Sur l'enseignement de la relation transitive a l'ecole elementaire

Abstract

A team, comprising teachers of mathematics and psychopedagogues, tried to define the prerequisites for the command of the transitive relation during the elementary period of education in France. The aim of this study was to bring to light the impact of teaching on a notion which was not specifically meant to be taught. After selecting a sample of pupils, the team set them a progressive test composed of transitive operations bearing on symbolic objects and structures. This study permitted us to observe what conditions are required for success, and how the command of the transitive relation develops.

The interpretation of the results leads us to stress several important factors. First, confirming the studies of Piaget's disciples, observation shows a characteristic threshold in the learning of that notion around the age of 6–8. However, if the command of transitive relation bearing on objects is almost complete towards the end of elementary education, a certain stagnation of results can be noticed in the case of symbolic relations, except for the pupils who get very good results in mathematics. The authors feel they have brought two obstacles into light. One is resulting from the number of elements to be combined. A combination of more than three terms seems to present a considerable difficulty for many children. The other obstacle comes from the nature of the exercises set at school. Apparently, they require the children to use a type of problem solving quite unattainable for many of them. On the whole, the authors feel that education, to be efficient, should be more selective about the notions to be learnt and the conditions of their teaching.