Object permanence
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Jean Piaget conducted experiments with infants which led him to conclude that this awareness was typically achieved at eight to nine months of age, during the sensorimotor stage of cognitive development. Infants before this age are too young to understand object permanence, which explains why infants at this age do not cry when their mothers are gone. "Out of sight, out of mind." A lack of Object Permanence can lead to A-not-B errors, where children reach for a thing at a place where it should not be.
In more recent years, the original Piagetian object permanence account has been challenged by a series of infant studies suggesting that much younger infants do have a clear sense of objects persisting when out of sight.
