Preschool Drawing and School Mathematics: The Nature of the Association

Abstract

The study examined the aetiology of individual differences in early drawing and of its longitudinal association with school mathematics. Participants (N = 14,760), members of the Twins Early Development Study, were assessed on their ability to draw a human figure, including number of features, symmetry and proportionality. Human figure drawing was moderately stable across six months (average r = .40). Individual differences in drawing at age 4½ were influenced by genetic (.21), shared environmental (.30) and non-shared environmental (.49) factors. Drawing was related to later (age 12) mathematical ability (average r = .24). This association was explained by genetic and shared environmental factors that also influenced general intelligence. Some genetic factors, unrelated to intelligence, also contributed to individual differences in drawing.

Drawing can fulfil different functions in children’s development, such as helping them to explore their ideas about the surrounding world, improve their spatial visualisation and orientation skills, and enable them to create visual representations of their thoughts and feelings (Brook, 2009). Drawing skills emerge during the second year of life and change significantly over the course of childhood (Braswell & Rosengren, 2008). Two year-old children already show some understanding of the link between intention, action and interpretation necessary for drawing production; and by the age of three to four children are able to apply this understanding to their drawings (Golomb, 1974).

A drawing can be described as having a dual nature: it is a thing in itself (e.g., a mark on a page), but also refers to a phenomenon in the internal or external world. To appreciate the dual nature of a picture, young children are required to flexibly adjust their thinking, for example conceiving objects in two ways simultaneously (Malchiodi, 2012). Cognitive flexibility, required for successful drawing, develops gradually, reaching appropriate levels around four years of age, when children start appreciating that pictures are representations of items as well as items themselves (Jolley, 2008). Drawing ability and cognitive flexibility continue to be positively related throughout childhood. For example, spatial drawing ability, the ability to use depth cues while reproducing a three-dimensional object, was found to be positively related (r = .35) to cognitive flexibility in 7 to 11 year-old children (Ebersbach & Hagedorn, 2011).

The notion that children’s drawing ability is linked to their cognitive development has been around for more than a century. Cooke (1885) was the first to describe the successive developmental stages of children’s drawing. His work was followed by that of Ricci, who published his theory on children’s drawing development in 1887 (Kamphaus & Pleiss, 1991). The scientific interest in children’s drawing reached its peak at the beginning of the 20th century, with studies finding links between drawing and intelligence (Kamphaus & Pleiss, 1991). Piaget incorporated drawing in his developmental learning theory describing it as an activity that indexed the child’s cognitive maturity (Brooks, 2009). Piaget described the developmental stages of drawing, arguing that drawing performance was emblematic of a child’s cognitive competence. The stage-like development of the drawing ability is also exemplified by the observation that children can progress to a more complex representational ability only once they can master a more basic representation (e.g., Karmiloff-Smith, 1990).

Early research into human figure drawing ability resulted in the development of two measures that assess performance based on whether the necessary features of the human body are present: Goodenough-Harris Draw-a-Person (DAP) Test (Harris, 1963) and the Draw-A-Child (DAC) Scale (McCarthy, 1972). Both the DAP and the DAC are considered valid and reliable instruments for measuring the ability to draw a human figure, and have been shown to correlate with general intelligence in children (Reynolds, 1978). The tests are fast and easy to administer, and have been shown to be suitable for administration cross-culturally (Naglieri and Bardos, 1987). Both tests include clear scoring guidelines for clinicians and have been used in clinical settings, including with nonverbal children (Kampaus & Pleiss, 1991).

However, recently the validity of using drawing tests as measures of cognitive ability and development has been challenged as only moderate relationships are observed between drawing and cognitive abilities (e.g., Willcock, Imuta & Hayne, 2011). For example, one study found a moderate positive correlation (.40) between performance in the Draw-A-Person test and measures of cognitive ability, such as the Wechsler Intelligence Scale in 5–6 year-old children (Willcock et al., 2011). In addition, very little is known about the stability of the observed drawing – intelligence relationship.

Moreover, the aetiology of individual differences in human figure drawing and of its association with general cognitive ability (g) remains poorly understood. Drawing ability is characterised by a consistent, universal and sequential progression, with very little influence from adults on drawing development (Kellogg 1969, in Brooks, 2009) - suggesting a genetically governed developmental process. However, individual differences in maturity of drawing are likely to be related to both, genetic and environmental factors. For example, drawing quality and timing of progression to a more advanced stage of the drawing ability have been shown to be at least partly related to parental involvement (Dunst & Gorman, 2009). To date only one study has looked at the aetiology of early human figure drawing ability and its relationship to later g (Arden, Trzaskowski, Garfield & Plomin, 2014). The study used data from the large longitudinal population based Twins Early Development Study (TEDS) and found human figure drawing ability to be moderately heritable (approximately .3) with environmental factors being largely of the nonshared type (approximately .5). No sex differences were found in the aetiology of the individual differences in human figure drawing ability: the same genetic and environmental factors were involved in differences among boys and differences among girls (Arden et al., 2014). The study also found that the relationship between early drawing and g at age 14 (r = .20) was 99% explained by genetic factors.

It is possible that early human figure drawing ability may be particularly related to specific aspects of cognitive development. Mathematical ability may be strongly related to drawing, both because it is linked to general cognitive ability and because of several specific features that mathematics may share with human figure drawing. For example, awareness of number of body features, proportionality, appropriate use of space and symmetry may all be specifically related to mathematical development.

