## A longitudinal analysis of sex differences in math

Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found pan-culturally, in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains i. In particular, males consistently outperform females in the solving of mathematical word problems and in geometry. Sexual selection and any associated proximate mechanisms e.

First, sexual selection appears to have resulted in the greater elaboration of the neurocognitive systems that support navigation in 3-dimensional space in males than in females. Knowledge implicit in these systems appears to reflect an understanding of basic Euclidean geometry, and thus appears to be one source of the male advantage in geometry.

Males also co-opt these spatial systems in problem-solving situations more readily than females, which provides males with an advantage in word problems and geometry. Moreover, sex differences in social styles and interests, which also appear to be related, in part, to sexual selection, result in sex differences in engagement in mathematics-related activities, which further increases 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, sexual selection provides the primary theoretical context for examining the cross-national pattern of sex differences in mathematical abilities.

The argument is not that complex mathematical abilities, or any associated sex differences, have been directly shaped by evolutionary pressures, but rather that sexual selection appears to have directly shaped the social and cognitive styles of males and females, which, in turn, influence mathematical development and performance and contribute to sex differences in certain mathematical domains.

In order to fully consider the potential influence of evolutionary pressures on mathematical abilities, a general framework for making inferences about the relative degree of biological and cultural influences on cognition is needed Geary This is because children's mathematical development occurs primarily in school settings, and, as a result, the assessment of mathematical performance necessarily reflects some cultural influences.

In fact, the administration of all psychometric tests, such as the Scholastic Achievement Test SAT, formerly the Scholastic Aptitude Test necessarily reflects culturally-taught skills, such as reading.

Although performance on these measures must to a large degree reflect schooling and other sociocultural influences, this does not preclude more primary biological influences on psychometric test performance. In the first section below, a framework for making inferences about forms of cognition that are largely influenced by biological factors and forms of cognition that are more culturally-specific is presented; these respective forms of cognition are called biologically-primary and biologically-secondary Geary ; Rozin On the basis of this framework, a systematic assessment of sex differences in mathematical abilities requires a consideration of whether the differences in question are evident for biologically- primary or biologically-secondary mathematical domains, which are defined in Section 2.

If sexual selection were directly related to sex differences in mathematical abilities, then any such sex difference should be most evident for biologically-primary mathematical domains, those least affected by sociocultural influences e. In contrast, if there are no sex differences in biologically-primary mathematical domains but consistent sex differences in secondary mathematical domains, then there are two general potential sources of these sex differences.

The first and most obvious is a difference in the schooling of boys and girls, given that school is the primary cultural context within which secondary mathematical abilities appear to emerge Geary The second and less obvious source of sex differences in secondary mathematical domains is the secondary effects of sexual selection on the cognitive and social styles of boys and girls.

Section 3 presents a framework for considering any such secondary influences of sexual selection on sex differences in mathematical abilities. The present article is not the first to argue that cognitive sex differences in general and sex differences in mathematics in particular have biological origins. Indeed, there are many theoretical reviews in the literature on the potential biological influences on cognitive sex differences e.

Benbow, for instance, presented evidence suggesting that the greater number of males than females at the upper end of the distribution of SAT scores reflects, at least in part, a sex difference in the functional organization of the left- and right-hemisphere.

McGee argued that a sex difference in certain forms of spatial cognition has biological origins and contributes to sex differences in certain mathematical areas. Sherman , , in contrast, presented evidence suggesting that the sex difference in mathematics was primarily related to the greater mathematical confidence of boys than girls. On this view, the greater mathematical confidence of boys results in a sex difference in mathematical activities e.

The present article builds on and extends previous theoretical treatments of the source and nature of sex differences in mathematics in several ways. First, as noted above, potential biological influences on mathematical sex differences are considered explicitly within the context of sexual selection.

In particular, sexual selection is used as a theoretical context for examining sex differences in those cognitive and social domains that appear to influence mathematical development. As an example, it is argued in section 3. Second, the article provides a theoretical framework for examining how evolved cognitive abilities might be manifested in evolutionarily novel contexts such as schools. In the section below, it is argued that there are at least two ways in which biologically primary forms of cognition, such as certain spatial abilities, can be expressed in biologically secondary domains, such as complex mathematics.

