Comments on Donna Crumley's comments [dc]:
> The pattern of results suggests that there are no sex differences in
> biologically-primary mathematical abilities. This conclusion seems to
> be especially sound for preschool and kindergarten children, because
> the results are robust across studies and across cultures. For the
> infancy research, however, this conclusion must be considered
> tentative, because the measures used in these studies, combined with
> the small sample sizes, might not be sensitive enough to detect any
> potentially more subtle differences. Nevertheless, given the results
> for preschool children, there appears to be little reason to
> suspect that more subtle sex differences exist in these basic skills.
> In other words, the later sex differences in mathematical problem
> solving and geometry do not appear to have their antecedents in
> fundamental numerical abilities.
dc> Donna's response: Geary seems to be implying here that
dc> something other than biological ability - socialisation for
dc> example lies behind later sex differences in mathematical
dc> problem solving.
My comments:I personally think that Geary is warning that
infancy research may have some methodological flaws: the
sample size and measures may not be sensitive enough to
detect subtle sex differences that may be good indicators of
later secondary abilities.
dc> Here Geary is suggesting that it is not until adolescence
dc> that sex differences are shown. The differences come about
dc> as a result of the Mathematical Reasoning Factor. I^m not
dc> sure that I agree with this. Surely males don^t suddenly
dc> become mathematical genius^, leaving their female
dc> counterparts behind. I believe that the process
dc> of socialisation reinforces biological ability from an early
dc> age. Survival of the fittest has never required that females
dc> need to be good at mathematical problem solving/ spatial
dc> ability. The female has always ensured the safety of her off
dc> spring. The male on the other hand has had an underlying
dc> necessity to be good at mathematics/ spatial ability.
dc> He needs to be able to protect and provide for his mate and
dc> off spring.
My comments: I think it is perfectly feasible to suggest
there is a mathematical reasoning factor that comes into play
in adolescence. Whilst I am sure socialisation plays a role
in this ability, it is important to remember that genes do
not always show their effects at the moment of conception.
Effects can be turned on and off - just like a child's
physical development occurs in spurts and lags. This is the
same with cognitive development - one cognitive spurt occurs
around 2 years of age when language develops.
> 4.2.4. Sex differences in gifted samples. Children who scored in the
> top 2 to 5% on standard mathematics achievement tests in the seventh
> grade were invited to take the SAT. The mathematics section of the
> SAT, the SAT-M, assesses the individual's knowledge of some arithmetic
> concepts, such as fractions, as well as basic algebraic and geometric
> skills (Stanley et al. 1986). Across cohorts, American boys, on
> average, have been found to consistently outperform American girls on
> the SAT-M by about 30 points (about 1/2 of a standard deviation). This
> sex difference has also been found in the former West Germany and in
> mainland China (Benbow 1988; Stanley et al. 1986), although it is of
> interest to note that the mean performance of gifted Chinese girls (M
> = 619) was between 50 and nearly 200 points higher, depending on the
> cohort, than the mean of the American boys identified through SMPY
> (Stanley et al. 1986). Stanley et al. argued that the advantage of
> gifted Chinese children over gifted American children on the SAT-M was
> probably due to more homework in China and the fact that some of the
> material covered on the SAT-M is introduced in the seventh grade in
> China, but not until high school in the United States. The finding
> that Chinese individuals do not have better developed spatial
> abilities than Americans indicates that this national difference in
> SAT-M performance is not related to a national difference in spatial
> abilities (Stevenson et al. 1985).
dc> Donna's response:The above evidence suggests that
dc> socialisation does have a part to play in giftedness. More
dc> school work in China led to higher results in the tests -
dc> for females as well as males. Giftedness then, it seems is
dc> not innate, but the result of early learning and practice.
My comments: I disagree that giftedness is a result of early
learning and practice: whilst it certainly improves
performance - Chinese girls outperform American boys - but do
they still outperform their own counterparts (Chinese boys).
It seems that they don't (This sex difference has been found
in mainland China). Certainly lots of learning, good
teaching and practice enhances performance, I don't think it
can account for giftedness.
> 4.2.5. Summary and conclusion. Consistent sex differences in
> mathematical performance are found in some domains, such as geometry
> and word problems, but not other domains, such as algebra (Hyde et al.
> 1990). It has generally been argued that when a sex difference in
> mathematical skills is found, it is typically not found until
> adolescence (Benbow 1988; Hyde et al. 1990). This conclusion has been
> based, for the most part, on comparisons of American children.
> Multinational studies, in contrast, show that a male advantage in the
> solving of arithmetic word problems and on tasks that are solvable
> through the use of spatial skills, such as visualizing geometric
> shapes, is often evident in elementary school (Lummis & Stevenson
> Senk and Usiskin (1983), in a large-scale national (U.S.) study, found
> no sex difference in high-school students' ability to write geometric
> proofs, after taking a standard high-school geometry course, even
> though adolescent males typically perform better than their female
> peers on geometric ability tests (Hyde et al.1990). Thus, the male
> advantage in geometry also appears to be selective, that is,
> associated with certain features of geometry rather than the entire
dc> Donna's response: The Spatial advantage which males have
dc> could account for their advantage in geometry, this is
dc> particularly because females showed the same level of
dc> competency in writing geometric proofs. However, I still
dc> find it difficult to understand why these differences do not
dc> appear until adolescence.
Multinational studies show a male advantage in the solving of
arithmetic word problems and on tasks that are solvable
through the use of spatial skills in elementary schools.
Perhaps our measures of cognitive ability are not finely
tuned enough to detect subtle differences: I believe that
sex differences are probably evident in elementary children
but are very slight - furthermore, we haven't devised precise
enough tests to test them. As the child reaches adolescence -
both genes and environment will encourage the child's natural
ability. I don't think that you can say it is nature vs
nurture. Both work in cooperation.
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