The sensorimotor stage is when children come to realize that objects exist and tend to experiment greatly by throwing stuff around or putting it in their mouth. They know the object is real even if they can’t see it. This is a sign that intelligence is developing. This stage occurs from birth up to about 2 years.
Then there’s the pre-operational stage when the child becomes egocentric, they have problems distinguishing their thoughts and perception from that of others. This occurs between the ages of 2 to 7.
The Concrete operational stage is when children begin to realize that their feelings and opinions are unique and may not be in unison with everyone else. (7-11 years)
Lastly the Formal operational stage is when adolescents can relate a relative thought to an abstract scenario. This is when problem solving comes into play and sometimes the individual can solve the problem before it even happens.
One of the limitations to this theory is that Piaget underestimates the ability of the infants and even individuals at other stages because it has been proven that even infants have a certain intellectual capacity and may surpass what is known as the norm for babies. One of the accomplishments would be that Piaget has provided a framework by which psychologists can work with and can also be used as a baseline for further upcoming understandings of cognitive development. The fact is that this is the more widely accepted theory to describe intellectuality in people throughout the duration of their lives.