By more fully articulating the potential relation between primary spatial abilities and secondary mathematical abilities, this framework expands on McGee's position that the sex difference in certain mathematical areas is secondary to more primary sex differences in certain spatial abilities.

Finally, the review of sex differences in mathematical abilities is more comprehensive in many ways than other treatments of this issue e. Specifically, the review of mathematical sex differences provides a greater emphasis on cross-national patterns than have most previous reviews and includes a review of potential sex differences in very early numerical competencies, those that appear to be biologically primary.

Evolution, culture and cognition In some respects, all forms of cognition are supported by neurocognitive systems that have evolved to serve some function or functions related to reproduction or survival. However, some forms of cognition, such as reading, emerge in some cultures and not others.

This pattern suggests that while the emergence of some domains of cognition are driven largely by biological influences, other domains emerge only with specialized cultural practices and institutions, such as schools, that are designed to facilitate the acquisition of these cognitive skills in children Geary Thus, when assessing the source of group or individual differences in cognitive abilities, it seems necessary to consider whether the ability in question is part of a species-typical biologically-primary cognitive domain, or whether the ability in question is culturally-specific, and therefore biologically-secondary.

Although biologically-secondary abilities appear to emerge only in specific cultural contexts, at least for large segments of any given population, they must perforce be supported by neurocognitive systems that have evolved to support primary abilities. Indeed, these culture-specific abilities might involve the co-optation of biologically-primary neurocognitive systems or access to knowledge implicit in these systems for purposes other than the original evolution-based function S.

The basic premise is that in terms of children's cognitive development, the interface between culture and biology involves the co-optation of highly specialized neurocognitive systems to meet culturally-relevant goals. In this section, a basic framework for distinguishing between primary and secondary abilities is presented a more complete presentation can be found in Geary One way to organize our understanding of both biologically-primary and biologically-secondary forms of cognition is to hierarchically organize them into domains, abilities, and neurocognitive systems.

Domains, such as language or arithmetic, represent constellations of more specialized abilities, such as language comprehension or counting. The goal of counting, for instance, is to determine the number of items in a set of objects. Counting is achieved by means of procedures, such as the act of pointing to each object as it is counted. Counting behavior, in turn, is constrained by conceptual knowledge or skeletal principles for the initial emergence of primary domains , so that, for instance, each object is pointed at or counted only once.

First, inherent in the neurocognitive systems that support primary abilities is a system of skeletal principles Gelman Skeletal principles provide the scaffolding upon which goal structures and procedural and conceptual competencies emerge. Second, it appears, at least initially, that the knowledge that is associated with primary domains is implicit. That is, the behavior of children appears to be constrained by skeletal principles, but children cannot articulate these principles Geary ; Gelman While the initial structures for the cognitive competencies that might be associated with primary abilities appear to be inherent, the goal structures as well as procedural and conceptual competencies for secondary abilities are likely to be induced or learned from other people e.

For the latter, there appear to be two possibilities. As noted above, the first involves the co- optation of the neurocognitive systems that support primary abilities. Second, knowledge that is implicit in the skeletal principles of primary abilities can be made explicit and used in ways unrelated to the evolution of these principles Rozin For a germane example, consider the possibility that the development of geometry as a formal discipline involved, at least in part, the co-optation of the neurocognitive systems that have evolved to support navigation in the three-dimensional physical universe and access to the associated implicit knowledge.

Arguably all terrestrial species, even invertebrates e. Gould ; Landau et al. Cheng and Gallistel , for instance, showed that laboratory rats appear to develop a "Euclidean representation of space for navigational purposes" p. Implicit in the functioning of the associated neurocognitive systems is a basic understanding of geometric relationships amongst objects in the physical universe. So, for example, even the behavior of the common honey bee Apis mellifera reflects an implicit understanding that the fastest way to move from one location to another is to fly in a straight line J.

