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Formal operations (11 years and above)
A person capable of formal operations can view a problem from several positions without making a move. While a child is still in stage 3, the ability to reason depends on the evidence of his or her senses. But as children approach and continue through adolescence, they can think more abstractly.
By associating things that have qualities in common, a pre-adolescent begins to form concepts. Symbols—words, numbers, or other signs—play a more important part in thinking. Adolescents have a concept of space apart from their own experience in it. They can organize facts and events in mature fashion. They can figure out possible moves and likely outcomes.
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