Jean Piaget (1896–1980) was a Swiss developmental psychologist who is best known for his theory of cognitive development in children. His theory outlined a number of stages of development. Piaget describes differences between children of different ages.
The Pre-Operational Stage: Let us turn now to the development of representational thinking proper. We observe it first in play, in imaginary games with their fictitious qualities and symbolic aspects, play in which one thing comes to be represented by means of another thing. Differentiated imitation, for instance of various people in the child’s environment, and a variety of other symbolic acts belong to this stage. Such representational thinking greatly enlarges the range of intellectual activity … All this takes place in the period which extends from the beginning of language at one end to the age of about seven or eight years at the other end. During this period we can already speak of thought, of representation, but not yet of logical operations defined as interiorized reversible action systems … We can ask the child to put blue beads into container A and red beads into container B, and we make sure that each time he places a blue bead into container A he also places a red bead into the other container B, so that there will be the same number of beads in each of the two containers. The child is then told to pour the beads from container B into a new [taller and thinner] container C, thereupon we ask him if there are the same number of beads in C and in A—those in A having remained there and those from B having been poured into C. Now a curious thing happens. Until approximately the age of 6½ years the child believes that the number of beads has changed, that there are more beads in container C because it is higher than B, or that there are fewer beads in container C because it is thinner than B. If you ask him ‘Where do these extra beads come from?’ or ‘What happened to the beads that are no longer there?’ he is very much surprised at your question. He is totally uninterested in the mechanism of the transformation. What interests him is the gross perceptual configuration which is different in the two situations; even in the case of these discrete entities there is no conservation of absolute quantities.
The Stage of Concrete Operations: Towards the age of seven or so the problems of conservation become resolved … How have they been resolved? They have been resolved as a function of three arguments which children always give you, irrespective of the experimental problem. The first argument is: the quantity, or the number is the same—for example, in the bead problem, nothing has been added and nothing has been taken away. I call this the identity argument, because it takes place entirely within the single, self-contained system without any attempt at transcending the boundaries of that system …
The child’s second argument tells us the reason. I call this the argument of simple reversibility. The child says: ‘you have done nothing except to pour the beads in the other container, so it looks different, but all you have to do is to pour them back and you will see that they are the same’. In other words, it is no longer the perceptual configuration which is interesting, it is their displacement and the resultant transformation. This transformation is apprehended as something that can take place in both directions, that is reversible …
The third argument used by the children is again based on a kind of reversibility, but now in the form of a pattern of relationships. The child tells you: ‘Here is more height but a little less width; what you gain in height you lose in width; that evens it out’. This implies a pattern of relationships, a multiplication of relationships and their mutual compensation; it is once more a type of reversibility. In other words these three arguments, that of identity, that of simple reversibility and that of patterned relationships show you the beginnings of operations as we have defined them. These operations, that can be observed between the ages of seven years and eleven or twelve years, are already logical operations. Their structure is essentially logical, even though the available implications of that logic are still rather limited … These operations always center around an action or an application to specific objects. For this reason we call them ‘concrete operation’.
The Stage of Propositional Operations: Let us proceed to the last stage which begins approximately at the age of 12 years and which is characteristic of the whole adolescent development. This is the period during which new logical operations appear: prepositional operations, the logic of propositions, implication, and so forth. These are superimposed onto the earlier concrete operations. The adolescent is no longer limited to concrete reasoning about objects, he begins to reason hypothetically. Starting from a theoretical assumption he can reason that if it is true, then certain consequences must follow. This is the hypothetico deductive method that presupposes implication, disjunction, compatibility, and all the other operations of the logic of propositions.
Piaget, Jean. 1976. An Introduction to Jean Piaget Through His Own Words. edited by Sarah F. Campbell. New York: John Wiley & Sons, Inc. pp.2–11. Amazon || WorldCat