ABSTRACT
The concept of change of position is fundamental for Euclidean metrics. These changes form a mathematical ‘group’, and can be represented in terms of a three-dimensional space structured by a coordinate system. The subject has already been touched on in two earlier investigations. The first of these was concerned with the organization of changes of position at the level of sensori-motor intelligence, during the first eighteen months of life. 2 The second was devoted to the study of spatial representation between the ages of 4 and 12 3 : we saw how younger children described changes of position in terms of end-positions only, while older children compared paths of movement. Dimensions and coordinate systems have also been investigated in an earlier work in which we showed how gradually children learn to structure their space in terms of horizontal and vertical axes and went on to trace the stages of development in the construction of a ground-plan like that of a village. 4 We have yet to study how children come to reconstruct changes of position in terms of a comprehensive system of references, or coordinate system.
