Did Piaget's four stages really describe how children think?

Partly. Jean Piaget proposed that children move through four stages of thinking. Piaget himself recognised that his theory supports sharp stages rather than continuous development, and later infant studies challenged his timetable.

It began in 1919 at the Alfred Binet Laboratory School in Paris, where Piaget noticed that children of different ages made different kinds of mistakes on the same problems. He concluded that the difference was in the quality, not the quantity, of their intelligence. His four stages were sensorimotor (infants learn through grasping, sucking and stepping), preoperational (play turns checkers into snacks and a box into a table, and the child struggles to see other viewpoints), concrete operational (from about 7 to 11, logic arrives), and formal operational (from about 11 to 15, abstract thought).

A famous test of the third stage is the water task. A child watches liquid being poured from a small glass into a tall, thin one and is asked whether the amount has changed. Understanding that it has not is called conservation: the quantity does not change because the appearance does.

Piaget's own account of how children move between stages was assimilation and accommodation. Assimilation fits new information into an existing schema, and accommodation changes the schema. In a common textbook illustration, a farm boy who sees an elephant and shouts "look mommy, Horsey!" is assimilating, because he has no scheme for elephants; learning that elephants are a different animal means adjusting his animal schema.

The theory had limits that Piaget acknowledged: it supports sharp stages rather than continuous development. Later researchers added more: three-month-old infants seem surprised by impossible events, long before Piaget's timetable allowed, and critics argue that culture and language matter more than he thought.