Date: Tue, 03 Aug 1999 10:21:01 -0500

Sender: Chris

Subject: cognitive development as related to learning mathematics
I am doing an independent study for my Math theory course at Evergreen State College, WA. I am looking into teaching Math to elementary students "as a language". I need information on cognitive development to tie to this idea of language development. I only know of Piaget. There must be others who are more recent. Can you help?

My name is Christopher

I am a junior at Evergreen State College

Hi Chris,

I am suspicious of analyzing 'mathematics as a language' at a cognitive
level.

It appears to me that recent studies indicate that, at a cognitive level
'mathematics' is many different things, one of which is 'a language',
others of which are 'spatial', and probably other intelligences as well.

For example, there was a recent study (written up in Science in late
April or
early May) which studied bilingual people (Russian /English) doing two
kinds
or 'arithmetic calculation": exact, and approximation ( a > b). For the
exact
calculation, it mattered what language the problem was given in, and the
'language' part of the brain was activated. For the approximation, the
language did NOT matter and the parietal lobes were activated (the area
where, say the number line would be represented as a geometric /
topological
object). So one skill is probably cognitively a 'language' skill - but
how it
is done depends on 'language' in a sense other than mathematics AS a
language,
rather mathematics IN a language. The other is cognitively not much
connected
to language.

Gardner ( a cognitive scientist) distinguishes logic/ algebra (which he
calls
'logic / mathematics' from language AND from spatial cognition:

Howard Gardener, Frames of Mind: the theory of multiple intelligences,
Basic Books, 1985.

There are continuing studies of spatial cognition (for mathematics, as
well as
for geography, mechanical drawing, navigation etc.) A book with a lot
of this
is:

Spatial Cognition: Brain Bases and Development, ed Stiles-Davis,
Kritchevsky and Bellugi, Lawrence Erlbaum Hillsdale New Jersey, 1988.
This includes some updates
on Piaget's work on learning geometries (i.e. learning topology first and
euclidean
geometry last - the opposite of the curriculum ... )

Another is:

I.S Yamkimanskaya, The Development of Spatial Thinking in School
Children, Soviet Studies in Mathematics Education Volume 3 (1980),
translated by Robert H. Silverman, NCTM, Reston Virginia, 1991.

However, there certainly IS an analogy between mathematics teaching and
'whole language teaching": the need to give a wide range of experiences,
the practice the use in meaningful contexts, to use mathematics for
communication
among students etc. However, that seems to have more to do with issues
like
constructivism etc.

Cheers

Walter Whiteley

York University