Final answer:
Jean Piaget utilized the case study research method, where he closely observed and analyzed the behavior and cognitive development of his own children to form his theories.
Step-by-step explanation:
Jean Piaget's Research Method
The developmental psychologist Jean Piaget based his insights into child development on in-depth examinations of his own three children. This approach is best characterized as the case study research method. Case studies are a research strategy where the development of one individual, or a very small group, is studied in depth over a period of time.
Piaget's work focused on how children's cognitive abilities develop through specific stages, representing a discontinuity approach to development. His observations and analyses of his own children's behavior helped inform his Cognitive Theory of Development. The findings from such case studies are invaluable; however, they are oftentimes difficult to generalize to a larger population.
Another example of the case study method can be found in Sigmund Freud's work, particularly his study of a child known as "Little Hans" which informed his theories of psychosexual development. Likewise, Piaget's scrutiny into his children's development played a pivotal role in shaping his theories on the development of self, which accounted for a balance between internal cognitive processes and external social experiences.