Learn. Disabil. 50, 408–421. doi: 10.1177/0022219415618500

Preacher, K. J., and Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behav. Res. Methods 40, 879–891. doi: 10.3758/BRM.40.3.879

Purpura, D. J., Schmitt, S. A., and Ganley, C. M. (2017). Foundations of mathematics and literacy: the role of executive functioning components. J. Exp. Child Psychol. 153, 15–34. doi: 10.1016/j.jecp.2016.08.010

Roth, B., Becker, N., Romeyke, S., Schäfer, S., Domnick, F., and Spinath, F. M. (2015). Intelligence and school grades: a meta-analysis. Intelligence 53, 118–137. doi: 10.1016/j.intell.2015.09.002

Ruan, Y., Georgiou, G., Song, S., Li, Y., and Shu, H. (2018). Does writing system influence the associations between phonological awareness, morphological awareness and reading? A meta-analysis. J. Educ. Psychol. 110, 180–202. doi: 10.1037/edu0000216

Seymour, P., Aro, M., and Erskine, J. (2003). Foundation literacy acquisition in European orthographies. Br. J. Psychol. 94, 143–174. doi: 10.1348/000712603321661859

Simmons, F. R., and Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia 14, 77–94. doi: 10.1002/dys.341

Slot, E. M., van Viersen, S., de Bree, E. H., and Kroesbergen, E. H. (2016). Shared and unique risk factors underlying mathematical disability and reading and spelling disability. Front. Psychol. 7:803. doi: 10.3389/fpsyg.2016.00803

Tabachnick, B. G., and Fidell, L. S. (2012). Using Multivariate Statistics, 6th Edn. London: Pearson.

Torgesen, J. K., Wagner, R. K., and Rashotte, C. A. (1994). Longitudinal studies of phonological processing and reading. J. Learn. Disabil. 27, 276–286. doi: 10.1177/002221949402700503

Torgesen, J. K., Wagner, R. K., and Rashotte, C. A. (2011). Test of Word Reading Efficiency, 2nd Edn . Austin, TX: Pro-ED.

Torgesen, J. K., Wagner, R. K., Rashotte, C. A., Burgess, S., and Hecht, S. (1997). Contributions of phonological awareness and rapid automatic naming ability to the growth of word-reading skills in second-to fifth grade children. Sci. Stud. Read. 1, 161–185. doi: 10.1207/s1532799xssr0102_4

Vanbinst, K., Ghesquière, P., and De Smedt, B. (2015). Does numerical processing uniquely predict first graders' future development of single-digit arithmetic? Learn. Individ. Differ. 37, 153–160. doi: 10.1016/j.lindif.2014.12.004

Wagner, R., Torgesen, J. K., Rashotte, C. A., and Pearson, N. A. (2013). Comprehensive Test of Phonological Processing, 2nd Edn . Austin, TX: Pro-Ed. doi: 10.1037/t52630-000

Wagner, R. K., and Torgesen, J. K. (1987). The nature of phonological processing and its causal role in the acquisition of reading skills. Psychol. Bull. 101, 192–212. doi: 10.1037/0033-2909.101.2.192

Wechsler, D. (2002). Wechsler Individual Achievement Test (WIAT-II), 2nd Edn . San Antonio, TX: The Psychological Corporation. doi: 10.1037/t15173-000

Wechsler, D. (2009). Wechsler Individual Achievement Test-third edition (WIAT-III), 2nd Edn . San Antonio, TX: The Psychological Corporation.

Willcutt, E. G., Petrill, S. A., Wu, S., Boada, R., DeFries, J. C., Olson, R. K., et al. (2013). Comorbidity between reading disability and math disability: concurrent psychopathology, functional impairment, and neuropsychological functioning. J. Learn. Disabil. 46, 500–516. doi: 10.1177/0022219413477476

Wolf, M., and Denckla, M. B. (2005). Rapid Automatized Naming and Rapid Alternating Stimulus Tests (RAN/RAS) . Austin, TX: Pro-ED.

Woodcock, R. W. (1998). Woodcock reading mastery test-revised . Washington, DC: American Guidance Service.

Yang, X., and McBride, C. (2020). How do phonological processing abilities contribute to early Chinese reading and mathematics? Educ. Psychol. 40, 893–911. doi: 10.1080/01443410.2020.1771679

Yang, X., McBride, C., Ho, C. S.-H., and Chung, K. K. H. (2021). Longitudinal associations of phonological processing skills, Chinese word reading, and arithmetic. Read. Writing 33, 1679–1699. doi: 10.1007/s11145-019-09998-9

Zhang, X., and Lin, D. (2018). Cognitive precursors of word reading versus arithmetic competencies in young Chinese children. Early Child. Res. Q. 42, 55–65. doi: 10.1016/j.ecresq.2017.08.006

Zoccolotti, P., De Luca, M., Marinelli, C. V., and Spinelli, D. (2020). Predicting individual differences in reading, spelling, and math in a sample of typically developing children: a study in the perspective of comorbidity. PLoS ONE 15:e0231937. doi: 10.1371/journal.pone.0231937

Keywords: reading fluency, arithmetic fluency, rapid automatized naming, phonological awareness, speed of processing, working memory, number sense

Citation: Georgiou GK, Inoue T and Parrila R (2021) Do Reading and Arithmetic Fluency Share the Same Cognitive Base? Front. Psychol. 12:709448. doi: 10.3389/fpsyg.2021.709448

Received: 13 May 2021; Accepted: 05 July 2021; Published: 28 July 2021.

Reviewed by:

Copyright © 2021 Georgiou, Inoue and Parrila. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: George K. Georgiou, georgiou@ualberta.ca

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

New evidence on the benefits of small group math instruction for young children

• Download the full report

Subscribe to the Center for Economic Security and Opportunity Newsletter

Robin jacob and robin jacob research associate professor, co-director of youth policy lab - university of michigan institute for social research brian a. jacob brian a. jacob walter h. annenberg professor of education policy; professor of economics, and professor of education - university of michigan, former brookings expert.

June 7, 2018

We describe the findings from a randomized evaluation of a one-year kindergarten math enrichment program, the High 5s program. The program was designed to provide small-group math enrichment in a fun, club-like format to children who had received enriched math instruction the prior year. Participants included 655 kindergarten students in 24 low-income schools in New York City. Students were randomly assigned to either the “business as usual” control group or to participate in the High 5s math clubs, which met outside of class in small groups with a trained facilitator three times per week. The High 5s program produced a positive impact on kindergarten math skills.

introduction

Over the last few decades there has been a heavy emphasis on increasing literacy skills among low-income children, with federal and state initiatives designed to ensure that all children can read by grade 3. State and federal dollars have been spent to improve reading curricula, hire reading coaches and provide tutoring and small group support for struggling readers. However, much less emphasis has been placed on improving the early math skills of students in low-income schools. Kindergarten classes typically devote less than one hour per day to math compared with over 1.5 hours for literacy. Moreover, kindergarten math instruction is often very basic, covering topics that students know when they enter kindergarten such as simple counting and shape recognition. 1

This is true despite research having shown that math skills are highly correlated not only with later math achievement but also with later reading achievement, high school completion, and college attendance. 2

A possible response to this situation would be small-group interventions designed to build young children’s math skills. Such interventions have a long history in literacy, and a strong research base suggests that small group literacy instruction is effective. 3 In the area of math, there are few well-developed programs to provide supplemental math support or enrichment to young children, let alone rigorous research to determine whether such programs are effective. 4

Here we report findings from research on such a program that one of us (Robin Jacob) helped design and evaluate. The study suggests that small group math instruction for kindergarteners is a promising strategy for improving early mathematical competency.

the high 5s program

The High 5s program was developed in the context of a larger MDRC project to evaluate Building Blocks , a 30-week, pre-K math curriculum designed to take into account children’s natural developmental progression in math. 5 Developed by researchers at the University of Michigan with support from MDRC and the developers of Building Blocks , the goal of High 5s was to provide a consistent instructional approach and alignment of content from the pre-K math curriculum to kindergarten. Importantly, High 5s was designed as a hands-on program to foster interest in math, critical thinking, and broad knowledge of mathematical concepts including not only numeracy, but geometry, patterning, and measurement as well.

Students in the High 5s program met for 30 minutes three times a week in “math clubs,” which took place either before or after school or during lunch. The clubs met for roughly 28 weeks from October through May. Activities in the clubs are delivered in a game-like format and are intended to be fun, engaging, interactive, and developmentally appropriate.

Each club includes 3-4 children working with a trained facilitator. Most facilitators had a BA degree, but limited formal teaching experience. They were paid a salary commensurate with that of a paraprofessional teacher in the New York City public schools (around $25 per hour, depending on experience).

In the study reported here, facilitators received a substantial amount of training and supervision over the course of the year. 6 They received 16 days of training before clubs began and an additional eight throughout the school year. In addition, supervisors from Bank Street College of Education provided ongoing support in weekly meetings that included 4-5 facilitators with one supervisor. These meetings included support regarding logistics, curriculum review, reflection about student learning, and guidance and training in small-group management. Supervisors also met individually with facilitators regularly and provided coaching in the field as needed.    

Students were eligible to participate in the High 5s program if they had attended one of the 24 public preschools that participated in the Making Pre-K Count project described above and the student stayed in the same school between pre-K and kindergarten. These schools served predominantly low-income, Black and Hispanic students. With the exception of one, all schools had fewer than 50% of their students scoring proficient or above in reading and mathematics at the end of third grade. On average, roughly 50% of the students were Hispanic and 43% were Black. All schools had at least 70% of students who were eligible for free or reduced price lunch (FRPL) and nine of the 24 schools had 100% of students with FRPL eligibility.

Individual children were randomly assigned within schools in the fall of the kindergarten year to receive the High 5s program in addition to their regular kindergarten math instruction (n=320), or to a “kindergarten-as-usual” control group (n=335). 7 The researchers were able to obtain student outcome data from 613 of the 655 students who were randomly assigned as part of the study, and attrition was similar for the program and control groups. There were no statistically significant differences in measured baseline demographic characteristics between children in the High 5s and the kindergarten-as-usual groups.

Kindergarten classrooms contained students from both program and control groups as well as other students who were not part of the study. To reduce the likelihood that control students would be exposed to any High 5s instruction, the clubs were held in pre-K classrooms or other multi-use spaces (e.g., a resource room), and not in kindergarten classrooms. In an effort to keep teachers informed, kindergarten teachers were provided with a few example activities from the clubs, but otherwise teachers did not have access to the High 5s curriculum. Most of the interactions that High 5s facilitators had with teachers were brief, and mostly focused on dropping off or picking up students from the classroom.

Consistently, one of the key challenges of education interventions is implementation. Using a combination of daily logs completed by facilitators and observations of the clubs conducted by external staff, researchers concluded that the program was implemented with a high degree of fidelity. Student attendance was 87 percent, which is quite high for a supplemental program conducted outside of the typical school day. Logs indicate that 93 percent of scheduled club sessions were completed, and that facilitators followed the intended pacing of the curriculum and activities. According to external observers, the majority of facilitators met or exceeded standards for quality instruction. More generally, observers reported that the facilitators had a good rapport with students and created a positive instructional climate.

Related Content

Diane Whitmore Schanzenbach, Stephanie Howard Larson

April 13, 2017

Brookings Institution, Washington DC

1:30 pm - 3:30 pm EDT

Deborah A. Phillips, Mark W. Lipsey, Kenneth A. Dodge, Ron Haskins, Daphna Bassok, Margaret R. Burchinal, Greg J. Duncan, Mark Dynarski, Katherine A. Magnuson, Christina Weiland

April 17, 2017

student achievement effects

The study analyzed two different measures of math achievement: the Woodcock-Johnson applied problems subscale and the REMA-K. The Woodcock-Johnson is a widely used standardized assessment of mathematical thinking that provides a global measure of math ability. The REMA-K was adapted from an assessment designed by the developers of the  Building Blocks Pre-K program. 8  The REMA-K is a longer and more discriminating measure of mathematical knowledge, with questions designed to assess discrete math skills. For example, the REMA-K asks “How many pennies are left if I have 5 and cover these 3?” while, the Woodcock-Johnson asks “How much money do I have if I add three pennies and two nickels together?” The latter requires multi-step addition as well as knowledge regarding the value of different coins, while the former is a simple one-step subtraction problem.

