ABSTRACT
The mind does not jump directly from the perceptual notion of continuity to a conceptual schema constructed to express this. A long process of intellectual elaboration is needed to arrive at the two complementary schemas of the decomposition of a line or surface into points and the recomposition of the line or surface from these points. The relations so far considered (of order and surrounding) are only extensions of those of proximity, and it is necessary to go on to the operations of subdivision and reunion of the separated parts. These then lead eventually to the final fully reversible schema referred to above. Thus ‘subdivision’ is the key-notion through which the study of children’s ideas about both continuity and points needs to be approached.
