Final answer:
Martin, at six months old, is in the sensorimotor stage of Piaget's theory of cognitive development, where he is learning about the world through his senses and has not yet fully developed object permanence.
Step-by-step explanation:
The stage of cognitive development that Martin, who is six months old, is currently in, according to Piaget's theory, is the sensorimotor stage. This is the first stage in Piaget's theory, spanning from birth to about 2 years old. During this period, a child learns about the world through senses and motor behavior, and develops object permanence, which is the understanding that objects continue to exist even when they cannot be seen or heard. Martin's belief that the blanket had disappeared when Desmond hid it suggests that Martin has not yet fully developed object permanence, a milestone that typically develops between 5 and 8 months old.