The Child's Conception of Number

The Child's Conception of Number

The Child's Conception of Number

The Child's Conception of Number

Excerpt

In our earlier books (The Language and Thought of the Child, Judgement and Reasoning in the Child, The Child's Representation of the World, and The Child's Conception of Physical Causality), we analysed various verbal and conceptual aspects of the child's thought. Later on, we examined the beginnings of thought on the practical and sensory-motor planes (La Naissance de l'Intelligence and La Construction du Réel chez l'Enfant). It now remains, in order to discover the mechanisms that determine thought, to investigate how the sensory-motor schemata of assimilating intelligence are organized in operational systems on the plane of thought. Beyond the child's verbal constructions, and in line with his practical activity, we now have to trace the development of the operations which give rise to number and continuous quantities, to space, time, speed, etc., operations which, in these essential fields, lead from intuitive and egocentric pre-logic to rational co-ordination that is both deductive and inductive.

In dealing with these new problems, appropriate methods must be used. We shall still keep our original procedure of free conversation with the child, conversation which is governed by the questions put, but which is compelled to follow the direction indicated by the child's spontaneous answers. Our investigation of sensory-motor intelligence has, however, shown us the necessity for actual manipulation of objects. In The Child's Conception of Physical Causality, we saw, though it was not possible to take full advantage of the fact, that conversation with the child is much more reliable and more fruitful when it is related to experiments made with adequate material, and when the child, instead of thinking in the void, is talking about actions he has just performed. As far as the study of number is concerned, this is an essential condition, and the gifts of Mlle Szeminska have made it possible to discover techniques adapted to the various problems which needed to be solved and analysed separately. In another volume, written with the collaboration of Mlle Inhelder, the same methods will be used in the description of continuous quantities as the product of quantification of physical qualities (weight, volume, etc.).

In the present volume, it has not been possible to include all that we should have wished to say on the subject of the evolution of number. In particular, there is an inexhaustible mine of . . .

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