Jean Piaget developed a theory of cognitive development that included four stages: sensorimotor, preoperational, concrete operational, and formal operational stage. Piaget suggested all humans encounter environmental challenges by either assimilation (interpreting new information into existing schemas) or accomodation (adapting current schemas to incorporate new information). Criticisms of Piaget's theory have included the following: lack of understanding of culture on cognition (Dasen, 1994), modularity or domain-specificity (Callaghan, 2004), and the role of language in cognitive development.
On a more interesting note (at least to me) James Fowler (1981) modeled his theory of faith development on PIaget's theory as well as Kohlberg's theory of moral development. Fowler's theory of faith development was the first well known attempt to identify "religious cognition," which has since been challenged by Pascal Boyer and Justin Boyer, who have cited modularity for the cognitive byproduct explanation of religion.
- Boyer, Pascal. Religion Explained: The Evolutionary Origins of Religious Thought Basic Books, 2001
- Boyer, Pascal. "Religious Thought and Behavior as By-Products of Brain Functions," Trends in Cognitive Sciences 7, pp 119–24
- Piaget, J. (1977). The role of action in the development of thinking. In Knowledge and development (pp. 17–42). Springer US
- Barrett, J.L. "Cognitive Science of Religion: What Is It and Why Is It?" Religion Compass 2007, vol 1.
- Barrett, J.L. "Exploring the Natural Foundations of Religion." Trends in Cognitive Sciences 2000, vol. 4 pp 29–34
- Barrett, J.L. Why Would Anyone Believe in God? AltaMira Press, 2004.