We investigated the extent to which genetic influences on mathematics performance also affect reading and g, as predicted by the generalist genes hypothesis. The results supported the generalist genes hypothesis in that the genetic correlations are 0.74 between mathematics and reading and 0.67 between mathematics and g. This finding implies that most of the genes that contribute to individual differences in mathematics ability also affect reading and g. Of course not all of the genetic effects are general: a third of the total genetic variance in mathematics is specific to mathematics. However, the more surprising finding is that most of the genetic action is general rather than specific to mathematics. That is, a common set of genes affects mathematics, reading and g. In addition, there are some genetic effects shared between mathematics and reading that are independent of g.
The results of the present study have several implications. The most straightforward implication is for molecular genetics: When the genes associated with any of these traits are identified, some of these genes will also be related to the other traits; and in the case of mathematics and reading, the overlap is expected to be very large. Finding generalist genes will facilitate research that attempts to understand the cognitive and brain systems responsible for the genetic overlap between mathematics, reading, and g.
One of the main reasons for such overlap is likely to be the complexity of these domains as assessed behaviorally. A great variety of non-specific abilities, such as long-term memory, working memory and attention are involved in mathematical ability as well as in reading and g. For example, if the ability to retrieve arithmetic facts and word meanings from long-term memory rely on the same mechanisms, comorbid mathematical and reading disabilities and correlated abilities should be expected. Phonological processing abilities and verbal IQ have also been implicated as a link between reading and mathematics in that they seem to explain most of the covariance between the two traits (e.g. Hecht et al., 2001
; Light et al., 1998
). Visuo-spatial ability, which has been implicated in at least some forms of mathematical disability (Geary, 2004
), may also be involved in some aspects of general cognitive ability. Although many brain and cognitive processes are likely to contribute to the phenotypic overlap among different cognitive abilities and g, the point of the present results is that the same set of genes is largely responsible for genetic influence in these seemingly diverse domains (for more discussion on this issue see Plomin & Kovas, in press
One might be tempted to say that what is in common between mathematics and reading is intelligence. However, our view is that this does not take us much farther in terms of understanding mechanisms because we do not know what the g factor is any more than we know what causes the general factor that pervades learning disabilities and abilities. It will be difficult to resolve these issues of the nature of the g factor and its relationship to learning disabilities and abilities at the behavioral or cognitive levels of analysis. As Spearman noted in 1927, ultimate understanding of the g factor “must needs come from the most profound and detailed direct study of the human brain in its purely physical and chemical aspects” (Spearman, 1927
p. 403). However, even the neural level of analysis cannot definitively disentangle causation from correlation because behavior can affect the brain as well as the brain affecting behavior. DNA is not subject to this direction of effects confusion—neural, cognitive and behavioral functioning does not change the structure of DNA. For this reason, we suggest that finding generalist genes associated with learning disabilities and abilities will be particularly useful in clarifying the nature of the g factor and its relationship to learning disabilities and abilities. Identifying these generalist genes will make it possible to investigate gene expression, proteomic and neural mechanisms by which these genes ultimately have their pleiotropic effects on learning disabilities and abilities as well as on the g factor (Plomin & Kovas, in press
It should be emphasized that our results also show some genetic specificity for mathematics performance. Again, many cognitive processes might mediate this effect. For example, research in cognitive psychology and neuropsychology has identified a specific ability to assess and compare approximate numerosities, which does not depend on the modality in which the numerical information is presented. This ability seems to be separate from formally learned aspects of mathematics, such as exact calculations (e.g. Russell & Ginsburg, 1984
; Xu & Spelke, 2000
). This number-processing ability appears to emerge in infants at a very early age is present in animals (Landerl, Bevan, & Butterworth, 2004
), and has specific parietal brain areas associated with it (e.g. Dehaene, Molko, Cohen, & Wilson, 2004
; Dehaene, Piazza, Pinel, & Cohen, 2003
). Another unique aspect of mathematics might be the ability to calculate small exact numerosities, which can also be demonstrated in infants (Xu, 2003
). These two processes have been shown to be differentiated in the brain (e.g. Dehaene et al., 2004
). It is possible that these abilities have etiologies unique to mathematics. Future research on the specificity of mathematics development will be facilitated by the use of more refined measures of mathematics, including tasks that have been specifically developed to assess ostensibly mathematics-specific processes such as calculation of approximate and exact small numerosities.
