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Quote Comment on Section 6 of the Geary article:

*> 6. Culture, sexual selection, and sex differences
*

*> in mathematical abilities: An integrative model
*

*> In this section, an integrative consideration of cultural and
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*> biological influences on
*

*> mathematical development and the earlier
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*> described sex differences in mathematical
*

*> performance is presented.
*

*> The general level of mathematical achievement within any given culture
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*> influences the
*

*> degree to which sex differences in
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*> biologically-secondary mathematical domains (e.g.,
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*> mathematical
*

*> problem solving) are expressed, but is not the primary cause of these sex
*

*> differences. In fact, given that sex differences only appear to
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*> emerge for secondary, and not
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*> primary, mathematical domains, these
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*> differences will only emerge in societies with
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*> prolonged formal
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*> mathematical instruction. Although the mode of instruction (i.e.,
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*> competitive versus cooperative classrooms) appears to differentially
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*> influence the
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*> mathematical development of boys and girls,
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*> instructional differences are not likely to be
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*> the only source of the
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*> sex differences in mathematical abilities. Rather, math instruction in
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*> school provides an important context within which more primary sex
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*> differences (e.g.,
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*> spatial abilities) can be expressed.
*

This quote really emphasises the importance of the teaching context as

a way of influencing the mathematical development of boys and girls,

and the type of context in which the child is taught will provide the

environmental influences that shape the way that the more primary sex

differences can be expressed.

*> Moreover, the finding that males tend to be more variable in
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*> mathematical and other
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*> cognitive abilities and more sensitive to
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*> environmental influences (see Section 3.3) in
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*> comparison to females,
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*> suggests that the degree to which sex differences in mathematical
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*> performance are expressed should vary directly with the overall degree
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*> of mathematical
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*> development.
*

This raises the question of why then do males have such a significant

overall advantage in their mathematical abilities than females, as

emphasised in the earlier part of this article.

*> Thus, the overall level of skill development influences the expression
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*> of sex
*

*> differences in mathematical abilities, but is not likely to be
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*> the primary causes of these
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*> differences. Stated differently, sex
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*> differences in mathematical performance appear to be the
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*> largest,
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*> especially by adolescence, in those cultures that greatly facilitate
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*> the mathematical
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*> development of children. As the emphasis on
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*> mathematics achievement declines within a
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*> culture, such as the United
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*> States, the performance of boys appears to fall more quickly than
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*> that
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*> of girls. As a result, any sex differences in component abilities will
*

*> likely be masked.
*

This section stresses the the fact that the cultural influences will

not express their effects on mathematical performance until

adolescence, which shows the extended time curse of cultural influences

on an individual.

*> Nevertheless, there do appear to be some more specific cultural
*

*> influences that contribute to
*

*> the magnitude of the sex differences in
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*> mathematical performance, that is, sex-role
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*> stereotypes and cultural
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*> influences on perceived mathematical competence.
*

*> However, in comparison to the sex difference in social preferences
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*> (described below),
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*> stereotypes and perceived competencies probably
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*> have a relatively minor, but nonetheless
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*> important, influence on
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*> participation in mathematics course taking and related activities.
*

*> Fennema et al. (1981), for instance, found that focusing on the
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*> utility of mathematics had a
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*> stronger effect on increasing girl's
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*> mathematics course taking than did changing sex-role
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*> stereotypes.
*

It can be seen that sex-role stereotypes are tied up with socially

learned aspects, and are actually a part of cultural influences on

perceived mathematical competence, rather than a separate entity as

Geary suggests. Fennema's (1981) finding that emphasizing the use and

importance of mathematics had a greater effect on increasing girl's

maths course taking than did changing the sex-role stereotypes, makes

sense since sex-role stereotypes are well defined and established, and

have been developed over a longer period of time and thus are more

difficult to change; whereas, highlighting the advantages and utility

of maths willl be more easily taken on and accepted by the individual

girl, since no preconceptions have been established with regard to the

utility of maths.

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

Social preferences is another key factor, which will, in turn influence

eventually the the sex differences in maths course taking.