As shown in in Figure 1, High 5s had a positive effect on one of two measures of student math skills. Students in High 5s scored 0.19 SD higher than control students on the REMA-K, which is equivalent to roughly two-and-a-half months of learning on the assessment. There was a positive but not statistically significant impact on the Woodcock-Johnson Applied Problems assessment (effect size = 0.09). 9

Somewhat surprisingly, the study did not find a significant effect on children’s math attitudes. 10 Researchers speculate that the reason for this is that when children answered survey items about their views of math they were thinking about their regular math class. Qualitative research suggests students greatly enjoyed the activities in the clubs. The following exchange, as reported by one of the facilitators during the last week of the clubs, captures this difference:

While filling out their “why we like math” page, the children [in this club] all concluded that they didn’t like math. I [the facilitator] said that was strange because they’ve been doing math in High 5s all year and were loving it and were so happy. They clarified that they like math in High 5s but they don’t like it in school. R explained in his words that “In school, you do math and you be quiet and look down at your paper. They just tell you that you’re wrong. And then nobody talks to you. It’s just wrong and you have to be quiet. But in High 5s we have you. You never say we did it wrong and we all talk and figure it out and then nobody’s wrong. That’s why I’m happy when I do math in High 5s.”

The research identified several potential mechanisms through which High 5s may have enhanced children’s math skills. First, students in the High 5s program received substantially more math instruction than control students. Kindergarten teachers spent an average of 52 minutes per day on math, for a total of about 4 hours and 20 minutes per week. High 5s added an additional 75 minutes of math instruction – an increase of roughly 30 percent.

Second, the instructional approach and content in High 5s differed considerably from the standard math instruction observed in kindergarten classrooms. In math classes in the study, students spent 83 percent of their time in whole-group instruction or seat work, and most activities involved either workbooks or no materials at all. In contrast, High 5s featured small group interactive activities with a variety of manipulatives. In addition, High 5s exposed students to somewhat more advance and a wider range of mathematical topics relative to the classroom math instruction.

Finally, the instructional climate in clubs differed substantially from the climate in classrooms. As illustrated by the child’s quote above (and consistent with the more general qualitative research findings), students enjoyed the math activities in High 5s. External observations of the clubs and the regular math classes indicate that facilitators in the clubs were somewhat more likely to ask open-ended questions, encourage mathematical reflection, and differentiate instruction.

Related Books

Daniel S. Hamilton, Joe Renouard

April 1, 2024

Michael E. O’Hanlon

February 15, 2024

Clifford Winston, Jia Yan Scott Dennis, Austin J. Drukker, Hyeonjun Hwang, Jukwan Lee, Vikram Maheshri, Chad Shirley, Xinlong Tan

December 1, 2023

conclusions

Small group reading instruction is ubiquitous in elementary schools. This type of intervention provides the opportunity for more tailored, individualized instruction, which may help to motivate as well as instruct students. It also provides greater opportunities for conversation and interaction among teachers and students. Prior research has demonstrated the efficacy of this approach for improving students’ early literacy skills, yet small group instruction is used much less frequently for math.

This study provides some preliminary evidence that small group instruction may be a promising approach for math instruction as well. Students who participated in the High 5s small group math instruction made statistically significant and substantively meaningful gains on one of two measures of math skills. Researchers will continue to follow students who participated in the study through elementary school to assess whether the gains made by the children who participated in High 5s are sustained or fade over time.

Although the program was delivered by facilitators who had little formal teaching experience and who were paid a salary commensurate with that of a paraprofessional staff member, the High 5s model tested in this study was resource intensive. 11 Because clubs were only offered outside of regular instructional time (before school, after school, or during lunch), each facilitator could only run a few clubs per week and facilitators had to travel from school to school to serve students, which added both time and transportation costs. Facilitators were also offered substantial training and support to implement the clubs.

The researchers are now working to develop a model for such small-group math instruction that requires fewer resources and could be more easily scaled. For example, one might conduct small groups in classrooms themselves or via pull-out services, using paraprofessional staff already employed by schools.

If a more cost-effective model can be developed, small group math instruction may be a promising approach for elementary schools to consider in the future.

The authors did not receive any financial support from any firm or person for this article or from any firm or person with a financial or political interest in this article. They are currently not an officer, director, or board member of any organization with an interest in this article.

• Engel, M., Claessens, A., & Finch, M. A. 2013. Teaching students what they already know? The (Mis) Alignment between mathematics instructional content and student knowledge in kindergarten. Educational Evaluation and Policy Analysis, 35(2), 157-178; Engel, M., Claessens, A., Watts, T., & Farkas, G. (2016). Mathematics Content Coverage and Student Learning in Kindergarten. Educational Researcher.
• Jordan N., Kaplan D., Ramineni C., Locuniak M. 2009. Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867; Duncan, Greg J., Chantelle J. Dowsett, Amy Claessens, Katherine Magnuson, Aletha C. Huston, Pamela Klebanov, Linda S. Pagani, Leon Feinstein, Mimi Engel, and Jeanne Brooks-Gunn. 2007. “School Readiness and Later Achievement.” Developmental Psychology 43, 6: 1428-1446; Duncan, Greg J., and Katherine Magnuson. 2009. “The Nature and Impact of Early Skills, Attention, and Behavior.” Paper presented at the Russell Sage Foundation Conference on Social Inequality and Educational Outcomes, New York City.
• Slavin, Robert E., Cynthia Lake, Susan Davis, and Nancy A. Madden. 2010. Identifying What Works for Struggling Readers: Educator’s Guide. Best Evidence Encyclopedia. Center for Data-Driven Reform in Education, Johns Hopkins University. Website: www.bestevidence.org .
• Among older children, there is evidence that one-on-one or small group tutoring can be effective; e.g. Ritter, G. W., Barnett, J. H., Denny, G. S., & Albin, G. R. 2009. The effectiveness of volunteer tutoring programs for elementary and middle school students: A meta-analysis. Review of Educational Research, 79(1), 3–38; Fryer, R. 2011. Injecting successful charter school strategies into traditional public schools: A field experiment in Houston. (Working Paper 17494). Retrieved from National Bureau of Economic Research website: http://www.nber.org/papers/w17494. There is also evidence that computer-aided math instruction, which students engage with individually, can improve math achievement; e.g. Steenbergen-Hu, Saiying, and Harris Cooper. 2013. “A Meta-Analysis of the Effectiveness of Intelligent Tutoring Systems on K–12 Students’ Mathematical Learning.” Journal of Educational Psychology 105(4): 970-87; Cheung, Alan CK, and Robert E. Slavin.. 2013. “The Effectiveness of Educational Technology Applications for Enhancing Mathematics Achievement in K-12 Classrooms: A Meta-Analysis.” Educational Research Review 9(1): 88-113.
• Making Pre-K Count was developed by MDRC in partnership with the Robin Hood Foundation, Overdeck Family Foundation, the Heising-Simons Foundation, and other funders as part of the Robin Hood Early Childhood Research Initiative to design and test interventions aimed at improving outcomes for children living in poverty in New York City. For more information about the project, including the published reports, see here .
• Bank Street College of Education provided training, supervision, and support for the facilitators in this program.
• Among the children who planned to stay in the same school between pre-K and kindergarten, 738 parents (99% of eligible children) gave consent at the end of pre-K for their student to participate in the second phase of the study. Some students who were assigned to the High 5s program group did not participate in the program or discontinued their participation before the end of the year. All students who were assessed at the end of kindergarten, regardless of their participation, were included in analyses. 
• An item-by-item analysis of the REMA-K showed that fewer than 10% of the items on the test were aligned with specific Building Blocks or High 5s activities.
• Children in the High 5s study had all participated in Making Pre-K Count and therefore had all been exposed to the Building Blocks math curriculum in preschool. 
• The study found no significant effects on language or executive functioning skills.
• For a detailed discussion of costs, see the High 5s implementation report. 

Economic Studies

Center for Economic Security and Opportunity

Larry Cooley, Jenny Perlman Robinson

March 8, 2024

The Brookings Institution, Washington DC

9:00 am - 5:00 pm EDT

Nicol Turner Lee, Jennifer Huddleston , Christopher Wood

January 29, 2024

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• HHS Author Manuscripts

Cognitive Prediction of Reading, Math, and Attention: Shared and Unique Influences

Robin l. peterson.

Children’s Hospital Colorado and University of Colorado School of Medicine, 13123 E. 16 th Ave, B285, Aurora, CO 80045

Richard Boada

Children’s Hospital Colorado and University of Colorado School of Medicine, 13123 E. 16 th Ave, B155, Aurora, CO 80045

Lauren M. McGrath

American University, 4400 Massachusetts Avenue, NW, Gray Hall, Washington, DC 20016-8030

Erik G. Willcutt

University of Colorado Boulder, Muenzinger D244, 345 UCB, Boulder, CO 80309

Richard K. Olson

Bruce f. pennington.

University of Denver, 2155 S. Race Street, Denver, CO 80238

The current study tested a multiple-cognitive predictor model of word reading, math ability, and attention in a community-based sample of twins aged 8 to 16 years (N = 636). The objective was to identify cognitive predictors unique to each skill domain, as well as cognitive predictors shared among skills that could help explain their overlap and thus help illuminate the basis for comorbidity of related disorders (reading disability, math disability, and attention deficit hyperactivity disorder). Results indicated that processing speed contributes to the overlap between reading and attention as well as math and attention, while verbal comprehension contributes to the overlap between reading and math. There was no evidence that executive functioning skills help account for covariation among these skill domains. Instead, specific executive functions differentially related to certain outcomes (i.e., working memory to math and inhibition to attention). We explored whether the model varied in younger versus older children and found only minor differences. Results are interpreted within the context of the multiple deficit framework for neurodevelopmental disorders.

Introduction

Understanding the basis of the comorbidity among neurodevelopmental disorders has been a very active area of research in recent years. One of the most rigorously examined phenotypic associations is the comorbidity between reading disability (RD, or dyslexia) and Attention Deficit Hyperactivity Disorder (ADHD), for which there is now evidence of both shared cognitive and genetic risk factors ( McGrath et al., 2011 ; Willcutt et al., 2010 ). However, the association between RD and ADHD is not exclusive; various other comorbidities have been identified in children, including reading disability and math disorder (MD, or dyscalculia) ( Landerl & Moll, 2010 ), as well as math disorder and ADHD ( Capano, Minden, Chen, Schacher, & Ickowicz, 2008 ). Rarely, though, have all three symptom dimensions been studied in a large enough sample of children to allow for an investigation of the underlying cognitive relationships among them. The main goal of this study is to advance these important lines of inquiry by modeling the shared and unique cognitive risk factors that predict reading, math, and attention using data from a large community-based sample of twins from the Colorado Learning Disabilities Research Center (CLDRC).

How these three skill dimensions, and their associated disordered states, relate to one another at cognitive and etiologic levels of analysis is a central issue in the field of developmental neuropsychology, with clinical and theoretical implications. Apparent comorbidity among neurodevelopmental disorders can arise for various artifactual reasons, such as referral biases, definitional overlap, or assortative mating. Another possible explanation is a phenocopy phenomenon, in which symptoms of one disorder lead to secondary expression of the symptoms in another disorder. For example, perhaps children with poor attention struggle with academic skills not because they have a primary learning disability but because they are not able to benefit from instruction to the same extent as their peers. Previous research suggests that these artifactual explanations are unlikely to fully account for overlap among the symptom dimensions that are the focus of this paper ( Pennington, Willcutt, & Rhee, 2005 ).

The theoretical model that guides the current study is the multiple cognitive deficit model of neurodevelopmental disorders ( Pennington, 2006 ). In this investigation, we extend this deficit-focused model to account for individual differences across the full range of abilities. According to the multiple deficit framework, each symptom dimension can be predicted by several underlying cognitive factors. Genuine comorbidity among symptom dimensions or disorders arises because some of the underlying cognitive skills are shared by disorders. The overlap at the symptom level is less than 100% because each dimension also has unique predictors. This model has been applied successfully to several sets of symptom dimensions or disorders ( Archibald, Cardy, Joanisse, & Ansari, 2013 ; Carroll & Myers, 2010 ; Christopher et al., 2012 ). In the sections that follow, we will provide a brief overview of the various two-way comorbidities embedded in this study. Subsequently, we will outline a rationale for the proposed set of hypotheses that we will test in this dataset in order to understand more clearly the relations among reading, math, and attention.

