Spatial ability as a predictor of math achievement: the importance of sex and handedness patterns

Development and Validation of a New Measure of Mental Rotation for Preadolescent and Adolescent Groups

Measurement of mental rotation presents a serious challenge to cognitive researchers owing to the lack of a single comprehensive measure that can be applied across the developing age groups. Objective of the present study was to develop and validate a new measure of mental rotation for preadolescent and adolescent age groups. Items were conceptualized and constructed based on existing theories. Study I checked the suitability of these items among preadolescent and adolescent age groups. After revisions, Study II was done to evaluate the item properties using item response theory. Subsequently done Confirmatory Factor Analysis provided evidence for the construct validity of the new measure. Finally, Study III was done to develop the age wise and gender wise norms for preadolescent and adolescent age groups. The newly developed measure was found to have sufficient reliability and validity and hence can be widely applied for measuring mental rotation of preadolescents and adolescents.

Mathematics Meets Science in the Brain

Mathematics and science are highly integrated disciplines, but the brain association between mathematics and science remains unclear. The current study used functional magnetic resonance imaging (fMRI) scans of 34 undergraduates (17 males, mean age = 20.3±1.64 years old) while they completed mathematical, physical and chemical principles, arithmetic computation, and sentence comprehension. We examined neural activation level, neural activation pattern, and neural connectivity to investigate the neural associations between mathematics and science (including physics and chemistry). The results showed that mathematical, physical, and chemical principles elicited similar neural activation level and neural activation pattern in the visuospatial network (mainly in the middle frontal gyrus and inferior parietal lobule), which were different from those elicited by sentence comprehension; those three principles also elicited similar neural activation level and neural activation pattern in the semantic network (mainly in the middle temporal gyrus, angular gyrus, inferior frontal gyrus, and dorsomedial prefrontal cortex), in contrast to that elicited by arithmetic computation. Effective connectivity analyses showed stronger connectivity between the middle temporal gyrus and inferior parietal lobule for mathematical, physical, and chemical principles than for sentence comprehension. The results suggest that visuospatial and semantic networks were critical for processing both mathematics and science.

Arithmetic in developmental cognitive disabilities

This paper reviews and discusses research on arithmetical strengths and weaknesses in children with specific developmental cognitive disabilities. It focusses on children with dyslexia, developmental language disorder, attention deficit hyperactivity disorder and autism. In general, studies show that arithmetical weaknesses are commoner in children with any of these disorders than in controls. Autism is sometimes associated with specific strengths in arithmetic; but even in autism, it is commoner for arithmetic to be a relative weakness than a relative strength. There may be some genetic reasons why there is an overlap between mathematical difficulties and other developmental learning difficulties; but much of the reason seems to be that specific aspects of arithmetic are often influenced by other factors, including language comprehension, phonological awareness, verbal and spatial working memory and long-term memory, and executive functions. The findings discussed here will be discussed in relation to Pennington's (2006) Multiple Deficit Model.

Assessment of executive function using the Tinkertoy test

The Tinkertoy test (TTT) has often been used to assess executive function. Despite its clinical importance, there are few published normative data for it. Thus, the primary aim of this study was to fill this gap. Moreover, as there exists a sex difference in many cognitive abilities and neuropsychological tests, a secondary aim was to examine whether sex influences TTT performance. We administered the TTT to 25 healthy men and 25 healthy women whose average age was 28 years. Performances were scored based upon Lezak's (1982) original TTT criteria. On average, our participants used 43 pieces to complete their construction (SD=8), with a range of 21-50, and their complexity scores ranged from 7 to 12, with a mean score of 9.68 (SD=1.35). Overall performance did not differ based on sex; yet, when examining individual scoring criteria, we found that men scored significantly higher on the symmetry measure. Efforts towards the development of adequate normative data for the TTT and different tests of executive functioning are crucial to neuropsychologists' and other healthcare providers' ability to reliably diagnose and treat disorders of cognition that affect executive function. The present data go some way towards enhancing the utility of the TTT.

