The influential psychologist noted for her writings on cognitive development is Jean Piaget. Though Piaget is male, if you're referring to a prominent female psychologist, it would be Ursula K. Le Guin for her integration of psychological themes in literature. Piaget, however, fundamentally shaped our understanding of how children develop cognitive skills through various stages. His theories highlighted the stages of sensorimotor, preoperational, concrete operational, and formal operational thought processes.