RD and ADHD

Although RD and ADHD each occur in approximately 5–10% of children in the population, 15 to 30% of children with either RD or ADHD also meet criteria for the other disorder, a higher-than-chance comorbidity ( Willcutt et al., 2012 ). Research suggests that these disorders, along with virtually all other behaviorally defined disorders, represent the low tail of ability in a normal distribution ( Pennington, 2014 ; Rodgers, 1983 ). Thus, the categorical diagnoses represent somewhat arbitrary cut-offs in continuous variables.

Twin studies have shown a significant genetic association between RD and ADHD, particularly between single word reading and the inattentive symptom dimension ( Willcutt, Pennington, Olson, & DeFries, 2007 ). Neuropsychological studies have sought to identify cognitive deficits unique to each disorder. In the RD literature, there is ample support for a deficit in phonological awareness (PA) and other aspects of phonological processing ( Boada & Pennington, 2006 ; Olson, Forsberg, & Wise, 1994 ; Vellutino, Fletcher, Snowling, & Scanlon, 2004 ). However, weaknesses have been identified in several other cognitive domains, such as broader speech and language processing ( Bishop & Adams, 1990 ), naming speed (NS) ( Compton, Olson, DeFries, & Pennington, 2002 ; Purvis & Tannock, 2000 ; Semrud-Clikeman, Guy, Griffin, & Hynd, 2000 ; Wolf & Bowers, 1999 ), processing speed (PS) ( Caravolas, Volin, & Hulme, 2005 ; Catts, Gillispie, Leonard, Kail, & Miller, 2002 ; Kail & Hall, 1994 ; Shanahan et al., 2006 ; Willcutt, Pennington, Olson, Chhabildas, & Hulslander, 2005 ), and verbal working memory (VWM) ( Rucklidge & Tannock, 2002 ; Swanson, Mink, & Bocian, 1999 ; Willcutt et al., 2001 ; Willcutt et al., 2005 ).

In the case of ADHD, there is less agreement about core neuropsychological deficits. Various aspects of executive functioning have been implicated, including response inhibition ( Barkley, 1997 ), and organization/planning and working memory (WM) ( Willcutt et al., 2005 ). Deficits in PS ( Shanahan et al., 2006 ; Willcutt et al., 2005 ), NS ( Rucklidge & Tannock, 2002 ; Shanahan et al., 2006 ; Willcutt et al., 2005 ), and reaction time variability ( Kuntsi & Klein, 2012 ) have also been reported.

Our group has previously investigated the cognitive and etiologic overlap of RD and ADHD. Shanahan et al. (2006) showed that PS was a likely shared cognitive deficit that could account for the comorbidity between these disorders. Extending this work, McGrath et al. (2011) tested a multiple cognitive deficit model of RD and ADHD using multiple latent cognitive factors to predict three latent symptom dimensions (word reading, attention, and hyperactivity/impulsivity). Each symptom dimension had several significant predictors. PA, NS and PS predicted reading, while inhibition and PS predicted inattention and hyperactivity/impulsivity. PS was the only cognitive predictor shared by all three symptom dimensions. With PS in the model, the covariance between reading-attention and reading-hyperactivity/impulsivity became nonsignificant. Thus, the authors concluded that PS primarily accounted for the significant correlation (i.e., comorbidity) between the two symptom dimensions.

PS has also been shown to share common genetic influence with RD and ADHD symptom dimensions. Willcutt et al. (2010) used a Cholesky decomposition analysis in the CLDRC twin sample to estimate the shared and independent genetic influences on reading, inattention, hyperactivity/impulsivity, and PS and NS. After accounting for genetic influences shared by PS, reading, inattention, and hyperactivity/impulsivity, there were no other genetic influences shared by reading and either ADHD symptom dimension. These results suggest that comorbidity between reading difficulties and ADHD is primarily attributable to common genetic influences that lead to slow PS.

RD and MD co-occur in 30–70% of individuals with either disorder, again a higher-than-chance overlap ( Badian, 1999 ; Kovas et al., 2007 ; Landerl & Moll, 2010 ). Twin studies suggest that some of the same genetic influences contribute to both disorders ( Light & DeFries, 1995 ; Plomin & Kovas, 2005 ). However, relatively few studies have examined possible shared cognitive predictors.

The existing literature suggests that MD is associated with a pronounced weakness in numerosity, the understanding of different conceptual properties of numbers ( Cirino, Fletcher, Ewing-Cobbs, Barnes, & Fuchs, 2007 ; Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007 ). In addition, some previous studies have reported that individuals with MD have weaknesses in PA ( Geary et al., 2007 ), WM ( Passolunghi & Cornoldi, 2008 ; Raghubar, Barnes, & Hecht, 2010 ), set shifting ( van der Sluis, de Jong, & van der Leij, 2004 ), and PS and NS ( Andersson & Lyxell, 2007 ; Geary et al., 2007 ). Since several of these cognitive weaknesses have also been implicated in RD, a logical step is to investigate which might help account for the overlap of the two disorders.

A few studies have now investigated unique and shared cognitive predictors of RD and MD. Using multiple regression models, Willcutt and colleagues (2013) reported that PA and NS were unique predictors of RD, while set shifting uniquely predicted MD. The two disorders shared weaknesses in WM, PS and verbal comprehension (VC).

Cirino and colleagues (2013) also tested the association of RD and MD with various cognitive predictors, including language skills (PA, NS and vocabulary), WM, PS, and foundational numerical competencies. PA predicted RD while PS, non-verbal problem solving and foundational math competencies predicted MD. WM predicted both disorders. PS was assessed using a speeded perceptual discrimination task that had reduced linguistic and graphomotor demands, which may explain the lack of association with RD.

Moll and colleagues (2014) investigated a slightly different set of cognitive risk factors that included PS, WM, and temporal processing (a time reproduction task). The authors argued that the predictors were chosen because all three have been associated with ADHD, which is also comorbid with both RD and MD. Results of this study converged with Cirino et al. (2013), with VWM being associated with both disorders. PS and NS predicted RD uniquely, while temporal processing and visuospatial WM predicted MD.

Across these studies, there is convergence that WM may be an important shared cognitive deficit contributing to the comorbidity between RD and MD. Results are more variable for PS, partly depending on the specific tasks used. These results highlight that specific model results can vary depending on the constructs included, the tasks used to assess each construct, and sample characteristics (i.e., a population sample versus a learning disabilities sample).

MD and ADHD

Fewer studies have investigated the comorbidity between MD and ADHD. In a study of 476 children with ADHD, Capano et al. (2008) found a prevalence rate of 18.1% for comorbid MD + ADHD. There was no effect of age, sex, ADHD subtypes or comorbid conduct disorder on the frequency of MD. Children who had both disorders attained lower IQ, language, and academic scores compared to children with ADHD alone. Children who had ADHD, MD and RD were the most impaired, and had distinct deficits in receptive and expressive language skills.

Twin studies have shown that genetic factors account for a significant portion of the comorbidity between MD and ADHD ( Hart et al., 2010 ; Polderman et al., 2011 ). Additionally, as has been shown with RD, there is a stronger phenotypic association between MD and inattention than between MD and hyperactivity/impulsivity ( Rodriguez et al., 2007 ). Since both ADHD symptoms and math ability have also been shown to be genetically associated with reading and general cognitive ability ( Hart, Petrill, Thompson, & Plomin, 2009 ), the association between ADHD and math could possibly be confounded by the genetic factors shared with reading or IQ. However, Greven et al. (2014) found that the genetic association between inattention and math ability could only be partially accounted for by reading and IQ. Thus, there are likely to be unique as well as shared influences among the three disorders.

To date, no study has specifically investigated potential cognitive risk factors that could account for the comorbidity between MD and ADHD. Additionally, there has been no study that has attempted to model all three symptom dimensions (reading, math, and attention) at once to test which cognitive predictors may be unique and which may be shared by two or more disorders. The current study aims to fill these gaps in the literature. Because of the evidence described above that the inattention symptom dimension of ADHD is more strongly related to reading and math than is hyperactivity/impulsivity, we focused only on the former symptom dimension in the current investigation. It is also important to place these models in a developmental context. Although there is evidence to suggest that core deficits likely persist across development in conditions such as RD, MD, and ADHD, it is not clear whether the relative importance of risk factors remains constant over time. In fact, the reading literature would suggest that this is likely not the case. Constructs such as PA, semantic knowledge, and NS may predict different amounts of variance in reading depending on a child’s stage of reading acquisition (i.e., early literacy where accurate decoding is emphasized vs. later stages of reading acquisition where reading fluency and comprehension is emphasized) ( de Jong & van der Leij, 2002 ). This issue extends to the modeling of comorbidity, and as such, it will be important to test these models at different ages.

We addressed several specific questions in the current study. First, we asked whether a phenocopy phenomenon could possibly explain the symptom overlap among reading, math, and attention. It is possible that poor attention more globally impacts children’s ability to acquire academic skills, and conversely, that good attention supports acquisition of both reading and math. We thought this possibility was unlikely to account for most of the overlap among reading, math, and attention based on previous literature showing that the comorbidity between reading-related and attention problems emerges early in development ( Boetsch, 1996 ) and arises from shared cognitive and etiologic risk factors ( Ebejer et al., 2010 ), but thought it important to explicitly test in this data set. Thus, we hypothesized that attention would not fully account for the overlap between reading and math.

Second, we tested a multiple cognitive predictor model of the overlap among individual differences in reading, math, and attention. We developed specific hypotheses based primarily on previous results from this sample, with additional consideration for the broader learning disorders literature reviewed above. First, we predicted that PS would be a significant predictor of all three outcomes, and would help explain all three pairs of symptom overlap. Second, we expected that VC would additionally help account for the overlap between reading and math. Third, we expected to find cognitive predictors unique to each outcome. Specifically, we hypothesized that phonological awareness (PA) and NS would uniquely predict reading and inhibition would uniquely predict attention. For math, we predicted that measures of nonverbal problem solving (in our sample, captured by the Wechsler perceptual organization (PO) factor) and WM would be unique predictors. Specific measures of numerosity were not available in this sample, unfortunately. In a follow-up analysis, we tested an alternative model to see if executive functions (WM and inhibition) could account for the comorbidity among symptom dimensions. Thus, we allowed these cognitive factors to predict all three outcomes and evaluated whether inclusion of these additional paths improved model fit relative to our first hypothesized model. There is empirical support for relationships between reading-WM, attention-WM, and math-inhibition in the broader literature. However, previous studies in the current sample have not found these associations to be significant after accounting for the other cognitive factors included in this study.

Participants

Participants included a total of 636 children and adolescents (305 males and 331 females), 8–16 years. The participants were recruited as part of the Colorado Learning Disabilities Research Center (CLDRC) twin study, which is an ongoing population-based study of the etiology of learning disorders, described elsewhere ( DeFries et al., 1997 ; Willcutt et al., 2005 ). In brief, permission was sought from parents of all twin pairs between 8–18 years in 22 local school districts to review school records. If either member of a twin pair had a history of reading or attention difficulties, the pair and any siblings were invited to participate in the study. A comparison group of control twins was selected from the overall sample of pairs who did not meet the screening criteria for learning problems. Inclusion criteria included the following: (1) English-speaking home, (2) no evidence of neurological problems or history of brain injury, (3) no uncorrected visual or auditory deficits, and (4) no known genetic disorders or syndromes. Additional criteria specific to this study were (1) a Full Scale IQ of at least 70 on the Wechsler Intelligence Scale for Children-Revised (WISC-R; Wechsler, 1974 ) and (2) age range between 8–16 years to minimize missing data due to test version differences associated with age. To preserve the statistical assumption of independence, one twin was randomly chosen from the twin pair, regardless of diagnostic status, to be included in the analyses for this study. Further details regarding the sample demographics are provided in Table 1 .

