I've often been surprised at how much people in education(and laypersons as well) take for granted that Jean Piaget's work may be false. Although we question many aspects of our lives, such as religion, politics, even the decision to vaccinate children against viruses and cancers, we often do not question "big names" in psychology.
Well, we should.
I'm not going to go into the intricacies of Piaget's theory. If you are interested, you should reference the Wikipedia article on his life and work. However, in general, Piaget's theory indicates that children progress intellectually through four stages of development: Sensorimotor, Preoperational, Concrete Operations and Formal Operations. At each one of these levels, Piaget posited, there were different challenges that the child needed to deal with. He also indicated that unless the child mastered the tasks in the one stage, he or she could not master the tasks in other stages.
There are problems that are inherent in all theories which posit "stages" of development. Development does not occur in discrete stages - it occurs whenever the environment places increased demands and/or provides less support to the individual. In our society, it simply appears that we all tend to place these demands on children at around the same time - this makes it appear that we are witnessing "stages" of development.
Zimmerman conducted a series of various studies beginning around the 1960's and up until today demonstrating that if the environment placed certain demands, then children would surpass what was expected of them.
Here are some other studies:
Baillargeon et al. (1985). Infants could identify, to a reasonable degree, events which violated the laws of physics, even though, Piaget noted that infants at the "sensorimotor" stage could not do so.
Das Gupta & Bryant (1988). Children were able to follow simple transformations, even though, Piaget noted that children at the "pre-operational" stage could not do so.
Hughes (1978). Children were able to take the perspective of multiple people even though, Piaget noted that children at the "pre-operational" stage could not do so.
Light, Buckingham & Robbins (1979). When children were taught to pay attention to the concrete properties of an event (e.g., pouring liquids into different sized beakers), then they were able to do so, even though, Piaget noted that children at the "pre-operational" stage could not do so.
McCarrigle (1978). When given discrete instruction about the super-ordinate and sub-ordinate categories, children were able to classify information effectively.
Piaget was instrumental in getting people to think about children as individuals who are developing. However, children develop in radically different ways. Assessments of intelligence (WISC-IV) appreciate this as these children tend to go through items as much as possible. There is no cap on how much a child can or cannot do on a particular set of items.