The cognitive developmental theory was developed by Jean Piaget; Lev Vygotsky developed Sociocultural Theory of Development. Eric Erikson is identified with psycho-social development theory eight stages of development. Include whether each theory is classical or contemporary.
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As you describe the cognitive developmental theory by Jean Piaget, I deem it as classical. This theory reflects the beliefs that people "actively organize their world into coherent systems" (http://faculty.weber.edu/jabird/chf2750/Psychological/Piaget%20Intro.pdf) using schema.
This theory also relies heavily upon four life stages. Piaget suggests, "As the person matures and develops his/her structural abilities for organizing new information, thinking becomes more complex - this produces stages" (http://faculty.weber.edu/jabird/chf2750/Psychological/Piaget%20Intro.pdf).
Like steps on a ladder, Piaget's theory is also rooted in predictable patterns. Piaget believes that development happens in a pattern where "A person must pass through each stage before going on to a new, more complex. Each stage sees the elaboration of new mental abilities that set the limit and determine the character of what can be learned at that period" ...
Developmental theories are briefly clarified and validated by resources.