As spatial ability has been found to be uniquely associated with mathematical ability (Rohde & Thompson, 2007), the spatial nature of drawing may mean that drawing and mathematics are related above and beyond their relationship with g. A large body of research has investigated the relationship between mathematics and spatial ability – the ability to produce, recall, store and modify images of objects (Lohman, 1996). Moderate correlations are consistently observed between mathematics and spatial ability across several measures, and this relationship appears to be universal; it has been observed in different cultures (e.g. Krajewski & Schneider, 2009; van Garderen, 2006; Wei, Yuan, Chen, & Zhou, 2012). The association has been observed at every level of proficiency; for example, one study found that mathematically gifted adolescents also excelled in spatial ability (Dark & Benbow, 1991). Furthermore, the observed overlap between mathematics and spatial ability cannot be fully explained by their relationship with g. One study of young adults found that spatial ability predicted mathematics achievement (R² = .13) after accounting for g (Rohde & Thompson, 2007). Support for the relationship between mathematics and spatial ability was also observed at the aetiological level (Tosto et al., 2014). Although both spatial and mathematical ability at age 12 were only moderately heritable (.27 and .43 respectively), the correlation between them (r = .43) was largely explained by shared genetic factors (60%), most of which were also associated with g.

Existing measures of human figure drawing ability, such as the McCarthy Scale (McCarthy, 1972), mainly focus on whether children’s drawings contain the necessary bodily features (e.g. one head, two arms, two legs etc.). Although valid and reliable, these measures might not be tapping into all of the cognitive skills involved in human figure drawing production. In fact, the relationship between early drawing and several other cognitive skills, such as spatial and mathematical abilities, might be revealed by other characteristics of children’s human figure drawing, including symmetry, proportionality, and the position of the drawing on the page. In order to overcome these limitations, we developed the Drawing Maturity Scale (DMS). The DMS explores eight aspects of early human figure drawing ability designed to tap into: (a) general cognitive development (emotionality, maturity of the lines, realism and developmental stage of the drawing); and (b) spatial cognition (symmetry, proportionality, position of the drawing on the page and percentage of the page that children used to produce their drawing. We hypothesize that both general and spatial features would be important for later mathematical development.

It is important to explore sex differences in early human figure drawing ability as they may be related to sex differences in mathematical ability. Previous research found mixed results in other cognitive domains, such as spatial and mathematical abilities. For most spatial and mathematical abilities no significant sex differences have been consistently found (Miller & Halpen, 2014). Some studies found a small female advantage in some aspects of the spatial domain, such as remembering object locations (e.g. Voyer et al., 2007). Males were found to show an advantage in other spatial tasks, such as 2D and 3D mental rotation (e.g. Voyer et al., 1995). As these latter abilities seem more closely related to drawing, we predict a small male advantage in the human figure drawing task.

The present study used the data on drawing ability at ages 4 and 4½ and mathematical ability at age 12 from children participating in the longitudinal TEDS study. Measures of g at age 4 and 12 were also available. We extended previous research on preschool drawing (Arden et al., 2014) by examining human figure drawing at 4½, approximately 6 months after the initial assessment, and by developing a new measure of human figure drawing ability, the DMS. The goal of this research was threefold as we investigated: (1) stability of human figure drawing over a six-month period in preschool boys and girls; (2) genetic and environmental aetiology of human figure drawing ability at age 4½; (3) the aetiology of the association between early drawing of the human figure and later mathematical abilities accounting for general intelligence. In addition, the large sample used in this study allowed us to investigate sex differences in early human figure drawing ability.

Method

Sample

The sample of the present investigation includes twins from the Twins Early Development Study (TEDS). All families with live twin births born in England and Wales between 1994 and 1996 were contacted by the Office of National Statistics on behalf of the study and over 15,000 families participated at first contact. Regular comparisons with the general population show that families in TEDS remain closely representative of the British population in socio-economic distribution, ethnicity and parental occupation (Oliver & Plomin, 2007). Informed, written consent was obtained from all of the families who agreed to take part in the study. TEDS focuses on investigating cognitive and behavioural traits across development. In 2014 all participants turned 18 and more than 8,000 twins remain actively involved in the study. More than 300 scientific papers have been published based on the TEDS data, and several spin-off projects have emerged from TEDS (for detailed information on TEDS see Haworth, Davis & Plomin, 2013). The N of participants, whose data were used in the present analyses, is reported separately for each measure in the Measures and Results sections.

Measures and Procedure

Human Figure Drawing Ability at age 4

The Draw-a-Man test (McCarthy, 1972) was administered separately to each twin (N = 14,580 – 4,999 MZ and 9,581 DZ twins) by their parents when they were four years old. Each child completed the drawing in the booklet provided to the family (one booklet per twin). All children were given the same instructions: ‘draw me a picture of a girl (or boy if the child was a male). Do the best that you can. Make sure that you draw all of her’. Parents were instructed to encourage the children in case they hesitated by saying things like: ‘you draw it all on your own, and I’ll watch you. Draw the picture any way you like, just do the best picture you can’. Parents were asked not to help the children by, for example, mentioning any missing body parts, and to make sure the child was finished with the drawing before putting the booklet away. The drawings were scored following the McCarthy’s standardized procedure (McCarthy, 1972) by trained raters. These scoring criteria are based on the presence and absence of certain features (body parts such as head, hair, trunk and arms) and require the rater to score each feature from 0, if the feature is absent, to 1, if the feature is depicted well. This created a maximum score of 12 for drawing ability at age 4.

Human Figure Drawing Ability at age 4½

When the twins were 4½, they completed a similar task -The Draw-a-Child test (McCarthy, 1972). This test was administered directly by experimenters during a home visit to a subset of twins (N = 1,517 – 559 MZ and 958 DZ). The instructions, scoring and coding procedure were the same as for the Draw-a-man task (McCarthy, 1972). The scores ranged from 0 to a maximum 16 for drawing ability at 4½.

