Piaget's ideas of moral realism and morality of cooperation play a role inKohlberg's theory. Children in Piaget's stage of moral realism believe thatrules are absolute and can't be changed. Punishment should be determined by howmuch damage is done, and the intention of the child is not taken intoaccount.
For example, a child operating in the stage of moral realism would believe thata child who accidentally breaks three cups should be punished more than a childwho breaks one cup on purpose.
Gradually, as a child matures, he or sheunderstands that people make rules and people can change them: the beginningsof Piaget's morality of cooperation. Eventually, both the damage done and theintention of the offender in a given moral dilemma are considered in this stageof moral development (Reference).
Kamii, Constance. (1991). Toward autonomy: The importance of criticalthinking and choice making. School Psychology Review, 20(3): 382-388.
Kavathatzopoulos, Iordanis. (1991). Kohlberg and Piaget: Differences andsimilarities. Journal of Moral Education, 20(1): 47-54.