Another important implication of this study is the need to examine critically the role of environmental factors in the development of individual differences in mathematical ability. It should be emphasized that our finding of substantial heritability on individual differences in mathematics does not imply limited malleability of mathematical achievement overall. First, our results indicate that environmental influences are important—heritabilities are not 100%. However, environmental influences are largely not shared by children growing up in the same families and attending the same school. More generally, quantitative genetic results only describe genetic and environmental influences as they exist in a particular sample at a particular time. Even if a trait is highly heritable, a new environmental intervention such as a novel educational program, could have a major impact on children’s mathematics learning.
Moreover, finding that the salient environmental influences are nonshared has far-reaching implications for investigations of educationally relevant environments. It is commonly believed that environments, such as home environment and formal education, play an important role in shaping individual differences in mathematics and other cognitive abilities. In the field of educational psychology some environmental variables, such as aspects of classroom environment, teaching styles, and school environment, have been identified as significantly related to mathematical learning (e.g. Turner et al., 2002
). Although the present study does not implicate specific environments, the important feature of the results is the modest effects of shared aspects of both home and school environments. The results suggest that shared environmental influences account for less than 10% of variance in mathematical ability as assessed by the teachers. In addition, an important multivariate finding is that approximately 70% of these shared environmental influences are the same as those affecting reading. This is not surprising if we assume that at least some of the variance is due to teachers, since both reading and mathematics are taught by the same teacher at this age.
Interestingly, the kind of influences that make the two twins in the same family, school, and class different rather than similar were found to be mostly ability-specific in this study. In other words, what makes a child perform similarly across the domains is largely due to genetic influences; most environmental influences act in a way as to make a child perform differently across the domains. To date none of these domain-specific environmental influences have been discovered.
What are the implications of these findings for educational research and practice? One direction for research is to identify the nonshared environmental factors that are experienced differently by twins, even identical twins, even in the same classroom and that contribute to differences in children’s relative performances in mathematics and reading. In terms of genetics, we suggest that the generalist genes hypothesis has received such consistent support that it would be useful to begin to consider its implications for teaching mathematics and reading. The immediate reaction is likely to be to focus on the smaller group of children with specific impairments, for example, children with problems in learning mathematics but whose performance in reading and general cognitive ability is not impaired. However, in reading where specific reading disability has been a focus of research, the difficulties of such discrepancy models have been increasingly recognized (e.g. Fletcher, Francis, Rourke, Shaywitz, & Shaywitz, 1992
). The consistent support for the generalist genes hypothesis suggests that there is merit in focusing on what is in common between problems in reading and mathematics and their relationship with general cognitive ability. As noted earlier, investigation of the mechanisms responsible for this overlap will be facilitated when generalist genes are identified.
It should be noted that our environmental results may not generalize beyond the population of England and Wales. Most notably, having a common national curriculum as in the UK might lead to decrease in variation in mathematical ability, with the relative role of environment being smaller and the relative role of genetic influences being larger than in countries with different educational practices.
Potential assessment limitations of the present study should also be mentioned. It is important to demonstrate that the observed correlations between the traits are not due to the way the traits are measured. For example, if reading is necessary for the assessment of mathematics and general cognitive ability, then we would expect the traits to correlate simply for this reason. In our study, general cognitive ability was assessed over the telephone and reading was not involved in this assessment. Mathematics was assessed by teachers based on the pupil’s performance over the whole academic year, and it is unlikely that such measure can be seriously confounded by reading ability. Nonetheless, the use of teacher ratings for both mathematics and reading could inflate the overlap between them and with g if for example teachers’ ratings of mathematics and reading are influenced by their general impression of the children’s intelligence. For this reason, we are currently collecting data from children as well as teachers in order to directly test the validity of the teacher assessments and to enrich our findings.
To conclude, the study reported here has contributed to understanding the etiology of individual differences in mathematical ability by conducting the first multivariate genetic analysis using the data on mathematics, reading and general verbal and nonverbal cognitive ability from a large population-based sample of twins. The results of this study can be used to inform future multidisciplinary investigations in this area aimed to clarify the genetic and environmental mechanisms that underlie individual differences in mathematical cognition. A better understanding of these mechanisms will have important implications for mathematics education as well as diagnosis and prevention of mathematical learning disability.