Piaget observed the cognitive development of three infants - Laurent, Lucienne, and Jacqueline. His observations showed that in the first months of life, infants develop the ability to coordinate senses like vision and touch. They progress from reflexive behaviors to intentionally grasping objects and repeating circular reactions with objects. By 12-18 months, infants display curiosity and experimentation, and begin to understand means-ends and object permanence.