Final answer:
A child displaying egocentric thinking is in the preoperational stage, the second of Piaget's stages of cognitive development, which occurs from approximately 2 to 7 years old.
Step-by-step explanation:
In Piaget's theory of cognitive development, a child who has just begun to demonstrate egocentric thinking is in the preoperational thought stage. A child who has just begun to demonstrate egocentric thinking is in the preoperational stage of Piaget's stages of cognitive development. This stage occurs from approximately 2 to 7 years old. During the preoperational stage, children can use symbols to represent words, images, and ideas, and engage in pretend play. However, they are not yet able to understand adult logic or mentally manipulate information. They also display egocentrism, meaning they cannot take on the perspectives of others and think that everyone sees, thinks, and feels just as they do.