Sample characteristics

The study protocol was approved by the Institutional Review Boards at the University of Colorado, Boulder and the University of Denver. After obtaining informed consent at both institutions, two testing sessions were completed at the University of Colorado, and a third testing session was scheduled approximately one month later at the University of Denver. Participants taking psychostimulant medication were asked to withhold medication for 24 hours prior to each testing session.

Detailed descriptions of the tasks administered have been published in previous reports ( Gayan & Olson, 2001 ; Willcutt et al., 2005 ). As a result, Table 2 is limited to a brief description of the tasks grouped according to construct along with a basic definition of each cognitive construct. Descriptive statistics for the overall sample for all measures with standardized scores available are provided in Table 3 . As can be seen, the sample performed within the average range overall although slightly above the population mean on most measures. These higher scores may reflect a Flynn effect in part, since several older tests are used in the CLDRC to maximize consistency in measures across many years. Similar to other volunteer research studies, there may also be some ascertainment bias contributing to this effect. All models utilized continuously distributed scores of the cognitive and symptom dimensions. A dimensional Attention score was calculated for parent and teacher raters by averaging the ratings on the nine DSM-IV inattention items on the Disruptive Behavior Rating Scale (DBRS; Erford, 1993 ).

Indicators for the symptom and cognitive dimensions. Basic definitions of the cognitive dimensions are provided for reference.

Descriptive statistics for cognitive and symptom variables with standardized scores available.

Data Cleaning

Raw scores from the tasks in Table 2 were used in the analyses and were reflected, when necessary, so that higher scores were associated with better performance. Outliers were winsorized to 4 SD, and variables were checked for extreme departures from normality ( Kline, 2005 ). We controlled for possible linear and nonlinear effects of age by regressing the raw scores on age and age squared and saving the unstandardized residuals for further analyses.

For the cognitive indicators, missing data was minimal. For the symptom dimensions, missing data was minimal for the indicators of the Single Word Reading and Math factors (<1% missing). For the Attention symptom dimension, it was more common to have missing data because information was gathered from multiple raters: mothers (4% missing), fathers (22% missing), and teachers (16% missing).

SEM analyses were run with AMOS 22.0 using maximum likelihood estimation and imputation of missing data using full information maximum likelihood estimation. We used the following general guidelines for reasonable model fit: Χ 2 /df<3, Comparative Fit Index (CFI)>.90, Root Mean Square Error of Approximation (RMSEA)<.08 ( Kline, 2005 ).

As described in the hypotheses section above, we planned to compare two multiple predictor models: a first model in which specific hypothesized cognitive predictor-symptom relationships were based heavily on previous results in the current sample, and a second model emphasizing the contribution of executive functioning skills to symptom overlap. After identifying a model that fit the data well, we examined how well the model accounted for comorbidity by examining the correlations among the reading, math, and attention error terms. The logic was that if the included cognitive predictors fully explain symptom overlap, the correlations among any residual symptom variance (i.e., the error terms) should be null. Finally, we tested more specifically which shared cognitive predictors could account for comorbidity by dropping them, one at a time, from the final model. The logic in this case was that if a given predictor accounted for symptom covariance/comorbidity, when that predictor is removed from the model then the correlation between symptom error terms should increase again.

Measurement Models

Symptom dimensions.

Our measurement model for the symptom dimensions of reading, math, and attention is displayed in Figure 1 . The latent factors represent continuously distributed symptom dimensions underlying the diagnostic categories of the related disorders (RD, MD, and Inattentive ADHD). Our proposed model fit the data well (Χ 2 (17)=50.48, p< .001; χ 2 /df=2.97; CFI=.99; RMSEA=0.06) and was accepted without further modification. The significant correlations among all three symptom dimensions represent the continuous comorbidities that we will seek to explain with the cognitive dimensions using structural equation models.

Measurement model of symptom dimensions.

Notes. Read=Single word reading; Attn=attention; PIAT Rec= PIAT Reading Recognition; TLORT=Time Limited Oral Reading Test.

Standardized weights shown.

Cognitive dimensions

Our proposed model for the cognitive dimensions of VC, PO, PA, VWM, NS, PS, and inhibition (Inhib) is displayed in Figure 2 and Table 4 . Again, the model fit the data well (χ 2 (253)=663.41, p< .001; χ 2 /df=2.62; CFI=.94; RMSEA=0.05) and was accepted without further modification.

Measurement model of cognitive dimensions.

Notes. VC=Verbal Comprehension; PO=Perceptual Organization; PA = Phonological Awareness; VWM=Verbal Working Memory; PS=Processing Speed; NS=Naming Speed; Inhib=Inhibition.

For ease of reference, correlations among latent constructs are shown in Table 4 .

Correlations among latent cognitive constructs.

All correlations are significant at p<.001 level, except PO-NS correlation p-value = .002.

Phenocopy Hypothesis

Next, we evaluated whether the symptom overlap might arise from a phenocopy phenomenon in which attention impacts the acquisition of academic skills across domains. We tested a very simple model in which the latent trait of attention predicted the latent traits of both reading and math. Error terms for the reading and math traits were correlated. The key question was whether this model would significantly reduce the correlation between these error terms compared to the zero-order correlation of .77 (as shown in Figure 1 ). Fit statistics for this model were good (χ 2 (17)=15.48, p< .001; χ 2 /df=2.97; CFI=.99; RMSEA=0.06). However, the correlation between reading and math error terms was essentially unchanged (r = .73, p < .001). This result is consistent with our hypothesis and suggests that the three-way symptom overlap does not primarily arise from a phenocopy phenomenon. Instead, it appears that cognitive constructs are needed to explain the overlap among reading, math, and attention.

Multiple Deficit Models

Next, we tested a comorbidity model in the full sample in which cognitive dimensions predicted symptom dimensions. We began with a hypothesis-driven model based on the overall learning disorders literature as well as on previous results in this sample. Specifically, we allowed VC, PA, PS, and NS to predict reading; VC, PO, VWM, and PS to predict math; and VC, PO, PS, and Inhibition to predict attention. Model fit was good (χ 2 (458)=1153.53, p< .001; χ 2 /df=2.52; CFI=.94; RMSEA=0.05). Results were largely consistent with our predictions and with prior results, with a few exceptions. PS did not explain significant unique variance in reading. Furthermore, PO did not explain significant unique variance in any outcome. We thought these findings might at least partly reflect the construct overlap between PO and PS, given that the PO subtests are completed under time pressure. We therefore tested a second model that did not include PO and was otherwise identical to the first. Model fit remained good (χ 2 (348)=907.94, p< .001; χ 2 /df=2.61; CFI=.95; RMSEA=0.05) and consistent with considerable previous literature, PS now explained significant unique variance in reading. We therefore accepted this second model, which is shown in Figure 3 .

Comorbidity model in full sample.

Note. Standardized weights shown. Solid paths are statistically significant at the p<.05 level. Dotted paths are not statistically significant (p>.05).

Several aspects of this model are worth highlighting. Each symptom is predicted by multiple cognitive dimensions, some of which are shared across symptoms (PS predicting reading, math, and attention; VC predicting reading and math) and some of which are unique to a particular symptom (PA and NS for reading; VWM for math; and inhibition for attention). The cognitive predictors fully explained the comorbidity among the symptoms; correlations among all sets of error terms became nonsignificant. The cognitive predictors explained 79%, 88%, and 28% of the variance in reading, math, and attention, respectively.

To test which specific predictors explained the comorbidity among symptoms, we dropped PS from the final model, then dropped VC from the final model. Without PS as a predictor, the correlation between the reading and attention error terms became significant (r=.13, p=.03), as did the correlation between the math and attention error terms (r=.18, p=.04). However, the correlation between the reading and math error terms remained close to 0 and nonsignificant. In contrast, when VC was dropped from the full model, the correlation between the reading-attention and math-attention error terms remained nonsignificant, but the correlation between reading and math became large and statistically significant (r=.46, p<.001). Overall, these results suggest that PS accounts for much of the overlap of attention with both reading and math, but that the overlap of reading and math owes to VC.

Next, we evaluated an alternative model to test whether executive functions (working memory and inhibition) helped account for the comorbidity among symptoms. To the model in Figure 3 , we added paths allowing VWM to predict both reading and attention, and paths allowing inhibition to predict both reading and math. Addition of these paths did not significantly improve model fit (Δχ 2 (4)=2.97, p> .4), and none of the new paths was statistically significant. This model provided no evidence that these executive functions helped account for the overlap among symptoms.

We conducted a follow-up analysis to better understand the relationship of verbal skills to math achievement. We wondered whether this relationship was carried mainly by a link between VC and PIAT Math, which includes many word problems. In contrast, our other math measure (WRAT-R Math) emphasizes computation. We therefore ran the final model shown in figure 3 , but using only WRAT-R Math (treated as an observed variable) as the math outcome. Model fit remained good (χ 2 (322)=844.94, p< .001; χ 2 /df=2.62; CFI=.95; RMSEA=0.05), and the overall pattern of results was very similar to that reported above. Specifically, VC, PS, and VWM all continued to be significant predictors of math outcome (with standardized path weights of .33, .20, and .33), and the overlap among all three symptom dimensions remained nonsignificant. The cognitive predictors explained 54% of the variance in WRAT-R math. It is expected that the proportion of variance explained will decrease somewhat, since the observed variable includes error variance.

Multiple Groups Analyses

We formally tested whether the final model varied as a function of age using multi-group SEM analyses. We compared groups based on a median age split. There were 325 younger children (<10.33 years) and 315 older children (≥10.33 years).

First, we tested whether measurement weights could be constrained to be equal across the two groups without significant loss of fit. Results indicated significant model differences across age groups (χ 2 (20)=88.42, p< .001). To understand this finding, we evaluated each measurement weight individually for age group differences. We applied a Bonferroni correction for multiple testing. Seven of 29 individual weights were significantly different in younger versus older children, including observed variables that loaded on VC (Information, Similarities), PA (Phoneme Deletion 1 and 2, Pig Latin), and Math (PIAT Math and WRAT-R Math). Although the differences in unstandardized weights for these variables were statistically different in the two groups, the magnitude of the differences was generally small. Furthermore, the standardized loadings were very similar in every case, because the direction of variance differences aligned with the direction of the loading differences.

Next, we tested whether structural weights could be constrained to be equal across the two groups without significant loss of fit. Results again indicated significant model differences across age groups in the omnibus test (χ 2 (10)=24.95, p=.005). However, none of the individual structural weights significantly varied in older vs. younger children after correction for multiple comparisons.

Finally, we constrained the correlations among the error terms for the symptom dimensions (representing any remaining covariance after accounting for shared cognitive predictors) to be equal across older and younger groups. There was no evidence that these relationships varied as a function of age (χ 2 (3)=1.00, p=.80).

The goal of the current study was to better understand the basis for the overlap among word reading, mathematics skill, and attention across the full range of individual differences in a community-based sample of twins aged 8 to 16. These three skills are moderately to highly correlated, and the corresponding neurodevelopmental disorders of RD, MD, and inattentive ADHD co-occur at greater-than-chance levels. We asked which cognitive skills underlie these relationships. As predicted, results did not support a phenocopy hypothesis in which low reading and math achievement both arise from poor attention. Instead, results were consistent with a multiple deficit or multiple predictor framework in which the shared variance among each pair of symptoms could be attributed to a single common cognitive predictor. Also consistent with the predictions of a multiple deficit/multiple predictor framework, each symptom also had at least one unique predictor that was not shared with other outcomes. Important novel findings included that verbal-conceptual skills specifically contributed to the overlap between reading and math, while PS contributed to the overlap between math and attention.

As expected based on previous work in this sample, PS helped account for the overlap between reading and attention. Since PS weaknesses have also been linked to MD, we had initially hypothesized that this single cognitive factor might contribute to overlap among all three symptom dimensions. This hypothesis was partially supported. PS did explain significant variance in each symptom outcome, and accounted for the overlap between math and attention. However, VC rather than PS explained the strong relationship between reading and math achievement. This pattern continued to be evident when math was assessed with a single measure that emphasized calculation skills rather than word problems. Unique predictors for each symptom were consistent with previous research and included PA and NS for reading, VWM for math, and response inhibition for attention.

