Geary 4

From: Crumley, Donna (dhc195@soton.ac.uk)
Date: Tue Feb 24 1998 - 14:41:16 GMT


> This section focuses on potential sex differences, or a lack thereof,
> in biologically-primary and biologically-secondary mathematical
> abilities. In preview, research in these domains suggests no sex
> differences in biologically-primary mathematical abilities, but
> consistent differences, favoring males, in some biologically secondary
> areas, in particular mathematical problem solving and geometry.

Geary gives examples of studies conducted in an attempt to discover
whether these differences exist.

> Of particular interest with the infancy studies is whether boys and
> girls differ in their sensitivity to numerosity, and in their basic
> understanding of the effects of addition and subtraction on quantity
> (Starkey et al. 1983; Wynn 1992); sex effects were not assessed in the
> ordinality studies. Those studies that did examine sex differences are
> very consistent in their findings: Boy and girl infants do not differ
> in their ability to discriminate small numerosities (Antell & Keating
> 1983; Starkey et al. 1990; Strauss & Curtis 1981).

He also gives examples of studies conducted across different races.
Again he finds no evidence to suggest that males and females have
different abilities with regard to primary mathematical ability.
There were no sex differences, across race or social class, in the
ability to count and enumerate, or on any task that assessed basic
counting and number knowledge.

> 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.

Geary seems to be implying here that something other than biological
ability - socialisation for example lies behind later sex differences
in mathematical problem solving.

> Mathematical problem solving and geometry. Sex differences in general
> samples. The results described in this section are from large-scale
> studies of what appear to be representative samples of boys and girls
> from many different nations. These studies represent differences
> across a broad range of abilities, including the gifted. Hyde et al.
> 1990), and others before them (e.g., Dye & Very 1968), argued that the
> sex difference in mathematical problem solving, for instance, is not
> evident until adolescence. As described in Section 2.2, factor-
> analytic studies suggest that the Mathematical Reasoning factor does
> not emerge until high school, and it is the emergence of this factor
> that is typically associated with the emergence of sex differences in
> mathematical skills, at least in the United States (Very 1967).

Here Geary is suggesting that it is not until adolescence that sex
differences are shown. The differences come about as a result of the
Mathematical Reasoning Factor. I'm not sure that I agree with this.
Surely males don't suddenly become mathematical genius', leaving their
female counterparts behind. I believe that the process of
socialisation reinforces biological ability from an early age. Survival
of the fittest has never required that females need to be good at
mathematical problem solving/ spatial ability. The female has always
ensured the safety of her off spring. The male on the other hand has
had an underlying necessity to be good at mathematics/ spatial ability.
He needs to be able to protect and provide for his mate and off
spring.

> Error patterns suggested that girls found translating relational
> information into appropriate equations more difficult than boys
> (Marshall & Smith 1987).

> In all, these studies indicate that beginning in the elementary-school
> years and continuing into adulthood, boys often show an advantage over
> girls in the solving of arithmetical and algebraic word problems.

> Except for the solving of algebraic word problems, there appear to be
> no other consistent sex differences in algebraic skills (Hyde et al.
> 1990), but modest sex differences are found in geometry and calculus.
> As noted earlier, Harnisch et al. (1986) found a consistent male
> advantage (of about 1/2 of a standard deviation) in geometry for both
> 13- and 17-year-olds across ten nations.

Geary again reinforces the notion that these sex differences are cross
cultural and that males are more competent than females in the majority
of mathematical areas.

> 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).

The above evidence suggests that socialisation does have a part to play
in giftedness. More school work in China led to higher results in the
tests - for females as well as males. Giftedness then, it seems is not
innate, but the result of early learning and practice.

> 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
> 1990).

> 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
> domain.

The Spatial advantage which males have could account for their
advantage in geometry, this is particularly because females showed the
same level of competency in writing geometric proofs. However, I still
find it difficult to understand why these differences do not appear
until adolescence.



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