A parallel argument has been made for some time in the case of
scientific discourse for the 'Thing-ization' of physical
processes (and scientific practices) as a _semantic_ shift,
traced historically by Halliday in _Writing Science_ (ref. below)
from the linguistic evidence, interpreted in a model that links
grammatical constructions (e.g. nominalizations of finite verbs)
to meaning shifts. Halliday had made some general observations of
this sort as early as the 60s, and I had discussed the phenomenon
for scientific discourse in a paper on technocratic ideology
(abbreviated as Ch 4 in _Textual Politics_) as an example of
semantic 'condensation', in which the complex thematics of
activities are re-represented by naming the activity (but in
which the meaning _intertextually_ remains complex for expert,
but not for other, readers -- a gap exploited by technocratic
modes of discourse as distinct from technical ones).
In these analyses the 'reification' is not seen as a 'universal
psychological process' but as a very linguistically, culturally,
and historically specific discourse practice, with rather
definite ideological functions.
An application of the argument has been made recently to
discourses of school mathematics in a recent dissertation by Kay
O'Halloran (Murdoch University, Australia).
I will be very interested to make comparisons particularly with
Sfard's views. O'Halloran's work compares across social class
(and gender) and may provides an interesting counterpoint to
Confrey & Costa. It is possible that, as with technocratic abuse
of technical discourse conventions, it is only when the expert-
assumed practices of unpacking the condensations are not
successfully taught alongside the super-condensed meanings of
symbolic mathematics that the divergence between mathematicians'
views of their practices and students' needs become acute.
Certainly semantic condensation imposes some additional
information-processing burden, but it may seem more significant
and mysterious as a 'cognitive' process than it does as a
linguistic-semantic one. I really doubt that by itself it
presents major hurdles to students' understanding. More likely
the obstacles derive from (1) lack of systematic unpacking, which
prevents many mathematical abstractions from ever rising to the
concrete level where alone they are ever understood by anyone,
and (2) the very real extensions of natural language semantics
which exist only in mathematical discourse (because of its
special historical functions) and cannot be comprehended in the
verbal modes most of us are used to (though visual and motor-
manipulative modes, combined with verbal, offer a critical
assist).
JAY.
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JAY LEMKE.
City University of New York.
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