The Relationship between Handedness and Mathematics Is Non-linear and Is Moderated by Gender, Age, and Type of Task

The relationship between handedness and mathematical ability is still highly controversial. While some researchers have claimed that left-handers are gifted in mathematics and strong right-handers perform the worst in mathematical tasks, others have more recently proposed that mixed-handers are the most disadvantaged group. However, the studies in the field differ with regard to the ages and the gender of the participants, and the type of mathematical ability assessed. To disentangle these discrepancies, we conducted five studies in several Italian schools (total participants: N = 2,314), involving students of different ages (six to seventeen) and a range of mathematical tasks (e.g., arithmetic and reasoning). The results show that (a) linear and quadratic functions are insufficient for capturing the link between handedness and mathematical ability; (b) the percentage of variance in mathematics scores explained by handedness was larger than in previous studies (between 3 and 10% vs. 1%), and (c) the effect of handedness on mathematical ability depended on age, type of mathematical tasks, and gender. In accordance with previous research, handedness does represent a correlate of achievement in mathematics, but the shape of this relationship is more complicated than has been argued so far.

From High Intellectual Potential to Asperger Syndrome: Evidence for Differences and a Fundamental Overlap-A Systematic Review

Background: An increasing number of clinicians point to similar clinical features between some children with High Intellectual Potential (HIP or "Giftedness" = Total IQ > 2 SD), and children with Autism Spectrum Disorder (ASD) without intellectual or language delay, formerly diagnosed with Asperger Syndrome. Some of these common features are social interaction impairments, special interests, and in some cases high-verbal abilities. The aim of this article is to determine whether these similarities exist at more fundamental levels, other than clinical, and to explore the literature in order to provide empirical support for an overlap between ASD and HIP. Method: First, comparative studies between ASD and HIP children were sought. Because of a lack of data, the respective characteristics of ASD and HIP subjects were explored by a cross-sectional review of different areas of research. Emphasis was placed on psychometric and cognitive evaluations, experimental and developmental assessments, and neurobiological research, following a "bottom-up" procedure. Results: This review highlights the existence of similarities in the neurocognitive, developmental and neurobiological domains between these profiles, which require further study. In addition, the conclusions of several studies show that there are differences between HIP children with a homogeneous Intellectual Quotient profile and children with a heterogeneous Intellectual Quotient profile. Conclusion: HIP seems to cover different developmental profiles, one of which might share features with ASD. A new line of investigation providing a possible starting-point for future research is proposed. Its implications, interesting from both clinical and research perspectives, are discussed.

Semantic, Executive, and Visuospatial Abilities in Mathematical Reasoning of Referred College Students

Semantic retrieval (SR) and executive-procedural (EP), but not visuospatial (VS) skills, have been found to be uniquely predictive of mathematical calculation skills in a sample of clinically referred college students. This study set out to cross-validate these results in an independent sample of clinically referred college students (N = 337) as well as extend them by examination of the contributions of these cognitive domains to math reasoning skills. Results indicate that these cognitive domains were able to predict 30% of the variance in calculation skills and 50% of the variance in math reasoning; however, in both cases, only the domains of semantic retrieval and visuospatial skill contributed uniquely. Differences between studies, and the lack of unique contribution of the EP domain to either type of math skill, may be due to measurement and sampling differences, the degree of shared relations among domains, and the choice of measures that represent the EP domain. Implications and future directions are explored.

Children’s Play Preferences, Construction Play with Blocks, and Visual-spatial Skills: Are they Related?

Fifty-one preschoolers’ play preferences, skills at assembling block structures, and spatial abilities were recorded in this study. There were no sex differences in children’s visual-spatial skills, and play with art materials and children’s free and structured play with blocks were related to spatial visualisation. Two patterns emerged from the findings: (1) activity and performance representing skills in spatial visualisation and visual-motor coordination; and (2) creativity, or the ability to break set and to produce varied solutions using visual materials. Future research might examine the extent to which children’s play activities and experiences predict these types of skills.

The relation between children's constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

The scientific literature shows that constructive play activities are positively related to children's spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children's constructive play and their performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children's constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance.

