The concrete-operations stage is the third of the four levels of children's cognitive development, according to Swiss psychologist Jean Piaget. During this stage, children are becoming more logical, but they have difficulty dealing with abstract and hypothetical concepts. This stage lasts from about ages 7 to 11, when the formal-operations stage begins.
Piaget believed that, prior to the concrete-operations stage, babies and toddlers learn about their environment during the sensorimotor stage. This is followed by the preoperational stage, which is characterized by language development, burgeoning use of symbols and egocentrism. The concrete-operations stage builds off of earlier understandings. This allows children to start using their past experiences in order to make generalizations. However, at this point, children are not capable of predicting specific outcomes based on generalizations.
Reversibility is acquired during this stage, when children learn that steps move both forward and backward. For example, children at this age are able to see that, while addition puts numbers together, subtraction is used to separate those same numbers. Children are capable of seeing multiple parts of a problem simultaneously.
During the concrete-operations stage, children become less egocentric, recognizing that others have different perspectives, knowledge and beliefs. However, children are not yet able to identify the nature of others' thoughts. Children's understanding of the physical world also increases. They learn that some physical variations, such as different containers, do not change the nature of substances. In addition, children become familiar with the relationships between distance, time and speed.