According to Parten, what category of play does not involve games with rules?

The correct answer is associative play, as this type of play involves children playing alongside each other while engaging in similar activities, but without any structured rules governing their interactions or the play itself. In associative play, children may share toys and communicate, but they do not organize themselves into a fixed structure or establish formal rules for their activities. This contrasts with cooperative play, where children work together towards a common goal and establish clear rules for their interactions, making it more structured and rule-oriented.

Solitary play, where a child plays alone, inherently lacks interaction and games with rules since the focus is solely on the individual child. Onlooker play is characterized by a child observing others play without joining in, which does not involve any gameplay or rules either. Thus, associative play is distinct in its nature of being social but not rule-based, making it the correct categorical choice among the options presented.