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There has been growing interest in the links between reading and mathematics, both to
determine the factors contributing to individual differences in these domains and to better
understand why children with reading difficulties often have co-occurring difficulties with
mathematics. Much of this research has been hampered, however, by assessment issues. In
particular, studies of reading and mathematics have typically used only a single measure of
word decoding or a global measure, such as overall reading achievement. This is
problematic because word decoding skills (word recognition) are demonstrably distinct from reading comprehension (e.g., Nation & Angell, 2006), and thus may have different
relationships with mathematics. Clarifying the nature of the relationships among word decoding, reading comprehension and mathematics may provide a more solid understanding
of reading and mathematics development. In the present study, we sought to examine the
relationships among word decoding, reading comprehension and mathematics skill from
both phenotypic and genetic perspectives. We focus specifically on the middle school years.
Word decoding, reading comprehension, and mathematics
Word decoding and reading comprehension are robustly correlated during middle childhood
(e.g., Catts, Hogan, & Adlof, 2005; Betjemann, Willcutt, Olson, Keenan, DeFries &
Wadsworth, 2008). This makes intuitive sense: when word decoding skills are weak, words
are likely to be misidentified and fewer cognitive resources can be devoted to the processing
of meaning. Moreover, word decoding and reading comprehension draw on many of the
same skills, such as word knowledge, syntactic competence and verbal working memory.
Nonetheless, word decoding and reading comprehension are also dissociable. Word
decoding does not account for all of the variance in reading comprehension, indicating that
the ability to recognize words does not guarantee comprehension (e.g., Catts et al., 2005;
Cutting & Scarborough, 2006). In addition, the trajectories of word decoding and reading
comprehension differ, with word decoding being the focus of early reading, and reading
comprehension becoming more important once children have become relatively proficient at
word decoding (Verhoeven & van der Leeuwe, 2008).
The high but imperfect association between word decoding and reading comprehension has
led to growing recognition that the skills required for comprehending texts are partly distinct
from those required for word decoding (Oakhill, Cain, & Bryant, 2003). According to the
triangle model (Bishop & Snowling, 2004), word decoding depends on the ability to
recognize the systematic correspondences between letters and phonemes (phonological
processing), as well as exceptions to these regularities (orthographic knowledge). In learning
to read, children gradually apply these skills with greater speed and accuracy so that words
are recognized fluently and automatically. Reading comprehension, on the other hand,
depends substantially on listening comprehension skills that enable the reader to form a
coherent representation of the content of text (Rapp & van den Broek, 2005). For example,
the reader must be able to derive the meanings of individual words and sentences, determine
the key ideas or themes and make inferences to fill information that is implicit in text..
Against this background, the relationship of word decoding and reading comprehension to
mathematics is intriguing. There is robust evidence for a phenotypic relationship between
mathematics and reading, with studies reporting moderate to high correlations (~.24 to .62)
(e.g., Durand, Hulme, Larking, & Snowling, 2005; Hart, Petrill, Thompson, & Plomin,
2009; Hecht, Torgesen, Wagner, & Rashotte, 2001). In most cases, these studies have
focused on word decoding or global measures of reading, in conjunction with global
measures of mathematics or arithmetic. Similarly, there is substantial comorbidity between
difficulties in word reading and mathematics (e.g., Dirks, Spyer, van Lieshout, & de
Sonneville, 2008; Landerl & Moll, 2011). The overlap between reading and mathematics has
typically been attributed to language and working memory processes that are required for
both, such as phonological processing skills (e.g., de Smedt et al., 2010; Hecht et al., 2001),
We argue that it is equally important to determine the relation of reading comprehension to
mathematics. Recent evidence for a connection comes from Pimperton and Nation (2010),
who examined the mathematical profiles of poor comprehenders aged 7-8 years. These
children did not differ significantly from controls (matched for word decoding and
nonverbal ability) on a numerical operations task, but they performed at a significantly
lower level on a mathematical reasoning task. The authors argue that results from this study demonstrate that oral language may act as limiting factor on aspects of math that test
children’s abilities through verbally-presented items, irrespective of basic arithmetic skills.
The importance of language for mathematics is particularly relevant in the middle school
years. During this time, mathematical learning is principally concerned with developing
mathematical reasoning skills and mastering complex mathematical procedures (e.g., multi-
digit arithmetic) (Geary, 1994). These skills are typically taught and assessed using
mathematical texts, which pose several challenges (Freitag, 1997). First, they tend to be very
concise: each word and symbol must be read and understood with precision. Second, they
use a high density of information-bearing words, including ‘everyday’ words with new
meanings in mathematical contexts (e.g., product, odd, per). Third, mathematical texts often
contain more concepts per sentence than other content areas, and complex grammatical
processes are often used to compress complex ideas into just a few words (e.g., in “There is
an even number between 200 and 300 that is divisible by 5 and 9; what is that number?”,
divisible is shorthand for can be divided by). These characteristics place an onus on good
reading skills. They also directly raise the question of whether word decoding and reading
comprehension differ in their links with mathematics. To date, few studies have explicitly
examined this issue. In the present study, we examine the links among mathematics, word
decoding, and reading comprehension from a multivariate behavioral genetic perspective.
