id: 02368677
dt: j
an: 2006c.01581
au: Duval, Raymond
ti: A cognitive analysis of problems of comprehension in a learning of
mathematics.
so: Educ. Stud. Math. 61, No. 1-2, 103-131 (2006).
py: 2006
pu: Springer Netherlands, Dordrecht
la: EN
cc: D20 C30 E20
ut: cognitive paradox; figural organization; knowledge object; language;
learning; recognition; multifunctional and monofunctional registers;
noncongruence; representation; representation conversion; semiotic
representation; semiotic systems; thinking processes; treatment;
MD2005c.01390
ci:
li: doi:10.1007/s10649-006-0400-z
ab: To understand the difficulties that many students have with comprehension
of mathematics, we must determine the cognitive functioning underlying
the diversity of mathematical processes. What are the cognitive systems
that are required to give access to mathematical objects? Are these
systems common to all processes of knowledge or, on the contrary, some
of them are specific to mathematical activity? Starting from the
paramount importance of semiotic representation for any mathematical
activity, we put forward a classification of the various registers of
semiotic representations that are mobilized in mathematical processes.
Thus, we can reveal two types of transformation of semiotic
representations: treatment and conversion. These two types correspond
to quite different cognitive processes. They are two separate sources
of incomprehension in the learning of mathematics. If treatment is the
more important from a mathematical point of view, conversion is
basically the deciding factor for learning. Supporting empirical data,
at any level of curriculum and for any area of mathematics, can be
widely and methodologically gathered: some empirical evidence is
presented in this paper. (Authorâ€™s abstract)
rv: