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168 PILLAR 2 Development and LearningPreoperational children develop language skills, but their communication is often egocentric. Egocentrism is the inability to consider another person%u2019s point of view. This means that preoperational children are likely to say whatever is on their mind without taking into account what others have said. Egocentrism shows up in the actions and statements of young children. For example, many years ago, my oldest daughter used to close her eyes when she didn%u2019t want anybody to see her. Ask a 4-year-old why the sun shines in the morning, and you might hear the answer, %u201cTo wake me up.%u201dWe%u2019ve learned that taking another%u2019s viewpoint, a form of symbolic thinking, appears earlier in the preoperational mind than Piaget thought. In one study, 3-year-olds were able to use a scale model of a real room to locate a hidden stuffed animal. If the stuffed animal was hidden under a pillow in the scale model, 3-year-olds knew to look under the pillow in the real room 80 percent of the time. However, only 30 percent of 2%u00bd-year-olds knew where to look for the stuffed animal in the real room.35 Piaget probably would have been surprised that symbolic thinking could be shown at such an early age, and that 6 months made such a difference in children%u2019s ability to use the scale model of a room as a symbol.Concrete Operational StagePiaget believed that in the concrete operational stage (from about age 6 or 7 to about age 11), children gain the mental skills that enable them to think logically about concrete events. Concrete operational children comprehend that mass and volume stay the same despite changes in the forms of objects (a sign of understanding conservation). They know that a change in shape does not affect quantity. Whether you roll a batch of dough into one big loaf of bread or divide it into a dozen rolls, a child at the concrete operational stage knows that you still have the same amount of dough.In the concrete operational stage, Piaget said that children could also comprehend mathematical transformations. For example, they enjoy math-based jokes that used to fly over their heads, like this one:A king asked his baker to bring him a pie. When the baker brought a pie cut in six pieces, the king yelled at the baker, %u201cWhy didn%u2019t you bring me a pie cut in two pieces? I could never eat six!%u201dEvidently, that king can%u2019t conserve. Concrete operational children understand the joke (even if it%u2019s not that funny).Formal Operational StageConcrete reasoning requires actual experience. In the formal operational stage(age 12 and over), children begin to think logically about abstract concepts and form strategies about things they may not have experienced. The ability to create and use the strategies necessary to play chess is a sign of formal operational thought. Think of the abstract reasoning necessary to understand chemical equations and the laws of physics. Concrete thinkers would struggle in these classes. Young adolescents, said Piaget, become capable of solving hypothetical problems. They can figure out the answer to If this, then what questions, such as the egocentrism In Piaget%u2019s theory, the inability of the preoperational child to take another person%u2019s point of view or to understand that symbols can represent other objects.concrete operational stage In Piaget%u2019s theory, the stage of cognitive development (from about 6 or 7 to 11 years of age) during which children gain the mental skills that enable them to think logically about concrete events.formal operational stage In Piaget%u2019s theory, the stage of cognitive development (beginning about age 12) during which people begin to think logically about abstract concepts and form strategies about things they may not have experienced.%u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.