La Genèse du nombre and Le Développement des Quantités chez l'Enfant were the last volumes we devoted to the development of rational thought in the child. These dealt with the construction of the various systems of operations involved in logical and mathematical functions when the mind is confronted with the real world. They were thus concerned with intuitive or representational thought only in a somewhat negative way, our main object being to indicate its shortcomings and show the necessity for completing and correcting it by means of operations properly so called. But imaged or intuitive representation as such raises a series of problems which need to be discussed in their own right. We need to consider the function of the development of representation and not only its ultimate inclusion within the framework of operations (or rather, that is to say, we need to consider the progressive articulations which gradually transform representation into operational, reversible thought). It is therefore important to give an account of the beginnings of representation and to attempt to understand its specific method of functioning. Only when this has been done is it possible to clarify the connection between intuition and operations, both in those cases where the first is produced into the second, and in those, which may be equally numerous, where imaged representation retains an existence of its own apart from operations, as in play, imitation, and symbolic thought.
In two previous volumes, La Naissance de l'Intelligence and La Construction du Réel chez l'Enfant, we studied sensory motor intelligence in the pre-verbal stage, i.e., that aspect of intelligence which is a preparation in the field of elementary activity for what will much later become the operations of reflective thought. What now therefore requires to be done is to bridge the gap between sensory-motor activity prior to representation, and the operational forms of thought. The problem again becomes that of describing the beginnings of representational thought and of placing its evolution with respect to the sensory-motor stage at one end and the operational stage at the other.
Obviously these problems involve the question of the role of language, which has already been much studied. In our first two volumes, Le Langage et la Pensée chez l'Enfant and Le Jugement et le Raisonnement chez l'Enfant, we considered this question from the point of view of the socialisation of thought. We shall come back to it here only in connection with the first verbal schemas and with "preconcepts," so characteristic of the two to four-year-old stage. We shall rather try to show that the acquisition of language is itself subordinated to the working of a symbolic function which can be seen . . .