In addition, the same drawings from a subsample of twins (N = 517 – 163 MZ and 354 DZ) were evaluated using The Drawing Maturity Scale (DMS, see Appendix S2) that was specifically created and validated for this study. DMS aims to complement the existing measures of human figure drawing ability that mainly focus on presence or absence of the main body parts. Other aspects of children’s drawings, such as emotionality, position on a page and symmetry, may also index the level of child’s cognitive competence. DMS was specifically developed for this study to evaluate such features. The development of the DMS involved three piloting phases and the present study represents a further step towards the validation of the measure (see Appendix S1 for details of the scale development and use). The DMS includes 8 items assessing emotionality, symmetry, maturity of lines, realism, proportionality, percentage of paper used, position of the drawing on the page and the developmental stage shown by the picture. The scale has good internal validity, with a Cronbach’s alpha of .86.

Mathematical ability at age 12

Teachers assessed twins’ mathematical ability on the basis of the UK National Curriculum for Key Stage 3 (Qualification and Curriculum Authority, 2003). Completed teacher questionnaires were received in the post. Teachers rated each child (N = 6,140 – 2,245 MZ and 3,895 DZ) on a 9-point scale, from 1 being very poor to 9 being exceptional performance. The scale corresponds to the National Curriculum levels of achievement that UK teachers use for assessing pupils. For example, most 12-year-old students are expected to achieve Level 4 in mathematics. Teachers assessed four aspects of mathematical ability: using and applying mathematics; numbers; shapes, space and measures; and handling data. Due to the high correlations between them (average r = .80; Oliver, Harlaar, Hayiou-Thomas, Kovas, Walker, Petrill, et al., 2004), the four aspects were collapsed into a composite score (Teacher-rated mathematics composite at age 12).

At age 12, mathematical ability was also assessed by means of an internet-based test battery, developed from the National Foundation for Educational Research (5–14) Mathematics Series (nFerNelson, 1999). The battery contained three subcomponents: understanding numbers, non-numerical processes and computation, and knowledge. Examples of questions include: (a) ‘Identify the missing number and type it into the appropriate box: 15 x 6 = 90; __ x 6 = 96’; and (b) the twins (N = 8,846 – 3,098 MZ and 5,348 DZ) were presented with the picture of a partly-shaded segmented circle, they were asked to identify which fraction corresponded to the shaded part out of 5 options. Due to the strong correlations between the three tests, the three subcomponents were combined into a Web-measured mathematics score at age 12 (for a detailed description of the measures see Kovas, Haworth, Petrill, and Plomin, 2007; for additional information on the reliability and validity of this measure see Haworth, Harlaar, Kovas, Davis, Oliver, et al., 2007).

We included both teacher-rated and web-measured mathematics at age 12 as they reflect, at least partly, different aspects of mathematical ability. Of relevance to drawing, a more global teacher- rating might reflect such specific characteristics as motivation and creativity.

General cognitive ability (g) at ages 4 and 12

General cognitive ability was derived using principal component analysis, separately at each age. At age 4, parents administered 2 non-verbal and 1 verbal test to their children (N = 15,123 – 5,209 MZ and 9,914 DZ). The nonverbal tests included: an oddity task asking the twins to select a matching pair out of three items (Bayley, 1993) and puzzles (Raven, Court, & Raven, 1996). The verbal cognitive test assessed vocabulary (Receptive Picture Vocabulary Test, based on the Peabody Picture Vocabulary Test Revised -PPVT-R; Dunn and Dunn, 1981). Scores from these three tests were combined with scores of the Parent Report of Children’s Abilities (PARCA; Saudino, Dale, Oliver, Petrill, Richardson et al., 1998). Parents reported on their children’s conceptual knowledge, syntax, expressive vocabulary, and abstract language. The PARCA shows good internal consistency (α = .74) and moderate to strong correlation (r = .55) with the Mental Development Index (MDI) of the second edition of the Bayley Scales of Infant Development (BSID-II; Oliver et al., 2002).

At age 12, g was measured (N = 7,280 – 2,696 MZ and 4,584 DZ) via two verbal tests: the Multiple Choice Information and Multiple Choice Vocabulary test (WISC-III-PI; Wechsler, 1992); and two non-verbal reasoning tests: the Picture Completion (WISC-III-UK; Wechsler, 1992) and Raven’s Standard and Advanced Progressive Matrices (Raven, Raven, & Court, 1998).

Results

Descriptive statistics for all variables are presented in Table 1. All variables met the criteria for normal distribution. Only one twin out of each pair was randomly selected for phenotypic analyses in order to account for non-independence of observation (i.e. the fact that the children are twins).

Table 1.

Descriptive statistics for all standardized variables and raw scores for the drawing measures.

Variable	M	SD	Min	Max	Skewness	Kurtosis	N*
Draw 4	.00	1.01	2.47	1.89	−.65	.006	7290
Draw 4 raw score	6.71	2.88	0	12	−.70	.032	7290
Draw 4½	−.01	1.01	1.88	2.35	−.33	−.50	758
Draw 4½ raw score	6.89	3.91	0	16	−.31	−.62	758
DMS	−.06	.99	2.38	2.05	−.22	−.63	258
DMS raw score	24.17	6.67	9.33	38.00	−.27	−.63	258
Teacher Maths 12	−.02	.93	2.67	2.89	−.02	.22	3070
Web Maths 12	.03	.95	2.96	1.83	−.76	.10	4423
g 4	.02	.96	3.00	2.66	−.40	−.89	7561
g 12	.01	.98	2.86	2.76	−.37	−.19	3640

Note: The variables were standardized on the whole sample and then one twin out of each pair was selected for further analysis in order to control for non-independence of observation. The means and standard deviations were estimated after excluding outliers. Deviations of means and standard deviations from 0 and 1 respectively are a result of this selection; draw = drawing score; DMS = Drawing Maturity Scale score; Teacher Maths 12 = teacher ratings of mathematics at age 12; Web Maths 12 = mathematics web test total score age 12; g = general cognitive ability;

^*One twin out of each air was selected to account for non-independence of observation. We utilised all data available for each measure. The small N for the 4½ drawing measure and for the DMS measure is based on the in-home data collection wave that involved only a subsample of the Twins Early Development Study (TEDS).

Gender differences in drawing ability

Three Univariate between-subjects ANOVAs were carried out on raw scores of one twin from each pair to identify potential sex differences in performance across the three drawing variables (Drawing at age 4, Drawing at age 4½, and the Drawing Maturity Scale at age 4½). We found that girls outperformed boys on all measures of human figure drawing (see Table S4 in Appendix S3). Sex differences were significant (p < .001), with sex explaining between 4 and 7% of the variance in drawing ability. Levene’s test showed that variances were comparable.

Despite these average sex differences, we did not expect sex differences in the aetiology of individual differences in human figure drawing. Differences between groups may stem from different factors from those affecting individual differences within groups (see Kovas, Haworth, Dale, & Plomin, 2007). Previous research, applying a sex limitation model fitting to the human figure drawing data at age 4, found that the same genetic and environmental factors contributed to variation in drawing in boys and girls to the same extent (Arden et al., 2014).

Phenotypic associations

Correlations between measures of drawing, mathematics and g are shown in Table 2. Although the two drawing measures at 4½ assessed different aspects of human figure drawing ability (number of features vs. drawing maturity), the correlation between them was strong (.74). The correlation between Draw 4 and Draw 4½, and between Draw 4 and DMS 4½ were .35 and .50, respectively – suggesting moderate stability of drawing across approximately 6 months. The drawing measures correlated modestly with the measures of mathematics and g at ages 4 and 12.

Table 2.

Phenotypic correlations and number of participants (N)

	Draw4	Draw4½	DMS4½	MT 12	MW 12	g 4	g 12
Draw 4	1
Draw 4½	.35**	1
DMS 4½	.50**	.74**	1
MT12	.20**	.14**	.31**	1
MW12	.20**	.20**	.15**	.52**	1
g 4	.28**	.28**	.34**	.21**	.23**	1
g 12	.18**	.26**	.24**	.47**	.63**	.25**	1

Note:

^*p < .05,

^**p < .01 (two-tailed);

Drawing 4 = drawing score at age 4; Drawing 4½ = drawing score at age 4½; DMS 4½ = Drawing Maturity Scale scores; g 4 and 12 = general cognitive ability at age 4 and 12; MT12 = teacher-rated mathematics at 12; MW12 = web-measured mathematics at 12; N = only one twin out of each pair was randomly selected.

Predicting mathematical performance from human figure drawing maturity

Two separate linear regressions were carried out to examine the predictive power of human figure drawing at 4½, as measured by the DMS, specifically developed for the purpose of this study to capture mathematically relevant processes. We evaluated the prediction from drawing to: (1) teacher-rated mathematics at 12; and (2) web-measured mathematics at age 12. DMS at 4½ was a significant predictor of the two mathematical outcomes, explaining 12.3%, and 4.7% of the variance in teacher-rated and web-measured mathematics at 12, respectively.

The regressions were repeated, including a contemporaneous measure of g (at age 12) to assess whether DMS at 4½ had any specific association with later mathematics beyond a more general association with g. The results, reported in Table S4 (Appendix S3), show that drawing ability at 4½ measured with the DMS, remained a significant predictor of teacher-rated mathematics at 12 after accounting for g at the same age. The overall model was significant (F (2,105) = 21.312, p< .001, R² = .29). In contrast, general cognitive ability at 12 was the only significant predictor of web-assessed mathematics at 12 (F (2,141) = 46.041, p< .001, R² = .39).

The same regressions were run replacing the DMS with the McCarthy scale at 4 and 4½. The McCarty scale at age 4 was a significant predictor of the two measures of mathematics at age 12, explaining 3.8% of the variance in teacher-rated mathematics and 4.5% of the variance in web-measured mathematics. When g was included in the analyses, the McCarthy measure at age 4 remained a significant predictor of teacher rated and web-assessed mathematics at age 12, although g explained most of the variance. The McCarthy scale at age 4½ was a significant predictor of the two mathematical outcomes, explaining 1.9%, and 4.4% of the variance in teacher-rated and web-measured mathematics at age 12, respectively. After controlling for g, the McCarthy measure at age 4½ was not a significant predictor of later mathematical ability. The results suggest that most of the longitudinal association between early human figure drawing measures and later mathematical ability is not unique to mathematics, but rather reflects the stability of general cognitive ability. The DMS scale, developed specifically to tap into mathematically relevant abilities, was largely not uniquely related to mathematics at age 12, as most of the variance in the association between drawing at 4½ and mathematics at age 12 was also shared with g at 12.

Genetic and environmental aetiology of individual differences in human figure drawing ability at 4½

Comparing similarities between monozygotic (MZ) and dizygotic (DZ) twins allows for an estimation of the relative contribution of genetic and environmental factors to individual differences in a given trait (Rutter, 2006). The ACE model allows us to assess the proportion of the variance in a phenotypic trait that is explained by additive genetic (A), shared environment (C) and non-shared environment (E) by comparing the similarity between MZ twins, who share 100% of their genes, and DZ twins, who on average share 50% of their segregating genes. Consequently, the ACE model posits that similarities between MZ twins for a specific trait could be explained by shared genetic and/or common environmental factors, whereas differences between MZ twins are due to non-shared environmental factors and measurement error. On the other hand, differences between DZ twins could be due not only to non-shared environmental influences and measurement error, but also to their genetic differences (Rijsdijk & Sham, 2002). Genetic influence can be estimated by comparing intraclass correlations for MZ and DZ twins. A greater similarity between MZ twins than between DZ twins for a specific trait indicates a degree of genetic influence on the variance of that specific trait. Heritability, the amount of variance in a trait that can be attributed to genetic variance, can be calculated as double the difference between the MZ and DZ twin correlations.

