ABSTRACT
This chapter examines what happens with series in which there are only additive relations between discrete elements, in the form of numerical additions; or in which there are varied alternations ranging over poker chips; or even alternations ranging over the number of sides for geometric figures. The demands imposed by this type of series may look entirely elementary, but we will soon be noting the unexpected difficulties. These difficulties are not; however, at the same level that F. Orsini has called 'asymmetric alternations', in her studies of 'natural regularities. 'The full study later appeared in Jean Piaget, Francine Orsini, Marianne Meylan-Backs, and Hermina Sinclair, from regularities to proportions, in Jean Piaget, Jean-Blaise Grize, Epistemology and psychology of functions. But what is of principal interest in our findings about Stage I is rather the difficulty of the empirical or pseudo-empirical abstraction that would allow the child to take correct actions based on the characteristics of the model and conform to them.
