Re: Geary 2

From: Chan Dorothy (
Date: Thu Feb 12 1998 - 21:25:48 GMT

[jc = Jennifer Chalmers]

jc> From: "Chalmers Jennifer" <>
jc> To: "Yr 3 Course Discussion List" <>
jc> Subject: Geary 2
jc> Date: Thu, 12 Feb 1998 13:56:27 GMT

jc> To anyone who may be interested!
> Section 2 Geary.
> Potential primary and secondary mathematical abilities
> > Biologically-primary mathematical abilities.
> > There is some evidence for the
> > pan-cultural existence of a biologically-primary
> > numerical domain which consists
> > of at least four numerical abilities; numerosity,
> > ordinality, counting, and simple
> > arithmetic.
jc> Geary suggests that there are biologically primary abilities- evidence
jc> of which are given for infants as young as 5 months and a pretty
jc> rhesus monkey called Abel. He suggests that these primary abilities
jc> are the necessary precursors to mathematical ability and that they
jc> are the building block for acquiring secondary mathematical abilities
jc> (those acquired through instruction from parent, teachers, etc)
jc> Geary also states that differences may lie in our ability to co-opt our
jc> primary abilities that is use our 'evolutionary functional' abilities
jc> for unrelated purposes such as mathematical reasoning or reading.
jc> Although, as we are talking about sex differences I am not sure where
jc> these are supposed to lie (there's a suprise!) Does this suggest that
jc> sex differences are biological determined? or that it is in the way we
jc> apply our 'given' abilities?. What about the arguement that males
jc> have a superior RH (right hemisphere not hand!) due to testosterone
jc> during the fetal period?

I think the author is trying to distinguish clearly between the
biologically-primary and secondary mathematical abilities so that we
can determine whether there is sex differences in general
mathematical abilities. Because if there is evidence that proves
that such differences do exist in primary "level", then evolution
must have resulted the advantages that males have in mathematics.
However, if differences in the secondary "level", then other factors
must play roles in causing the sex differences between females and
males (as found in many studies).

I should think sex difference is biologically determined as
Benbow(1988) has shown that there is sex difference in the functional
organisation of the left- and right-hemisphere and the fact that the
sex chromosomes in males and females are different.

> > These general abilities are often subsumed under
> > the terms general intelligence
> > (g) or fluid and crystallized intelligence and
> > appear to represent cognitive skills,
> > such as speed of processing or working memory,
> > that support performance in
> > many cognitive domains (e.g., Kyllonen & Christal 1990; Vernon 1983).
jc> Surely whenever we talk of general intelligence we must consider the
jc> fact that when making average (mean) comparisons between
jc> subgroups (males
jc> vs females) there is likely to be great variation
jc> within groups as well as between.
jc> Therefore some girls may have a greater mathematical
jc> ability than most boys.
jc> If there are sex differences shouldn't we be considering those
jc> 'outliers' who can perform better than boys- at maths!

Although indeed there are "outliers" within each category, however,
these "gifted" people are still subject to psychosocial factors which
would influence their eventual achievements in maths. For example,
how much attention they were given in class by their teachers or how
much they actually value their achievements in maths. Their gifted
abilities might be submerged by other psychosocial factors

> >Biologically-secondary mathematical abilities.
> The argument that certain features of counting, number, and arithmetic are
> > biologically primary should not
> > be taken to mean that all numerical and arithmetical
> > abilities are biologically
> > primary. In fact, there are many features
> > of counting and arithmetic that are
> > probably biologically secondary......
> > These features include skills and knowledge
> > taught by parents (e.g., the names of
> > number words), concepts that are induced by
> > children during the act of counting
> > (e.g., that counted objects are usually
> > tagged from left to right), and skills
> > that are formally taught in school
> > (e.g., the base-10 system, trading, fractions
> > multiplication, exponents, etc.)
jc> Parental and school input is very important
jc> - think about talented musicians etc
jc> (then see LIZ)!

I agree very much! For exampe, the societal stereotypes for "what
girls should do or should be good at" could can impacts on the sex
differences in maths rather than immediately jumping into the
conclusion that the sex difference was purely biologically

> > Moreover, it is likely that most features of
> > complex mathematical domains, such
> > as algebra, geometry, and calculus are
> > biologically- secondary, given that the
> > associated abilities only emerge with formal education.
jc> The ability to do algebra and geometry etc will only be apparent when
jc> given instruction this would suggest that we would not be able to do
jc> geometry, algebra etc without being taught! - Yep!

Moreover, evidences have shown that males are more able to co-opt
their primary abilities to learn or develop their secondary
abilitites, does that mean that females have to work extremely hard
just to have similar achievements in maths as males?
> > This is because the knowledge that
> > appears to be implicit in the neurocognitive
> > systems that support navigation is limited and imprecise.
jc> Geary then suggests that primary abilities may
jc> facilitate the learning of complex
jc> maths such as geometry but the majority of it will need to be
jc> taught. This could suggest that there are no sex differences in the
jc> primary abilities needed for complex maths but occur after prolonged
jc> tuition.

As I have mentioned earlier, other "non-evolutionary" factors in fact
play more major roles in the resulted differences in maths
> > Mathematical problem-solving abilities are
> > typically assessed by the solving of
> > arithmetical and algebraic word problems.
> > The solving of mathematical word
> > problems requires the ability to spatially
> > represent mathematical relations,
jc> Again isn't this the problem? The degree of sexual difference may be
jc> an artifact of the test being used.

I should imagine, the emphasis on school subjects are not
standardised between countries or even within countries. For
example, some schools might have more emphasies on maths or
maths-related subjects but other schools might not. So, not only the
kind of tests that were being used to examine the difference but also
the degree of sex difference is actually an artifact of the different
emphasizes in school subjects.
> > The point is that the abilities that are subsumed by the
> > Mathematical Reasoning factor only appear to emerge with sustained
> > mathematical instruction, and are therefore
> > more likely to represent secondary
> > abilities rather than primary abilities. In other words,
> > it appears that for
> > most individuals direct instruction
> > (e.g., teaching the use of diagrams to solve
> > word problems; Lewis 1989) is necessary for the co-optation of
> > primary abilities and the eventual emergence of a coordinated system of
> > secondary mathematical abilities.
jc> This suggests that sex differences may not be apparent until we are
jc> taught as this facilitates our ability to co opt our primary
jc> abilities and apply them activities which are unrelated to our
jc> primary function.

Again, as in many other debates, we should not only restrict
ourselves to the "nature" factor(s) but also looking at "nurture"
factor(s) as well.

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