Together, cognitive factors accounted for the large majority (approximately 80–90%) of the variance in reading and math skills. As expected, variance accounted for in attention was much lower (<30%). Even this figure is at the higher end of variance in attention that researchers have been able to explain with neuropsychological tasks, likely because we modeled attention as a latent trait that removed error variance. The consistent failure across studies to account for more variance in attention probably arises from several factors, including: 1) method variance (of the three outcomes and six predictors included in Figure 3 , eight are assessed with objective cognitive tasks while only attention is assessed with rating scales); 2) restricted variance at the high end of the scale (like most attention rating scales, those used in the current study are designed to measure problematic behaviors but have limited ability to detect individual differences at the other end of the spectrum); and 3) perhaps a less mature neuropsychological theory of inattentive ADHD in comparison to MD and certainly to RD.

As illustrated by the current special issue, there is growing interest in the role that executive functions play in academic skill development. One hypothesis is that executive functions contribute in a general fashion to achievement across skill domains, and thus help account for comorbidity or covariation among symptom dimensions. The current study provided no evidence to support such a hypothesis. Instead, we found that specific executive functions differentially related to certain outcomes (i.e., VWM to math and inhibition to attention), but did not help account for the overlap between any two symptoms. Two important caveats are: 1) The current study emphasized basic reading skills, while our math composite tapped a mix of basic and complex skills. A very different pattern could emerge with more detailed measurement of higher-level skills such as reading comprehension, math problem solving, and written composition; and 2) Model results can vary substantially depending on which predictors are included, and as made clear in the introduction, exactly which tasks are used to assess those constructs. Thus, for example, if we had eliminated PA and NS or if we had used speeded measures emphasizing only perceptual speed or more basic reaction time rather than graphomotor speed, it is possible that VWM could have appeared to serve as a shared predictor of reading and math. A related point is that several of the cognitive constructs included in the current study were derived in part or in full from one of the Wechsler instruments, and some of them load strongly on Spearman’s “ g ” or a general intelligence factor. Of course, essentially all cognitive or neuropsychological tests correlate with g at least to an extent ( Pennington, 2008 ), so this interpretive issue is not unique to measures that are given as part of an IQ test. We obtained different patterns of results for VC, PO, PS, and VWM, which suggests that there is at least some specificity to the relationships between these cognitive factors and symptom domains. However, we did not explicitly test the extent to which common cognitive variance or g contributes to symptom covariance and this is an important question for future research that will require a different methodological approach.

The large age range included in the current study allowed us to test whether the relationships between cognitive predictors and symptom dimensions shifted as children grew older. The overall pattern of relationships was quite similar in younger and older participants. We found a few small but statistically significant differences in measurement aspects of the model. However, there was not compelling evidence that cognitive variables differentially related to symptom outcomes or to comorbidity in younger versus older children. Of note, however, our older and younger subgroups still included significant age variance. It is possible that results could look different in a very large sample allowing for comparison of results across narrower age bands, or in individuals younger or older than those included in the current study.

Results have several implications. Because presence of comorbid learning disorders is associated with increased functional impairment ( Willcutt et al., 2013 ), early identification of children at risk for more than one disorder is especially important. The current study adds to a growing body of evidence suggesting that weak processing speed is a risk factor for multiple poor outcomes. Thus, the educational and clinical utility of very early screening for processing speed deficits should be investigated by future research. Similarly, early screening for children with poor verbal skills could likely identify those at risk for academic difficulties across the curriculum. The current finding of a similar pattern of results across age groups, in conjunction with previous work showing very high stability of individual differences in academic skills over time ( Hulslander, Olson, Willcutt, & Wadsworth, 2010 ) suggests that school age assessment should predict adolescent cognitive and educational profiles fairly well. However, group findings never generalize perfectly to every individual in the distribution, so individual classification and prediction is inevitably challenging ( Pennington et al., 2012 ). Thus, for educational and clinical decision making at the individual level (e.g., determining whether a particular child qualifies for continued services), periodic re-evaluation is likely to remain appropriate.

Limitations

These results should be interpreted in the context of several limitations. First, our cross sectional sample and study design do not allow us to draw firm conclusions about causality. Working within the paradigm of developmental neuropsychology, we assume that discrete cognitive processes underlie, or cause, observed symptoms. However, it is also possible that the causal direction runs the other way, or that there are bidirectional relations. In fact, empirical evidence supports such a bidirectional relationship between reading and PA ( Morais, Cary, Alegria, & Bertelson, 1979 ) as well as reading and vocabulary (one part of VC) ( Stanovich, 1986 ).

Second, as previously mentioned, interpretation of results can be heavily influenced by the variables that are included in the model. Readers of some of our previous studies have been surprised that VWM does not play a more important role in the prediction of reading, for example. However, in the current sample, we have consistently found that when both PA and VWM are included, PA “wins” the competition and VWM does not explain significant unique variance in reading. Of course this does not mean that reading does not involve VWM. As is evident in Table 4 , all the cognitive predictors overlap to some extent with one another, and PA tasks certainly also tap into working memory skill to a degree.

A third important limitation is that we tested our model across the full range of individual differences and not only in a disordered sample to maximize variance and sample size. Based on evidence that essentially all behaviorally-defined developmental disorders represent the low tail of a continuously distributed symptom dimension ( Pennington, 2014 ), we think results have important implications for understanding the comorbidities among the common and impairing disorders of RD, MD, and ADHD as well. However, a somewhat different pattern of results could emerge in a sample more heavily selected for learning disabilities.

Future directions

In sum, results provide support for a multiple cognitive predictor model of three domains important in children’s educational achievement: reading, math, and attention. Findings suggest several important directions for future research. One set of questions concerns the mechanisms through which shared cognitive predictors influence multiple outcomes. For example, some researchers have proposed that slowed PS serves as a “bottleneck” that limits children’s abilities to master various skills ( Dennis, 2000 ). Alternatively, PS may simply serve as a proxy for some other variable, such as white matter integrity ( Penke et al., 2010 ), that influences performance across domains. Similarly, why do verbal skills underlie the relationship between reading and math achievement? Is it because so much teaching takes place in a verbal context or some other reason more internal to the child? As noted in the limitations sections above, it will also be important to test related models in longitudinal samples that include measures of both basic and complex academic skills. Future studies should also elucidate links to other levels of analysis, including brain bases and etiologic risk and protective factors. Finally, the potential relevance of these findings for early identification and remediation of children at risk for multiple disorders will need to be rigorously evaluated by future studies.

Acknowledgments

This research was supported by a Learning Disability Research Center grant from NICHD (HD027802).

Contributor Information

Robin L. Peterson, Children’s Hospital Colorado and University of Colorado School of Medicine, 13123 E. 16 th Ave, B285, Aurora, CO 80045.

Richard Boada, Children’s Hospital Colorado and University of Colorado School of Medicine, 13123 E. 16 th Ave, B155, Aurora, CO 80045.

Lauren M. McGrath, American University, 4400 Massachusetts Avenue, NW, Gray Hall, Washington, DC 20016-8030.

Erik G. Willcutt, University of Colorado Boulder, Muenzinger D244, 345 UCB, Boulder, CO 80309.

Richard K. Olson, University of Colorado Boulder, Muenzinger D244, 345 UCB, Boulder, CO 80309.

Bruce F. Pennington, University of Denver, 2155 S. Race Street, Denver, CO 80238.

