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
Geary suggests that there are biologically primary abilities- evidence
of which are given for infants as young as 5 months and a pretty
rhesus monkey called Abel. He suggests that these primary abilities
are the necessary precursors to mathematical ability and that they
are the building block for acquiring secondary mathematical abilities
(those acquired through instruction from parent, teachers, etc)
Geary also states that differences may lie in our ability to co-opt our
primary abilities that is use our 'evolutionary functional' abilities
for unrelated purposes such as mathematical reasoning or reading.
Although, as we are talking about sex differences I am not sure where
these are supposed to lie (there's a suprise!) Does this suggest that
sex differences are biological determined? or that it is in the way we
apply our 'given' abilities?. What about the arguement that males
have a superior RH (right hemisphere not hand!) due to testosterone
during the fetal period?
> 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).
Surely whenever we talk of general intelligence we must consider the
fact that when making average (mean) comparisons between subgroups
(males vs females) there is likely to be great variation within groups
as well as between. Therefore some girls may have a greater
mathematical ability than most boys. If there are sex differences
shouldn't we be considering those 'outliers' who can perform better
than boys- at maths!
> 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.)
Parental and school input is very important - think about talented
musicians etc (then see LIZ)!
> 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.
The ability to do algebra and geometry etc will only be apparent when
given instruction this would suggest that we would not be able to do
geometry, algebra etc without being taught! - Yep!
> This is because the knowledge that appears
> to be implicit in the neurocognitive
> systems that support navigation is limited and imprecise.
Geary then suggests that primary abilities may facilitate the learning
of complex maths such as geometry but the majority of it will need to
be taught. This could suggest that there are no sex differences in the
primary abilities needed for complex maths but occur after prolonged
> 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,
Again isn't this the problem? The degree of sexual difference may be
an artifact of the test being used.
>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.
This suggests that sex differences may not be apparent until we are
taught as this facilitates our ability to co opt our primary abilities
and apply them activities which are unrelated to our primary function.
I don't think I've convinced anyone that I know what I'm talking
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