Understanding left-handedness

BACKGROUND

The human cerebrum is asymmetrical, consisting of two hemispheres with differing functions. Recent epidemiological and neurobiological research has shed new light on the development of the cerebral lateralization of motor processes, including handedness. In this article, we present these findings from a medical perspective.

METHOD

We selectively searched the PubMed online database for articles including the terms "handedness," "left handedness," "right handedness," and "cerebral lateralization." Highly ranked and commonly cited articles were included in our analysis.

RESULTS

The emergence of handedness has been explained by physiological and pathological models. Handedness arose early in evolution and has probably been constitutive for the development of higher cognitive functions. For instance, handedness may have provided the basis for the development of speech and fine motor skills, both of which have played a critical role in the evolution of mankind. The disadvantages of certain types of handedness are discussed, as some cases seem to be associated with disease.

CONCLUSION

The consideration of handedness from the epidemiological, neurobiological, and medical points of view provides insight into cerebral lateralization.

Effects of a 'learn to think' intervention programme on primary school students

BACKGROUND

Methods for teaching thinking may be described as out-of-context or infusion. Both approaches have potential to raise students' general cognitive processing ability and so raise academic achievement, but each has disadvantages.

AIMS

To describe and evaluate a theory-based learn to think (LTT) curriculum for primary school students, which draws on the strengths of both out-of-context and infusion approaches.

SAMPLE

One-hundred and sixty-six students in three classes of Grade 1 (6+ years old), Grade 2 (7+ years old), and Grade 3 (8+ years old) in a primary school in Shanxi province, China, randomly ascribed to experimental (90) and control (76) groups.

METHODS

All students were pre-tested for non-verbal intelligence and academic achievement. Experimental students followed the LTT curriculum (one activity every 2 weeks) for 4 school years. All were post-tested on three occasions for thinking ability and four times for academic achievement.

RESULTS

Grade 1 and Grade 2 students showed effects of LTT from 1 year after their start and increasing: on thinking ability d= .78-1.45; on Chinese d= .68-1.07; on maths .58-.87. Grade 3 students showed effects from 6 months after their start: on thinking ability .90-1.37; Chinese .77-1.32; maths .65-1.29. The effects were concentrated in students in the middle band of initial ability.

CONCLUSIONS

A curriculum for teaching thinking based on a structured theoretical model that combines elements of out-of-context and infusion methods has been shown to have long-term far transfer effects on students' thinking ability and academic achievement. More work is needed to meet the needs of a wider range of abilities.

All sex differences in cognitive ability may be explained by an X-Y homologous gene determining degrees of cerebral asymmetry

Male superiority in mathematical ability (along with female superiority in verbal fluency) may reflect the operation of an X-Y homologous gene (the right-shift-factor) influencing the relative rates of development of the cerebral hemispheres. Alleles at the locus on the Y chromosome will be selected at a later mean age than alleles on the X, and only by females.

Still far too sexy a topic

Geary is highly selective in his use of the literature on gender differences. His assumption of consistent female inferiority in mathematics is not necessarily supported by the facts.

Mating, math achievement, and other multiple relationships

Although Geary's partitioning of mathematical abilities into those that are biologically primary and secondary is an advance over most sociobiological theories of cognitive sex differences, it remains untestable and ignores the spatial nature of women's traditional work. An alternative model based on underlying cognitive processes offers other advantages.

How important is spatial ability to mathematics?

This commentary focuses on one of the many issues raised in Geary's target article: the importance of gender differences in spatial ability to gender differences in mathematics. I argue that the evidence for the central role of spatial ability in mathematical ability, or in gender differences in it, is tenuous at best.

Spatial visualization and sex-related differences in mathematical problem solving

Spatial visualization as a key variable in sex-related differences in mathematical problem solving and spatial aspects of geometry is traced to the 1960s. More recent relevant data are presented. The variability debate is traced to the latter part of the nineteenth century and an explanation for it is suggested. An idea is presented for further research to clarify sex-related brain laterality differences in solving spatial problems.

Sexual selection and sex differences in mathematical abilities

The principles of sexual selection were used as an organizing framework for interpreting cross-national patterns of sex differences in mathematical abilities. Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found in all cultures as well as in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains (i.e., those that emerge primarily in school) are found throughout the industrialized world. In particular, males consistently outperform females in the solving of mathematical word problems and geometry. Sexual selection and any associated proximate mechanisms (e.g., sex hormones) influence these sex differences in mathematical performance indirectly. First, sexual selection resulted in greater elaboration in males than in females of the neurocognitive systems that support navigation in three-dimensional space. Knowledge implicit in these systems reflects an understanding of basic Euclidean geometry, and may thus be one source of the male advantage in geometry. Males also use more readily than females these spatial systems in problem-solving situations, which provides them with an advantage in solving word problems and geometry. In addition, sex differences in social styles and interests, which also appear to be related in part to sexual selection, result in sex differences in engagement iii mathematics-related activities, thus further increasing the male advantage in certain mathematical domains. A model that integrates these biological influences with sociocultural influences on the sex differences in mathematical performance is presented in this article.

Why are some people left-handed? An evolutionary perspective

Since prehistoric times, left-handed individuals have been ubiquitous in human populations, exhibiting geographical frequency variations. Evolutionary explanations have been proposed for the persistence of the handedness polymorphism. Left-handedness could be favoured by negative frequency-dependent selection. Data have suggested that left-handedness, as the rare hand preference, could represent an important strategic advantage in fighting interactions. However, the fact that left-handedness occurs at a low frequency indicates that some evolutionary costs could be associated with left-handedness. Overall, the evolutionary dynamics of this polymorphism are not fully understood. Here, we review the abundant literature available regarding the possible mechanisms and consequences of left-handedness. We point out that hand preference is heritable, and report how hand preference is influenced by genetic, hormonal, developmental and cultural factors. We review the available information on potential fitness costs and benefits acting as selective forces on the proportion of left-handers. Thus, evolutionary perspectives on the persistence of this polymorphism in humans are gathered for the first time, highlighting the necessity for an assessment of fitness differences between right- and left-handers.

Separating "Rotators" From "Nonrotators" in the Mental Rotations Test: A Multigroup Latent Class Analysis

Items of mental rotation tests can not only be solved by mental rotation but also by other solution strategies. A multigroup latent class analysis of 24 items of the Mental Rotations Test (MRT) was conducted in a sample of 1,695 German pupils and students to find out how many solution strategies can be identified for the items of this test. The results showed that five subgroups (latent classes) can be distinguished. Although three of the subgroups differ mainly in the number of items reached, one class shows are very low performance. In another class, a special solution strategy is used. This strategy seems to involve analytic rather than mental rotation processes and is efficient only for a special MRT item type, indicating that not all MRT items require a mental rotation approach. In addition, the multigroup analysis revealed significant sex differences with respect to the class assignment, confirming prior findings that on average male participants perform mental rotation tasks faster and better than female participants. Females were also overrepresented in the analytic strategy class. The results are discussed with respect to psychometric and substantive implications, and suggestions for the optimization of the MRT items are provided.

Kindergarten Predictors of Math Learning Disability

The aim of the present study was to address how to effectively predict mathematics learning disability (MLD). Specifically, we addressed whether cognitive data obtained during kindergarten can effectively predict which children will have MLD in third grade, whether an abbreviated test battery could be as effective as a standard psychoeducational assessment at predicting MLD, and whether the abbreviated battery corresponded to the literature on MLD characteristics. Participants were 226 children who enrolled in a 4-year prospective longitudinal study during kindergarten. We administered measures of mathematics achievement, formal and informal mathematics ability, visual-spatial reasoning, and rapid automatized naming and examined which test scores and test items from kindergarten best predicted MLD at grades 2 and 3. Statistical models using standardized scores from the entire test battery correctly classified ~80-83 percent of the participants as having, or not having, MLD. Regression models using scores from only individual test items were less predictive than models containing the standard scores, except for models using a specific subset of test items that dealt with reading numerals, number constancy, magnitude judgments of one-digit numbers, or mental addition of one-digit numbers. These models were as accurate in predicting MLD as was the model including the entire set of standard scores from the battery of tests examined. Our findings indicate that it is possible to effectively predict which kindergartners are at risk for MLD, and thus the findings have implications for early screening of MLD.