*> some of these sex differences in social preferences are influenced by
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*> stereotypes and
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*> perceived competencies; in fact, it is likely that
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*> preferences and stereotypes have
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*> bidirectional influences on one
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*> another..
*

But does this bidirectional influence not suggest that they are of

fairly equal importance?

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

This quote plays down the importance of cultural factors that were

previously emphasized, and it must be noted that it is impossible to

quantify or define precisely cultural influences in the long term.

*> the sex difference in social preferences, that is, object versus
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*> people orientations, and social
*

*> styles might arise, at least in part,
*

*> from biological sex differences. I argued in Section 3.1
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*> that sexual
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*> selection might have operated to make the nature of social
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*> relationships different
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*> for males and females. For instance,
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*> developing intimate social relationships seems to be an
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*> end in itself
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*> for young females but not young males (Block 1993). Young males, of
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*> course,
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*> have companions and develop social alliances, but these might
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*> be more of a means to an
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*> end, rather than an end in itself.
*

*> Regardless, the point is that males and females differ in
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*> terms of the
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*> importance of social relationships and interests in objects, which
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*> appear to
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*> influence career aspirations. Career aspirations appear to
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*> influence the perceived utility of
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*> mathematics, which, in turn,
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*> influences participation in mathematics-related activities (and
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*> other
*

*> types of activities, as well).
*

This section highlights the role of biological sex differences, and I

agree that these will certainly interplay with cultural influences.

This quote goes on to make a direct link in causation between the

importance of social relationships to each sex and its influence on

career aspirations, but I do not believe that these factors can be so

directly related, rather they are correlated, and there are several

other important factors involved.

*> It was also suggested that sexual selection operated to make males
*

*> more competitive than
*

*> females, and, as such, might influence how boys
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*> and girls perform, in mathematics and
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*> other academic areas, in
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*> competitive and cooperative classroom environments.
*

But, is it sexual selection that makes males competitive, or rather

cultural stereotypes inherent in society, that have the greatest

influence?

*> sex differences in mathematical areas that are not facilitated by
*

*> spatial abilities. For these
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*> areas, sex differences would be primarily
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*> driven by sex differences in mathematics course
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*> taking and related
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*> experiences. As a result, sex differences in these areas, if they
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*> arise, are
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*> expected to be smaller than for geometry and mathematical
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*> word problems, and emerge
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*> only after the emergence of sex differences
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*> in mathematics course taking (i.e., the latter part
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*> of high school).
*

This quote notes the possibility that the relationship could occur in

the reverse direction; that is that the maths course taking in itself

may influence the sex differences in regard to mathematical areas not

facilitated by spatial abilities.

*> Finally, in closing, even though I have argued that biological sex
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*> differences are an
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*> important source, though not the only source, of
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*> the sex differences that emerge for some
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*> 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.
*

*> 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 does
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*> not disappear
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*> (Johnson 1984). Third, highly competitive classroom
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*> environments should be avoided;
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*> highly cooperative environments should
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*> be avoided as well, since the achievement of boys
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*> appears to drop in
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*> these environments. Classroom teaching styles should either be gender
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*> neutral, or boys and girls should be educated in separate classrooms.
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*> Finally, relative to
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*> international standards, the mathematical
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*> development of American children, boys and girls,
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*> is very poor. As
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*> noted earlier, with improved mathematical instruction, American girls
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*> should be able to develop a level of mathematical skill that far
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*> exceeds the current level of
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*> their male peers. At the same time, a
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*> greater emphasis on mathematical instruction in the
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*> United States will
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*> not likely result in disappearing sex differences. In fact, based on
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*> cross-national studies, sex differences in mathematics are likely to
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*> increase, as the level of
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*> mathematical achievement increases.
*

This conluding section of the article provides some applicable

suggestions for reducing the sex differences in mathematical abilities,

yet, with their implementation, although girls will greatly improve,

boys will also improve so that the sex differences will still exiust at

a higher overall level.

----------------------

Dearns Rachael

rld195@soton.ac.uk

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