• Andersson U, Lyxell B. Working memory deficit in children with mathematical difficulties: A general or specific deficit? Journal of Experimental Child Psychology. 2007; 96 (3):197–228. [ PubMed ] [ Google Scholar ]
• Archibald LM, Cardy JO, Joanisse MF, Ansari D. Language, reading, and math learning profiles in an epidemiological sample of school age children. Plos One. 2013; 8 (10):e77463. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Badian NA. Persistent arithmetic, reading, or arithmetic and reading disability. Annals of Dyslexia. 1999; 49 (1):43–70. [ Google Scholar ]
• Barkley RA. Behavioral inhibition, sustained attention, and executive functions: constructing a unifying theory of ADHD. Psychological Bulletin. 1997; 121 (1):65. [ PubMed ] [ Google Scholar ]
• Bishop DVM, Adams C. A prospective study of the relationship between specific language impairment, phonological disorders and reading retardation. Journal of Child Psychology & Psychiatry. 1990; 31 (7):1027–1050. [ PubMed ] [ Google Scholar ]
• Boada R, Pennington BF. Deficient implicit phonological representations in children with dyslexia. Journal of Experimental Child Psychology. 2006; 95 (3):153–193. [ PubMed ] [ Google Scholar ]
• Boetsch EA. Unpublished doctoral dissertation. University of Denver; 1996. A longitudinal study of the relationship between dyslexia and socioemotional functioning in young children. [ Google Scholar ]
• Capano L, Minden D, Chen SX, Schacher R, Ickowicz A. Mathematical learning disorder in school-age children with attention-deficit hyperactivity disorder. Canadian journal of psychiatry Revue canadienne de psychiatrie. 2008; 53 (6):392–399. [ PubMed ] [ Google Scholar ]
• Caravolas M, Volin J, Hulme C. Phoneme awareness is a key component of alphabetic literacy skills in consistent and inconsistent orthographies: evidence from Czech and English children. J Exp Child Psychol. 2005; 92 (2):107–139. [ PubMed ] [ Google Scholar ]
• Carroll JM, Myers JM. Speech and language difficulties in children with and without a family history of dyslexia. Scientific Studies of Reading. 2010; 14 (3):247–265. [ Google Scholar ]
• Catts HW, Gillispie M, Leonard LB, Kail RV, Miller CA. The role of speed of processing, rapid naming, and phonological awareness in reading achievement. J Learn Disabil. 2002; 35 (6):509–524. [ PubMed ] [ Google Scholar ]
• Christopher ME, Miyake A, Keenan JM, Pennington B, DeFries JC, Wadsworth SJ, Olson RK. Predicting word reading and comprehension with executive function and speed measures across development: A latent variable analysis. Journal of Experimental Psychology: General. 2012; 141 (3):470. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Cirino PT, Fletcher JM, Ewing-Cobbs L, Barnes MA, Fuchs LS. Cognitive arithmetic differences in learning difficulty groups and the role of behavioral inattention. Learning Disabilities Research & Practice. 2007; 22 (1):25–35. [ Google Scholar ]
• Cirino PT, Fuchs LS, Elias JT, Powell SR, Schumacher RF. Cognitive and mathematical profiles for different forms of learning difficulties. Journal of Learning Disabilities. 2015; 48 :156–175. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Compton DL, Olson RK, DeFries JC, Pennington BF. Comparing the relationships among two different versions of alphanumeric rapid automatized naming and word level reading skills. Scientific Studies of Reading. 2002; 6 (4):343–368. [ Google Scholar ]
• de Jong PF, van der Leij A. Effects of phonological abilities and linguistic comprehension on the development of reading. Scientific Studies of Reading. 2002; 6 (1):51–77. [ Google Scholar ]
• Decker SN. Cognitive processing rates among disabled and normal young adults: A nine year follow-up study. Reading and Writing. 1989; 2 :123–134. [ Google Scholar ]
• DeFries JC, Filipek PA, Fulker DW, Olson RK, Pennington BF, Smith SD, Wise BW. Colorado Learning Disabilities Research Center. Learning Disability Quarterly. 1997; 7–8 :19. [ Google Scholar ]
• Denckla MB, Rudel RG. Rapid ‘automatized’ naming (R.A.N.): Dyslexia differentiated from other learning disabilities. Neuropsychologia. 1976; 14 (4):471–479. [ PubMed ] [ Google Scholar ]
• Dennis M. Developmental plasticity in children: the role of biological risk, development, time, and reserve. Journal of communication disorders. 2000; 33 (4):321–332. [ PubMed ] [ Google Scholar ]
• Dunn LM, Markwardt FC. Examiner’s manual: Peabody Individual Achievement Test. Circle Pines, MN: American Guidance Service; 1970. [ Google Scholar ]
• Ebejer JL, Coventry WL, Byrne B, Willcutt EG, Olson RK, Corley R, Samuelsson S. Genetic and environmental influences on inattention, hyperactivity-impulsivity, and reading: Kindergarten to grade 2. Scientific Studies of Reading. 2010; 14 (4):293–316. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Erford B. Disruptive Behavior Rating Scale parent/treacher manual. East Aurora, NY: Slosson Educational Publications; 1993. [ Google Scholar ]
• French JW, Ekstrom RB, Price LA. Manual for kit of reference tests for cognitive factors (revised 1963) DTIC Document 1963 [ Google Scholar ]
• Gayan J, Olson RK. Genetic and environmental influences on orthographic and phonological skills in children with reading disabilities. Developmental Neuropsychology. 2001; 20 (2):483–507. [ PubMed ] [ Google Scholar ]
• Geary DC, Hoard MK, Byrd-Craven J, Nugent L, Numtee C. Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child development. 2007; 78 (4):1343–1359. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Gordon M. Gordon Diagnostic System. DeWitt, NY: Gordon Systems; 1983. [ Google Scholar ]
• Greven CU, Kovas Y, Willcutt EG, Petrill SA, Plomin R. Evidence for shared genetic risk between ADHD symptoms and reduced mathematics ability: a twin study. Journal of Child Psychology and Psychiatry. 2014; 55 (1):39–48. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Hart SA, Petrill SA, Thompson LA, Plomin R. The ABCs of math: A genetic analysis of mathematics and its links with reading ability and general cognitive ability. Journal of educational psychology. 2009; 101 (2):388. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Hart SA, Petrill SA, Willcutt E, Thompson LA, Schatschneider C, Deater-Deckard K, Cutting LE. Exploring how symptoms of attention-deficit/hyperactivity disorder are related to reading and mathematics performance general genes, general environments. Psychological Science. 2010; 21 (11):1708–1715. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Hulslander J, Olson RK, Willcutt EG, Wadsworth SJ. Longitudinal stability of reading-related skills and their prediction of reading development. Scientific Studies of Reading. 2010; 14 (2):111–136. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Jastak SR, Wilkinson GS. Wide Range Achievement Test: WRAT-R. Western Psychological Services; 1984. [ Google Scholar ]
• Kail R, Hall LK. Processing speed, naming speed, and reading. Developmental Psychology. 1994; 30 (6):949–954. [ Google Scholar ]
• Kline RB. Principles and Practice of Structural Equation Modeling. 2. New York: Guilford Press; 2005. [ Google Scholar ]
• Kovas Y, Haworth C, Harlaar N, Petrill SA, Dale PS, Plomin R. Overlap and specificity of genetic and environmental influences on mathematics and reading disability in 10-year-old twins. Journal of Child Psychology and Psychiatry. 2007; 48 (9):914–922. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Kuntsi J, Klein C. Behavioral Neuroscience of Attention Deficit Hyperactivity Disorder and Its Treatment. Springer; 2012. Intraindividual variability in ADHD and its implications for research of causal links; pp. 67–91. [ PubMed ] [ Google Scholar ]
• Kuntsi J, Stevenson J, Oosterlaan J, Sonuga-Barke EJ. Test-retest reliability of a new delay aversion task and executive function measures. British Journal of Developmental Psychology. 2001; 19 (3):339–348. [ Google Scholar ]
• Landerl K, Moll K. Comorbidity of learning disorders: prevalence and familial transmission. Journal of Child Psychology and Psychiatry. 2010; 51 (3):287–294. doi: 10.1111/j.1469-7610.2009.02164.x. [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Light JG, DeFries JC. Comorbidity of Reading and Mathematics Disabilities Genetic and Environmental Etiologies. Journal of Learning Disabilities. 1995; 28 (2):96–106. [ PubMed ] [ Google Scholar ]
• Lindamood CH, Lindamood PC. Lindamood Auditory Conceptualization Test. Allen, TX: DLM Teaching Resources; 1979. [ Google Scholar ]
• Logan GD, Schachar RJ, Tannock R. Impulsivity and inhibitory control. Psychological Science. 1997; 8 (1):60–64. [ Google Scholar ]
• McGrath LM, Pennington BF, Shanahan MA, Santerre-Lemmon LE, Barnard HD, Willcutt EG, Olson RK. A multiple deficit model of reading disability and attention-deficit/hyperactivity disorder: Searching for shared cognitive deficits. Journal of Child Psychology and Psychiatry. 2011; 52 (5):547–557. doi: 10.1111/j.1469-7610.2010.02346.x. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Moll K, Göbel SM, Gooch D, Landerl K, Snowling MJ. Cognitive Risk Factors for Specific Learning Disorder Processing Speed, Temporal Processing, and Working Memory. Journal of Learning Disabilities. 2014 0022219414547221. [ PubMed ] [ Google Scholar ]
• Morais J, Cary L, Alegria J, Bertelson P. Does awareness of speech as a sequence of phones arise spontaneously? Cognition. 1979; 7 (4):323–331. [ Google Scholar ]
• Olson R, Forsberg H, Wise B, Rack J. Measurement of word recognition, orthographic, and phonological skills. In: Lyon GR, editor. Frames of Reference for the Assessment of Learning Disabilities: New Views on Measurement Issues. Baltimore, MD: Paul H. Brookes Publishing; 1994. pp. 243–278. [ Google Scholar ]
• Olson RK, Forsberg H, Wise B. Genes, environment, and the development of orthographic skills. In: Berniger VW, editor. The varieties of orthographic knowledge I: Theoretical and developmental issues. Dordrecht, the Netherlands: Kluwer; 1994. pp. 27–71. [ Google Scholar ]
• Olson RK, Wise B, Connors F, Rack J, Fulker D. Specific deficits in component reading and language skills: Genetic and environmental influences. Journal of Learning Disabilities. 1989; 22 :339–348. [ PubMed ] [ Google Scholar ]
• Passolunghi MC, Cornoldi C. Working memory failures in children with arithmetical difficulties. Child Neuropsychology. 2008; 14 (5):387–400. [ PubMed ] [ Google Scholar ]
• Penke L, Maniega SM, Murray C, Gow AJ, Hernández MCV, Clayden JD, Deary IJ. A general factor of brain white matter integrity predicts information processing speed in healthy older people. The Journal of Neuroscience. 2010; 30 (22):7569–7574. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Pennington BF. From single to multiple deficit models of developmental disorders. Cognition. 2006; 101 (2):385. [ PubMed ] [ Google Scholar ]
• Pennington BF. Diagnosing Learning Disorders: A Neuropsychological Framework. 2. New York: Guilford Publications; 2008. [ Google Scholar ]
• Pennington BF. Explaining Abnormal Behavior: A Cognitive Neuroscience Perspective. New York: Guilford Publications; 2014. [ Google Scholar ]
• Pennington BF, Santerre–Lemmon L, Rosenberg J, MacDonald B, Boada R, Friend A, Willcutt EG. Individual prediction of dyslexia by single versus multiple deficit models. Journal of abnormal psychology. 2012; 121 (1):212–224. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Pennington BF, Willcutt E, Rhee SH. Analyzing comorbidity. In: Kail RV, editor. Advances in child development and behavior. Vol. 33. San Diego, CA US: Elsevier Academic Press; 2005. pp. 263–304. [ PubMed ] [ Google Scholar ]
• Plomin R, Kovas Y. Generalist genes and learning disabilities. Psychological Bulletin. 2005; 131 (4):592. [ PubMed ] [ Google Scholar ]
• Polderman TJ, Huizink AC, Verhulst FC, van Beijsterveldt CE, Boomsma DI, Bartels M. A genetic study on attention problems and academic skills: Results of a longitudinal study in twins. Journal of the Canadian Academy of Child and Adolescent Psychiatry. 2011; 20 (1):22. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Purvis KL, Tannock R. Phonological processing, not inhibitory control, differentiates ADHD and reading disability. J Am Acad Child Adolesc Psychiatry. 2000; 39 (4):485–494. [ PubMed ] [ Google Scholar ]
• Raghubar KP, Barnes MA, Hecht SA. Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences. 2010; 20 (2):110–122. [ Google Scholar ]
• Rodgers B. The identification and prevalence of specific reading retardation. British Journal of Educational Psychology. 1983; 53 (3):369–373. [ PubMed ] [ Google Scholar ]
• Rodriguez A, Järvelin MR, Obel C, Taanila A, Miettunen J, Moilanen I, Kotimaa AJ. Do inattention and hyperactivity symptoms equal scholastic impairment? Evidence from three European cohorts. BMC Public Health. 2007; 7 (1):327. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Rucklidge JJ, Tannock R. Neuropsychological profiles of adolescents with ADHD: effects of reading difficulties and gender. Journal of Child Psychology & Psychiatry. 2002; 43 (8):988–1003. [ PubMed ] [ Google Scholar ]
• Semrud-Clikeman M, Guy K, Griffin JD, Hynd GW. Rapid naming deficits in children and adolescents with reading disabilities and attention deficit hyperactivity disorder. Brain Lang. 2000; 74 (1):70–83. [ PubMed ] [ Google Scholar ]
• Shanahan MA, Pennington BF, Yerys BE, Scott A, Boada R, Willcutt EG, DeFries JC. Processing speed deficits in attention deficit/hyperactivity disorder and reading disability. J Abnorm Child Psychol. 2006; 34 (5):585–602. [ PubMed ] [ Google Scholar ]
• Stanovich KE. Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. Reading Research Quarterly. 1986; 21 (4):360–406. [ Google Scholar ]
• Swanson HL, Mink J, Bocian KM. Cognitive processing deficits in poor readers with symptoms of reading disabilities and ADHD: More alike than different? Journal of Educational Psychology. 1999; 91 (2):321–333. [ Google Scholar ]
• van der Sluis S, de Jong PF, van der Leij A. Inhibition and shifting in children with learning deficits in arithmetic and reading. Journal of Experimental Child Psychology. 2004; 87 (3):239–266. [ PubMed ] [ Google Scholar ]
• Vellutino FR, Fletcher JM, Snowling MJ, Scanlon DM. Specific reading disability (dyslexia): what have we learned in the past four decades? Journal of Child Psychology and Psychiatry. 2004; 45 (1):2–40. [ PubMed ] [ Google Scholar ]
• Wechsler D. Wechsler Intelligence Scale for Children--Revised. New York: The Psychological Corporation; 1974. [ Google Scholar ]
• Willcutt EG, Betjemann RS, McGrath LM, Chhabildas NA, Olson RK, DeFries JC, Pennington BF. Etiology and neuropsychology of comorbidity between RD and ADHD: The case for multiple-deficit models. Cortex. 2010; 46 (10):1345–1361. doi: 10.1016/j.cortex.2010.06.009. [ PMC free article ] [ PubMed ] [ CrossRef ] [ Google Scholar ]
• Willcutt EG, Nigg JT, Pennington BF, Solanto MV, Rohde LA, Tannock R, Lahey BB. Validity of DSM-IV attention deficit/hyperactivity disorder symptom dimensions and subtypes. Journal of abnormal psychology. 2012; 121 (4):991. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Willcutt EG, Pennington BF, Boada R, Ogline JS, Tunick RA, Chhabildas NA, Olson RK. A comparison of the cognitive deficits in reading disability and attention-deficit/hyperactivity disorder. Journal of Abnormal Psychology. 2001; 110 (1):157–172. [ PubMed ] [ Google Scholar ]
• Willcutt EG, Pennington BF, Olson RK, Chhabildas N, Hulslander J. Neuropsychological Analyses of Comorbidity Between Reading Disability and Attention Deficit Hyperactivity Disorder: In Search of the Common Deficit. Developmental Neuropsychology. 2005; 27 (1):35–78. [ PubMed ] [ Google Scholar ]
• Willcutt EG, Pennington BF, Olson RK, DeFries JC. Understanding comorbidity: A twin study of reading disability and attention-deficit/hyperactivity disorder. American Journal of Medical Genetics Part B: Neuropsychiatric Genetics. 2007; 144 (6):709–714. [ PubMed ] [ Google Scholar ]
• Willcutt EG, Petrill SA, Wu S, Boada R, DeFries JC, Olson RK, Pennington BF. Comorbidity Between Reading Disability and Math Disability Concurrent Psychopathology, Functional Impairment, and Neuropsychological Functioning. Journal of Learning Disabilities. 2013; 46 (6):500–516. [ PMC free article ] [ PubMed ] [ Google Scholar ]
• Wolf M, Bowers PG. The double-deficit hypothesis for the developmental dyslexias. Journal of educational psychology. 1999; 91 (3):415–438. [ Google Scholar ]

