6 month old Jerome is in the stage of cognitive development. Thus, when his mother shows Jerome a ball and then hides it behind her back, we would expect him to .

Sensorimotor stage, looks for the ball.

Explanation:

Jean Piaget theory states  that Humans progress through four developmental stages, The Senorimotor stage begins at birth and lasts till the acquisition of language. In this stage infants understand the words by experiences of hearing and vision by interacting physically with objects. They gain knowledge by various physical action they perform.  Object permanence also occurs during this stage, it means that a child understands that objects continue to exist even if he cannot hear or see it and by end of its period they develop a sense of self  and objects.