The univariate ACE model fitting analysis is a more comprehensive way of estimating the proportion of phenotypic variance that can be attributed to genetic and environmental factors. As opposed to the estimates that can be derived from cross-twin correlations, model fitting allows us to assess the goodness of fit of the model including the latent variables A, C and E, by comparing it to the saturated model (which is the model based on the observed data), and to more parsimonious models (e.g. models only including the latent factors A and E, or A and C, or only the latent factor E). Models are usually compared using maximum likelihood, Akaike Information Criterion (AIC), or Bayesian Information Criterion (BIC). The univariate model also estimates confidence intervals for all parameters (see Plomin, DeFries, Knopik & Neiderhiser, 2013 for details of the twin methodology; see Neale, Boker, Bergeman & Maes, 2005 for the model fitting procedures). We conducted the univariate ACE model-fitting analysis to assess the aetiology of individual differences separately in each measure. The results of these analyses are presented in Table S6, with the exception of the results for human figure drawing ability (McCarthy measure) at age 4½, which are presented below.

As can be seen in Table 3, MZ correlations exceeded DZ correlations – indicating significant genetic influences on this ability. As the DZ correlations were more than half of the MZ correlations, significant shared environmental effects were also indicated. As MZ correlations were only about .5, about half of the variance in drawing was explained by non-shared (individual-specific) factors, which also include measurement error.

Table 3.

Intraclass correlations, ACE estimates and fit indices for drawing at age 4½

	rMZ (95% CI)	rDZ (95%CI)
Drawing age 4 ½	.52 (.43-.60) 279	.38 (.30-.46) 478
ACE Estimates	A	C	E
	.21 (.09 – .41)	.30 (.30 – .45)	.49 (.21 – .58)
Goodness of fit indices for drawing at 4 ½ (McCarthy measure)
	-2LL	AIC	BIC
Saturated Model	4138.84	1112.84	−9379.98
ACE Model	4144.92	1106.92	−9427.51

Note: Drawing age 4½ = as measured by McCarthy Scale; rMZ = intraclass correlation for monozygotic twins; rDZ = intraclass correlation for dizygotic twins; 95% CI = 95% confidence intervals; both same sex and opposite sex DZ twin pairs were included in the analyses; a smaller, more negative, Bayesian Information Criteria (BIC) indicates better fit.

The model fitting analysis showed that genetic factors explained 21% of the variance in drawing ability at age 4½. Shared and non-shared environment explained 30% and 49% of the variance respectively. These results are highly similar to previous results from the TEDS sample at age 4 (Arden et al., 2014).

Aetiology of the relationship between early human figure drawing ability and school mathematics at 12

The univariate method can be extended to assess the aetiology of the covariation between variables. We used the trivariate Cholesky decomposition model (Neale et al., 2005) to examine to what extent common genetic and environmental influences explained the correlations between our three variables of interest: drawing, mathematics and g. The Cholesky model decomposes phenotypic variance and covariance between traits into common and independent genetic (A), shared environmental (C) and non-shared environmental (E) sources of variance and covariance (e.g. Wang et al., 2014). The model works similarly to a hierarchical regression analysis, as the independent contribution of a predictor variable to the dependent variable is estimated after accounting for the variance it shares with other predictors (Luo, Kovas, Haworth, & Plomin, 2011).

Table 4 reports cross-twin cross-trait correlations for each pair of variables. Cross-twin cross-trait correlations describe the association between two variables, with twin 1 score on variable 1 correlated with twin 2 score on variable 2. Cross-twin cross-trait correlations were calculated separately for MZ and DZ twins. A higher cross-twin cross-trait correlation for MZ than for DZ twins indicates that genetic factors have a degree of influence on the phenotypic relationship between the two traits. For example, the correlation between g for twin 1 and drawing for twin 2 is .28 for MZ and .19 for DZ twins. The correlations were very similar when the traits were swapped for Twin 1 and Twin 2.

Table 4.

Cross-twin cross-trait correlations for the associations between g at age 4, drawing at age 4 and mathematics (both teacher-rated and web-measured) at age 12; and for the associations between the McCarthy measure of drawing at 4½, g at 4 and mathematics at 12.

Pairs of variables	rMZ	rDZ
g 4 & Drawing 4	.28	.19
g 4 & Maths T12	.16	.14
Drawing 4 & Maths T12	.22	.13
g 4 & Maths W12	.23	.18
Drawing 4 & Maths W12	.21	.15
g 4 & Drawing 4½	.23	.18
Drawing 4½ & Maths T12	.31	.09
Drawing 4½ & Maths W12	.27	.10

Note: g = general cognitive ability at 4; Drawing 4 = drawing score at 4 measured with the McCarthy Draw-a-man scale; MathsT12 = teacher ratings of mathematics at 12; MathsW12= Mathematics web test scores at 12; Drawing 4½ = drawing score at age 4½ measured with the McCarthy Draw-a-child scale.

Four separate trivariate models were run using the McCarthy drawing measure at age 4 and at 4½ and mathematics measures (teacher-rated and web-assessed) at age 12, with g at age 4 added to each model. The results of the analyses of the two drawing measures were similar overall, but, due to a sample size reduction, the measure that children completed at 4½ produced very wide confidence intervals. We therefore report only the two multivariate analyses run on drawing at age 4, for which the largest sample size was available.