Advertisement

The State of Current Reading Intervention Research for English Learners in Grades K–2: a Best-Evidence Synthesis

• Meta-Analysis
• Published: 10 July 2021
• Volume 34 , pages 335–361, ( 2022 )

Cite this article

• Garrett J. Roberts   ORCID: orcid.org/0000-0003-1128-5577 1 ,
• Colby Hall   ORCID: orcid.org/0000-0002-0779-1322 2 ,
• Eunsoo Cho   ORCID: orcid.org/0000-0002-8828-484X 3 ,
• Brooke Coté 1 ,
• Jihyun Lee   ORCID: orcid.org/0000-0002-0172-9106 4 ,
• Bingxin Qi   ORCID: orcid.org/0000-0002-2732-641X 5 &
• Jacklyn Van Ooyik 1  

2277 Accesses

7 Citations

9 Altmetric

Explore all metrics

A Correction to this article was published on 09 August 2021

This article has been updated

This best-evidence synthesis reviews the past 20 years of rigorous reading intervention research to identify effective programs of instruction for Grade K–3 English Learners (ELs), as well as to determine the average effect of reading instruction on reading outcomes for this population. We identified 10 studies, all of which only included students in Grades K, 1, and/or 2. These studies evaluated the effects of seven programs, reporting 76 effect sizes. We did not identify any studies that included Grade 3 ELs. To guide researchers and practitioners, we describe each program and discuss associated effect sizes in foundational skills, fluency, comprehension, and oral language. Proactive Reading , delivered in a small group setting, produced some of the largest effects on foundational skills, fluency, and reading comprehension outcomes. Sound Partners was also shown to be effective even when delivered for a shorter duration, in a one-to-one setting. Finally, for practitioners and researchers aiming to improve oral language outcomes, Early Vocabulary Connection , delivered to small groups of students for 20 weeks, had the largest effects on oral language outcome measures. The primary limitation of this review was the small number of studies meeting the best-evidence synthesis criteria. Future research is needed to better understand the impact of reading interventions on reading outcomes for ELs in Grades 2–3 and the impact of meaning-focused intervention on reading outcomes. In particular, additional research is needed to identify interventions that have the potential to meaningfully improve reading comprehension and oral language outcomes for K–3 ELs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

The impact of tier 1 reading instruction on reading outcomes for students in grades 4–12: a meta-analysis.

Elizabeth Swanson, Elizabeth A. Stevens, … Christy R. Austin

Meta-Analyses of the Effects of Tier 2 Type Reading Interventions in Grades K-3

Jeanne Wanzek, Sharon Vaughn, … Philip Capin

Reading Instruction for English Learners in the Middle Grades: a Meta-Analysis

Colby Hall, Garrett J. Roberts, … Sharon Vaughn

Change history

09 august 2021.

A Correction to this paper has been published: https://doi.org/10.1007/s10648-021-09632-7

Note that standard errors may be unreliable when degrees of freedom is less than 4 in random effects model with RVE

Adams, G., & Engelmann, S. (1996). Research on direct instruction: 25 years beyond DISTAR . Educational Achievement Systems.

Adlof, S., & Catts, H. (2015). Morphosyntax in poor comprehenders. Reading and Writing, 28 (7), 1051–1070. https://doi.org/10.1007/11145.2015.95623 .

Article   Google Scholar  

Adlof, S., Catts, H., & Lee, J. (2010). Kindergarten predictors of second versus eighth grade reading comprehension impairments. Journal of Learning Disabilities, 43 (4), 332–345. https://doi.org/10.1177/00222.2010.0369067 .

Al Otaiba, S., Connor, C. M., Foorman, B., Schatschneider, C., Greulich, L., & Sidler, J. F. (2009). Identifying and intervening with beginning readers who are at-risk for dyslexia: advances in individualized classroom instruction. Perspectives on Language and Literacy, 35 , 13–19.

Google Scholar  

Babayiğit, S. (2014). The role of oral language skills in reading and listening comprehension of text: a comparison of monolingual (L1) and bilingual (L2) speakers of English language. Journal of Research in Reading, 37 (1), S22–S47. https://doi.org/10.1111/j.1467-9817.2012.01538.x .

Baker, S., Lesaux, N., Jayanthi, M., Dimino, J., Proctor, C. P., Morris, J., Gersten, R., Haymond, K., Kieffer, M. J., Linan-Thompson, S., & Newman-Gonchar, R. (2014). Teaching academic content and literacy to English learners in elementary and middle school (NCEE 2014-4012). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website: http://ies.ed.gov/ncee/wwc/publications_reviews.aspx .

*Baker, D., Burns, D., Kame’enui, E., Smolkowski, K., & Baker, S. (2016). Does supplemental instruction support the transition from Spanish to English reading instruction for first-grade English learners at risk of reading difficulties? Learning Disability Quarterly , 39 , 226-239. https://doi.org/10.1177/073.2016.715616757 , 4

Boscardin, C., Muthén, B., Francis, D., & Baker, E. (2008). Early identification of reading difficulties using heterogeneous developmental trajectories. Journal of Educational Psychology, 100 (1), 192–208. https://doi.org/10.1037/00220663.100.1.192 .

Capps, R. (2005). The new demography of America’s schools . Urban Institute.

Chall, J. S., & Jacobs, V. A. (1983). Writing and reading in the elementary grades: developmental trends among low SES children. Language Arts, 60 , 617–626.

Cheung, A., & Slavin, R. E. (2005). Effective reading programs for English language learners and other language-minority students. Bilingual Research Journal, 29 (2), 241–267. https://doi.org/10.1080/15235882.2005.10162835 .

Cheung, A., & Slavin, R. (2012). Effective reading programs for Spanish-dominant English language learners (ELLs) in the elementary grades. Review of Educational Research, 82 (4), 351–395. https://doi.org/10.3102/0034654312465472 .

Cho, E., Capin, P., Roberts, G., Roberts, G., & Vaughn, S. (2019). Examining sources and mechanisms of reading comprehension difficulties: comparing English learners and non-English learners within the simple view of reading. Journal of Educational Psychology, 111 (6), 982–1000. https://doi.org/10.1037/edu0000332 .

Daniel, S. S., Walsh, A. K., Goldston, D. B., Arnold, E. M., Reboussin, B. A., & Wood, F. B. (2006). Suicidality, school dropout, and reading problems among adolescents. Journal of Learning Disabilities, 39 (6), 507–514. https://doi.org/10.1177/00222194060390060301 .

Cosentino de Cohen, Deterding, C. N., & Clewell, B. C. (2005). Who’s left behind? Immigrant children in high and low LEP schools. Urban Institute (NJ3) .

*Ehri, L. C., Dreyer, L. G., Flugman, B., Gross, A. (2007). Reading rescue: an effective tutoring intervention model for language-minority students who are struggling readers in first grade. American Education Research Journal , 44 , 414-448. https://doi.org/10.3102/2F0002831207302175 , 2

Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2018). Learning disabilities: from identification to intervention . Guilford Publications.

*Foorman, B. R., Herrera, S., & Dombek, J. (2018). The relative impact of aligning tier 2 intervention materials with classroom core reading materials in grades K-2. The Elementary School Journal , 118 , 477-504. https://doi.org/10.1086/696021 , 3

Francis, D. J., Shaywitz, S. E., Stuebing, K. K., Shaywitz, B. A., & Fletcher, J. M. (1996). Developmental lag versus deficit models of reading disability: a longitudinal, individual growth curves analysis. Journal of Educational Psychology, 88 (1), 3–17. https://doi.org/10.1037/00220663.88.1.3 .

Fry, R., & Gonzales, F. (2008). One-in-five and growing fast: a profile of Hispanic public school students. Pew Research Center.

Fuchs, D., Fuchs, L. S., Al Otaiba, S., Thompson, A., Yen, L., McMaster, K. N., Svenson, E., & Yang, N. J. (2001). K-PALS: Helping kindergartners with reading readiness: teachers and researchers in partnerships. Teaching Exceptional Children, 33 (4), 76–80. https://doi.org/10.1177/2F004005990103300411 .

Gersten, R., Haymond, K., Newman-Gonchar, R., Dimino, J., & Jayanthi, M. (2020). Meta-analysis of the impact of reading interventions for students in the primary grades. Journal of Research on Educational Effectiveness, 13 (2), 401–427. https://doi.org/10.1080/19345747.2019.1689591 .

Gottardo, A., Mirza, A., Koh, P. W., Ferreira, A., & Javier, C. (2018). Unpacking listening comprehension: the role of vocabulary, morphological awareness, and syntactic knowledge in reading comprehension. Reading and Writing, 31 (8), 1741–1764. https://doi.org/10.1007/s11145-017-9736-2 .

Grant, A., Gottardo, A., & Geva, E. (2011). Reading in English as a first or second language: the case of grade 3 Spanish, Portuguese, and English speakers. Learning Disabilities Research & Practice, 26 (2), 67–83.

Greenberg, E., Dunleavy, E., & Kutner, M. (2007). Literacy behind bars: results from the 2003 national assessment of adult literacy prison survey. NCES 2007-473. National Center for Education Statistics.

Hall, C., Roberts, G. J., Cho, E., McCulley, L. M., Carroll, M., & Vaughn, S. (2017). Reading instruction for English language learners in the middle grades: a synthesis of the research. Educational Psychology Review, 29 (4), 763–794. https://doi.org/10.1007/s10648-016-9372-4 .

Hedges, L. V. (1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6 (2), 107–128.

Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods, 1 (1), 39–65. https://doi.org/10.1002/jrsm.5 .

Hernandez, D. J. (2011). Double jeopardy: how third-grade reading skills and poverty influence high school graduation . Annie E. Casey Foundation. http://www.aecf.org/m/resourcedoc/AECF-Double-Jeopardy-2012-Full.pdf

Hernandez, D. J., Denton, N. A., & Macartney, S. E. (2008). Children in immigrant families: looking to America’s future. Society for Research in Child Development, 22 , 1–24. https://doi.org/10.1002/j.23793988.2008.tb00056.x .

Hussar, B., Zhang, J., Hein, S., Wang, K., Roberts, A., Cui, J., Smith, M., Bullock Mann, F., Barmer, A., & Dilig, R. (2020). The condition of education 2020 (NCES 2020-144). U.S. Department of Education . National Center for Education Statistics Retrieved March 1, 2020, from https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2020144 .

Hutchinson, J. M., Whiteley, H. E., Smith, C. D., & Connors, L. (2004). The early identification of dyslexia: children with English as an additional language. Dyslexia, 10 (3), 179–195. https://doi.org/10.1002/dys.275 .

Institute of Education Sciences. (2020). What Works Clearinghouse standards handbook version 4.1. Retrieved from https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-Standards-Handbook-v4-1-508.pdf

Irby, B. J., Lara-Alecio, R., Quiros, A. M., Mathes, P., & Rodriguez, L. (2004). English Language and Literacy Acquisition evaluation research program (Project ELLA): Second annual evaluation report. U.S. Department of Education, Institute for Educational Sciences.

Irby, B. J., Tong, F., Lara-Alecio, R., Mathes, P. G., Acosta, S., & Guerrero, C. (2010). Quality of instruction, language of instruction, and Spanish-speaking English language learners’ performance on a state reading achievement test. Texas Association for Bilingual Education, 12 , 1–42.

Kieffer, M. J., & Lesaux, N. K. (2012). Development of morphological awareness and vocabulary knowledge in Spanish-speaking language minority learners: a parallel process latent growth curve model. Applied PsychoLinguistics, 33 (1), 23–54. https://doi.org/10.1017/S0142716411000099 .

Lakeshore Learning Materials. (1997). Question of the day. Author.

Leafstedt, J. M., Richards, C. R., & Gerber, M. M. (2004). Effectiveness of explicit phonological-awareness instruction for at-risk English learners. Learning Disabilities Research & Practice, 19 (4), 252–261. https://doi.org/10.1111/j.1540-5826.2004.00110.x .

