Boys' advantage on the fractions number line is mediated by visuospatial attention: Evidence for a parietal-spatial contribution to number line learning

The study tested the hypotheses that boys will have an advantage learning the fractions number line and this advantage will be mediated by spatial abilities. Fractions number line and, as a contrast, fractions arithmetic performance were assessed for 342 adolescents, as was their intelligence, working memory, and various spatial abilities. Boys showed smaller placement errors on the fractions number line (d = -0.22) and correctly solved more fractions arithmetic problems (d = 0.23) than girls. Working memory and intelligence predicted performance on both fractions measures, and a measure of visuospatial attention uniquely predicted number line performance and fully mediated the sex difference. Visuospatial working memory uniquely predicted fractions arithmetic performance and fully mediated the sex difference. The results help to clarify the nuanced relations between spatial abilities and formal mathematics learning and the sex differences that often emerge in mathematical domains that have a visuospatial component.

Language-Related Longitudinal Predictors of Arithmetic Word Problem Solving: A Structural Equation Modeling Approach

We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10 to 9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children's later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed.

Mental Arithmetic as a Function of Computerized Digit Rates, Gender, and Size of Audience

Mental-arithmetic tests were given to 117 undergraduate volunteers (40 men and 77 women) using three rates (between groups) of digit presentation (1 sec., 2 sec., and 3 sec.) under three (within-group) sizes of audience (2 observers, 1 observer, and alone condition). Subjects were instructed to sum mentally three sets of 25 numerals ranging from 1 to 5 in computer-generated random sequences, under each of the three audience conditions. A mixed 2×3×3 split-plot analysis of variance of correct scores showed a significant main effect for rate of digit presentation, and post hoc Scheffé tests of multiple comparisons showed significant differences between the 1-sec. rate and each of the other rates (2 sec. or 3 sec.), yet no significance between 2-sec. and 3-sec. rates indicating a “critical threshold” has been identified with implications for computer-scrolled numerical information. Also, there was a significant two-way interaction between gender and size of audience. Post hoc Newman-Keuls comparisons showed women scored higher than men in the one-observer condition while men scored higher than women in the two-observer condition. Interpretations regarding interpersonal relationships and social inhibition were offered.

The Effect of Mathematics Self-Concept on Girls' and Boys' Mathematical Achievement

Norwegian elementary schoolboys showed significantly higher mathematics self-concept than girls. Boys also had a significantly higher mathematical achievement score than girls. However, controlling for mathematics self-concept produced several interesting results. First, there was no significant effect of gender on overall mathematical achievement. Second, although the gender difference in achievement favouring boys increased with increasing task difficulty, no significant effects of gender were found in subsamples of difficult tasks. Finally, a significant effect of gender favouring girls appeared in subsamples of easy tasks and in routinizing well-defined procedural tasks. These results indicate that mathematics self-concept is an important variable accounting for differences in elementary schoolgirls' and boys' mathematical achievement.

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.

A longitudinal analysis of sex differences in math and spatial skills in primary school age children

We report on a longitudinal study designed to assess possible sex differences in math achievement, math ability, and math-related tasks during the primary school age years. Participants included over 200 children from one public school district. Annual assessments included measures of math ability, math calculation achievement scores, rapid naming and decoding tasks, visual perception tests, visual motor tasks, and reading skills. During select years of the study we also administered tests of counting and math facts skills. We examined whether girls or boys were overrepresented among the bottom or top performers on any of these tasks, relative to their peers, and whether growth rates or predictors of math-related skills differed for boys and girls. Our findings support the notion that sex differences in math are minimal or nonexistent on standardized psychometric tests routinely given in assessments of primary school age children. There was no persistent finding suggesting a male or female advantage in math performance overall, during any single year of the study, or in any one area of math or spatial skills. Growth rates for all skills, and early correlates of later math performance, were comparable for boys and girls. The findings fail to support either persistent or emerging sex differences on non-specialized math ability measures during the primary school age years.