The first model considered the trivariate association between g at age 4, human figure drawing at age 4 and teacher-rated mathematics at age 12. The best model to fit the data was selected on the basis of goodness of fit, as previously done for the univariate analysis. The full ACE model was found to be the best fit for the data (see Appendix S4, Table S7 for goodness of fit and standardized squared path estimates).

The results of the trivariate Cholesky decomposition, shown in Figure 1, indicate that the aetiology of g at age 4 was due largely to shared environmental factors (C1 = 62%), with moderate genetic influence (A1 = 24%) and a smaller portion of variance explained by non-shared environmental factors (E1 = 14%) that also include error. About 5% of the genetic factors (the path from A1 to drawing) and 4% of the shared environmental factors (the path from C1 to drawing) that influenced g also influenced individual differences in drawing at 4. Similarly, 3% and 2% of genetic and shared environmental factors, respectively, influenced both g at age 4 and teacher-rated mathematics at age12.

Figure 1.

Variation in mathematics at age 12 was explained by genetic (48%), shared environmental (31%), and non-shared environmental (21%) factors. For example, looking at the model in Figure 1, the heritability of teacher-rated mathematics at age12 can be obtained by adding up the estimates of all the paths linking the latent factors A to teacher-rated mathematics at age 12 (A1, A2 and A3 in this model). Therefore, the heritability of teacher-rated mathematics at age 12 is estimated at .48 (√.34 + √.11 + √.03 = √.48). The results also show that aetiology of the individual differences in mathematics at age12 is largely independent from that of general cognitive ability and drawing ability at age 4. The strongest influences on mathematics come from the latent factors A3 (34%), C3 (29%) and E3 (21%), which represent the proportion of genetic (A3), shared environmental (C3) and non-shared environmental (E3) variance in teacher-rated mathematics at 12 that is not shared with g and drawing at age 4. The latent factors A2, C2 and E2 indicate the proportion of the variance in the aetiology of mathematics at age12 that is shared with drawing at age 4, independent of g at age 4. As indicated by the path from latent variable A2 to mathematics at 12, 11% of the heritability of teacher-rated mathematics at 12 was shared with drawing but independent of g at age 4. As indicated by the path from the latent variable A1 to mathematics at 12, only 3% of the heritability of mathematics at age12 was shared with both drawing and g at age 4. Shared and non-shared environmental effects were largely specific to each trait. For example, the paths from latent variables E1 to drawing and mathematics; and from E2 to mathematics were non-significant.

Another way of looking at the aetiology of the interrelationship across the measures is to look at the genetic, shared environmental and non-shared environmental correlations between variables. From these estimates it is possible to derive the proportion of the phenotypic correlation between variables that can be attributed to genetic, shared and non-shared environmental influences. The proportion of the phenotypic correlation that can be attributed to genetic influences common to both variables is known as bivariate heritability. In the same way, bivariate shared environment is the proportion of the phenotypic correlation that can be attributed to shared environmental factors common to both variables. Finally, bivariate non-shared environment is the proportion of the phenotypic correlation that can be attributed to non-shared environmental factors common to both variables. Table 6 presents the pairwise phenotypic correlations among the three measures, which were overall modest (average .24). The table also presents genetic and environmental correlations. Average genetic correlation was moderate (.40) and average shared environmental correlation was modest (.28). The average non-shared environmental correlation was negligible (.04).

The bivariate heritability and environmentalities for each pairwise association were derived using the following formula: (√h² (draw) x √h² (maths) x r_G)/r_P for genetic effects; (√c² (draw) x √c² (maths) x r_C)/r_P for shared environment; and (√e² (draw) x √e² (maths) x r_E)/r_P for non-shared environment (see Table 5). The largest proportion of the modest phenotypic correlation (.24) between drawing at age 4 and teacher-rated mathematics at age 12 was explained by genetic factors (82%), with a smaller portion explained by shared environment (18%). The modest phenotypic association (.21) between g at age 4 and teacher-rated mathematics at age 12 was explained mostly by shared environment (56%) and genetic factors (40%), with a minor proportion explained by non-shared environmental influences (5%). The modest correlation (.28) between drawing and g at age 4 was explained mostly by shared environmental (56%) and genetic (38%) influences.

Table 5.

Phenotypic (r_P), genetic (r_G), shared (r_C) and non-shared environmental (r_E) correlations and bivariate heritability/environmentalities for the trivariate association between g at 4, drawing at age 4 and teacher-rated mathematics at age 12.

Variables	Bivariate h2 *	Bivariate c2	Bivariate e2
	&	&	&
	rG (95% CI)	rC (95% CI)	rE (95% CI)
g 4 & drawing rP = .28 (.27 – .30)	.38	.56	.06
	41(.30 – .53)	.40 (.33 – .47)	.07 (.03- .10)
g 4 & maths T12 rP = .21 (.18 – .24)	.40	.56	.04
	.25 (.12 – .37)	.27 (.17 – .37)	.06 (.04 – .13)
Drawing 4 & maths T12 rP = .24 (.21 – .26)	.82	.18	.00
	.53 (.37 – .70)	.16 (-.02 – .34)	.01 ( .08 – .04)

Note: g = general cognitive ability at age 4; drawing = drawing ability at age 4 measured with the McCarthy scale; maths T12 = teacher-rated mathematics at age 12; The phenotypic correlation estimates are slightly different from the correlations previously reported as these were obtained after the data was regressed for age and gender, as is standard practice in the data preparation for ACE model fitting;

^*Bivariate heritability/environmentalities = the proportion of the phenotypic correlation (r_P) explained by common genetic, shared and non-shared environmental factors.

