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.


Walter Whiteley
York University

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