
02368677
j
2006c.01581
Duval, Raymond
A cognitive analysis of problems of comprehension in a learning of mathematics.
Educ. Stud. Math. 61, No. 12, 103131 (2006).
2006
Springer Netherlands, Dordrecht
EN
D20
C30
E20
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
doi:10.1007/s106490060400z
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. (Author's abstract)