Gender Differences in Arithmetic Strategy Use: A Function of Skill and Preference

This study was designed to examine whether first-grade boys' use of retrieval and first-grade girls' use of manipulatives reflected gender differences in their abilities to use these strategies or gender differences in preferences for strategy use. Eighty-four first-grade students, 42 boys and 42 girls, from two suburban elementary schools participated in this study. The children solved basic arithmetic problems under two conditions: a free-choice condition in which they were allowed to solve the problems any way they preferred and a game condition in which the children's strategy use was constrained so that all children used the same strategies on the same arithmetic problems. Strategy use during the free-choice session replicated the findings of earlier research indicating that girls tend to use strategies utilizing manipulatives and boys tend to use retrieval. During the game condition, when we controlled the types of strategies children used on different problems we found that boys were as able as girls to calculate solutions using manipulatives. Girls, however, were not as capable as boys in their retrieval of answers to arithmetic problems from memory. No differences were found in error rates or speed of retrieval. Gender differences were found in the variability of correct retrieval, with boys being significantly more variable than girls. Copyright 2001 Academic Press.

Sex differences in spatial cognition, computational fluency, and arithmetical reasoning

Alternative explanations for the male advantage in arithmetical reasoning, as measured by the ability to solve complex word problems, include a male advantage in spatial cognition and a male advantage in computational fluency. The current study was designed to test these competing hypotheses. To this end, 113 male and 123 female undergraduates were administered arithmetical computations and arithmetical reasoning tests, along with an IQ test and a test of spatial cognition. There was no sex difference on the IQ test, but males showed significantly higher mean scores on the arithmetical computations, arithmetical reasoning, and spatial cognition measures. A series of structural equation models indicated that individual differences in arithmetical reasoning were related to individual differences in IQ, spatial abilities, and computational fluency. Moreover, the results suggested that the male advantage in arithmetical reasoning is mediated by the male advantages in both computational fluency and spatial cognition.

Student gender and teaching methods as sources of variability in children's computational arithmetic performance

An experimental study of the effects of a didactic teaching approach and a constructivist teaching approach on 3rd- and 5th-grade boys' and girls' performance on arithmetic computation problems was conducted. Two groups of children, matched on the basis of initial computation performance as well as grade and gender, were taught how to solve arithmetic problems using one of these two instructional approaches. Analysis of subsequent computation test performance revealed that 5th graders scored higher than 3rd graders, and there was a significant interaction between gender and instruction group. After instruction, girls in the didactic group outperformed boys in both instruction groups and girls who had been taught using constructivist approaches. Gender differences in computation performance can appear relatively early, by 3rd grade, if didactic instruction strategies are used to teach computational rules. The pattern of gender differences suggests that didactic teaching does not handicap boys. Rather, it appears that didactic instruction enhances computational performance in girls.

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.

We are far from understanding sex-related differences in spatial-mathematical abilities despite the theory of sexual selection

I have provided evidence that Geary's model does not explain male dominance in spatial abilities by sexual selection. The current literature concerning the relations of nonverbal IQ to testosterone, hand preference, and right- and left-hand skill, as well as the organizing effects of testosterone on cerebral lateralization during the perinatal period, does not support Geary's arguments.

Do gender differences in spatial skills mediate gender differences in mathematics among high-ability students?

Based on Geary's theory, intelligence may determine which males utilize innate spatial knowledge to inform their mathematical solutions. This may explain why math gender differences occur mainly with higher abilities. In support, we found that mental rotation ability served as a mediator of gender differences on the math Scholastic Assessment Test for two high-ability samples. Our research suggests, however, that environment and biology interact to influence mental rotation abilities.

