
02311855
j
1996c.01689
Duval, R.
The obstacle of splitting mathematical objects. (L'obstacolo dello sdoppiamento degli oggetti matematici.)
Mat. Didatt., No. 1, 432 (1996).
1996
Pitagora Editrice, Bologna
IT
E63
This paper was originally published in French in "Educational Studies in Mathematics" (Nov 1993) v. 14(4) p. 385414, 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 onetoone 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.)