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Response to Quote/ Comments on Section 6 of the Geary article:

*> 6. Culture, sexual selection, and sex differences
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*> in mathematical abilities: An integrative model
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*> In this section, an integrative consideration of cultural and
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*> biological influences on
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*> mathematical development and the earlier
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*> described sex differences in mathematical
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*> performance is presented.
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*> The general level of mathematical achievement within any given
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*> culture influences the degree to which sex differences in
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*> biologically-secondary mathematical domains (e.g., mathematical
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*> problem solving) are expressed, but is not the primary cause of
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*> these sex differences. In fact, given that sex differences only
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*> appear to emerge for secondary, and not primary, mathematical
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*> domains, these differences will only emerge in societies with
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*> prolonged formal mathematical instruction. Although the mode of
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*> instruction (i.e., competitive versus cooperative classrooms)
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*> appears to differentially influence the mathematical development of
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*> boys and girls, instructional differences are not likely to be the
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*> only source of the sex differences in mathematical abilities.
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*> Rather, math instruction in school provides an important context
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*> within which more primary sex differences (e.g., spatial abilities)
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*> can be expressed.
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-The assertion that instructional technique influences the mathematical

ability of girls/boys has intuitive appeal; however I would have

thought that instructional differences, even if applied energetically

at early school stages may only have a minimal influence relative to

other socio-cultural factors. Also, does instructional style act as a

context in which socially mediated sex differences could be expressed?

*> Thus, the overall level of skill development influences the
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*> expression of sex differences in mathematical abilities, but is not
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*> likely to be the primary causes of these differences. Stated
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*> differently, sex differences in mathematical performance appear to
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*> be the largest, especially by adolescence, in those cultures that
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*> greatly facilitate the mathematical development of children. As the
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*> emphasis on mathematics achievement declines within a culture, such
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*> as the United States, the performance of boys appears to fall more
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*> quickly than that of girls. As a result, any sex differences in
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*> component abilities will likely be masked.
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-What grounds does Geary have for asserting that the overall level of

skill development does not have a primary cause of the expression of

sex differences in mathematical abilities?

*> Nevertheless, there do appear to be some more specific cultural
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*> influences that contribute to the magnitude of the sex differences
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*> in mathematical performance, that is, sex-role stereotypes and
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*> cultural influences on perceived mathematical competence. However,
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*> in comparison to the sex difference in social preferences (described
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*> below), stereotypes and perceived competencies probably have a
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*> relatively minor, but nonetheless important, influence on
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*> participation in mathematics course taking and related activities.
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*> Fennema et al. (1981), for instance, found that focusing on the
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*> utility of mathematics had a stronger effect on increasing girl's
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*> mathematics course taking than did changing sex-role stereotypes.
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-Note that there is still not unequivocal evidence to support the

argument that perceived competence has only a minor role in

precipitating sex differences. I (tentatively) argue that a robust

perceived competence in maths (i.e confidence) is conducive to

attainment of greater mathematical aptitude. Thus, perceived

competence may have a significant impact on the development of

mathematical ability, and it is possible that sex differences in maths

are greatly magnified by the subjective perceived competence (i.e.

confidence) of a boy or girl. Clearly any substantial role of

confidence would only be mediated by a base level of acquired ability.

But boys, having attained a superior proficiency in some aspects of

maths than girls will receive more encouragement from their more

numerous successes, continually reinforcing self confidence in maths

ability. This will be conducive to greater maths achievement. The

opposite arrangement will hold true for girls.

*> Sex differences in social preferences and general interests appear
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*> to be important influences on the sex difference in the perceived
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*> utility of mathematics and the resulting sex difference in
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*> mathematics course taking (Lubinski et al. 1993).
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-Sex differences in social preferences and general interests are

arguably key influences in the cultivation of mathematical ability and

hence sex differences in the area. There is a genetic component to

social preferences and gen.interests of an individual. But, given the

widely held view that general interests and social preferences are

also profoundly influenced by the rearing environment of the child,

particularly the parents, differential treatment of boys and girls may

mediate expression of the innate maths advantage of boys. Some facet

of differential treatment could for instance, allow a boy instead of a

girl to gain early practice in skills such as spatial ability which

are thought to promote achievement in certain aspects of maths.