Genetic influences on sex differences in outstanding mathematical reasoning ability

Sexual selection provides an adequate partial explanation for the difference in means between the distributions, but fails to explain the difference in variance, that is, the overrepresentation of both boys with outstanding mathematical reasoning ability (OMRA) and boys with mental retardation. Other genetic factors are probably at work. While spatial ability is correlated with OMRA, so are other cognitive abilities. OMRA is not reducible to spatial ability; hence selection for navigational skill is unlikely to be the only mechanism by which males have gained an advantage in OMRA.

Sexual-selection accounts of human characteristics: Just So Stories or scientific hypotheses?

We evaluate three of Geary's claims, finding that (1) there is little evidence for sex differences in object- vs. person-orientation; (2) sex differences in competition, even if biologically caused, lead to sex differences in mathematics only given a certain style of teaching; and (3) sex differences in mental rotation, though real, are not well explained in a sociobiological framework or by the proximate biological variables assumed by Geary.

A critic with a different perspective

To the extent that Geary's theory concerning biologically primary and secondary behaviors depends on factor analytic methods and findings, it is woefully weak. Factors have been mistakenly called primary mental abilities, but the adjective “primary” represents reification of a mathematical dimension defined by correlations. Fleshing out a factor beyond its mathematical properties requires much additional quantitative experimental and correlational research that goes far beyond mere factoring.

Omissions relevant to gender-linked mathematical abilities

Analyses of bodies of data usually omit some relevant studies. Geary omits (1) some studies looking at functional correlates of basic biological data, (2) studies of developmental implications for functioning, and (3) the recent achievement of acceleration of cognitive development.

Resources dimorphism sexual selection and mathematics achievement

Geary's model is a worthy effort, but ambiguous on important issues. It ignores differential resource allocation, although this follows directly from sexual selection via differential parental investment. Dimorphism in primary traits is arbitrarily attributed to sexual selection via intramale competition, rather than direct evolutionary pressures. Dubious predictions are made about the consequences of raising mathematics achievement.

The logic of the sociobiological model Geary-style

Geary's is the traditional view of the sexes. Yet each part of his argument – the move from sex differences in spatial ability and social preferences to a sex difference in mathematical ability, the claim that the former are biologically primary, and the sociobiological explanation of these differences – requires considerable further work. The notion of a biologically secondary ability is itself problematic.

Some problematic links between hunting and geometry

Geary's emphasis on hunting ignores the possible importance of other human activities, such as scavenging and gathering, in the evolution of spatial abilities. In addition, there is little evidence that links spatial abilities and math skills. Furthermore, such links have little practical importance given the small size of most differences and girls' superior performance in mathematics classrooms.

Quantitative information presentation and gender: an interaction effect

The authors investigated whether performance on mathematical test items would be influenced by an interaction between presentation format and gender. One hundred fourteen students in a management accounting course were randomly assigned either to a tabular format or to a graphics format. There were significant main effects for gender and presentation format; men outperformed women, and the subjects who received the tabular format outperformed the subjects who received the graphics format. A significant interaction supported the existence of a conditional relationship between performance on mathematical test items and presentation format. This relationship varied as a function of gender (symmetry permits the interchange of presentation format and gender). Simple effects for the interaction determined that the women who received the graphics presentation did not perform as well as their male counterparts, or as well as other women and men who received the tabular format. The results of this study indicate that presentation format is an important consideration in gender differences for mathematics performance.

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

In accordance with major theories of handedness and brain organization, differential predictors for math achievement were found as a function of sex and handedness subgroups among eighth graders. Although there was no difference in absolute levels of performance as a function of either sex or handedness, predictive structures did differ. Regression analyses showed that spatial ability predicts math achievement for: (1) girls with anomalous dominance (non-right-handers and right-handers with non-right-handed relatives), and (2) all boys (independent of handedness group). In contrast, for the standard dominance girls who are right-handed with all right-handed relatives (considered strongly left-hemisphere dominant for language), spatial ability did not predict for math achievement. These findings occurred, even when scholastic aptitude and verbal achievement factors were controlled. It was concluded that further studies of sex differences in math achievement should consider subgroup differences within the sexes, based on handedness patterns.