While presented in a series of discrete progressive stages even Piaget believed that development does not always follow such a smooth and predictable path. September 161980 Age 84 Parents. Piaget S Theory Of Cognitive Development The Psychology Notes Psychology Notes Piaget Theory Cognitive Development The fourth and last stage of cognitive development is called the Formal Operational Stage. . Piagets stages of development are. This contradicts Piagets concept. He is thought by many to have been the major figure in 20th-century developmental psychology. Piagets theory of cognitive development suggests that at this stage children are so engrossed in egocentric thoughts that they believe their view of the world is shared by everyone else. Vygotsky does not refer to stages in the way that Piaget does. Piagets theory of cognitive development suggests that children progress through a series of stages of mental development.