Lemons, C. J., Fuchs, D., Gilbert, J. K., & Fuchs, L. S. (2014). Evidence-based practices in a changing world: reconsidering the counterfactual in education research. Educational Researcher, 43 (5), 242–252. https://doi.org/10.3102/2F0013189X14539189 .

Lesaux, N. K., Rupp, A. A., & Siegel, L. S. (2007). Growth in reading skills of children from diverse linguistic backgrounds: findings from a 5-year longitudinal study. Journal of Educational Psychology, 99 (4), 821–834.

Liberatti, A., Altman, D. G., Tetzlaff, J., Mulrow, C., Gotzsche, P. C., Ioannidis, J., Clarke, M., Devereaux, P. J., Kleijnen, J., & Moher, D. (2009). The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: explanation and elaboration. PLoS Medicine, 6 (10), 1–28. https://doi.org/10.1016/j.jclinepi.2009.06.006 .

Lipka, O., & Siegel, L. S. (2012). The development of reading comprehension skills in children learning English as a second language. Reading and Writing, 25 (8), 1873–1898. https://doi.org/10.1007/s11145-011-9309-8 .

Lovett, M. W., Frijters, J. C., Wolf, M., Steinbach, K. A., Sevcik, R. A., & Morris, R. D. (2017). Early intervention for children at risk for reading disabilities: the impact of grade at intervention and individual differences on intervention outcomes. Journal of Educational Psychology, 109 (7), 889–914. https://doi.org/10.1037/edu0000181 .

Ludwig, C., Guo, K., & Georgiou, G. K. (2019). Are reading interventions for English language learners effective? A meta-analysis. Journal of Learning Disabilities, 52 (3), 220–231. https://doi.org/10.1177/0022219419825855 .

Mathes, P. G., & Torgesen, J. K. (2005 ). Early interventions in reading , level 1 . SRA/McGraw-Hill.

*McMaster, K. L., Kung, H., Han, I., & Cao, M. (2008). Peer-assisted learning strategies: a “tier 1” approach to promoting English learners’ response to intervention. Exceptional Children , 74 , 194-214. https://doi.org/10.1177/001440290807400204 , 2

McNamara, J. K., Scissons, M., & Gutknecth, N. (2011). A longitudinal study of kindergarten children at risk for reading disabilities: the poor really are getting poorer. Journal of Learning Disabilities, 44 (5), 421–430. https://doi.org/10.1177/0022219411410040 .

Montgomery, J. (2007). Bridge of vocabulary. Pearson.

National Reading Panel. (2000). Report of National Reading Panel: teaching children to read . National Institute of Child Health and Human Development.

Nelson, J. R., & Vadasy, P. F. (2007). Early vocabulary connections: first words to know and decode. Sopris West.

*Nelson, J. R., Vadasy, P. F., & Sanders, E. A. (2011). Efficacy of a tier 2 supplemental root word vocabulary and decoding intervention with kindergarten Spanish-speaking English learners. Journal of Literacy Research , 43 , 184-211. https://doi.org/10.1177/1086296X11403088 , 2

O’Connor, R. E., Bocian, K. M., Beach, K. D., Sanchez, V., & Flynn, L. J. (2013). Special education in a 4-year Response to Intervention (RtI) environment: characteristics of students with learning disability and grade of identification. Learning Disabilities Research & Practice, 28 (3), 98–112. https://doi.org/10.1111/ldrp.12013 .

Phillips, B. (2014). Promotion of syntactical development and oral comprehension: development and initial evaluation of a small-group intervention. Child Language Teaching and Therapy, 30 (1), 63–77. https://doi.org/10.1177/0265659013487742 .

Proctor, C. P., Carlo, M., August, D., & Snow, C. (2005). Native Spanish-speaking children reading in English: toward a model of comprehension. Journal of Educational Psychology, 97 (2), 246–256. https://doi.org/10.1037/0022-0663.97.2.246 .

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/

Richards-Tutor, C., Baker, D. L., Gersten, R., Baker, S. K., & Smith, J. M. (2016). The effectiveness of reading interventions for English learners: a research synthesis. Exceptional Children, 82 , 144–169. https://doi.org/10.1177/0014402915585483 .

Risher, Tipton and Zhipeng (2017). robumeta: robust variance meta regression. R package version 2.0. https://CRAN.R-project.org/package=robumeta

Samson, J. F., & Lesaux, N. K. (2009). Language-minority learners in special education: rates and predictors of identification for services. Journal of Learning Disabilities, 42 (2), 148–162. https://doi.org/10.1177/0022219408326221 .

Scammacca, N. K., Roberts, G., Vaughn, S., & Stuebing, K. K. (2015). A meta-analysis of interventions for struggling readers in grades 4–12: 1980–2011. Journal of Learning Disabilities, 48 (4), 369–390. https://doi.org/10.1177/0022219413504995 .

Scammacca, N. K., Roberts, G. J., Cho, E., Williams, K. J., Roberts, G., Vaughn, S. R., & Carroll, M. (2016). A century of progress: reading interventions for students in grades 4–12, 1914–2014. Review of Educational Research, 86 (3), 756–800. https://doi.org/10.3102/0034654316652942 .

Slavin, R. E. (1986). Best-evidence synthesis: an alternative to meta- analytic and traditional reviews. Educational Researcher, 19 , 141–162 jstor.org/stable/42900104 .

Slavin, R. E., & Lake, C. (2008). Effective programs in elementary mathematics: a best-evidence synthesis. Review of Educational Research, 78 (3), 427–515. https://doi.org/10.3102/0034654308317473 .

Slavin, R. E., & Smith, D. (2009). The relationship between sample sizes and effect sizes in systematic review in education. Educational Evaluation and Policy Analysis, 31 (4), 500–506. https://doi.org/10.3102/2F0162373709352369 .

Slavin, R. E., Cheung, A., Groff, C., & Lake, C. (2008). Effective reading programs for middle and high schools: a best-evidence synthesis. Reading Research Quarterly, 43 (3), 290–322. https://doi.org/10.1598/RRQ.43.3.4 .

Slavin, R. E., Madden, N. A., Chambers, B., & Haxby, B. (2009). 2 million children: Success for All (2nd ed.). Corwin Press.

Sullivan, A. L. (2011). Disproportionality in special education identification and placement of English language learners. Exceptional Children, 77 (3), 317–334. https://doi.org/10.1177/2F001440291107700304 .

Tipton, E. (2015). Small sample adjustments for robust variance estimation with meta-regression. Psychological Methods, 20 (3), 375–393. https://doi.org/10.1037/met0000011 .

Tong, F., Irby, B. J., Lara-Alecio, R., & Mathes, P. G. (2008a). English and Spanish acquisition by Hispanic second graders in developmental bilingual programs: a 3-year longitudinal randomized study. Hispanic Journal of Behavioral Sciences, 30 (4), 500–529. https://doi.org/10.1177/0739986308324980 .

Tong, F., Lara-Alecio, R., Irby, B., Mathes, P., & Kwok, O. (2008b). Accelerating early academic oral English development in transitional bilingual and structured English immersion programs. American Educational Research Journal, 45 (4), 1011–1044. https://doi.org/10.3102/2F0002831208320790 .

Tong, X., Deacon, S. H., & Cain, K. (2014). Morphological and syntactic awareness in poor comprehenders: another piece of the puzzle. Journal of Learning Disabilities, 47 (1), 22–33. https://doi.org/10.1177/2F0022219413509971 .

Torgesen, J. K. (2002). The prevention of reading difficulties. Journal of School Psychology, 40 (1), 7–26. https://doi.org/10.1016/S0022-4405(01)00092-9 .

*Vadasy, P. F. & Sanders, E. A. (2010). Efficacy of supplemental phonics-based instruction for low-skilled kindergarteners in the context of language minority status and classroom phonics instruction. Journal of Educational Psychology , 102 , 786-803. https://doi.org/10.1037/a0019639 , 4

*Vadasy, P. F. & Sanders, E. A. (2011). Efficacy of supplemental phonics-based instruction for low-skilled first graders: how language minority status and pretest characteristics moderate treatment response. Scientific Studies of Reading , 15 , 471-497. https://doi.org/10.1080/10888438.2010.501091 , 6

Vadasy, P., & Sanders, E. (2012). Two-year follow-up of a kindergarten phonics intervention for English learners and native English speakers: contextualizing treatment impacts by classroom literacy instruction. Journal of Educational Psychology, 104 (4), 987–1005. https://doi.org/10.1037/a0028163 .

Vadasy, P., Sanders, E., & Peyton, J. (2006). Code-oriented instruction for kindergarten students at risk for reading difficulties: a randomized field trial with paraeducator implementers. Journal of Educational Psychology, 98 (3), 508–528. https://doi.org/10.1037/0022-0663.98.3.508 .

Vadasy, P., Sanders, E., & Abbott, R. (2008). Effects of supplemental early reading intervention at 2-year follow up: reading skill growth patterns and predictors. Scientific Studies of Reading, 12 (1), 51–89. https://doi.org/10.1080/10888430701746906 .

*Vaughn, S., Cirino, P. T., Linan-Thompson, S., Mathes, P. G., Carlson, C. D., Cardenas-Hagen, E., Pollard-Durodola, S. D., Fletcher, J. M., & Francis, D. J. (2006a). Effectiveness of a Spanish intervention and an English intervention for English-language learners at risk for reading problems. American Educational Research Journal , 43 , 449-487. https://doi.org/10.3102/2F00028312043003449 , 3

*Vaughn, S., Mathes, P., Linan-Thompson, S., Cirino, P., Carlson, C., Pollard-Durodola, S., Cardenas-Hagen, E., & Francis, D. (2006b). Effectiveness of an English intervention for first-grade English language learners at risk for reading problems. The Elementary School Journal , 107 , 153-180. https://doi.org/10.1086/510653 , 2

Vaughn, S., Elbaum, B. E., Wanzek, J., Scammacca, N., & Walker, M. A. (2014). Code sheet and guide for education-related intervention study syntheses . The Meadows Center for Preventing Educational Risk.

Ventriglia, L., & González, L. (2000). Santillana Intensive English. Santillana USA.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36 (3), 1–48 http://www.jstatsoft.org/v36/i03/ .

Wanzek, J., Vaughn, S., Scammacca, N., Gatlin, B., Walker, M. A., & Capin, P. (2016). Meta-analyses of the effects of tier 2 type reading interventions in grades K-3. Educational Psychology Review, 28 (3), 551–576.

Wanzek, J., Stevens, E. A., Williams, K. J., Scammacca, N., Vaughn, S., & Sargent, K. (2018). Current evidence on the effects of intensive early reading interventions. Journal of Learning Disabilities, 51 (6), 612–624. https://doi.org/10.1177/2F0022219418775110 .

Download references

Author information

Authors and affiliations.

Department of Teaching and Learning Sciences, Morgridge College of Education, The University of Denver, 1999 E. Evans Ave, Denver, CO, 80210, USA

Garrett J. Roberts, Brooke Coté & Jacklyn Van Ooyik

School of Education and Human Development, The University of Virginia, 417 Emmet Street South, P.O. Box 400273, Charlottesville, VA, 22904, USA

Department of Counseling, Educational Psychology, and Special Education, College of Education, Michigan State University, 620 Farm Lane, East Lansing, MI, 48824, USA

Department of Educational Psychology, The University of Texas at Austin, 1912 Speedway STE 504, Austin, TX, 78712, USA

Department of Research Methods and Information Science, Morgridge College of Education, The University of Denver, 1999 E. Evans Ave, Denver, CO, 80210, USA

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Garrett J. Roberts .

Additional information

Publisher’s note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

(PDF 164 kb)

Rights and permissions

Reprints and permissions

About this article

Roberts, G.J., Hall, C., Cho, E. et al. The State of Current Reading Intervention Research for English Learners in Grades K–2: a Best-Evidence Synthesis. Educ Psychol Rev 34 , 335–361 (2022). https://doi.org/10.1007/s10648-021-09629-2

Download citation

Accepted : 01 July 2021

Published : 10 July 2021

Issue Date : March 2022

DOI : https://doi.org/10.1007/s10648-021-09629-2

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Intervention
• Elementary school
• English language learner
• Best-evidence
• Find a journal
• Publish with us
• Track your research