Piaget proposes that there are three types of knowledge: physical, social, and logical mathematical. According to Piaget, "Intelligence is an adaptationTo say that intelligence is a particular instance of biological adaptation is thus to suppose that it is essentially an organization and that its function is to structure the universe just as the organism structures its immediate environment". "Piaget also called his view constructivism, because he firmly believed that knowledge acquisition is a process of continuous self-construction. That is, Knowledge is not out there, external to the child and waiting to be discovered. But neither is it wholly performed within the child, ready to emerge as the child develops with the world surrounding her...Piaget believed that children actively approach their environments and acquire knowledge through their actions". Piaget declared that he is neither an innatist nor an empiricist. He believes that we always interpret according to our own structure. Innatists believe that every individual is born with preexisting ideas present in the mind. Empiricists, on the other hand, believe that experience, especially of the senses, are the only sources of knowledge. Piaget argues that for empiricists, knowledge is a copy of objects. But actually, knowledge is always an assimilation or interpretation. In drawing a geometrical shape, the child does not draw what he sees, rather, he draws his idea of it - he draws what he knows of it. To look at it a clearer perspective, the child actually draws his interpretation of the object, and not the exact object itself. Asking a child to draw a diamond shape, showing the child a model of that shape, would give the child an idea of what you want him to do. He may see the diamond shape as a square with some points on it, so he may draw a square with a point in it or with a point beside it.
In the light that Piaget believes knowledge is primarily operative, he points out that children who are in the concrete operations stage (seven to eleven years old), and in the formal operations stage (twelve years old and up) constructs their perception of the world through the cognitive development which results from the child's interaction with the environment. The interiorisation of this interaction then forms internal models of reality or "operational structures" which forms the basis of perception upon which the child acts.
In the seriation demonstration, four children were asked to arrange a set of rods in order of length. Barbara is 3.5 years old, Renaud is 4 years old, Matthieu, 6.5 years old, and Catherine who is 9 years old. Among the four children, Catherine mastered the seriation structure as she can comprehend the processes of relating, corresponding, ordinal estimation, measurement, and classification. Catherine is at the age wherein she has mastered the nature of coordination. Barbara, on the other hand, being the youngest in the group, at 3.5 years old, she in the stage wherein she is motivated by biological and social impulses, also she has no sense of obligation to rules. She is the one with the poorest seriation structure among the group. Renaud is a few months older than Barbara, and similar results are expected from him regarding the seriation process, but better, as he is more