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Here you are looking at Piaget's cognitive theory of development. In order to determine if the child is behaving and developing according to Piaget's schedule you must first determine what stage of development the child should be in. At four years old the child should be in the preoperational stage of development which is characterized by use of symbols to represent concepts, language development, and an egocentric perspective (focus on self over focus on others). It is important to note that the concept of conservation is not present and abstract thought has not yet developed.
In order to answer this question you will want to observe the child and record their behaviors. You may want to utilize several small tests to see if the child can identify a picture of a horse to identify the concept of a horse. You could run a conservation activity to see if the child has started to move into the concrete operational stage. It is important to note that the age ranges outlined within this theory are not concrete; some children may develop early while some may develop later. However, if there is a lag of several years there begins to be a concern regarding cognitive development.
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