Final answer:
Jean Piaget and Bärbel Inhelder's Three-Mountain Task was designed to assess egocentrism during the preoperational stage by testing if a child could understand perspectives different from their own when viewing a model.
Step-by-step explanation:
The task that Jean Piaget and Bärbel Inhelder developed to demonstrate egocentrism during the preoperational stage is known as the Three-Mountain Task. In this task, children are presented with a model of three mountains, each differing in size, color, and features. They are asked to choose what they can see from their own perspective and then predict what a figure placed at different points around the model would be able to see.
This allows researchers to assess whether the child is able to take another's perspective or if they are still experiencing egocentrism—a characteristic of the preoperational stage where a child assumes that others share their viewpoint. Piaget's research through this task indicated that, at this stage, children tend to attribute their own perspective to others, revealing a lack of understanding that other people may have different thoughts, views, and feelings.