Another model, out of the four Cholesky decompositions, examined the association between g at age 4, human figure drawing at 4 and web-assessed mathematics at 12 (see Appendix S5). Overall, results were consistent with those obtained for teacher-rated mathematics at age12. Individual differences in general cognitive ability at age 4, drawing ability at 4, and web-assessed mathematics at 12 were found to have largely different aetiology. Approximately 5% of the heritability of drawing at age 4 and 6% of the heritability of web-measured mathematics at age12 was due to genetic factors shared with g at age 4. Drawing at age 4 and web-measured mathematics at age 12 shared only 3% of their heritability beyond that already shared with g at age 4.

In addition to the four analyses, another trivariate Cholesky decomposition was run looking at the aetiology of the covariation between human figure drawing at age 4, g at age 12 and teacher-rated mathematics at age 12 (see Appendix S6). Results were consistent with those obtained when looking at the covariance between g at age 4, human figure drawing at age 4 and teacher-rated mathematics at age 12. Approximately 6% of the heritability of g at age 12 was due to genetic factors shared with drawing at age 4. Interestingly, around 12% of the heritability of teacher-rated mathematics at age 12 was due to genetic factors shared with drawing at age 4 that were not shared with g at age 12. Independently of drawing at age 4, g at age 12 and teacher-rated mathematics at age 12 shared 6% of their heritability.

Discussion

The aim of the present study was to investigate early human figure drawing ability in its relation to later mathematical ability. Specifically, we addressed three main questions: (1) the stability of drawing over six months in preschool boys and girls; (2) the aetiology of individual differences in human figure drawing ability at age 4½; and (3) the aetiology of the longitudinal relationship between preschool drawing, school mathematics and g (measured at age 4 and 12).

Human figure drawing ability was found to be reasonably stable from 4 to 4½ years of age (average r = .42). Human figure drawing ability at age 4 was measured with the McCarthy Draw-a-man scale (1972); human figure drawing ability at 4½ was measured using the McCarthy Draw-a-child scale (1972), as well as the Drawing Maturity Scale (DMS) developed specifically for the purpose of this investigation. The relationship between the two drawing measures reflects the stability of individual differences in drawing performance over development and also demonstrates the validity of the new DMS scale. Although six months seems a short period, it is a large portion of a child’s life at this age, with several stages happening during this time in the development of drawing production (Malchiodi, 2012).

To our knowledge this study is the first to test the stability of human figure drawing ability longitudinally in a large representative sample. In fact, research findings on drawing development are too often limited by small sample sizes that lack adequate power to allow longitudinal analyses. Furthermore, our sample was homogeneous in age (all children were close to 4 and 4½ when tested); this is often not the case in the drawing literature, which is characterized by large age ranges. Large age gaps between participants are particularly problematic if the aim is to assess drawing development during childhood, as drawing production changes significantly over a relatively short developmental time.

Our large sample also allowed us to explore sex differences in human figure drawing ability with sufficient power. We found that sex differences in drawing performance explained between 4% and 7% of the variance in human figure drawing ability at age 4 and at age 4½, with girls scoring higher than boys at both ages and across the three measures (McCarthy Draw-a-man, McCarthy Draw-a-child and DMS). However, the aetiology of individual differences was the same for boys and girls, as suggested by findings from a previous study that ran sex limitation models on the same drawing data at age 4 (Arden et al., 2014). This is in line with a previous investigation of into the aetiology of spatial ability and its relationship with mathematics that found no gender differences in the aetiology of both abilities (Tosto et al., 2014).

The strong correlation observed between the two measures of human figure drawing ability at age 4½ (r = .74) suggests that the newly developed DMS scale is a valid instrument to measure individual differences in drawing performance in preschool children. The observed association between the DMS and the McCarthy Draw-a-child scale at 4½ partly reflects general cognitive ability. The association between drawing ability and g was found to be largely stable from age 4½ (average r = .30) to age 12 (average r = .25). This corroborates previous findings of a stable association between drawing at 4 and g at 14 (Arden et al., 2014) and extends it to another measure of human figure drawing ability (i.e. McCarthy measures as well as the DMS).

Similarly, the results on the aetiology of individual differences in early human figure drawing ability at age 4½, were in line with those previously obtained with a sample of 4-year-old twins (Arden et al, 2014): genetic (21%) and shared environmental (30%) influences were modest and non-shared (child specific) environmental influences explained the larger portion (49%) of the variance in drawing ability at 4½. However, a proportion of this variance could be due to error of measurement, as non-shared environmental effects include measurement error (Plomin, 2011), which is an important consideration when assessing young children’s abilities.

A further main aim of this investigation was to explore the specificity of the drawing-mathematics association over development. When we examined the association at the phenotypic level, we found that most of the variance in the prediction from drawing at age 4½ to mathematical ability at age 12 was also shared with g. In fact, regression analyses showed that drawing at age 4½ measured using the McCarthy Draw-a-child scale did not remain a significant predictor of mathematical ability at age 12 (both teacher-rated and web-measured) after controlling for g at 12. The prediction from the DMS at age 4½, developed specifically to tap into the drawing-mathematics association, to teacher-rated mathematics at age 12 remained significant after accounting for g; however, g explained a large portion of their relationship. On the other hand, the prediction from the DMS to web-measured mathematics at age 12 was not significant beyond g at age12. Our results suggest that the relationship between human figure drawing and mathematics is not specific, and in fact mostly accounted for by general intelligence. These results are in line with previous findings demonstrating links between drawing ability and other cognitive abilities (Gottling, 1990).

The overall absence of a unique relationship between drawing and mathematics goes against our prediction. We developed the DMS to specifically tap into those aspects of human figure drawing that could be more closely related to spatial and mathematical development, such as the position of the drawing on the page and the proportionality of the drawing. In fact, as previously observed for spatial ability (e.g. Rohde & Thompson, 2007), we expected the relationship between human figure drawing ability at age 4½ measured with the DMS and mathematical ability at age 12 to extend beyond their association with g. This was only partly supported when considering the relationship between the DMS and teacher-rated mathematics at age 12.

