Jean Piaget, answered from the texts and cited to the page.
The question is broad, so let me give you the center of gravity rather than a survey. Intelligence is not a fixed endowment the child receives; it is constructed, stage by stage, through the child's own activity on the world. At the beginning, the infant has only reflexes and the first acquired associations — yet within a few months it builds a system of schemata capable of unlimited combinations, a system that already presages logical concepts and relations.1
The mechanism is twofold: assimilation, by which the child takes in new experience according to its existing schemata, and accommodation, by which those schemata are reshaped by what resists them. The more numerous the links established among schemata through this dual process, the less thought remains centered on the subject's own activity and the more it becomes genuine comprehension and deduction.2
What drives invention — the genuinely new solution — is not a pre-formed structure waiting to unfold, nor is it the mere internal replay of external experiences already organized by the environment. Both the associationist and the Gestalt structuralist miss the same thing: that the essential is not the schema as a static structure but the structuring activity that gives rise to it.3
The schema only forms by functioning, and it only functions in experience; when, after many months of application to concrete data, the assimilatory activity finally operates on representative symbols alone, it extends itself rather than simply copying what came before.4 The transition from sensorimotor intelligence to reflective thought is not a simple translation upward.
Even when the child has constructed a coherent practical universe — objects that persist, causes that explain, a space and a time that hold together — it must rebuild all of that on the new plane of language and representation, and this reconstruction takes years.5 At each level, accommodation to perspectives outside the child's own reduces egocentrism and solidifies the universe, just as, at the social level, taking the point of view of others locates individual thought in a totality of perspectives that insures its objectivity.6
That, in brief, is the architecture: construction through action, assimilation and accommodation as the twin engines, an invariant sequence of stages each built from the one before, and a progressive decentering that moves the child from a world indistinguishable from its own activity toward a world it can represent, reason about, and share.
starting with the use of reflexes and the first acquired association, the child succeeds within a few months in constructing a system of schemata capable of unlimited combinations which presages that of logical concepts and relations.The Construction of Reality in the Child
The more numerous the links that are established among the schemata of assimilation, the less it remains centered on the subjectivity of the assimilating subject, in order to become actual comprehension and deduction.The Construction of Reality in the Child
the essential is, therefore, not the schema in so far as it is a structure, but the structuring activity which gives rise to the schemata.The Origins of Intelligence in Children
the assimilatory activity, trained by many months of application to the concrete data of perception, finally functions by itself by only using representative symbols. That does not mean at all, let us repeat, that this purification is a simple internalization of earlier experiences.The Origins of Intelligence in Children
In reality, things are far from being so simple... one might therefore expect that the totality of sensorimotor operations would merely pass from the plane of action to that of language and thought and that the organization of schemata would thus be directly extended in a system of rational concepts.The Construction of Reality in the Child
Just as accommodation to the point of view of others enables individual thought to be located in a totality of perspectives that insures its objectivity and reduces its egocentrism, so also the coordination of sensorimotor assimilation and accommodation leads the subject to go outside himself to solidify and objectify his universe.The Construction of Reality in the Child