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The concrete operational stage is one of four main stages within Piaget's model for cognitive development. According to Piaget it begins at approximately age 7 or 8 and is normally completed by age 11. The stage is characterized by the acquired ability to perform simple logical operations, conservation or the ability to know that, for example, if water from a full cup is transferred to another receptacle that it will retain the same quantity no matter what shape it is rearranged in. By this stage Piaget stated that they had mastered reversibility or the awareness that the subtraction of something is reversible by its addition, or vice versa. They no longer have centration or the ability to concentrate only on one "central" attribute such as height. No longer is the child limited to the illogical limitations of animism (the belief that all objects are animals and therefore have feelings), egocentrism (related to animism in that the children believe that all things are like them and therefore have feelings as do the children), and artificialism (the belief that all things were created by mankind) of the Preoperational stage. Children during this stage are limited by the lack of abstract thinking which they develop in the Formal operational stage.
The Theory of Cognitive development offered by Jean Piaget is often criticized by more recent psychologists who claim it underestimated the cognitive skills of younger children and overestimated the abilities of adolescents relative to adults. However, if the test of conservation he conducted is attempted - filling a glass of water and then transferring the water to another container of equal size and asking "which has more water, this or the other glass?", on children prior to the operational stage they normally will be unable to answer or will answer incorrectly due to, most likely, centration.