Even though an implicit understanding of geometric relationships appears to be a feature of the neurocognitive systems that support habitat representation and navigation, this does not mean that individuals have an explicit understanding of the formal principles of Euclidean geometry.

Rather, the development of geometry as a formal discipline might have been initially based on early geometer's access to the knowledge that is implicit in the systems that support habitat navigation. In keeping with this position, in the development of formal geometry, Euclid apparently "started with what he thought were self-evident truths and then proceeded to prove all the rest by logic" West et al. The implicit understanding, or "self-evident truth," that the fastest way to get from one place to another is to go "as the crow flies," was made explicit in the formal Euclidean postulate, "a line can be drawn from any point to any point" In Euclidean geometry, a line is a straight line " West et al ; p.

The former appears to represent implicit, biologically-primary knowledge i. Moreover, although the neurocognitive systems that support habitat navigation appear to have evolved in order to enable movement in the physical universe Shepard, , they can also be co-opted or used for many other purposes. For an example of what I would call cognitive co-optation, consider the use of spatial representations to aid in the solving of arithmetic word problems.

Lewis and Mayer showed that word problems that involve the relative comparison of two quantities are especially difficult to solve. For instance, consider the following compare problem from Geary She has one candy less than Mary. How many candies does Mary have? However, many adults and children often subtract rather than add to solve this type of problem; the keyword "less" appears to prompt subtraction rather than addition.

Moreover, the structure of the second sentence i. Lewis showed that one way to reduce the frequency of errors that are common with these types of relational statements is to diagram i.

It is very unlikely that the evolution of spatial abilities was in any way related to the solving of mathematical word problems. Nevertheless, spatial representations of mathematical relationships are used, that is co-opted, by some people to aid in the solving of such problems Johnson More important, there appear to be differences in the ease with which these systems can be used for their apparent evolution-based functions and co-opted tasks.

The use of spatial systems for moving about in one's surroundings or developing cognitive maps of one's surroundings appears to occur more or less automatically Landau et al. However, most people need to be taught, typically in school, how to use spatial representations to solve, for instance, mathematical word problems Lewis In short, the formal step-by-step procedures that can be used to spatially represent mathematical relationships are secondary with respect to the evolution of spatial cognition--these systems did not evolve for this purpose but nevertheless can be used for this purpose.

In other words, the practices that occur within some cultural institutions, such as schools, can, in a sense, create cognitive skills that otherwise would not emerge. Any such culture-based skill must perforce be built upon more primary forms of cognition Geary In general, I am arguing that the neurocognitive systems that have more likely evolved to support movement in the three- dimensional physical universe Gaulin ; Shepard can be adapted by human beings for purposes other than the original evolution-based function Rozin With regard to mathematics, there are two resulting predictions.

The first is that the relationship between spatial and mathematical abilities should be rather selective. Specifically, the prediction is that measures of 3-dimensional spatial abilities should be more strongly related to abilities in the domain of Euclidean geometry e.

The prediction is for tests of 3-dimensional spatial abilities because the neurocognitive systems that appear to support habitat navigation evolved in the 3-dimensional physical universe Shepard Second, in addition to Euclidean geometry, a relationship between spatial abilities and mathematical information that can be represented spatially is predicted.

Example of such areas would include the solving of word problems, tables, graphs, etc. From this perspective, a thorough assessment of sex differences in mathematical abilities should be based on a consideration of whether the abilities in question are likely to be biologically primary or biologically secondary.

For secondary domains, we should consider whether any differences that might emerge could possibly involve the co-optation of biologically primary cognitive systems or access to knowledge implicit in these systems. Thus, as noted earlier, the sections below provide a brief overview of potential primary and secondary mathematical domains.

Moreover, given the potential for co-optation, potential biologically-primary sex differences in cognitive and social styles that might influence mathematical development are considered in Section 3. Potential primary and secondary mathematical abilities The following subsections present a brief overview of potential biologically-primary and biologically-secondary mathematical domains.

There is some evidence for the pan-cultural existence of a biologically-primary numerical domain which consists of at least four numerical abilities; numerosity, ordinality, counting, and simple arithmetic see Geary