Challenges in identifying target skills for math disability screening and intervention

Gersten, Jordan, and Flojo (in this series) review their research on math difficulties, with an emphasis on applying current knowledge to inform practices of early identification and intervention. On a practical level, educators are in dire need of empirically based screening and intervention tools. From a scientific perspective, it is important to recognize the need to clearly define what we seek to identify and remediate, and to acknowledge that we are currently far from achieving this goal despite recent advances in the field. Among the studies reviewed by Gersten et al., as well as other studies by several other researchers, there is much variability in how mathematics difficulties are defined and measured, and even in the terms used to refer to them. I address the degree of consensus and controversy currently characterizing the state of math learning disabilities research, with an emphasis on the usefulness of a developmental perspective in appraising this young field.

The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds

A range of possible predictors of arithmetic and reading were assessed in a large sample (N=162) of children between ages 7 years 5 months and 10 years 4 months. A confirmatory factor analysis of the predictors revealed a good fit to a model consisting of four latent variables (verbal ability, nonverbal ability, search speed, and phonological memory) and two manifest variables (digit comparison and phoneme deletion). A path analysis showed that digit comparison and verbal ability were unique predictors of variations in arithmetic skills, whereas phoneme deletion and verbal ability were unique predictors of variations in reading skills. These results confirm earlier findings that phoneme deletion ability appears to be a critical foundation for learning to read (decode). In addition, variations in the speed of accessing numerical quantity information appear to be a critical foundation for the development of arithmetic skills.

CORRELATIONS BETWEEN NONVERBAL INTELLIGENCE AND NERVE CONDUCTION VELOCITIES IN RIGHT-HANDED MALE AND FEMALE SUBJECTS

A neurological theory of intelligence suggesting a direct correlation between nerve conduction velocity and psychometric intelligence was tested. Cattell's Culture Fair Intelligence Test was used to asses the nonverbal intelligence (IQ) of subjects. The motor median nerve conduction velocity from right hand of males was positively correlated with IQ. In subjects with no familial sinistrality (FS-), the motor ulnar-nerve conduction velocity from the right and left hands of males negatively correlated with IQ; there were inverse correlations between IQ and nerve conduction velocity (motor median nerve from right, sensory median nerve from right and left) in females. In subjects with familial sinistrality (FS+), IQ directly correlated with nerve conduction velocity from motor median (right and left), sensory median (right), and motor ulnar (right) nerves, but only in males. The speed hypothesis and neurological theory of intelligence were not supported by these results, which, in contrast, emphasized the importance of sex and familial sinistrality in any theory of intelligence.

Personality, manual preference and neuroendocrine reactivity in hirsute subjects

Behavioral and neuroendocrine differences may be postulated in hirsute subjects since central effects of gonadal steroids are well established. We conducted a controlled clinical study with 25 consecutive young hirsute participants compared with 20 consecutive controls. Neuropsychological evaluation included the Minnesota Multiphasic Personality Inventory (MMPI) and the Edinburgh Inventory of Manual Preference (EIMP). Neuroendocrine reactivity was assessed by the adrenocorticotropic hormone (ACTH) and cortisol responses to corticotropin releasing hormone (CRH). Hirsute participants presented a flattened personality profile with lower neurotic triad scores--146 +/- 20 versus 166 +/- 28. Left-hand preference was more common in hirsute participants--4/21 versus 0/20. Decreased ACTH [area under the curve (AUC)--36 +/-2 8 vs. 72 +/- 63 pg/ml h] and cortisol (AUC--18 +/- 4 vs. 25 +/- 10 microg/dl h) responses to CRH were found in the hirsute group. In the hirsute group, higher manual preference scores were associated with lower ACTH responses to CRH, while the opposite association was found in the control group. In the hirsute group, the hyporeactive hypothalamic-pituitary-adrenal (HPA) axis was associated with lower behavior-deviant scores, while in the control group, the hyporeactive HPA axis was associated with more psychopathology. We conclude that personality and HPA axis reactivity are different in hirsute female participants when compared with controls, with a trend for differences regarding handedness. Personality and handedness are differently associated with HPA reactivity. Distinctive features in hirsute participants are probably established very early during ontogenic development.

Familial handedness and spatial ability: a study with Chinese students aged 14-24

This study tested Annett's right-shift theory on spatial ability with two samples from China. The Vandenberg Mental Rotation Test (MRT), Edinburgh Handedness Inventory, and Family Handedness Questionnaire were administered to 266 high school students and 297 undergraduates. We found very few r++ or r-- among Chinese students. Most Chinese are either moderately right-handed or ambidextrous. Consistent with Casey's finding, we found using different methods to classify handedness leads to different conclusions. However, we did not find the effect of familial handedness that Casey found. Visual strategy is related to success on the MRT but handedness is not.

Neuropsychological concomitants of calculation skills in college students referred for learning difficulties

The contributions of 3 conceptual domains from a theoretical model of math skill (Geary, 1993) were examined in a large sample of college students referred for assessment of possible learning disorders. Measures were chosen from a comprehensive neuropsychological battery, and from the Wechsler Adult Intelligence Scale-Revised, to represent each of the 3 domains (semantic retrieval, executive-procedural, and visuospatial). The proposed model was examined using structural equation modeling (LISREL), and factors representing the 3 latent domains were derived. The domains of semantic retrieval and executive-procedural skills together accounted for approximately 17% of the variance in calculation skills. The domain of visuospatial skills failed to account for significant incremental variance.

Gender and teachers' rating of linguistic skills among second-grade schoolchildren

The aim of the study was to evaluate the possible differences in linguistic skills and school achievement between girls and boys. In a nation-wide study, the achievement of 1,936 second-grade Finnish girls and boys was appraised according to the teachers' rating. The results were compared with the linguistic test performance of 364 pupils from the nearby area. The mean rates of girls in writing, reading, oral performance and attention were significantly higher than those of boys as evaluated by the teachers (p < 0.01). Also, the risk of boys to be below the median in their achievement rates compared with girls was higher (risk ratios 1.3-1.6, 95% confidence intervals 1.2-1.7, p < 0.01). In multiple regression analysis where birth order, duration of nursery day care, number of otitis media episodes and parental education were controlled for, male gender proved to be a risk factor for linguistic skills as graded by the teachers. Yet, performance in linguistic tests did not support the superiority of girls in linguistic skills. Professionals taking care of linguistic problems in children should be aware that teachers' evaluations are influenced by the gender of the pupil.

Mean differences among subcomponents of Vandenberg's Mental Rotation Test

The current investigation was designed to answer three questions: is the sex difference on Vandenberg's Mental Rotation Test present in all five subsections, what is the relation with performance, and what are the estimates of split-half reliability. Undergraduate students (55 men and 52 women) enrolled in introductory psychology courses were administered Vandenberg's test and were given 6 min. to complete the test. An over-all significant sex difference indicated men's mean performance was significantly higher than women's "total item score" and "total ratio item score," but only for Section 4(D). This suggests that men were not significantly better at identifying all types of visual spatial items on all parts of Vandenberg's test and that the source of the sex difference may be due, at least in part, to performance factors. Reliability measures for Vandenberg's test were established for the 6-min. completion time. Spearman-Brown reliability coefficient was calculated for the "item score," "ratio item score," and "attempted item" scores (.86, .85, and .93, respectively).

On the biology and politics of cognitive sex differences

The male advantage in certain mathematical domains contributes to the difference in the numbers of males and females that enter math-intensive occupations, which in turn contributes to the sex difference in earnings. Understanding the nature and development of the sex difference in mathematical abilities is accordingly of social as well as scientific concern. A more complete understanding of the biological contributions to these differences can guide research on educational techniques that might someday produce more equal educational outcomes in mathematics and other academic domains.

