Final answer:
The statement about fast mapping is false. Fast mapping is a language acquisition process unrelated to the concepts of conservation and object permanence, which are cognitive development milestones identified by Jean Piaget.
Step-by-step explanation:
Fast mapping is the process by which children rapidly connect new words with their meanings after only a brief encounter; it is not directly related to conservation or object permanence. Therefore, the statement that fast mapping is the process through which a child comes to appreciate both conservation and object permanence is false. Conservation is the understanding that certain properties of objects remain the same despite changes in the objects' form or appearance and is typically developed during the preoperational stage of cognitive development. Object permanence is the understanding that objects continue to exist even when they cannot be seen, heard, or otherwise sensed, which develops in the sensorimotor stage. Both conservation and object permanence are concepts described by Jean Piaget, reflecting a child's cognitive development at different stages.