Behavioral genetic research on reading and mathematics
Multivariate behavioral genetic analysis decomposes the covariance among two or more
phenotypic (observed) traits into genetic and environmental effects. In the case of word
decoding and reading comprehension, we may expect that some of the genetic and
environmental factors that contribute to individual differences in one domain also overlap
with the other. Simultaneously, there may be sources of genetic and environmental variance
specific to each. Multivariate genetic research does not identify the specific genetic and
environmental factors involved, but it provides a window on the extent to which the
relationships among two or more variables are due to common genetic or common
environmental influences or both, which in turn may lead to new questions about the
processes by which reading and mathematics are associated.
Most quantitative genetic studies of reading and mathematics have used the twin design,
which takes advantage of the difference in genetic relatedness between monozygotic (MZ)
and dizygotic (DZ). Specifically, this design yields estimates of the proportion of variance
in the study population that is due to genetic and environmental influences. In general, twin
studies of word decoding and reading comprehension show substantial genetic effects that
are somewhat higher for word decoding (e.g., .68-.84) than for reading comprehension
(e.g., .51-.67) (e.g., Betjemann, Keenan, Olson, & DeFries, 2011; Betjemann et al., 2008;
Byrne et al., 2009; Byrne et al., 2007; Keenan, Betjemann, Wadsworth, DeFries, & Olson,
2006). For mathematical skills, genetic effects have varied widely, ranging from .20 to .90
(e.g., Hart, Petrill, & Thompson, 2010; Hart, Petrill, Thompson, & Plomin, 2009; Kovas,
Haworth, Petrill & Plomin, 2007; Polderman, Huizink, Verhulst, van Beijsterveldt,
Boomsma, & Bartels, 2011; Thompson, Detterman, & Plomin, 1991). Across both reading
and mathematics studies, shared (between-family) environmental effects have tended to be
small to moderate. All studies show nonshared (individual-specific) environmental effects
and measurement error.
Several studies have examined the etiological relationships among various reading or
mathematics ability tests. Typically these studies report genetic and environmental
correlations, which index the extent to which the genetic or environmental influences on one
trait correlate with those on a second trait. Genetic and environmental correlations can range from 1 (complete overlap) to 0 (no overlap). For reading, there is substantial genetic overlap
between word decoding and reading comprehension (e.g., Betjemann et al., 2011, 2008;
Byrne et al., 2007, 2009; Keenan et al., 2006). Furthermore, the magnitude of genetic
overlap decreases over time, consistent with evidence that word decoding and reading
comprehension correlate less highly as children move from an emphasis on word decoding
to reading comprehension (e.g., Byrne et al., 2007; Betjemann et al., 2008, 2011; Keenan et
al., 2006). The extent of environmental overlap is more difficult to determine: shared and
nonshared environmental correlations, as well as their confidence intervals, have varied
widely across studies. However, a majority of studies have reported substantial shared
environmental overlap (Betjemann et al., 2008, 2011; Keenan et al., 2006), and significant
nonshared environmental overlap between word decoding and reading comprehension
(Betjemann et al., 2008, 2011; Byrne et al., 2007, 2009). For mathematics, we are aware of
only one multivariate genetic study of different mathematical skills. In a sample of 10-year-
old twins (n = 1,250 pairs) from the Twins Early Development Study (TEDS), Kovas and
colleagues (2007) examined relationships among five mathematical tests: mathematical
application, numerical knowledge, computation skill, mathematical interpretation, and non-
numerical mathematical processes. These measures were almost perfectly correlated at a
genetic level (mean rA = .91). The substantial genetic correlation indicates that despite the
putative differences among mathematical tests used in this study, the same genes largely
affected individual differences in all five aspects of mathematics. Shared environmental
correlations were generally high (mean rC = .86; range = .61 - .99), but associated with
substantial confidence intervals; nonshared environmental correlations were generally
moderate (mean rE = .24; range = .13 - .35).
A few multivariate studies have examined reading and mathematics simultaneously.
Typically these have used general reading achievement test scores or composite scores,
rather than separate measures of word decoding and reading comprehension. In the TEDS
sample, genetic correlations between mathematics and reading were .75 at age 7 (Kovas,
Harlaar, Petrill, & Plomin, 2005), .57 at age 10 (Davis et al., 2008) and .75 at age 12 (Davis,
Haworth, & Plomin, 2009). Across these studies, shared environmental correlations were
substantial (close to 1.00), while nonshared environmental correlations ranged from .15 to .
59. An independent study of 6 to 12 year-old twins (n = 278 pairs) revealed a genetic
correlation of .98, shared environmental correlation of .92 and nonshared environmental
correlation of .28 between general measures of mathematics and reading achievement
(Thompson et al., 1991). Using a sample of 15 to 18-year-old Australian twins (n = 400
pairs), Wainwright et al. (2004) examined the relationships among arithmetic and two tests
of word decoding. The word decoding measures showed moderate genetic correlations with
arithmetic (mean rA = .56). No reading comprehension measures were available in this
study, however.
