Geary Commentators: Foss, Frith, Gilger

From: Dunn Christopher (
Date: Thu Feb 12 1998 - 14:47:37 GMT

Christopher Dunn

In Fidelman's commentary, he claims Geary ignored some pertinent
research on how males and females hemispheres and corpus callosum
differ in relation to information processing mechanisms for primary
mathematical abilities.


> Fidelman (1992a) suggested that the efficiency of the brain`s
> cognitive functions is determined by three factors. The first is the
> efficiency of the analytic mechanism which is lateralized mainly to the
> left hemisphere. This mechanism processes one datum after another
> analytically and transmits them to the synthetic mechanism, which is
> lateralized mainly to the right hemisphere. The second factor is the
> efficiency of this synthetic mechanism which synthesizes a new whole
> out of the the individual data obtained from the left hemisphere. This
> new whole is transmitted to the left hemisphere where it is procesed
> analyticaly as an individual datum. The third factor is the efficiency
> of the corpus callosum which transmits the data between the
> hemispheres. The left hemisphere of females is more efficient than that
> of males, while their right hemisphere is less efficient. The corpus
> callosum of females is larger than that of males, though their relative
> size is age-dependent (Fitch & Denenberg 1995). This relative size may
> indicate relative larger efficiency of the female corpus callosom.
> These observations are explained in Fidelman (1992a) by the suggestion
> that a right hemispheric brain which has larger synthetic power needs
> less interhemispheric transmissions of data in ord >According to Geary
> (section 4.1) "there are no sex differences in biologically primary
> mathematical abilities." This statement may be co matical abilities to
> the hemispheric mechanisms.<

> Acording to Geary (section 4.2.5) "when a sex difference in
> mathematical skills is found, it is typically not found until
> adolescence." This may be caused by the increased quantity of sex-
> hormenes at adolescence, and its influence on the hemispheres. They
> some changes to the curricula to aid learning.<

This commentary does provide some explanations for possible biological
differences and to its credit suggests some social policy, to aid
learning of maths by making separate curricula for those individuals
with differing hemisphericity. However whether this is a practical
solution in today's already overcrowded curriculum for example
subdividing for hemisphere and then again for personal ability is
another matter. Although this level of analysis may be useful to
explain the `base' of ability and illustrate biological limitations and
perhaps interventions to package the information we learn in a certain
way, to make it easier for some individuals to process. It ignores real
social application and context, can we assume that differences between
sexes is solely due just to biological differences, ignoring
motivation, social class, quality of teaching, stereotyping and self
fulfilling prophecies in the class room plus, social influences outside
the classroom. Even if these new techniques were implemented from this
area of research, how much improvement would we see, how much of it
would be `eaten up' by `real life' variables?


The commentary by Foss also picks up on this criticism. In Geary's
article social influences may be ignored and Geary's diagram of
influences of mathematical ability is flawed in its simplicity.

> Figure 1 makes the task look easier than it is, for all of the arrows
> flow out of the box at the top left: "Sexual Selection," which simply
> is to diagram the unproven assumption that ultimately the source of
> "Sex Differences in Mathematical Problem solving and Geometry" (box top
> right) must, like all biological phenomena, find their s rce in
> evolution. Unfortunately, there are other arrows which Figure 1 leaves
> out, such as, for example, the ones which must go into the box "Sex
> Differences in Social Preferences and Social Styles." Many things
> affect preferences and styles, and thus bear on this set of sexual
> differences, and not only nice scientific things like whether the
> culture is agrarian or industrial, but also quirky things, like Marilyn
> Monroe and Albert Einstein. Marilyn was not much of a mathematician,
> though Einstein was, and no doubt this has had some effect on some
> people's "social preferences and social styles," and thus, according to
> Geary, on sex differences in mathematical abilities. In other words,
> the system in Figure 1 is massively open!<

Foss points out that mathematical abilities do not develop in a vacuum,
they develop with social and cultural influence. Also Geary's "Pan
cultural" methodology is a pretty crap explanation for the filtering
out of cultural influences, by ignoring the fact that cultural
practices may mask or override biological influences.

> Which brings us to the first methodological stratagem Geary proposes:
> to hear the sexual signal through the cultural noise, we need only
> attend to evidence which is "pan-cultural" (p.9), so that varying
> cultural influences can cancel each other out. The methodological
> inference is of this form: pan-cultural, hence non-cultural, th efore
> biological in origin. For instance, if men are taller than women
> pan-culturally, then the difference is non-cultural, therefore
> biological in origin. But this form of inference is not generally
> reliable. Funerary practices are found everywhere (even where there is
> no mathematics) but surely there is no gene directing them. Likewise,
> news of Marilyn and Einstein pervades the mathematically educated
> world, but that hardly makes their effects non-cultural or biological.<

> Mathematics itself is a cultural phenomenon. Homo sapiens might well
> have prospered indefinitely without it: unlike the heart, it is
> biologically unnecessary. Future paleo- anthropologists will note that
> the fossil remains of math texts and calculating machinery appear in
> the same strata with remains of sophisticated tools, bu dings, musical
> instruments, automobiles, and Marilyn Monroe movies. The cultural
> changes which accompanied the invention of mathematics occurred over
> most of the globe within a few millennia of each other: people turned
> to agriculture, built cities, became more scientific, monotheistic, and
> monogamous. Given that mathematics is itself a rich cultural phenomenon
> lavishly embedded in yet other cultural phenomena, the purely
> biological effects of sex upon it cannot be isolated by Geary's simple
> pan-culturally stratagem.<

Although to ignore the fact that the parts of the brain that just
happen to be used in maths, may have differences in their ability to
process mathematical information (as in the Fidelman article) would be
foolish, our biological base must not be ignored. Foss claims that the
small difference that biology may have on maths ability, is pretty
irrelevant to the real world

> A second dubious element of Geary's method is used whenever he
> identifies sexual differences on social dimensions relevant to
> mathematical achievement. At these points he claims that "at least a
> portion of the sex differences on these social dimensions is
> biologically primary" (p. 15). This is a plausible assumption, but it
> ha essly renders Geary's conclusion unfalsifiable: void of empirical
> content. We begin with the idea that the sex differences in mathematics
> have either social or sexual causes, but if we then assume that the
> social causes are themselves, at least in part, the effects of sexual
> causes, then it is trivial that at least part of the differences in
> mathematics are the biological effects of sex itself., whatever the
> evidence has shown, or may show -- it is a mere tautology, and says
> nothing about the empirical world.<

The points Foss is making are extremely relevant it may be very easy to
become over concerned with the argument about how an ability evolved,
or whether it makes one sex better than the other. While ignoring how
this then applies to the here now and how relevant is this issue to
help us at this point in time, to make our lives bett . How it
interacts with the complex social world that we have created to help us
overcome some of our evolutionary limits.


Others (Frith and Happ) have offered alternative accounts to Geary for
sex differences, that cognitive strategies differ, subjects trying to
guess what the experimenter wants from them, and from cognitive
top-down or bottom-up processing

> As Geary points out, these problems are oddly phrased. In many
> respects the questions, as communications, violate Gricean maxims. In
> terms of relevance theory (Sperber & Wilson, 1986), the listener is
> justified in assuming that the speaker intends the most accessible
> interpretation. Anything else is trickery. The prediction uld be that
> you can improve performance by making the correct interpretation
> relevant, eg. by highlighting Mary.<

> Why should females be more sensitive to this pragmatic violation?
> Listeners will only be misled by these puzzles if they are trying to
> "read the speaker's mind". It is the normal concern with underlying
> meaning, versus surface form, which misleads. The same problem is seen
> in young children's failure to judge an inadequate messa as ambiguous -
> especially where the speaker's intention is clear (Beal & Flavell,
> 1984). Recognising speaker's intention depends upon theory of mind; the
> ability to attribute independent mental states to self and others
> (Premack & Woodruff, 1978). Greater sensitivity to mental states would
> therefore be a disadvantage in these word puzzles. Perhaps females have
> better developed theory of mind skill<

> Since children with autism typically fail tests of theory of mind
> (Frith, 1989), we would predict that they would be less misled (than
> verbal ability matched controls) by mathematical word problems. There
> is another reason, too, why children with autism might be relatively
> good at these puzzles. As mentioned above, children with autism show
> weak central coherence, attending to parts over wholes, and paying
> preferential attention to surface form versus gist. This cognitive
> style may be characterised in terms of greater bottom-up processing and
> less top-down influence. One way to fail the word puzzles is to leap to
> conclusions. In this case, incorrect answers will be given faster than
> correct ones, even though the arithmetical operations themselves are of
> equal difficulty. If top-down strategies cause failure, then inducing a
> bottom-up strategy should aid performance. This suggestion predicts
> that - in contrast to the other hypotheses - making the content of the
> word puzzles more artificial and unfamiliar would help. Interestingly,
> sex differences on Block Design and Embedded Figures (Voye Voyer &
> Bryden, 1995) suggest that females may have stronger central coherence
> than males.<


This commentary is moving in the right direction. By offering plausible
alternatives for Geary's work but again it is only focusing on one
thing, cognitive strategies in a specialist group, whose results may
not generalise to the general population. Gilger's commentary points out
although Geary has made some useful contributions, speculation over how
abilities evolved may be a fruitless exercise.

> There is much to comment on in this paper. To its' credit Dr. Geary's
> manuscript presents a thought provoking theory. At the outset, however,
> I feel compelled to state the obvious: while intriguing, the theory is
> perhaps another "just so" story. So many ideas that utilize
> evolutionary theory and base themselves on retrospe ive hypotheses are
> doomed to this criticism, and it is important to some day supplement
> "just so" stories with testable, a priori hypotheses. Primary versus
> Secondary Abilities in Mathematical Cognition<

Also once we have discovered that differing abilities in maths are due
to evolution and genetics, making one sex better than the other
(because of primary skills), so what? We could have seen that one sex
is better than the other from results from maths test. The question is
now that we have found that males are better at this nd females are
better at that, because of biology what are we going to do with these
findings. If the answer is nothing, then that would be wrong, as in the
Fidelman's commentary they suggested ways in which we could use this
knowledge to improve secondary skills or as Frith and Happ suggest to
remove or overcome the sex differences. It still remains that under
importance of environment and over importance of biology may be a bias
in these arguments.

> As my last comment, I would like to add to Dr. Geary's survey of
> hormonal and experiential effects on spatial skills. There can be no
> doubt that there are effects of hormones on cognitive abilities, and,
> that this area of study is quite complicated. Ther are two aspects of
> my own research that I would like to bring up that may have some
> bearing on Dr. Geary's review.<

> First, Dr. Geary's review indicates that past studies have shown
> female cycle effects on spatial test performance. In an earlier study,
> we (Ho, Gilger, & Brink, 1986) also tested females at different phases
> of their cycle on an information processing (chronometric) spatial
> relations task. We demonstrated that on the surface, there ere no cycle
> effects on ability, or the corrected score for the tests administered.
> However, signal detection analyses indicated that the subject's
> approach to the task, or the subject's task strategy (as assessed by
> between-phase variances and beta) was significantly different as a
> function of phase. In other words, women made more false alarms and
> responded more rapidly depending on the stage of their cycle, although
> their number of correct answers remained relatively stable. This
> suggests that studies that fail to look closely at the patterns of
> responses may miss the basis for any phase differences they may find:
> phase differences may not be due to hormonal effects per se on ability
> (d-prime in our study) but instead on mood or strategy<

> Second, Dr. Geary cites another of our papers (Gilger & Ho, 1989)
> where significant sex differences were found on the same
> two-dimensional spatial rotations tasks used in Ho et al. (1986). It is
> noteworthy that the sex difference noted on our chronometric task for a
> mental process was on the rotation parameter. Specifically, females
> were slower than males to mentally rotate the stimuli. Our study
> suggests that sex differences on corrected scores for such tasks are
> largely due to abilities on this internal mental rotation parameter.<

This archive was generated by hypermail 2b30 : Tue Feb 13 2001 - 16:23:19 GMT