id: 02311855
dt: j
an: 1996c.01689
au: Duval, R.
ti: The obstacle of splitting mathematical objects. (Lâ€™obstacolo dello
sdoppiamento degli oggetti matematici.)
so: Mat. Didatt., No. 1, 4-32 (1996).
py: 1996
pu: Pitagora Editrice, Bologna
la: IT
cc: E63
ut:
ci:
li:
ab: This paper was originally published in French in "Educational Studies in
Mathematics" (Nov 1993) v. 14(4) p. 385-414, see ZDM 1984 E53 2093. On
a task concerning the idea of infinity proposed to paired children
(twelve or thirteen years old), we have observed an obstacle
unconnected with this idea. Every pair has been introduced successively
to the argument of inclusion of perfect squares in the integer set,
then to the argument of one-to-one mapping between perfect squares and
integers. Most children rejected systematically the possibility of
bijection: they did not succeed in separating two properties attributed
to the same object (here the "number..."), which is necessary for
recognizing two distinct sets. This obstacle is not limited to the
comparison between an infinite set and its proper subset. The last part
of this study shows similar behaviours in other task. The splitting of
mathematical objects, and the inverse operation of identifying two
different expressions are obstacles encountered by most children at
every important stage of learning. (orig.)
rv: