Geary 1

From: Bollons Nik (
Date: Fri Feb 13 1998 - 14:04:32 GMT


David C. Geary

Part 1

This section talks about the evolutionary aspect of
mathematical ability and how we should see maths as a domain
comprising of lots of interlinking abilities all designed by
evolution. Some of these abilities directly tap into neural
mechanisms designed by evolution for things closely related
to mathematical like abilities - the laws of geometry tap
into neural circuits designed for navigation in the
environment. These abilities are primarily biological driven.
On the other hand, other abilities use neural mechanisms that
were not specifically designed for use in a maths
environment, but are learnt via culture (in schools, etc), to
be used in maths application. This, Geary calls,
co-optation, and formulates a primarily culture driven
ability. For example, spatial circuits designed by natural
seleciton to find way around a location, are used to create
spatial simulations of maths problems. By placing
mathematical ability in the context of evolutionary theory,
and specifically designed neural circuitry, the article falls
within a growing field of psychological thinking that places
weight on including an evolutionary perspective when
examining human abilities.

> neurocognitive systems that have evolved to serve some
>function or functions related to reproduction or survival

This section begins by making the point that many cognitive
abilities and processes found in all members of the human
species today - for example, language production - are there
because they aided our ancestors in survival and reproduction
in our evolutionary past.

> Thus, when assessing the source of group or individual
>differences in cognitive abilities, it seems necessary to
>consider whether the ability in question is part of a
>species-typical biologically-primary cognitive domain, or
>whether the ability in question is culturally-specific, and
>therefore biologically-secondary.

What this means is that '—some'“ cognitive abilities found in
all humans are predominatley driven by our biology - our
neural biology - and involve little learning via the
environment - for example, language. But that '—other'“
cognitve abilities - such as reading - are more dependent
upon the environment and learning, which builds upon existing
neural abilities, thus making our biology second.

The second point is made clearer in the next section, when
Geary describes how abilities which are more dependent on
learning in the environment - such as reading - can be
aquired because they build on, and use, neural circuits which
were designed for some other evolutionary purpose. A good
example would be the ability to skateboard. Humans can
skateboard because skateboarding uses balance organs and
neural circuits designed by evolution when we became bipedal
(started to walk upright). We have learnt to use these
circuits for abilities other than what they were designed
for, ie. skateboarding (this is called, if i got it right,
Baldwinian evolution). In relation to the study of maths
ability, Geary is highlighting the problem of how we should
look at mathematical ability as:

A) a primary neurobiological ability; with learning and
culture as secondary - like language
B) a primary cultural / learing ability, building on secondary
neurobiology - like skateboarding

>Indeed, these culture-specific abilities might involve the
>co-optation of biologically-primary neurocognitive systems
>or access to knowledge implicit in these systems for
>purposes other than the original evolution-based function
>(S. J. Gould & Vrba 1982; Rozin 1976).

Geary now moves on to explain some of the finer differences
between primary neural and primary learing abilities.

>Domains, such as language or arithmetic, represent
>constellations of more specialized abilities, such as
>language comprehension or counting.

>First, inherent in the neurocognitive systems that support
>primary abilities is a system of skeletal principles (Gelman
>1990). Skeletal principles provide the scaffolding upon
>which goal structures and procedural and conceptual
>competencies emerge.

What these two qutoes mean in other words, is that a primary
ability such as maths - which Geary transforms into a domain
- would not be linked to one single ability and neural area
of the brain - a maths area - but would be produced by a
number of '—abilities'“ in a number of areas. He then goes
onto suggest that these '—abilities'“ - that make up the
'—domain'“ - are themselves, based on '—skeletal'“ structures
which are implicit and innate within an individual. So what
you have is a break up of an ability into loads of
complicated parts:

Domain (maths) = number of different abilities (counting)
Number of different abilities (counting) = skeletal
principles Skeletal principles = procedural and conceptual
strategies Skeletal principles = innate and unlearned.

>While the initial structures for the cognitive competencies
>that might be associated with primary abilities appear to be
>inherent, the goal structures as well as procedural and
>conceptual competencies for secondary abilities are likely
>to be induced or learned from other people (e.g., teachers)

I got lost on the above!

>Even though an implicit understanding of geometric
>relationships appears to be a feature of the neurocognitive
>systems that support habitat representation and navigation,
>this does not mean that individuals have an explicit
>understanding of the formal principles of Euclidean
>geometry. Rather, the development of geometry as a formal
>discipline might have been initially based on early
>geometer's access to the knowledge that is implicit in the
>systems that support habitat navigation

What this section states is that some abilities that make up
a domain such as maths, may be tapping into innate neural
circuits that are closely related to the mathematical task in
hand. For example, some of the basis of mathematical geometry
may employ circuits that are used in navigation by our
ancestors around their environment. In this respect, this one
ability, which combines with others to make up the maths
domain, is biologically dependent.

> Lewis and Mayer (1987) showed that word problems that
involve the relative comparison of two quantities are
especially difficult to solve. For instance, consider the
following compare problem from Geary (1994): "Amy has two
candies. She has one candy less than Mary. How many candies
does Mary have?" The solution of this problem requires only
>simple addition, that is, 2+1. However, many adults and
>children often subtract rather than add to solve this type
>of problem; the keyword "less" appears to prompt subtraction
>rather than addition .... Lewis (1989) showed that one way
>to reduce the frequency of errors that are common with these
>types of relational statements is to diagram (i.e.,
>spatially represent)the relative quantities in the statements

>it is very unlikely that the evolution of spatial abilities
>was in any way related to the solving mathematical word
problems. Nevertheless, spatial representations of
>mathematical relationships are used, that is co-opted, by
>some people to aid in the solving of such problems (Johnson
>1984). The use of spatial systems for moving about in one's
>surroundings or developing ognitive maps of one's
>surroundings appears to occur more or less automatically
>(Landau et l. 1981). However, most people need to be taught,
>typically in school, how to use spatial representations to
>solve, for instance, mathematical word problems (Lewis

What this section states is that other abilities used to make
up the maths domain come from learning we obtain in our
lifetime, through school, education, etc. But that even this
primary cultural learning abilities, uses neural circuits
designed by natural selection for some other unrelated task -
what Geary calls, co-optation. The example given above shows
how being taught to use spatial simulations to solve maths
problems can aid in solving that problem. Because spatial
abilities develop in individuals with little learning and are
not subject to introspection we can conclude for an
evolutionary basis. But it is only through learning that
occurs during an individuals lifetime, is this ability
co-opted onto the maths domain.

> From this perspective, a thorough assessment of sex
>differences in mathematical abilities should be based on a
>consideration of ,whether the abilitity in question are
>likely to be biologically primary or biologically secondary.

This is the last part of the section and outlines the
proposals for the next few sections, in that: any differences
in maths ability by the sexes should be placed in context of
whether that particular tested ability falls into the
compartment of primary biological or primary culture ability.
If such primary cultural / learning abilities are identified
for maths, one must place them in the context of what innate
underlying structures they are employing inorder to do the
mathematical task - they were not designed for.

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