theory assumes that children learn gender-linked behaviors by observing and imitating others and through the rewards and punishments they receive for their imitation.

Social learning.

Explanation:

Let us first fill in the gap in the question above. Please note that the capitalized words are the missing words in the gap.

" SOCIAL LEARNING theory assumes that children learn gender-linked behaviors by observing and imitating others and through the rewards and punishments they receive for their imitation.''

When the ways of other people or Behaviors are learned through modeling then the theory that deals with such case or type of learning is known as social learning theory. The social learning believes that one can learn just by observing things around. This theory is so important to human beings as it has many uses and applications for instance now, the theory is used in the psychotherapy, moral development, criminology and so on.