Final answer:
Jean Piaget used the case study method to develop his theories on children's cognitive development, which involved detailed investigation of a few subjects over time.
Step-by-step explanation:
The research method Jean Piaget used to develop his ideas about children's thinking after carefully observing and questioning only a few children is known as a case study. Piaget conducted detailed investigations of his subjects, which allowed him to develop his theory of cognitive development. This approach enabled him to observe and record behaviors and to understand how children develop schemata to interpret the world. Piaget's method is characterized by the in-depth study of individual cases over extended periods of time.