Alternatively, adopting the nuturist's stance, these factors may

precipitate the sex differences in the first place.

*> the sex difference in object versus people orientations is evident
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*> in cultures where there are no scientists, mathematicians, or
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*> high-school mathematics curriculums, suggests that sex differences
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*> in social preferences and interests largely transcend specific
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*> cultural influences. Culture, will of course, influence how these
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*> preferences can be expressed, but is probably not the primary cause
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*> of these differences.
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-Leading on from my comment above, I see no reason to suggest that

culture is definitely not a (or amongst) the primary cause(s) of sex

differences in maths ability. How can this discrepancy in conviction

be resolved? On a broader note, are polarised viewpoints (i.e.

nature/nurture dichotomy) in such an intricate area an acceptable

attitude?

*> the sex difference in social preferences, that is, object versus
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*> people orientations, and social styles might arise, at least in
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*> part, from biological sex differences. I argued in Section 3.1 that
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*> sexual selection might have operated to make the nature of social
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*> relationships different for males and females. For instance,
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*> developing intimate social relationships seems to be an end in
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*> itself for young females but not young males (Block 1993). Young
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*> males, of course, have companions and develop social alliances, but
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*> these might be more of a means to an end, rather than an end in
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*> itself. Regardless, the point is that males and females differ in
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*> terms of the importance of social relationships and interests in
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*> objects, which appear to influence career aspirations. Career
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*> aspirations appear to influence the perceived utility of
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*> mathematics, which, in turn, influences participation in
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*> mathematics-related activities (and other types of activities, as
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*> well).
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The role of biological sex differences in influencing social

preferences, with the noted implications that social preferences have

for sex differences in maths is a viable argument. But how could this

preclude a primary role of the environment in the potentiation of sex

differences in social preferences? Moreover I do not believe this

precludes a primary role of the environment in the genesis of sex

differences in social preferences.

*> It was also suggested that sexual selection operated to make males
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*> more competitive than females, and, as such, might influence how
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*> boys and girls perform, in mathematics and other academic areas, in
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*> competitive and cooperative classroom environments.
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But, is it sexual selection that makes males competitive, or rather

cultural stereotypes inherent in society, that have the greatest

influence? -A very valid question to ask.

*> Finally, in closing, even though I have argued that biological sex
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*> differences are an important source, though not the only source, of
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*> the sex differences that emerge for some biologically-secondary
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*> mathematical domains, this should not be taken to mean that the
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*> mathematical development of girls cannot be improved.
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-It is important to emphasise that biological differences are not the

only (or even primary) determinants of sex differences in maths.

Obviously, to propose that the ability of girls could not be improved

would be ludicrous. Furthermore, I am still not convinced that there

is no possibility that manipulating and controlling the acknowledged

differential treatment of girls/boys by society could readdress and

diminish the gulf between each sexes mathematical ability.

*> even though girls do not appear to spontaneously use spatial
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*> representations in problem->solving situations as frequently as boys
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*> do, they can be taught to do so (Lewis 1989; Johnson 1984). Teaching
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*> girls to use diagrams during mathematical problem solving
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*> significantly improves their performance, but the male advantage
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*> does not disappear (Johnson 1984). Third, highly competitive
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*> classroom environments should be avoided; highly cooperative
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*> environments should be avoided as well, since the achievement of
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*> boys appears to drop in these environments. Classroom teaching
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*> styles should either be gender neutral, or boys and girls should be
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*> educated in separate classrooms. Finally, relative to international
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*> standards, the mathematical development of American children, boys
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*> and girls, is very poor. As noted earlier, with improved
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*> mathematical instruction, American girls should be able to develop a
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*> level of mathematical skill that far exceeds the current level of
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*> their male peers. At the same time, a greater emphasis on
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*> mathematical instruction in the United States will not likely result
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*> in disappearing sex differences. In fact, based on cross-national
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*> studies, sex differences in mathematics are likely to increase, as
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*> the level of mathematical achievement increases.
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-Yes according to Geary's position, the differences should remain.

However, I caution against unquestioning acceptance of this view

before more convincing evidence is presented.

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