To our knowledge, only one study has considered the relationship among mathematics and
separate indicators of word decoding and reading comprehension. Hart et al. (2010)
examined word decoding accuracy, word decoding fluency, reading comprehension, and
mathematics in 9-year-old twins (n = 228 pairs). A single genetic latent factor was sufficient
to account for the genetic covariance among these four domains. The three reading factors
had high and similar loadings on the common genetic factor (above .80 for each), while the
loading for mathematics on the common genetic factor was smaller but significantly
different from zero (.45). Word decoding fluency and mathematics also showed factor-
specific genetic variance, independent of the common genetic factor. All four factors loaded
on a single common shared environmental factor, where loadings were moderate for word
decoding accuracy (.29), word decoding fluency (.29), and reading comprehension (.39), and
substantial for mathematics (.74). In contrast, there was little evidence for overlap at the
level of nonshared environmental factors These findings present an intriguing picture. Word decoding and reading comprehension are
substantially correlated at a phenotypic level, yet are also clearly distinct. Etiologically, they
show substantial genetic correlations and moderate or substantial environmental
correlations. The overlap between genetic and environmental factors across word decoding
and reading comprehension is not perfect, however, indicating that there are genetic and
environmental factors unique to both aspects of reading. It remains unclear whether word
decoding and reading comprehension are differentially related to mathematics. The results
of Hart et al. (2010) suggest that word decoding (whether assessed as accuracy or fluency)
and reading comprehension show similar etiological relationships with mathematics;
however, this is a single study.
The goal of the present study was to examine the etiology of the relationships among
mathematics, word decoding, and reading comprehension at age 12. Do genetic and
environmental associations between mathematics and reading vary depending on which
aspect of reading is being assessed – word decoding or reading comprehension? Because
multiple measures of reading and mathematics were available, we examined this question at
the level of latent factors. The use of latent variables in a genetically-sensitive design is
highly informative, because it enables us to focus on genetic and environmental influences
that contribute to variance in the target ability (as indexed by the common variance among
measures), independent of measure-specific variance and uncorrelated measurement error.
In addition, estimates of relationships involving latent variables are more reliable (Loehlin,
2004).

Overlap between mathematics and reading comprehension
The most important new finding from the current study is that word decoding and reading
comprehension were also differentially related to mathematics. This was indicated by the
phenotypic and genetic correlations with mathematics, which were significantly higher for
reading comprehension than for word decoding. In addition, we found evidence for a
nonshared environmental link between reading comprehension and mathematics,
independent of word decoding.
We suggest that the specific link between mathematics and reading comprehension likely
reflects the importance of executive function skills such as working memory, inhibition,
strategic planning, and goal-directed preparedness to act. Executive function is vital for
developing skills that require focused attention and practice to acquire competence (Best &
Miller, 2010). Planning and organization skills would appear especially important for
reading comprehension, and in fact they have been shown to be more strongly associated
with reading comprehension than with word decoding (e.g., Locascio, Mahone, Eason, &
Cutting, 2010; Sesma, Mahone, Levine, Eason & Cutting, 2009). Similarly, in the mathematics domain, complex executive function skills are more closely related to
mathematical reasoning tasks compared with other tasks (e.g., calculation) (Best, Miller, &
Naglieri, 2011). Individual differences in executive function skills are highly heritable (e.g.,
Friedman, Miyake, Young, DeFries, Corley, & Hewitt, 2008); thus the genetic overlap
between reading comprehension and mathematics may reflect genetic influences on
common executive function processes.
Our finding of partly differential genetic overlap for word decoding and reading
comprehension with mathematics is inconsistent with that of Hart et al. (2010). Our
Cholesky decomposition analysis indicated that the genetic loadings from the first genetic
factor were significantly higher for mathematics and reading comprehension than for word
decoding, whereas Hart et al. (2010) found that word decoding accuracy, word decoding
fluency, and reading comprehension had high and very similar loadings on a general genetic
factor that also influenced mathematics. Several factors may account for this discrepancy.
For example, twins in Hart et al. (2010) were approximately two years younger than twins in
the current study. Reading comprehension may have stronger links with mathematics in
early adolescence than earlier, reflecting developmental and education-based changes that
increasingly emphasize higher-level comprehension in both domains. There are also
noteworthy differences in the reading comprehension measures in the two studies. Our
measures, the PIATrc and GOAL, tapped both literal and inferential reading comprehension
skills, whereas the measures used by Hart et al. (2010), the PIATrc and the Passage
Comprehension Subtest of the Woodcock-Johnson Reading Mastery Test (Woodcock,
1987), primarily reflect literal comprehension. Inferential comprehension draws on higher-
level verbal reasoning processes, some of which are likely to also be important for
mathematics.