In which verbal operant does the child follow a command such as 'clap your hands' without the therapist demonstrating the action?

The correct answer is rooted in understanding the nuances of verbal operants defined in the field of behavior analysis, particularly as it pertains to the way a child interacts based on verbal instructions. When a child follows a command like "clap your hands" without any demonstration, they are engaging in listener responding. This type of operant involves a child responding to another individual's verbal directive based on their understanding of the command, rather than mimicking an action they have just observed.

Listener responding is significant because it demonstrates comprehension and the ability to process verbal information in a meaningful way. The child is essentially demonstrating that they have learned the association between the command and the expected action, which is a critical skill in language development and learning.

In contrast, other operants such as mands involve requests made by the child to get something they want, imitation refers to copying observed behaviors after a model has demonstrated the action, and echoics involve repeating what another person has said. These types of verbal operants do not apply to the scenario where the child is simply following a direct command without prior demonstration, reinforcing the correctness of identifying listener responding as the appropriate answer here.