id: 02364816
dt: j
an: 2005d.01407
au: Duval, Raymond
ti: Cognitive conditions of the geometric learning: Developing visualisation,
distinguishing various kinds of reasoning and co-ordinating their
running. (Les conditions cognitives de l’apprentissage de la
géométrie: Développement de la visualisation, différenciation des
raisonnements et coordination de leurs fonctionnements.)
so: Ann. Didact. Sci. Cogn. 10, 5-53 (2005).
py: 2005
pu: IREM de Strasbourg (Institut de Recherche sur l’Enseignement des
Mathématiques), Université de Strasbourg, Strasbourg
la: FR
cc: C30 G10
ut: functional analysis (psychology); code; visualisation; counter-examples;
heuristic figural decomposition; dimensional building; definition;
straight lines; figures (geometry); proofs; proposition; figural unit
ci:
li: http://mathinfo.unistra.fr/fileadmin/upload/IREM/Publications/Annales_didactique/vol_10/adsc10-2005_001.pdf
ab: Geometry is a kind of knowledge area that requires the cognitive joining of
two representation registers: on one hand the visualisation of shapes
in order to represent the space and on the other hand the language for
stating some properties and for deducing from them many others. The
troubles of learning first come from the fact these two registers are
used in a way which is opposite to their cognitive use apart from
mathematics. The way of seeing a geometrical figure depends on the
activity for what it is used. Thus it can run in an iconic way or in a
non-iconic way. The non-iconic visualisation involves that the first
recognised shapes would be visually deconstructed. There are three
kinds of shape deconstruction: deconstruction by using tools in order
to construct any figure, the heuristic breaking down in order to solve
problems and the dimensional deconstruction. This one is the central
process of geometrical visualisation. The analysis of language in
geometry requires that three levels of discursive operations would be
separated: verbal designation, property statement and deduction. This
separation is important because the relation between visualisation and
language changes completely from one level to the other. This variation
conceals the most important cognitive phenomenon: the dimensional
hiatus. Comings and goings between visualisation and language involve a
jump into the number of dimensions in order to recognise the knowledge
objects that are represented within each register. Becoming aware of
the dimensional deconstruction of shapes and understanding the process
of the various discursive operations are the conditions for succeeding
in making the two registers run in synergy. There are the crucial
thresholds for learning in geometry. Is that really taken into account
in the teaching?.
rv: