id: 02370627
dt: j
an: 2009b.00251
au: Duval, Raymond
ti: Transformations of semiotic representations and the practice of
mathematical thinking. (Trasformazioni di rappresentazioni semiotiche e
prassi di pensiero in matematica.)
so: Mat. Didatt. 20, No. 4, 585-619 (2006).
py: 2006
pu: Pitagora Editrice, Bologna
la: IT
cc: E20 D20 C30
ut: cognitive analysis of mathematical activity; epistemology; tranformation of
semiotic representations; cognitive problems of representation; modes
of representation; cognitive obstacles; registers of representation;
theory of mathematics education
ci:
li:
ab: Summary: Recurring difficulties in learning that are caused by mathematics
compel us to examine not only the contents and the teaching procedures,
but also cognitive processes liable to mathematical practices. The aim
of this study is to introduce a cognitive analysis of mathematical
activity. The particular epistemological situation of mathematics, with
reference to other fields of knowledge, leads us to ascribe a
fundamental role to semiotic representations. First, they are the only
way by means we can approach mathematical objects, and this fact arises
the cognitive problem of the passage from a representation of an object
to another one, referred to the same object. Then, and above all,
mathematical practices closely imply the transformation of semiotic
representations. On the basis of some examples of different numerical,
visual and symbolic representations, we show that mathematical activity
fuses two kinds of semiotic representations transformations: one
corresponding to a change of the representation register, the other
consisting in the use of transformation possibilities typical for every
register. The first kind is pointed out to be the most difficult and
misleading for the students. Difficulties in the passage form a
representation in a certain register to a representation in another
register reveal the complexity, very often overlooked, of the
articulation between representation registers used in mathematics. We
finally show that the opposition between semiotic representations and
mental representations is based upon a confusion between the system
employed in order to produce a representation and the phenomenological
modality of this production. Frequently mental representations are
interiorized semiotic representations.
rv: