According to Jean Piaget's theory of cognitive development, when a child sees a new object or event and tries to fit it into their pre-existing schema without making any changes to their current mental structure (such as a young child seeing a 'dog' for the first time and assuming it is a 'cat' because both have four legs), what is this cognitive process called in Piaget's terminology?

According to Jean Piaget's theory of cognitive development, 'Assimilation' is the process in which a child attempts to fit new information or experiences into their pre-existing knowledge or schema without making any fundamental changes to it. In contrast, when the existing schema fails to handle new information and requires modification, it is called 'Accommodation'. For a detailed study on this topic, you can refer to the Wikipedia reference.