> A. Dowker.
> 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. This commentary will not deal with the issue of biological
> versus social origins of gender differences, or with the evolutionary
> theories that form a basis for part of the author's argument. Rather,
> it will focus on one topic raised in the target article: the issue of
> whether gender differences in spatial ability can adequately explain
> gender differences in arithmetic. Spatial ability has frequently been
> suggested (e.g. by Casey, Nuttall and Benbow, 1995) to be an important
> factor in mathematical performance in general, and in gender
> differences in mathematics in particular.
One surely cannot simply consider this without the consideration of
other factors such as environmental factors.
> Why indeed should spatial ability be expected to be important to
> mathematical performance? There seem to be three main ways in which
> spatial ability might contribute to mathematics: (1) Geometry
> emphasizes spatial relationships, However, only some forms of geometry
> emphasize THREE-DIMENSIONAL spatial relationships, which is the aspect
> of spatial ability that is most gender-differentiated. Trigonometry,
> for example, predominantly emphasizes two-dimensional geometry. While
> three-dimensional geometry is one important component of advanced
> mathematics, it is a relatively small and specialized one. (2) Some
> degree of spatial ability is necessary for the correct placement and
> alignment of digits, and as such must play a part in multi-digit
> arithmetic. Inversions, misplacements and misalignments of digits
> occur in what is sometimes referred to as "spatial dyscalculia" (c.f.
> Hartje, 1987). Once again, however, the relevant spatial abilities are
> two-dimensional. Moreover, as the author points out (pp.22-23), most
> studies of multi-digit arithmetic have either shown no gender
> differences or better performance by girls. (3) It is possible that
> spatial representations of the mathematical relationships in a word
> problem can facilitate its solution.
But why should there be gender differences in spatial ability? Also
one has to consider the other factors that are involved in
mathamatics, surely spatial ability is not the only important factor.
If there are other important factors, then what if they also have
> T. J. Crow
> The general finding to be explained is that (with great
> inter-individual variation) mean performance on indices of verbal
> fluency is greater in females, and is greater in males on tests of
> spatial (including mathematical) ability.
These are simply the mean measurements, one must also remember that
there will be variation in the case of male and female ability.
Therefore surely there are high performers who are female and those
who are male.
> Annett (1985) has proposed that a single gene (the right-shift-factor)
> can explain the transmission of handedness within families and
> postulates that this gene (with a random element) determines which
> hemisphere shall be dominant for language.
Again, there are other factors that affect handedness. Consider the
times when left handedness was considered to be wrong and children
were forced to be right handed. Also, does this suggest that there
are differeneces according to handedness for language ability? Has
this been proven?
> D. F. Bjorkland
> As cognitive developmental psychologists, we have never been very
> interested in sex differences. In fact, we admit to often treating sex
> differences only as error variance in our analyses, or treating sex as
> a "nuisance" variable -- something that must be controlled, like
> stimulus presentation order, but nothing that is of interest for its
> own sake. There have been several reasons for our disinterest. First,
> in agreement with Geary, most differences in cognitive abilities
> between the sexes are small in magnitude and are getting smaller with
> time. Second, and more important, we have ignored sex differences in
> our empirical research to date because we felt that there was no
> driving theoretical reason to assess them. We do not feel that
> male-female differences by themselves, with no theoretical basis,
> promote an understanding behind the differences.
Exactly. One has to consider other factors too, such as the
environmental factors. However, is sex simply a 'nuisance' variable?
Surely, it must play a part in some way.
> H. Davis
> In short, counting should mean counting, whether performed by a rat, a
> 6 year old child, or a mathematics professor.
Is there any proof that a rat can count? Also, consider the
differences in how a six year old and a professor count.
> If primary mathematical ability
> requires exposure to teachers or other social agents to make itself
> manifest, then perhaps so does the NC of animals.
Surely one can have mathematical skills present without exposure to
others. Surely there are many skills people have that haven't been
exposed to others.
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