Brain differences, anthropological stories, and educational implications

Geary's anthropological assumptions are questioned as he uses literature influenced by sociobiology to back the claim that Female humans do not engage in environmental orientation. Yet, female gatherers or migrators do need and use spatial skills. Geary's exploration of gender differences in math skills is speculation that hasharmful, ungrounded, and misleading educational implications and applications, particularly in light of research on the status of gender equity in education.

The twain shall meet: Uniting the analysis of sex differences and within-sex variation

Spatial and mathematical abilities may be “sex-limited” traits. A sex-limited trait has the same determinants of variation within the sexes, but the genetic or environmental effects would be differentially expressed in males and females. New advances in structural equation modeling allow means and variation to be estimated simultaneously. When these statistical methods are combined with a genetically informative research design, it should be possible to demonstrate that the genes influencing spatial and mathematical abilities are sex-limited in their expression. This approach would give an empirical confirmation of Geary's evolutionary speculations.

Sex differences and evolutionary by-products

From the perspective of evolutionary theory, we believe it makes more sense to view the sex differences in spatial cognition as being an evolutionary by-product of selection for optimal rates of fetal development. Geary does not convince us that his proposed selective factors operated with “sufficient precision, economy, and efficiency.” Moreover, the archaeological evidence does not support his proposed evolutionary scenario.

Between-sex differences are often averaging artifacts

The central problem in Geary's theory is how differences are conceptualized. Recent research has shown that between-sex differences on certain tasks are a consequence of averaging within sex differences. A mixture distribution models between-sex differences on several tasks well and does not appear congenial to a sexual-selection perspective.

Able youths and achievement tests

Achievement test differences between boys and girls and between young men and young women, mostly favoring males, extend far beyond mathematics. Such pervasive differences, illustrated here, may require an explanatory theory broader than Geary's.

Differences in male and female cognitive abilities: Sexual selection or division of labor?

In Darwinian terminology, “sexual selection” refers to purely reproductive competition and is conceptually distinct from natural selection as it affects reproduction generally. As natural selection may favor the evolution of sexual dimorphism by virtue of the division of labor between males and females, this possibility needs to be taken very seriously.

Arithmetic and old lace

Geary's project faces the severe methodological difficulty of tracing the biological effects of gender on mathematical ability in a system that is massively open. Two methodological stratagems he uses are considered. The first is that pancultural sex differences are biological in nature, which is dubious in the domain of mathematics, since it is completely culture-bound. The second is that sociosexual differences are partly caused by biosexual differences, which renders his thesis unfalsifiable and empirically empty.

Sex differences in mathematical abllity: Genes, environment, and evolution

Geary proposes a sociobiological hypothesis of how (and why) sex differences in math and spatial skills might have jointly arisen. His distinction between primary and secondary math skills is noteworthy, and in some ways analogous to the closed versus open systems postulated to exist for language. In this commentary issues concerning how genes might affect complex cognitive skills, the interpretation of heritability estimates, and prior research abilites are discussed.

Mary has more: Sex differences, autism, coherence, and theory of mind

We challenge the notion that differences in spatial ability are the best or only explanation for observed sex differences in mathematical word problems. We suggest two ideas from the study of autism: sex differences in theory of mind and in central coherence.

Is there a comparative psychology of implicit mathematical knowledge?

Geary suggests that implicit mathematical principles exist across human cultures and transcend sex differences. Is such knowledge present in animals as well, and is it sufficient to account for performance in all species, including our own? I attempt to trace the implications of Gearys target article for comparative psychology, questioning the exclusion of “subitizing” in describing human mathematical performance, and asking whether human researchers function as cultural agents with animals, elevating their implicit knowledge to secondary domains of numerical performance.

On an evolutionary model of sex differences in mathematics: Do the data support the theory?

The target article draws on evolutionary theory to formulate a biosocial model of sex differences in quantitative abilities. Unfortunately, the data do not support some of the crucial hypotheses. The male advantage in geometry is not appreciably greater than the male advantagi in algebra, and the greater male variability in mathematics cited by Gear is not cross-culturally invariant.