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Concrete operations (7-11 years)
The idea of formal logic plays an increasing role in cognitive growth at this stage of concrete operations. Children are able to make strides in learning measurement, class and set relationships, and concepts of space.
In stage 3, children also grasp the idea of conservation. The eleven-year-old boy above knows he is holding exactly one-half cup of butter. He checked the amount by dropping it into one cup of water; the combined total measured a cup and a half. Measuring displaced water when an object is immersed is a problem in conservation of volume solved correctly at about age 11.
Conservation of number, holding on to the knowledge of how many items there are after their position or arrangement is changed, is usually achieved at about age five or six. Conservation of area and weight are grasped between ages seven and ten.
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