id: 02370020
dt: j
an: 2006e.02979
au: Bagni, Giorgio T.
ti: Some cognitive difficulties related to the representations of two Major
concepts of set theory.
so: Educ. Stud. Math. 62, No. 3, 259-280 (2006).
py: 2006
pu: Springer Netherlands, Dordrecht
la: EN
cc: E63 C33 D23
ut: set theory; belonging to; inclusion; cognition; cultural context;
Euler-Venn diagrams; semiotic representations; theory of mathematics
education
ci:
li: doi:10.1007/s10649-006-8545-3
ab: The main focus of this paper is on the study of studentsâ€™ conceptual
understanding of two major concepts of Set Theory - the concepts of
inclusion and belonging. To do so, we analyze two experimental
classroom episodes. Our analysis rests on the theoretical idea that,
from an ontogenetic viewpoint, the cognitive activity of representation
of mathematical objects draws its meaning from different semiotic
systems framed by their own cultural context. Our results suggest that
the successful accomplishment of knowledge attainment seems to be
linked to the studentsâ€™ ability to suitably distinguish and
coordinate the meanings and symbols of the various semiotic systems
(e.g. verbal, diagrammatic and symbolic) that encompass their
mathematical experience. (orig.)
rv: