>Geary does not mention that tests of spatial and
>mathematical ability are not always gender neutral.
i.e. the tests used to determine whether one sex is better
than the other at a certain mathematical task, may be biased
in themselves. e.g. it might be the case that more males, on
average, find themselves in the situation where it is useful
to use certain mathematical reasoning (e.g. spatial
manipulation). This may be due to socially imposed norms
whereby male infants are encouraged to perform tasks which
engage these skills.
A test based on such mathematical skills which hopes to
reveal sex differences at a primary level (i.e. sex
differences which came about through processes of natural
selection in the environment of evolutionary adaptiveness)
may do little more than reveal socially imposed stereotypes;
since it would be hopelessly biased towards males socially
>Tests of spatial abilities may test the manipulation of
>objects used more frequently, by one sex, and mathematical
>word reasoning tests may use real world examples or linguistic
>constructions more familiar to one sex...tests for social
>preferences commonly elicit sex stereotypes rather than
However this is not to say that sexual differences in
mathematical abilities could not be partly due to 'primary'
causes after all, all behavior is ultimately the product of
genetically selected neural circuits.
Proudfoot goes on to examine whether the alleged differences
in males and females ability to perform spatial tasks is a
fair predictor of overall mathematical ability.
>A difference in spatial ability can adequately explain a
>difference in mathematical ability ONLY IF those
>mathematical problems that can be solved using spatial
>representations cannot be solved using a different strategy.
That is to say that making the assumption that a females poor
spatial ability is a predictor of her general mathematical
ability is dangerous, since not all mathematical tasks
require knowledge of spatial relations for their resolution.
> The relation between sex hormones and cognition is unclear:
>that the former affect test performance does not imply that
>a cognitive ability is biologically based in any sense
>except the uninteresting, namely that cognitive behavior in
>a biological entity is the causal consequence of biological
>processes in that entity
I.e. the cognitive behavior of a person is under the direct
influence of biological processes both in the sense of the
neural circuits which control the way we think and feel,
indeed all our behaviors, and also in the way that hormones
and other biological processes (e.g. genes) influence growth
> Geary can use this hypothesis [the sexual selection
>hypothesis] to account for a male advantage in mathematical
>problem solving, only if it is true that both the gathering
>activities of early human females did not involve habitat
>navigation and that specialized spatial abilities could not
>develop by other routes.
It would seem that Geary neglects to consider this
possibility. If Geary is willing to claim that increased
adeptness at spatial orientation tasks in maths is the
product of specialized neural circuits laid down in the
environment of evolutionary adaptiveness to aid navigation,
he must show how females could not develop the same trait,
since habitat navigation and object orientation would surely
have been of equal importance to them.
>Given the role of psychosocial factors in Geary's account of
>biologically secondary abilities, he can be claiming only
>that the sex difference in mathematical ability is
>biologically enabled, that is it occurs by way of biological
The claim made by Geary that social factors(such as
schooling) can influence the sex difference in mathematical
abilities, forces an acknowledgment that these abilities
have to be a product of both biological factors and
environmental factors: indeed ultimately social factors can
only have an impact on behavior because of the presence of
genetically selected innate neural mechanisms.
(2) David Rowe
> Whether sex difference has a bias in biology is highly
>...I propose another way of establishing biological sex
>differences using behaviour genetic modes of sex limited
>..."sex limited" applies to any trait that has the same
>underlying determinants in males and females but is more
>'expressed' in one sex than the other
This perhaps harps back to the Proudfoot commentary in that
ability at a given task( i.e. at some specific mathematical
ability) may vary between sexes because of differences in
the way that the trait is expressed,and primed, in the two
> In a sex limited trait, the underlying determinant of
>within sex variation would be identical in both sexes.
This would be chiefly due to the fact that "inheritance" of
the cognitive ability (spatial orientation) would be shared
amongst offspring both male and female. Some kin would share
the same spatial orientation gene.
