Final answer:
The cognitive process where new ideas are integrated into existing mental frameworks is called assimilation, a concept from Piaget's theory of cognitive development.
Step-by-step explanation:
The term for the cognitive process in which new ideas are added to existing mental frameworks is assimilation. This concept is part of Jean Piaget's theory of cognitive development, which states that when individuals encounter new information or experiences, they integrate this into their current schemata, or mental models, through assimilation. Should the new information be so different that it cannot fit into existing schemata, accommodation may occur, which involves altering the schemata to incorporate the new experiences. This process allows for the continuous evolution of our cognitive frameworks as we interact with our environment and is integral to our ability to organize and understand the world around us.