The lack of specificity of the relationship between the DMS and the two mathematics outcomes might also reflect the broad range of skills assessed by this new measure of human figure drawing ability. We explored this issue further by examining the prediction from factor 2 of the DMS (assessing the position of the drawing on the page and the percentage of paper occupied by the drawing), hypothesizing that these features could be more reflective of later mathematics competence. However, after controlling for g, factor 2 of the DMS did not remain a significant predictor of mathematics at 12 (See Table S5). It is possible that other aspects of drawing, not examined by the DMS, may be specifically associated with mathematics performance. On the other hand, it is also possible that human figure drawing ability is associated with other aspects of mathematics performance, such as numerical magnitude comparison and number line estimation.

At the aetiological level, the observed associations between human figure drawing at age 4 and general cognitive ability contemporaneous to drawing and mathematics at age12, were explained by overlapping genetic and shared environmental effects. The results of the trivariate analyses, where g at age 4 was also included, showed that common genetic influences on early drawing and later mathematics include mostly factors in common with g. The genetic associations between drawing at age 4 and mathematics at age 12 were largely similar after accounting for g with an indication of a slightly stronger relationship for the teacher-rated measure.

Overall, the results are consistent with the ‘generalist genes’ account of learning abilities and disabilities that proposes that most of the genes implicated in cognitive abilities and academic achievement are general as opposed to specific to each domain (Plomin & Kovas, 2005). The account is grounded in the two concepts of pleiotropy (one gene affects many traits) and poligenicity (several genes influence one trait) and proposes that genetic influences on different abilities, as well as disabilities, overlap. Several studies using multivariate genetic analyses have found support for the generalist genes theory (e.g. Plomin & Kovas 2005; Kovas, Harlaar, Petrill, & Plomin, 2005). Additionally, studies using genome-wide complex trait analysis (GCTA, Yang, Benyamin, McEvoy, Gordon, Henders et al., 2010), a method that allows for the estimation of heritability of complex traits from DNA samples of unrelated individuals, have also found support for the generalist genes account. The genetic correlations between g and language, reading and mathematical abilities obtained using GCTA exceeded .70 (Trzaskowski, Davis, DeGries, Yang, Visscher & Plomin, 2013); these results, in line with findings from twin studies, indicate the pleiotropic effects of the genes implicated in the variation in cognitive abilities. Evidence in support for the generalist genes hypothesis also comes from molecular genetic research. For example, most of the single nucleotide polymorphisms (SNPs) associated with early reading ability were also found to be associated with aspects of mathematics and general cognitive ability as well as with other components of literacy (Haworth, Meaburn, Harlaar, & Plomin, 2007).

The links between human figure drawing, mathematics and g could be related to motor development. For example, drawing scores may reflect maturity of lines that in turn depend on motor skills; close links have been found between the development of cognitive and motor skills in non-clinical populations (e.g. Martin, Tigera, Denckla, & Mahone, 2010). Moreover, recent neuroimaging research suggests that partly overlapping cortical and subcortical brain regions are associated with the development of both general cognitive ability and motor skills (Pangelinan, Zhang, VanMeter, Clark, Hatfield, et al., 2011).

A number of studies have explored the relationship between cognitive and motor abilities in clinical populations (e.g. Davis, Pass, Finch, Dean, & Woodcock, 2009). In particular, children with spina bifida – a congenital neurodevelopmental disorder characterised by motor deficits – showed impairments in several aspects of mathematics performance, from counting to magnitude comparison (i.e. English, Barnes, Taylor, & Landry, 2009). It is possible that deficits in fine motor skills, including finger function and precision in upper limb control, in infants and toddlers with spina bifida place early constraints on those aspects of counting and simple arithmetic that are supported by pointing, touching and finger counting. Further research is needed into the relationship between drawing ability and mathematics in children characterised by restricted motor abilities over an extended developmental time.

A key strength of this study is its large longitudinal sample that allowed us to have sufficient statistical power to examine the stability of human figure drawing ability, gender differences in performance, the aetiology of human figure drawing ability and its longitudinal association (phenotypically and aetiologically) with g and mathematics. A second strength of this investigation is that our data were obtained from several sources (parental reports, teacher assessments, child performance on cognitive and mathematical ability tests, and child drawing evaluations by trained raters) – minimizing the possible biases of single source information.

Although the richness of our twin sample allowed for the in depth investigation of the drawing-mathematics relationship, the fact that the children in this sample are twins comes with a few limitations. In fact, twin studies are based on a number of assumptions. One of these assumptions is the idea that environmental similarity is the same for MZ and DZ twin pairs growing up in the same family (equal environments assumption). Although evidence suggests that MZ twins are more likely to experience similar environments than DZ twins (e.g. they tend to be treated more similarly, to more often share the same playmates etc.), sharing more environmental experiences was not found to impact on the degree of their phenotypic concordance (Kendler, Kessler, Neale, Heath, & Eaves, 1993). A second limitation, particularly relevant to the present study, is the fact that evidence suggests that twins might be at a slight disadvantage during gestation and early development if compared to singletons (Martin, Boomsma & Machin, 1997). Therefore, before these findings can be extended, replication in a general population is required. A further limitation of the present investigation was that the DMS ratings were only available on a relatively small subsample of the children. Further investigations with a larger sample is necessary to test the added value of this scale over the traditional ‘number of features’ assessments of early drawing. Overall, the present investigation of individual differences in preschool human figure drawing ability represents a step forward in our understanding of the mechanisms through which early drawing ability relates to the overall cognitive development.