(3) Julia Sherman
> Geary proposes that a sex differnce in spatial
>visualization develops and then influences sex differences
>in mathematical problem solving and spatial aspects of
It must again be clarified as to how spatial orientation
abilities ( if truly selected in the environment of
evolutionary adaptiveness because they solved an adaptive
problem for males) can be seen to be predictors of general
> If male and female brains are differentiated for spatial
>visualization by gonadal hormones in early life, a further
>differentiation should occur during adolescence, resulting
>in increments in spatial visualization and mathematical
>problem solving being greater in the male than the female.
>The data from Sherman(1981) are consistent with this
>prediction for mathematical problem solving but not for
It is not clear what these data signal. That spatial
visualization is genetically determined (in the form of
specialized neural circuitry)from birth and hence remain
unchanged by hormonal changes? Or that spatial visualization
is relatively unimportant as a predictor for overall
mathematical ability, and that more emphasis should be placed
on mathematical problem solving between the sexes.
> Sex related differences in spatial visualization and
>mathematics variability...may be accounted for by natural
>selection, since far more males than females are conceived;
>more of them are born, but more males die in every decade of
>life. Male biologic venerability may account for the greater
>number of males at both the low and high ends of the
>distribution. At the low end of the distribution are males
>damaged but surviving, while males at the high end of the
>distribution represent the remnants of a more vigorous
>natural selection process than females experience...
>... in comparing the upper ends of human male and female
>distributions, more-select males are compared to less select
Variation in the male population is greater than variation
in the female population. ( This means that there are a
number of males who are more adept at mathematical problem
solving than females. Similarly there are a number of males
who are less adept at mathematical problem solving than
females. To illustrate this, imagine a scale of mathematical
ability where 10= highly adept and 0=very poor. The male
population would range from 0-10, with few individuals
scoring 0 or 10. However the female population may only
range from 3-7, simply because this population varies about
the mean (5) to a lesser degree). As such it would perhaps
be more wise to compare sexual differences in a trait around
the mean, since a better representation ofd skills within
and between sexes could be gleaned.
(4)Julian Stanley and Heinrich Stumpf
> Although mathematics has attracted the most interest in
>gender differences favoring males in several other subjects,
>especially European history tend to be higher.
It would be interesting to see how Geary would respond to
this, since his theory of selection suggests that successful
males tend to be object orientated. Surely European history
is people orientated. Perhaps social and cultural forces play
a major role here?
Uner Tan raises issues which would appear to contradict the
proposals stated by Geary.
>Geary argues that the male propensity toward agression,
>competitiveness and dominance is related to sexual
>selection during evolution, which resulted in greater
>elaboration of neurocognitive systems in males and females.
>If so the male hormone testosterone, must be associated
>with spatial abilities since testosterone was shown to be
>the main factor producing aggressive behavior in males
It turns out that
> It is generally accepted that the spatial mathematical
abilities are better in low testosterone males than those
with high testosterone.
As mentioned above Geary suggests that the genetic make up of
women predisposes them to be primarily interested in people,
where as men are genetically predisposed to be interested in
objects. (hence leading to their advantage in performing
object orientation tasks, and increasing their understanding
of related theories, e.g. geometry).
> Geary would probably find the people living in the eastern
black sea coast of Turkey very interesting. Men sit in
cafes. Women work in the fields carrying heavy bags. Grand
mother's look after the children. Women are primarily object
orientated. This is a bad example of Geary's model. Sexual
selection, if correct seems to be operating in reverse order
in this population.
However, does working in the fields make any woman any more
object orientated than those who do not? Indeed the role of
the older female is person orientated. Who is to say that the
men sitting in cafes do not contemplate geometry?
> Geary Clearly describes the complex relationship between
>spatial ability and mathematical reasoning ability (MRA),
>arguing that MRA cannot be reduced to spatial ability, as it
>does with other abilities, especially complex reasoning. It
>is not then reasonable to suggest that all the male
>advantage in outstanding mathematical ability has resulted
>from sexual selection, in which spatial orientation was the
>proximate selection variable.
The fact that spatial orientation may be confounded with other
mathematical variables suggests that proximal matematical
ability should not be assumed to be the result of distal
selections abased on spatial orientation abilities.
Fletcher, Emma Jane
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