Piaget and Vygotsky concluded that children use different concepts than adults to order the world, and these concepts gradually change as children grow. Piaget describes the schemas of a child, or groupings of concepts on how to understand the world, as something that is learned and shaped by experience and by behavior.
Piaget said he believed that a child goes through four stages of development. In each of these stages, the child learns new ways to order the world, which brings him closer to adulthood. Piaget believed that a child shapes his world based on personal and individual experience. Therefore, he saw it as the duty of the parent to leave a child alone as much as possible and allow her to freely explore the world without limitation.
Vygotsky said he believed that a child's behavior and language develops through social interactions with influential adults. He asserted that in order to study the knowledge of a child, their social interactions must be studied. In Vygotsky's model, a child talks to an adult. The adult then either validates or invalidates the remark made by this child. Based on the reaction of the adult, a child learns whether his behavior or language is "correct" and alters his knowledge based on this experience.
Piaget saw language as an outgrowth of thought, and labeled it a socially derived conventional system that was used by children simply to express their thought. Vygotsky found the development of language to be much more important. Since knowledge of the world, for Vygotsky, is based on interaction with influential adults, a child must be able to communicate with these adults to properly develop. Therefore language serves to facilitate the growth of knowledge and is integral for a child.