The final stage is known as the formal operational stage (adolescence and into adulthood, roughly ages 11 to approximately 15–20): Intelligence is demonstrated through the logical use of symbols related to abstract concepts. This form of thought includes "assumptions that have no necessary relation to reality."[43] At this point, the person is capable of hypothetical and deductive reasoning. During this time, people develop the ability to think about abstract concepts.
Piaget stated that "hypothetico-deductive reasoning" becomes important during the formal operational stage. This type of thinking involves hypothetical "what-if" situations that are not always rooted in reality, i.e. counterfactual thinking. It is often required in science and mathematics.
Abstract thought emerges during the formal operational stage. Children tend to think very concretely and specifically in earlier stages, and begin to consider possible outcomes and consequences of actions.
Metacognition, the capacity for "thinking about thinking" that allows adolescents and adults to reason about their thought processes and monitor them.[44]
Problem-solving is demonstrated when children use trial-and-error to solve problems. The ability to systematically solve a problem in a logical and methodical way emerges.
While children in primary school years mostly used inductive reasoning, drawing general conclusions from personal experiences and specific facts, adolescents become capable of deductive reasoning, in which they draw specific conclusions from abstract concepts using logic. This capability results from their capacity to think hypothetically.[45]
